CTAN sync 201909150300

124 files changed, 48987 insertions, 12 deletions

diff --git a/macros/latex-dev/required/amsmath/README.md b/macros/latex-dev/required/amsmath/README.md
new file mode 100644
index 0000000000..66a27edf03
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/README.md
@@ -0,0 +1,81 @@
+The amsmath bundle for LaTeX
+============================
+
+Release 2019-10-01 pre-release 3
+
+Overview
+--------
+
+The `amsmath` package is an extension package for LaTeX that provides
+additional features to facilitate mathematical typesetting. It has been
+developed by the American Mathematical Society (AMS) and released for general
+use as a service to the mathematical community. A number of smaller
+auxiliary packages are also distributed with the `amsmath` package.
+
+Effective in 2016, maintenance of `amsmath was transferred from AMS to
+the LaTeX Project; as `amsmath` is considered a "required" package, this
+centralizes control over the core LaTeX components.
+
+Installation
+------------
+
+We no longer distribute installation instructions for the various TeX
+implementations. All modern TeX systems include `amsmath` as-standard, and end
+users should in general use the release versions supplied in this way.
+
+Release distribution is carried out only through the CTAN archives.
+
+Documentation
+-------------
+
+The primary documentation for `amsmath` is in provided as `amsldoc.pdf`.
+
+Additional documentation files include:
+
+ - `diffs-m.txt`
+ - `subeqn.pdf`
+ - `technote.pdf`
+ - `testmath.pdf`
+
+which are included in the collection.  All of these can be accessed
+easily with most distributions by entering `texdoc` *filename* at the
+command line, or via [TeXdoc Online](http://texdoc.net).
+
+Change logs
+-----------
+
+The file `changes.txt` lists recent changes in reverse chronological order.
+
+The file `diffs-m.txt` contains information on development and changes
+prior to 2000.
+
+Reporting Bugs
+--------------
+
+If you wish to report a problem or bug in the `amsmath` bundle
+please use the [Issue Tracker for LaTeX2e on
+GitHub](https://github.com/latex3/latex2e/issues)
+and follow the guidelines that pop up if you press the "New issue" button.
+
+In particular, to check that you are really seeing a bug, please write
+a short, self-contained document that shows the problem. This should
+include the `latexbug` package, which will warn if your test file is
+not suitable for one or the other reason. See the [CONTRIBUTING
+guide](https://github.com/latex3/latex2e/blob/master/CONTRIBUTING.md)
+for further details, or if you need to obtain the `latexbug` package.
+
+If the bug turns out to be with third-party software then please
+contact the developer, and not us!
+
+License
+-------
+
+The contents of this bundle are distributed under the [LaTeX Project
+Public License](https://www.latex-project.org/lppl/lppl-1-3c/),
+version 1.3c or later.
+
+-----
+
+<p>Copyright (C) 2001-2004, 2007, 2008, 2010, 2011, 2013 American Mathematical Society. <br />
+<p>Copyright (C) 2016-2019 The LaTeX Project and American Mathematical Society. <br />
+
diff --git a/macros/latex-dev/required/amsmath/ams-external.txt b/macros/latex-dev/required/amsmath/ams-external.txt
new file mode 100644
index 0000000000..fa2dbea556
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/ams-external.txt
@@ -0,0 +1,547 @@
+%%% list of external commands used by amsmath (not totally correct)
+
+\!
+\"
+\(
+\*
+\,
+\-
+\.
+\/
+\:
+\;
+\=
+\Acute
+\AmS
+\AmSfont
+\And
+\AtBeginDocument
+\Bar
+\Big
+\Bigg
+\Biggr
+\Bigr
+\Breve
+\Check
+\DOTS
+\DOTSB
+\DOTSI
+\DOTSX
+\Ddot
+\DeclareFontEncoding
+\DeclareFontShape
+\DeclareMathAccent
+\DeclareMathDelimiter
+\DeclareMathOperator
+\DeclareMathSymbol
+\DeclareOption
+\DeclareRobustCommand
+\Dot
+\ExecuteOptions
+\GenericError
+\GenericInfo
+\GenericWarning
+\Grave
+\Hat
+\Leftarrow
+\Longleftarrow
+\Longleftrightarrow
+\Longrightarrow
+\MessageBreak
+\MultiIntegral
+\PackageError
+\PackageWarning
+\PackageWarningNoLine
+\PassOptionsToPackage
+\Pr
+\ProcessOptions
+\Relbar
+\RequirePackage
+\Rightarrow
+\Tilde
+\Umathaccent
+\Umathcar
+\Umathchar
+\Umathcharnumdef
+\Umathcode
+\Umathcodenum
+\Umathfractiondelsize
+\Vec
+\Vert
+\XeTeXcharclass
+\[
+\]
+\above
+\abovedisplayskip
+\abovewithdelims
+\accentedsymbol
+\acute
+\addtocounter
+\advance
+\aftergroup
+\allowbreak
+\allowdisplaybreaks
+\alph
+\arabic
+\arccos
+\arcsin
+\arctan
+\arg
+\array
+\arraycolsep
+\arraystretch
+\atop
+\atopwithdelims
+\badness<
+\bar
+\baselineskip
+\baselineskip6
+\begin
+\begingroup
+\belowdisplayskip
+\bgroup
+\big
+\bigcap
+\bigcup
+\bigg
+\biggr
+\bigodot
+\bigoplus
+\bigotimes
+\bigr
+\bigsqcup
+\biguplus
+\bigvee
+\bigwedge
+\binom
+\bmod
+\boldsymbol
+\box
+\boxed
+\breve
+\cases
+\cdotp
+\cdots
+\cfrac
+\char
+\chardef
+\check
+\cleaders
+\colon
+\columnwidth
+\coprod
+\copy
+\cos
+\cosh
+\cot
+\coth
+\cr
+\crcr
+\csc
+\csname
+\csnamen
+\csnamethe
+\dbinom
+\ddddot
+\dddot
+\ddot
+\def
+\deg
+\delimiter
+\delimiterfactor
+\delimitershortfall
+\det
+\dfrac
+\dim
+\displaybreak
+\displayindent
+\displaylimits
+\displaystyle
+\displaywidth
+\divide
+\do
+\dot
+\doteq
+\dots
+\dotsb
+\dotsc
+\dotsi
+\dotsm
+\dotso
+\dp
+\edef
+\egroup
+\else
+\end
+\endalign
+\endaligned
+\endarray
+\endcsname
+\endgather
+\endgroup
+\endmathdisplay
+\endmatrix
+\endmultline
+\endsplit
+\endsubarray
+\eqno
+\eqref
+\everycr
+\everydisplay
+\everymath
+\exp
+\expandafter
+\fbox
+\fi
+\fontchardp
+\fontcharht
+\fontdimen
+\fontencoding
+\fontfamily
+\frac
+\fracwithdelims
+\futurelet
+\gcd
+\gdef
+\genfrac
+\global
+\grave
+\halign
+\halignto
+\hat
+\hbox
+\hdots
+\hdotsfor
+\hfil
+\hfill
+\hfilneg
+\hfuzz
+\hom
+\hookleftarrow
+\hookrightarrow
+\hrule
+\hskip
+\ht
+\ialign
+\idotsint
+\if
+\ifDOTS
+\ifcase
+\ifdim
+\iff
+\iffalse
+\iffalse%initialvalue
+\ifhbox
+\ifinner
+\ifm
+\ifmacrostarts
+\ifmmode
+\ifnum
+\ifnum`
+\ifodd
+\iftrue
+\ifvmode
+\ifx
+\ignorespaces
+\ignorespacesafterend
+\iiiint
+\iiint
+\iint
+\impliedby
+\implies
+\inf
+\injlim
+\int
+\interdisplaylinepenalty
+\intertext
+\intop
+\joinrel
+\jot
+\ker
+\kern
+\l%
+\lVert
+\label
+\lastbox
+\lastkern
+\lastskip
+\lbrace
+\ldots
+\leavevmode
+\left
+\leftarrow
+\leftmargini
+\leftmarginiminus
+\leftroot
+\leqno
+\let
+\lg
+\lhook
+\lim
+\liminf
+\limits
+\lineskip
+\lineskiplimit
+\linewidth
+\llap
+\ln
+\log
+\long
+\longleftarrow
+\longleftrightarrow
+\longmapsto
+\longrightarrow
+\loop
+\lq
+\lvert
+\mapsto
+\mapstochar
+\mathaccent
+\mathaccentV
+\mathalpha
+\mathbin
+\mathchar
+\mathchardef
+\mathchoice
+\mathclose
+\mathcode
+\mathdisplay
+\mathellipsis
+\mathgroup
+\mathhexbox
+\mathinner
+\mathop
+\mathopen
+\mathord
+\mathpalette
+\mathpunct
+\mathrel
+\mathring
+\mathsurround
+\mathxxx
+\mathxxxtest
+\mathxxxx
+\matrix
+\max
+\maxdimen
+\mbox
+\meaning
+\medmuskip
+\medspace
+\min
+\minalignsep
+\mintagsep
+\mkern
+\mod
+\moveleft
+\mskip
+\mspace
+\multicolumn
+\multiply
+\multlinegap
+\multlinegap10pt
+\multlinetaggap
+\multlinetaggap10pt
+\negmedspace
+\negthickspace
+\negthinspace
+\newbox
+\newcommand
+\newcount
+\newcounter
+\newdimen
+\newenvironment
+\newhelp
+\newif
+\newmuskip
+\newskip
+\newtoks
+\noalign
+\nobreak
+\nobreakdash
+\nobreakspace
+\noexpand
+\noindent
+\nointerlineskip
+\nolimits
+\nonscript
+\nonumber
+\normalbaselines
+\normalcolor
+\normalfont
+\normallineskiplimit
+\not
+\notag
+\nottest
+\null
+\nulldelimiterspace
+\number
+\numberwithin
+\of
+\oint
+\ointop
+\omit
+\openup
+\operatorfont
+\operatorname
+\operatornamewithlimits
+\or
+\over
+\overleftarrow
+\overleftrightarrow
+\overline
+\overrightarrow
+\overset
+\overwithdelims
+\par
+\parshape
+\penalty
+\pmatrix
+\pmod
+\pod
+\postdisplaypenalty
+\predisplaypenalty
+\prevdepth
+\primfrac
+\prod
+\projlim
+\protect
+\providecommand
+\qopname
+\quad
+\rVert
+\raise
+\raisetag
+\rangle
+\rbrace
+\rbrack
+\rceil
+\ref
+\refstepcounter
+\relax
+\relaxo
+\relbar
+\renewcommand
+\renewenvironment
+\repeat
+\rfloor
+\rgroup
+\rhook
+\right
+\rightarrow
+\rlap
+\rmoustache
+\romannumeral
+\root
+\rootbox
+\rq
+\rvert
+\scriptfont
+\scriptscriptfont
+\scriptscriptstyle
+\scriptstyle
+\sec
+\selectfont
+\setbox
+\setcounter
+\shoveleft
+\shoveright
+\sideset
+\sim
+\sin
+\sinh
+\skewchar
+\smash
+\space
+\spaceor
+\span
+\spbreve
+\spcheck
+\spdddot
+\spddot
+\spdot
+\sphat
+\split
+\sptilde
+\sqrtsign
+\stepcounter
+\string
+\strut
+\strutbox
+\subarray
+\substack
+\sum
+\sup
+\symoperators
+\tabskip
+\tag
+\taghere
+\tan
+\tanh
+\tbinom
+\text
+\textellipsis
+\textfont
+\textstyle
+\textup
+\tfrac
+\the
+\theequation
+\theparentequation
+\thetag
+\thickmuskip
+\thickmuskip0mu
+\thickspace
+\thinmuskip
+\thinspace
+\tilde
+\tmspace
+\toks
+\typeout
+\u
+\underleftarrow
+\underleftrightarrow
+\underrightarrow
+\underset
+\unhbox
+\unhcopy
+\unpenalty
+\unskip
+\unvbox
+\unvcopy
+\uppercase
+\uproot
+\usefont
+\value
+\varDelta
+\varGamma
+\varLambda
+\varOmega
+\varPhi
+\varPi
+\varPsi
+\varSigma
+\varTheta
+\varUpsilon
+\varXi
+\varinjlim
+\varliminf
+\varlimsup
+\varprojlim
+\vbox
+\vcenter
+\vec
+\vee
+\veqno
+\vert
+\vrule
+\vskip
+\vss
+\vtop
+\wd
+\widehat
+\widetilde
+\xdef
+\xleaders
+\xleftarrow
+\xrightarrow
diff --git a/macros/latex-dev/required/amsmath/ams-internal.txt b/macros/latex-dev/required/amsmath/ams-internal.txt
new file mode 100644
index 0000000000..06a0c97f09
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/ams-internal.txt
@@ -0,0 +1,482 @@
+%%%% list of internal commands used by amsmath (not totally correct)
+
+\@@above
+\@@abovewithdelims
+\@@atop
+\@@atopwithdelims
+\@@eqno
+\@@italiccorr
+\@@leqno
+\@@over
+\@@overline
+\@@overwithdelims
+\@@sqrt
+\@@undefined
+\@@underline
+\@M
+\@addtoreset
+\@amsmath@err
+\@arrayboxrestore
+\@arrayparboxrestore
+\@backslashchar
+\@badmath
+\@car
+\@cdots
+\@centering
+\@checkend
+\@currentlabel
+\@currenvir
+\@declmathop
+\@depth
+\@display@init
+\@displaytrue
+\@eha
+\@ehc
+\@ehd
+\@elt
+\@empty
+\@emptytoks
+\@envbody
+\@eqnnum
+\@eqnswfalse
+\@eqnswtrue
+\@eqpen
+\@fleqntrue
+\@for
+\@genfrac
+\@getpen
+\@gobble
+\@gobblefour
+\@gobblethree
+\@gobbletwo
+\@gtempa
+\@height
+\@iden
+\@ifdefinable
+\@ifnextchar
+\@ifnotempty
+\@ifpackageloaded
+\@ifpackagewith
+\@ifstar
+\@ifundefined
+\@ignoretrue
+\@ldots
+\@let@token
+\@lign
+\@m
+\@mathmargin
+\@mathmeasure
+\@mathstyle
+\@namedef
+\@ne
+\@nil
+\@nocnterr
+\@nocounterr
+\@nx
+\@onlypreamble
+\@saveprimitive
+\@sptoken
+\@stpelt
+\@tempa
+\@tempb
+\@tempc
+\@tempcnta
+\@tempcntb
+\@tempd
+\@tempdima
+\@tempdimb
+\@tempdimc
+\@temptokena
+\@testopt
+\@totalleftmargin
+\@undefined
+\@width
+\@xp
+\@xp#1
+\DN@
+\DOTS@
+\DOTSCASE@
+\FN@
+\Invalid@@
+\Leftarrowfill@
+\Leftrightarrowfill@
+\Let@
+\Mathstrut@
+\Mathstrutbox@
+\RIfM@
+\Rightarrowfill@
+\SK@@label
+\SK@equationtrue
+\SK@tagform@
+\Umathch@
+\acc@check
+\acc@error
+\accentclass@
+\add@amp
+\add@amps
+\addto@envbody
+\addto@hook
+\align@
+\align@preamble
+\align@recover
+\aligned@a
+\alignedat@a
+\alignedspace@left
+\alignsafe@testopt
+\alignsep@
+\alignsep@-
+\alignsep@<
+\alt@tag
+\ams@DeclareRobustCommand
+\ams@def
+\ams@newcommand
+\ams@renewcommand
+\andhelp@
+\arrowfill@
+\bBigg@
+\begin@stack
+\big@size
+\bigcap@
+\bigcup@
+\bigodot@
+\bigoplus@
+\bigotimes@
+\bigsqcup@
+\biguplus@
+\bigvee@
+\bigwedge@
+\binrel@
+\binrel@@
+\black@
+\bold@false
+\bold@true
+\boldsymboldots@
+\boxz@
+\c@MaxMatrixCols
+\c@MaxMatrixColsc
+\calc@shift@align
+\calc@shift@gather
+\check@mathfonts
+\checkat@false
+\checkat@true
+\cl@@ckpt
+\classnum@
+\cmex@opt
+\collect@@body
+\collect@body
+\column@
+\column@plus
+\coprod@
+\count@
+\csname@@
+\csnamec@
+\csnamecl@
+\csnameemdf@
+\csnamem@gobble
+\csnamemb@
+\ctagsplit@false
+\ctagsplit@true
+\default@tag
+\delayed@
+\df@label
+\df@tag
+\dft@tag
+\dimen@
+\displ@y
+\displ@y@
+\displaywidth@
+\dotsb@
+\dotso@
+\dotsspace@
+\dspbrk@
+\dspbrk@context
+\dspbrk@lvl
+\dt@pfalse
+\dt@ptrue
+\emdf@L
+\emdf@La
+\emdf@R
+\emdf@Ra
+\emdf@U
+\emdf@Ua
+\endmathdisplay@a
+\endmathdisplay@fleqn
+\endmultline@math
+\env@cases
+\env@matrix
+\eqnshift@
+\every@math@size
+\ex@
+\ext@arrow
+\extra@
+\extrap@
+\f@series
+\f@size
+\field@lengths
+\fieldlengths@
+\finsm@sh
+\firstchoice@false
+\firstchoice@true
+\fracwithdelims@
+\frozen@everymath
+\gather@
+\gather@split
+\gdisplaywidth@
+\genfrac@choice
+\genfrac@rule
+\getdsp@pen
+\getmathch@
+\getmathcode@
+\gmeasure@
+\gobble@tag
+\gtest@false
+\gtest@true
+\hdots@for
+\hexnumber@
+\if@display
+\if@eqnsw
+\if@fleqn
+\ifbold@
+\ifcheckat@
+\ifctagsplit@
+\ifdt@p
+\iffirstchoice@
+\ifgtest@
+\ifinalign@
+\ifingather@
+\ifmeasuring@
+\ifshifttag@
+\ifst@rred
+\iftag@
+\iftagsleft@
+\iftagsleft@L
+\ifxxat@
+\ilimits@
+\inalign@false
+\inalign@true
+\incr@eqnum
+\inf@bad
+\ingather@false
+\ingather@true
+\insplit@
+\intdots@
+\intertext@
+\intkern@
+\ints@a
+\ints@b
+\ints@c
+\invalid@tag
+\keybin@
+\keybin@test
+\label@in@display
+\leavevmode@ifvmode
+\leftarrowfill@
+\leftrightarrowfill@
+\leftroot@
+\leftroot@mu
+\lendmultline@
+\lendsplit@
+\lineht@
+\ltx@label
+\m@gobble
+\m@ne
+\m@th
+\m@th$
+\macc@a
+\macc@adjust
+\macc@code
+\macc@depth
+\macc@group
+\macc@kerna
+\macc@kernb
+\macc@nested
+\macc@nested@a
+\macc@nucleus
+\macc@palette
+\macc@set@skewchar
+\macc@skewchar
+\macc@style
+\macc@test
+\macc@tmp
+\macro@
+\macro@@
+\make@df@tag
+\make@df@tag@@
+\make@df@tag@@@
+\make@display@tag
+\makesm@sh
+\maketag@@
+\maketag@@@
+\math@
+\math@bgroup
+\math@cr
+\math@cr@
+\math@cr@@
+\math@cr@@@
+\math@cr@@@align
+\math@cr@@@align@measure
+\math@cr@@@aligned
+\math@cr@@@alignedat
+\math@cr@@@gather
+\math@cr@@[
+\math@egroup
+\mathbin@
+\mathch@
+\mathdisplay@@pop
+\mathdisplay@@push
+\mathdisplay@pop
+\mathdisplay@push
+\mathdisplay@stack
+\mathrel@
+\mathsm@sh
+\matrix@check
+\matrix@error
+\maxcol@width
+\maxcolumn@widths
+\maxfields@
+\mb@b
+\mb@t
+\mb@tb
+\mdots@
+\mdots@@
+\meaning@
+\meaning@@
+\measure@
+\measuring@false
+\measuring@true
+\mmeasure@
+\multline@
+\multline@indent
+\new@ifnextchar
+\newmcodes@
+\newmcodes@m
+\newmcodes@o
+\next@
+\nextii@
+\nextiii@
+\nextiv@
+\nextix@
+\nextv@
+\nextvi@
+\nextvii@
+\nextviii@
+\nfss@text
+\nmlimits@
+\noaccents@
+\nogood@displaybreak
+\nolimits@
+\nomath@env
+\nonmatherr@
+\not@
+\operator@font
+\operator@fontlim$
+\operator@fontmod
+\overarrow@
+\p@
+\p@equation
+\place@tag
+\place@tag@gather
+\plainroot@
+\print@eqnum
+\process@envbody
+\prod@
+\protected@edef
+\push@begins
+\r@@t
+\raise@tag
+\relaxnext@
+\rendmultline@
+\rendsplit@
+\reset@equation
+\reset@strutbox@
+\resetMathstrut@
+\restore@hfuzz
+\restore@math@cr
+\restorealignstate@
+\restorecolumn@
+\restorecounters@
+\rightarrowfill@
+\rightdelim@
+\row@
+\savealignstate@
+\savecolumn@
+\savecounters@
+\savefieldlength@
+\saveshift@
+\savetaglength@
+\select@group
+\set@field
+\set@gather@field
+\set@mathaccent
+\setboxz@h
+\sf@size
+\shdots@for
+\shift@tag
+\shifttag@false
+\shifttag@true
+\sixt@@n
+\skip@
+\slimits@
+\split@
+\split@al@a
+\split@al@tagcheck
+\split@aligned
+\split@err
+\split@tag
+\split@warning
+\spread@equation
+\ssf@size
+\st@rredfalse
+\st@rredtrue
+\start@align
+\start@aligned
+\start@gather
+\start@multline
+\std@equal
+\std@minus
+\striplong@
+\strut@
+\strut@$
+\strutbox@
+\sum@
+\tag@false
+\tag@help
+\tag@in@align
+\tag@in@display
+\tag@in@display@a
+\tag@lengths
+\tag@shifts
+\tag@true
+\tag@width
+\tagform@
+\tagshift@
+\tagsleft@false
+\tagsleft@true
+\tagwidth@
+\tdots@
+\text@
+\textdef@
+\thecharacter@
+\thedots@
+\thr@@
+\toks@
+\too@wide
+\totwidth@
+\try@load@fontshape
+\tw@
+\underarrow@
+\uproot@
+\use@mathgroup
+\varlim@
+\varliminf@
+\varlimsup@
+\wdz@
+\x@calc@shift@lc
+\x@calc@shift@lf
+\x@calc@shift@rc
+\x@calc@shift@rf
+\x@lcalc@width
+\x@rcalc@width
+\xatlevel@
+\xxat@true
+\z@
diff --git a/macros/latex-dev/required/amsmath/amsbsy.dtx b/macros/latex-dev/required/amsmath/amsbsy.dtx
new file mode 100644
index 0000000000..890fbd0d82
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsbsy.dtx
@@ -0,0 +1,238 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society. 
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amsbsy}
+\GetFileInfo{amsbsy.sty}
+\begin{document}
+\title{The \pkg{amsbsy} package}
+\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amsbsy.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%
+%    The package \texttt{amsbsy}, first written in 1989, implements a
+%    few commands for producing \textbf{bold} characters in the `normal'
+%    \emph{math version}.
+% \begin{quote}\em
+%    Note: It is recommended nowadays to use the \pkg{bm} package, which
+%    became available in 1997.
+% \end{quote}
+%
+%    If we have bold fonts which contain the character in question then
+%    we will use these fonts to produce the wanted character. But
+%    sometimes math fonts are only available in a certain weight
+%    (e.g.\ the AMS symbol fonts).
+% \DescribeMacro\pmb
+%    For these cases we provide a command which is called \verb+\pmb+ (an
+%    acronym for \textbf{p}oor \textbf{m}an's \textbf{b}old) with one argument.
+%    The bolder weight is achieved by copying the argument three times in
+%    slightly different positions which is better than nothing but no
+%    match for a real bold font.
+%
+% \DescribeMacro\boldsymbol
+%    There also exists the \verb+\boldsymbol+ command which is better in
+%    all cases where bold fonts exists. This command will internally
+%    switch to the corresponding `bold' \emph{math version} typeset its
+%    argument in this version.
+%
+%    Both commands will preserve the nature of their arguments, i.e.\ if
+%    they get a relational atom their result will again be a relation as
+%    far as \tex/'s mathspacing is concerned.
+%
+%    Since it is good policy to make at least a small test we try to
+%    typeset the infinity sign ($\infty$) first with \verb+\pmb+ and then
+%    with \verb+\boldsymbol+.
+% \[
+%           \pmb{\infty} = \boldsymbol{\infty} \quad ?
+% \]
+% \StopEventually{}
+%
+%    Standard package info.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesPackage{amsbsy}[1999/11/29 v1.2d Bold Symbols]
+%    \end{macrocode}
+%
+% \section{The implementation}
+%
+%    We need some functions from the \pkg{amsgen} package.
+%    \begin{macrocode}
+\RequirePackage{amsgen}
+%    \end{macrocode}
+%
+%\begin{macro}{\boldsymbol}
+%    In implementing boldsymbol, we must take into account \tex/'s
+%    limitation of only 16 mathgroups (math families, in Knuth's
+%    terminology). If we wanted to maintain mathgroups for both the bold
+%    and non-bold version of each math font, it would not take long to
+%    run out of mathgroups. Therefore what we do instead for a bold
+%    symbol is embed it in an \verb|\hbox|; inside that \verb|\hbox|,
+%    when we start another math formula, we can change all the
+%    mathgroups to their bold equivalents.
+%
+%    However, to get the correct math style inside the hbox (display,
+%    text, script or scriptscript) we have to use \verb|\mathchoice|.
+%    Since \verb|\mathversion{bold}| has a lot of overhead, and
+%    \verb|\mathchoice| typesets the argument text four times, we would
+%    rather not put the \verb|\mathversion| command inside each
+%    \verb|\hbox| in the \verb|\mathchoice|; on the other hand,
+%    \verb|\mathversion| gives an error message if it's used in math
+%    mode. Therefore if we want to execute \verb|\mathversion{bold}|
+%    before starting the \verb|\mathchoice| we have to temporarily
+%    disable the \verb|\@nomath| error. (The error message is intended
+%    to keep people from accidentally emboldening a preceding part of a
+%    math formula, since only the mathgroups defined at the end of a
+%    math formula will determine the fonts used in that formula; but we
+%    are going to typeset our bold symbol not in the current formula but
+%    in an embedded formula, so that this danger doesn't apply here.)
+%    \begin{macrocode}
+\DeclareRobustCommand{\boldsymbol}[1]{%
+%    \end{macrocode}
+%    Start a group to localize the change of \verb|\@nomath|:
+%    \begin{macrocode}
+  \begingroup
+%    \end{macrocode}
+%    Disable \verb|\@nomath| so that we don't have to leave math
+%    mode before executing \verb|\mathversion|:
+%    \begin{macrocode}
+  \let\@nomath\@gobble \mathversion{bold}%
+%    \end{macrocode}
+%    \cs{math@atom} is a test macro which looks at its argument and
+%    produces a math atom of the proper class.
+%    \begin{macrocode}
+  \math@atom{#1}{%
+%    \end{macrocode}
+%    Although it is tempting to use \verb|\text| here, to save some
+%    main memory, that caused a bug in the past due to some internal
+%    interactions with \verb|\mathversion|.
+%    \begin{macrocode}
+  \mathchoice%
+    {\hbox{$\m@th\displaystyle#1$}}%
+    {\hbox{$\m@th\textstyle#1$}}%
+    {\hbox{$\m@th\scriptstyle#1$}}%
+    {\hbox{$\m@th\scriptscriptstyle#1$}}}%
+%    \end{macrocode}
+%    End the group we started earlier.
+%    \begin{macrocode}
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@atom}
+%    The macro \verb+\math@atom+ looks at its argument and produce a
+%    correct math atom, i.e.\ a primitive like \verb+\mathopen+.
+%    Until the day we have a real implementation for all cases we use
+%    the \verb+\binrel@+ command from \amstex/ which can distinguish
+%    between binary, relation and ord atoms.
+%    \begin{macrocode}
+\def\math@atom#1#2{%
+   \binrel@{#1}\binrel@@{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\pmb}
+%    Poor man's bold command, works by typesetting multiple copies of
+%    the given argument with small offsets.
+%    \begin{macrocode}
+\DeclareRobustCommand{\pmb}{%
+  \ifmmode\else \expandafter\pmb@@\fi\mathpalette\pmb@}
+%    \end{macrocode}
+%
+%    \cs{pmb@@} is called by \cn{pmb} in the non-math-mode case.
+%    Discard the first two arguments which are for the math-mode case.
+%    \begin{macrocode}
+\def\pmb@@#1#2#3{\leavevmode\setboxz@h{#3}%
+   \dimen@-\wdz@
+   \kern-.5\ex@\copy\z@
+   \kern\dimen@\kern.25\ex@\raise.4\ex@\copy\z@
+   \kern\dimen@\kern.25\ex@\box\z@
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newdimen\pmbraise@
+%    \end{macrocode}
+%    Note: because of the use of \cs{mathpalette}, if \cs{pmb@} is applied to a
+%    single math italic character (or a single character from some other
+%    slanted math font), the italic correction will be added. This will
+%    cause subscripts to fall too far away from the character in some
+%    cases, e.g., $\pmb{T}_1$ or $\pmb{\mathcal{T}}_1$.
+%    \begin{macrocode}
+\def\pmb@#1#2{\setbox8\hbox{$\m@th#1{#2}$}%
+  \setboxz@h{$\m@th#1\mkern.5mu$}\pmbraise@\wdz@
+  \binrel@{#2}%
+  \dimen@-\wd8 %
+  \binrel@@{%
+    \mkern-.8mu\copy8 %
+    \kern\dimen@\mkern.4mu\raise\pmbraise@\copy8 %
+    \kern\dimen@\mkern.4mu\box8 }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\def\binrel@#1{\begingroup
+  \setboxz@h{\thinmuskip0mu
+    \medmuskip\m@ne mu\thickmuskip\@ne mu
+    \setbox\tw@\hbox{$#1\m@th$}\kern-\wd\tw@
+    ${}#1{}\m@th$}%
+%    \end{macrocode}
+%    The \cn{noexpand} here should be unnecessary, but just in case
+%    \ldots
+%    \begin{macrocode}
+  \edef\@tempa{\endgroup\let\noexpand\binrel@@
+    \ifdim\wdz@<\z@ \mathbin
+    \else\ifdim\wdz@>\z@ \mathrel
+    \else \relax\fi\fi}%
+  \@tempa
+}
+%    \end{macrocode}
+%    For completeness, assign a default value for \cs{binrel@@}.
+%    \begin{macrocode}
+\let\binrel@@\relax
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \CheckSum{131}
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amsbsy.ins b/macros/latex-dev/required/amsmath/amsbsy.ins
new file mode 100644
index 0000000000..fe1cd5413d
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsbsy.ins
@@ -0,0 +1,50 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amsbsy.sty}{\from{amsbsy.dtx}{}}
+}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/amsmath/amsbsy.pdf b/macros/latex-dev/required/amsmath/amsbsy.pdf
new file mode 100644
index 0000000000..9a2dabfc88
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsbsy.pdf
diff --git a/macros/latex-dev/required/amsmath/amscd.dtx b/macros/latex-dev/required/amsmath/amscd.dtx
new file mode 100644
index 0000000000..2d0a35d685
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amscd.dtx
@@ -0,0 +1,322 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amscd}
+\GetFileInfo{amscd.sty}
+%    Dummy citation to avoid error in an example.
+\bibcite{fre:cichon}{C}
+\begin{document}
+\title{The \pkg{amscd} package}
+\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amscd.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+% \newcommand{\operatorname}[1]{\mathop{\mathrm{#1}}}
+% \newcommand{\per}{\operatorname{per}}
+% \newcommand{\cov}{\operatorname{cov}}
+% \newcommand{\non}{\operatorname{non}}
+% \newcommand{\cf}{\operatorname{cf}}
+% \newcommand{\add}{\operatorname{add}}
+% \newcommand{\End}{\operatorname{End}}
+%
+% \section{Introduction}
+%
+%    The \pkg{amscd} package provides a \env{CD} environment that
+%    emulates the commutative diagram capabilities of \amstex/ version
+%    2.x. This means that only simple rectangular diagrams are
+%    supported, with no diagonal arrows or more exotic features. Many
+%    users will be better served by one of the more powerful diagram
+%    packages such as \pkg{diagram}, \pkg{xypic}, or \pkg{kuvio}.
+%
+%    Example:
+%    \begin{equation}\begin{CD}
+%    S^{{\mathcal{W}}_\Lambda}\otimes T   @>j>>   T\\
+%    @VVV                                    @VV{\End P}V\\
+%    (S\otimes T)/I                  @=      (Z\otimes T)/J
+%    \end{CD}\end{equation}
+% \begin{verbatim}
+% \begin{equation}\begin{CD}
+% S^{{\mathcal{W}}_\Lambda}\otimes T   @>j>>   T\\
+% @VVV                                    @VV{\End P}V\\
+% (S\otimes T)/I                  @=      (Z\otimes T)/J
+% \end{CD}\end{equation}
+% \end{verbatim}
+%    (assuming \cn{End} is defined as an `operator name'.
+%
+%    Another example:
+%
+%    We will make liberal use of Cichon's Diagram \cite{fre:cichon}:
+%    \begin{equation}
+%    \begin{CD}
+%    \cov(\mathcal{L}) @>>> \non(\mathcal{K}) @>>> \cf(\mathcal{K}) @>>>
+%    \cf(\mathcal{L})\\
+%    @VVV @AAA @AAA @VVV\\
+%    \add(\mathcal{L}) @>>> \add(\mathcal{K}) @>>> \cov(\mathcal{K}) @>>>
+%    \non(\mathcal{L})
+%    \end{CD}\end{equation}
+% \begin{verbatim}
+% \begin{equation}\begin{CD}
+% \cov(\mathcal{L}) @>>> \non(\mathcal{K}) @>>> \cf(\mathcal{K}) @>>>
+% \cf(\mathcal{L})\\
+% @VVV @AAA @AAA @VVV\\
+% \add(\mathcal{L}) @>>> \add(\mathcal{K}) @>>> \cov(\mathcal{K}) @>>>
+% \non(\mathcal{L})
+% \end{CD}\end{equation}
+% \end{verbatim}
+%
+% \StopEventually{}
+%
+%    Standard package info.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesPackage{amscd}[2017/04/14 v2.1 AMS Commutative Diagrams]
+%    \end{macrocode}
+%    \begin{macrocode}
+\RequirePackage{amsgen}
+%    \end{macrocode}
+%      Better not to redefine \verb|\math@cr| if it is already defined,
+%      because for CD use only we want to omit the part of the code
+%      related to \verb|\dspbrk@lvl| (see \fn{amsmath.sty}).
+%
+%    [mjd,1999/11/04] These definitions have gone somewhat obsolete; but
+%    we had probably better leave them as they are for backward
+%    compatibility.
+%    \begin{macrocode}
+\@ifundefined{math@cr}{%
+  \def\math@cr{{\ifnum0=`}\fi
+    \@ifstar{\global\@eqpen\@M\math@cr@}%
+          {\global\@eqpen\interdisplaylinepenalty \math@cr@}}
+%    \end{macrocode}
+%    The following section merely duplicates some code from the
+%    \pkg{amsmath} package, in case the \pkg{amscd} package is used by
+%    itself. For documentation of the code refer to \fn{amsmath.dtx}.
+%    \begin{macrocode}
+  \def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
+  \def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@
+    \noalign{\vskip#1\relax}}
+  \def\restore@math@cr{\def\math@cr@@@{\cr}}
+}{}
+\restore@math@cr
+%    \end{macrocode}
+%    [mjd,1999/11/04] These definitions too are somewhat obsolete;
+%    but we had probably better leave them as they are for backward
+%    compatibility.
+%    \begin{macrocode}
+\@ifundefined{rightarrowfill@}{
+  \def\rightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+    $#1\copy\z@\mkern-6mu\cleaders
+    \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+    \mkern-6mu\mathord\rightarrow$}
+  \def\leftarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+    $#1\mathord\leftarrow\mkern-6mu\cleaders
+    \hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
+    \mkern-6mu\box\z@$}
+  \def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+    $#1\mathord\leftarrow\mkern-6mu\cleaders
+    \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+    \mkern-6mu\mathord\rightarrow$}
+}{}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
+\@ifundefined{Iat}{%
+  \DeclareRobustCommand{\Iat}{\FN@\at@}
+}{}
+\begingroup \catcode`\@=\active
+%    \end{macrocode}
+%    Define math \qc{\@} to replicate its mathcode-dictated behavior.
+%    This is in case \qc{\@} occurs outside of \env{CD}.
+%    \begin{macrocode}
+\csname if\string @compatibility\endcsname
+\else \fam=\mathcode`\@
+  \xdef @{\mathchar\number\fam\space }
+\fi
+\gdef\CDat{\let @=\Iat}
+\endgroup
+\mathcode`\@="8000 % make @ pseudo-active in math
+\def\at@{\let\next@\at@@
+ \ifcat\noexpand\next a\else
+ \ifcat\noexpand\next0\else
+ \ifcat\noexpand\next\relax\else
+ \let\next@\at@@@\fi\fi\fi\next@}
+\def\at@@#1{\expandafter
+  \ifx\csname\space @\string#1\endcsname\relax
+    \DN@{\at@@@#1}%
+  \else
+    \DN@{\csname\space @\string#1\endcsname}%
+  \fi\next@}%
+%    \end{macrocode}
+%    The following items should be defined only if they are not
+%    already defined, either to leave the package name untouched (in
+%    the case of \cs{PackageError}) or to avoid redundant allocation
+%    of token or dimen registers.
+%    \begin{macrocode}
+\@ifundefined{default@tag}{%
+  \def\default@tag{%
+    \def\tag{\PackageError{amscd}{\protect\tag\space not allowed
+      here}\@eha}}%
+}{}%
+\@ifundefined{at@@@}{%
+  \def\at@@@{\PackageError{amscd}{\Invalid@@ @}{\the\athelp@}\char64\relax}
+}{}
+\@ifundefined{athelp@}{\csname newhelp\endcsname\athelp@
+{Only certain combinations beginning with @ make sense to me.^^J%
+I'll assume you wanted @@ for a printed @.}}{}
+\@ifundefined{minaw@}{\newdimen\minaw@}{}
+\@ifundefined{bigaw@}{\newdimen\bigaw@}{}
+%    \end{macrocode}
+%
+%      Assignment of a couple of dimensions, and initialization of
+%      \verb=\ampersand@=. We check to see if we need to define
+%      \verb=\minaw@= and \verb=\bigaw@=.
+%    \begin{macrocode}
+\minaw@11.111pt
+\newdimen\minCDarrowwidth
+\minCDarrowwidth2.5pc
+\newif\ifCD@
+\let\ampersand@\relax
+%    \end{macrocode}
+%
+%      Added \verb|\restore@math@cr\default@tag| to fix line numbering
+%      problems, 7-JUN-1991. Suggested by I.~Zakharevich.
+%    \begin{macrocode}
+\newenvironment{CD}{%
+  \CDat
+  \bgroup\relax\iffalse{\fi\let\ampersand@&\iffalse}\fi
+  \CD@true\vcenter\bgroup\let\\\math@cr\restore@math@cr\default@tag
+  \tabskip\z@skip\baselineskip20\ex@
+  \lineskip3\ex@\lineskiplimit3\ex@\halign\bgroup
+  &\hfill$\m@th##$\hfill\crcr
+}{%
+  \crcr\egroup\egroup\egroup
+}
+%    \end{macrocode}
+%
+% \begin{macro}{\CD@check}
+%    This check is used by all macros that must not appear outside the
+%    \env{CD} environment. The first argument is the symbol to be used
+%    after \verb+@+, the second one the action to be performed.
+%
+%    Once again we use the trick of defining a temporary control
+%    sequence \verb+\next@+ and calling it after the final \verb+\fi+.
+%    This is not absolutely necessary, but it ensures that the
+%    conditional text is processed in one and the same column
+%    of the enclosing alignment.
+%    \begin{macrocode}
+\def\CD@check#1#2{\ifCD@\DN@{#2}\else
+  \DN@{\PackageError{amscd}{@\protect#1 not
+    allowed outside of the CD environment}\@eha}%
+  \fi\next@}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\atdef@>#1>#2>{\ampersand@
+  \ifCD@ \global\bigaw@\minCDarrowwidth \else \global\bigaw@\minaw@ \fi
+  \setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%
+  \ifdim\wdz@>\bigaw@\global\bigaw@\wdz@\fi
+%    \end{macrocode}
+%      If \verb|#2| is empty we can save some work.
+%    \begin{macrocode}
+  \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
+    \ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi}%
+ \ifCD@\enskip\fi
+   \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill@\displaystyle}}%
+     \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+ \ifCD@\enskip\fi \ampersand@}
+%
+\atdef@<#1<#2<{\ampersand@
+  \ifCD@ \global\bigaw@\minCDarrowwidth \else \global\bigaw@\minaw@ \fi
+  \setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%
+  \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
+  \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%
+    \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
+  \ifCD@\enskip\fi
+    \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill@\displaystyle}}%
+      \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+  \ifCD@\enskip\fi \ampersand@}
+%    \end{macrocode}
+%
+%      Variants of the above two arrows, using \verb|(| and \verb|)|
+%      characters instead of \verb|<| and \verb|>| characters, are
+%      provided for those whose keyboards don't have the latter.
+%    \begin{macrocode}
+\begingroup \catcode`\~=\active \lccode`\~=`\@
+\lowercase{%
+  \global\atdef@)#1)#2){~>#1>#2>}
+  \global\atdef@(#1(#2({~<#1<#2<}
+}% end lowercase
+\endgroup
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\atdef@ A#1A#2A{\CD@check{A..A..A}{\llap{$\m@th\vcenter{\hbox
+  {$\scriptstyle#1$}}$}\Big\uparrow
+  \rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
+%
+\atdef@ V#1V#2V{\CD@check{V..V..V}{\llap{$\m@th\vcenter{\hbox
+  {$\scriptstyle#1$}}$}\Big\downarrow
+  \rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
+%
+\atdef@={\CD@check={&\enskip\mathrel
+  {\vbox{\hrule\@width\minCDarrowwidth\vskip2\ex@\hrule\@width
+  \minCDarrowwidth}}\enskip&}}
+%
+\atdef@|{\CD@check|{\Big\Vert&&}}
+%
+\atdef@\vert{\CD@check\vert{\Big\Vert&&}}
+%
+\atdef@.{\CD@check.{&&}}
+%    \end{macrocode}
+%
+%    The \cn{pretend} command has weird syntax that doesn't fit well
+%    with standard \latex/ syntax so we leave it undone, at least for
+%    now. [mjd,1994/10/27]
+%    \begin{macrocode}
+%\def\pretend#1\haswidth#2{\setboxz@h{$\m@th\scriptstyle{#2}$}\hbox
+% to\wdz@{\hfill$\m@th\scriptstyle{#1}$\hfill}}
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \CheckSum{459}
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amscd.ins b/macros/latex-dev/required/amsmath/amscd.ins
new file mode 100644
index 0000000000..148c4cb32e
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amscd.ins
@@ -0,0 +1,50 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amscd.sty}{\from{amscd.dtx}{}}
+}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/amsmath/amscd.pdf b/macros/latex-dev/required/amsmath/amscd.pdf
new file mode 100644
index 0000000000..860352c44a
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amscd.pdf
diff --git a/macros/latex-dev/required/amsmath/amsgen.dtx b/macros/latex-dev/required/amsmath/amsgen.dtx
new file mode 100644
index 0000000000..5edc26b9cc
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsgen.dtx
@@ -0,0 +1,386 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society. 
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amsgen}
+\GetFileInfo{amsgen.sty}
+\begin{document}
+\title{The \pkg{amsgen} package}
+\author{American Mathematical Society\\Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amsgen.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%    This is an internal package for storing common functions
+%    that are shared by more than one package in the \amslatex/
+%    distribution. Some of these might eventually make it into the \latex/
+%    kernel.
+%
+% \StopEventually{}
+%
+%    Standard package info.
+%    Using \cs{ProvidesFile} rather than \cs{ProvidesPackage} because
+%    the latter, when input by, e.g, \cls{amsbook}, results in
+%    \texttt{LaTeX warning: You have requested document class `amsbook',
+%    but the document class provides `amsgen'.}
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesFile{amsgen.sty}[1999/11/30 v2.0 generic functions]
+%    \end{macrocode}
+%
+% \section{Implementation}
+%    Some general macros shared by \fn{amsart.dtx}, \fn{amsmath.dtx},
+%    \fn{amsfonts.dtx}, \dots
+%
+% \begin{macro}{\@saveprimitive}
+%    The \pkg{amsmath} package redefines a number of \tex/ primitives.
+%    In case some preceding package also decided to redefine one of
+%    those same primitives, we had better do some checking to make
+%    sure that we are able to save the primitive meaning for internal
+%    use. This is handled by the \cs{@saveprimitive} function. We
+%    follow the example of \cs{@@input} where the primitive meaning is
+%    stored in an internal control sequence with a |@@| prefix.
+%    Primitive control sequences can be distinguished by the fact that
+%    \cs{string} and \cs{meaning} return the same information.
+%    \begin{macrocode}
+\providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
+  \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
+  \ifx\@tempa\@tempb \global\let#2#1%
+  \else
+%    \end{macrocode}
+%    Check to see if \arg{2} was already given the desired primitive
+%    meaning somewhere else.
+%    \begin{macrocode}
+    \edef\@tempb{\meaning#2}%
+    \ifx\@tempa\@tempb
+    \else
+      \@latex@error{Unable to properly define \string#2; primitive
+      \noexpand#1no longer primitive}\@eha
+    \fi
+  \fi
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xp}
+% \begin{macro}{\@nx}
+%    Shorthands for long command names.
+%    \begin{macrocode}
+\let\@xp=\expandafter
+\let\@nx=\noexpand
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\@emptytoks}
+%    A token register companion for \cs{@empty}. Saves a little main mem and
+%    probably makes initializations such as |\toks@{}| run faster too.
+%    \begin{macrocode}
+\newtoks\@emptytoks
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\@oparg}
+%    Use of \cs{@oparg} simplifies some constructions where a macro
+%    takes an optional argument in square brackets. We can't use
+%    \cn{newcommand} here because this function might be previously
+%    defined by the \pkg{amsmath} package in a loading sequence such as
+% \begin{verbatim}
+% \usepackage{amsmath,amsthm}
+% \end{verbatim}
+%    \begin{macrocode}
+\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@ifempty}
+% \begin{macro}{\@ifnotempty}
+%    |\@ifnotempty| and |\@ifempty| use category 11 |@| characters to
+%    test whether the argument is empty or not, since these are highly
+%    unlikely to occur in the argument. As with \cn{@oparg}, there is a
+%    possibility that these commands were defined previously in
+%    \fn{amsmath.sty}.
+%    \begin{macrocode}
+\long\def\@ifempty#1{\@xifempty#1@@..\@nil}
+\long\def\@xifempty#1#2@#3#4#5\@nil{%
+  \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
+%    \end{macrocode}
+%    \cs{@ifnotempty} is a shorthand that makes code read better when
+%    no action is needed in the empty case. At a cost of double
+%    argument-reading---so for often-executed code, avoiding
+%    \cs{@ifnotempty} might be wise.
+%    \begin{macrocode}
+\long\def\@ifnotempty#1{\@ifempty{#1}{}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    Some abbreviations to conserve token mem.
+%    \begin{macrocode}
+\def\FN@{\futurelet\@let@token}
+\def\DN@{\def\next@}
+\def\RIfM@{\relax\ifmmode}
+\def\setboxz@h{\setbox\z@\hbox}
+\def\wdz@{\wd\z@}
+\def\boxz@{\box\z@}
+\def\relaxnext@{\let\@let@token\relax}
+%    \end{macrocode}
+%
+% \begin{macro}{\new@ifnextchar}
+%    This macro is a new version of \latex/'s \verb+\@ifnextchar+,
+%    macro that does not skip over spaces.
+%    \begin{macrocode}
+\long\def\new@ifnextchar#1#2#3{%
+%    \end{macrocode}
+%    By including the space after the equals sign, we make it possible
+%    for \cs{new@ifnextchar} to do look-ahead for any token, including a
+%    space!
+%    \begin{macrocode}
+  \let\reserved@d= #1%
+  \def\reserved@a{#2}\def\reserved@b{#3}%
+  \futurelet\@let@token\new@ifnch
+}
+%
+\def\new@ifnch{%
+  \ifx\@let@token\reserved@d \let\reserved@b\reserved@a \fi
+  \reserved@b
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@ifstar}
+%    There will essentially never be a space before the \qc{\*}, so
+%    using \cs{@ifnextchar} is unnecessarily slow.
+%    \begin{macrocode}
+\def\@ifstar#1#2{\new@ifnextchar *{\def\reserved@a*{#1}\reserved@a}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+%    The hook \cs{every@size} was changed to \cs{every@math@size} in the
+%    December 1994 release of \latex/ and its calling procedures changed.
+%    If \cs{every@math@size} is undefined it means the user has an older
+%    version of \latex/ so we had better define it and patch a couple of
+%    functions (\cs{glb@settings} and \cs{set@fontsize}).
+%    \begin{macrocode}
+\@ifundefined{every@math@size}{%
+%    \end{macrocode}
+%    Reuse the same token register; since it was never used except for
+%    the purposes that are affected below, this is OK.
+%    \begin{macrocode}
+\let\every@math@size=\every@size
+\def\glb@settings{%
+     \expandafter\ifx\csname S@\f@size\endcsname\relax
+       \calculate@math@sizes
+     \fi
+     \csname S@\f@size\endcsname
+      \ifmath@fonts
+%       \ifnum \tracingfonts>\tw@
+%          \@font@info{Setting up math fonts for
+%                  \f@size/\f@baselineskip}\fi
+        \begingroup
+          \escapechar\m@ne
+          \csname mv@\math@version \endcsname
+          \globaldefs\@ne
+          \let \glb@currsize \f@size
+          \math@fonts
+        \endgroup
+        \the\every@math@size
+      \else
+%       \ifnum \tracingfonts>\tw@
+%        \@font@info{No math setup for \f@size/\f@baselineskip}%
+%       \fi
+      \fi
+}
+%    \end{macrocode}
+%    Remove |\the\every@size| from \cs{size@update}.
+%    \begin{macrocode}
+\def\set@fontsize#1#2#3{%
+    \@defaultunits\@tempdimb#2pt\relax\@nnil
+    \edef\f@size{\strip@pt\@tempdimb}%
+    \@defaultunits\@tempskipa#3pt\relax\@nnil
+    \edef\f@baselineskip{\the\@tempskipa}%
+    \edef\f@linespread{#1}%
+    \let\baselinestretch\f@linespread
+      \def\size@update{%
+        \baselineskip\f@baselineskip\relax
+        \baselineskip\f@linespread\baselineskip
+        \normalbaselineskip\baselineskip
+        \setbox\strutbox\hbox{%
+          \vrule\@height.7\baselineskip
+                \@depth.3\baselineskip
+                \@width\z@}%
+%%%     \the\every@size
+        \let\size@update\relax}%
+  }
+}{}% end \@ifundefined test
+%    \end{macrocode}
+%
+% \begin{macro}{\ex@}
+%    The \cs{ex@} variable provides a small unit of space for use in
+%    math-mode constructions, that varies according to the current type
+%    size. For example, the \cn{pmb} command uses \cs{ex@} units.
+%    Since a macro or mu unit solution for the \meta{dimen} \cs{ex@} won't
+%    work without changing a lot of current code in the \pkg{amsmath}
+%    package, we set \cs{ex@} through the \cs{every@math@size} hook.
+%    The value of \cs{ex@} is scaled nonlinearly in a range of roughly
+%    0.5pt to 1.5pt, by the function \cs{compute@ex@}.
+%    \begin{macrocode}
+\newdimen\ex@
+\addto@hook\every@math@size{\compute@ex@}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \cs{compute@ex@} computes \cs{ex@} as a nonlinear scaling from 10pt
+%    to current font size (\cs{f@size}). Using .97 as the multiplier makes 1
+%    |ex@| $\approx$ .9pt when the current type size is 8pt and 1 |ex@|
+%    $\approx$ 1.1pt when the current type size is 12pt.
+%
+%    The formula is essentially
+% \begin{displaymath}
+% \newcommand{\points}{\mbox{pt}}
+% \newcommand{\floor}[1]{\lfloor#1\rfloor}
+%      1\points \pm (1\points - (.97)^{\floor{\vert 10 - n\vert}})
+% \end{displaymath}
+%    where $n$ = current type size, but adjusted to differentiate
+%    half-point sizes as well as whole point sizes, and there is a
+%    cutoff for extraordinarily large values of \cs{f@size} ($>$ 20pt)
+%    so that the value of \cs{ex@} never exceeds 1.5pt.
+%
+%    \begin{macrocode}
+\def\compute@ex@{%
+  \begingroup
+  \dimen@-\f@size\p@
+  \ifdim\dimen@<-20\p@
+%    \end{macrocode}
+%    Never make \cs{ex@} larger than 1.5pt.
+%    \begin{macrocode}
+    \global\ex@ 1.5\p@
+  \else
+%    \end{macrocode}
+%    Adjust by the reference size and multiply by 2 to allow for
+%    half-point sizes.
+%    \begin{macrocode}
+    \advance\dimen@10\p@ \multiply\dimen@\tw@
+%    \end{macrocode}
+%    Save information about the current sign of \cs{dimen@}.
+%    \begin{macrocode}
+    \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%
+%    \end{macrocode}
+%    Get the absolute value of \cs{dimen@}.
+%    \begin{macrocode}
+    \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
+    \advance\dimen@-\@m sp % fudge factor
+%    \end{macrocode}
+%    Here we use \cs{vfuzz} merely as a convenient scratch register
+%    \begin{macrocode}
+    \vfuzz\p@
+%    \end{macrocode}
+%    Multiply in a loop.
+%    \begin{macrocode}
+    \def\do{\ifdim\dimen@>\z@
+      \vfuzz=.97\vfuzz
+      \advance\dimen@ -\p@
+%\message{\vfuzz: \the\vfuzz, \dimen@: \the\dimen@}%
+      \@xp\do \fi}%
+    \do
+    \dimen@\p@ \advance\dimen@-\vfuzz
+    \global\ex@\p@
+    \global\advance\ex@ \@tempa\dimen@
+  \fi
+  \endgroup
+%\typeout{\string\f@size: \f@size}\showthe\ex@
+}
+%    \end{macrocode}
+%    Tests of the \cs{compute@ex@} function yield the following results:
+%
+% \begin{center}\begin{tabular}{rlrl}
+%    \cs{f@size}& \cs{ex@}&   \cs{f@size}& \cs{ex@}\\
+%    10&          1.0pt&      9&           0.94089pt\\
+%    11&          1.05911pt&  8.7&         0.91266pt\\
+%    12&          1.11473pt&  8.5&         0.91266pt\\
+%    14.4&        1.23982pt&  8.4&         0.88527pt\\
+%    17.28&       1.36684pt&  8&           0.88527pt\\
+%    20.74&       1.5pt&      7&           0.83293pt\\
+%    19.5&        1.4395pt&   6&           0.78369pt\\
+%                       &&    5&           0.73737pt\\
+%                       &&    1&           0.57785pt
+% \end{tabular}\end{center}
+%
+%  \begin{macro}{\@addpunct}
+%    Use of the \cs{@addpunct} function allows ending punctuation in
+%    section headings and elsewhere to be intelligently omitted
+%    when punctuation is already present.
+%    \begin{macrocode}
+\def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\frenchspacing}
+%    Change \cn{frenchspacing} to ensure that \cs{@addpunct} will
+%    continue to work properly even when `french' spacing is in effect.
+%    \begin{macrocode}
+\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
+  \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
+%    \end{macrocode}
+%  \end{macro}
+%
+% \subsection{Miscellaneous}
+%    \begin{macrocode}
+\def\nomath@env{\@amsmath@err{%
+  \string\begin{\@currenvir} allowed only in paragraph mode%
+}\@ehb% "You've lost some text"
+}
+%    \end{macrocode}
+%     A trade-off between main memory space and hash size; using
+%     \verb+\Invalid@@+ saves 14 bytes of main memory for each use of
+%     \verb+\Invalid@+, at the cost of one control sequence name.
+%     \verb+\Invalid@+ is currently used about five times and
+%     \verb+\Invalid@@+ is used by itself in some other instances,
+%     which means that it saves us more memory than \verb+\FN@+,
+%     \verb+\RIfM@+, and some of the other abbreviations above.
+%    \begin{macrocode}
+\def\Invalid@@{Invalid use of \string}
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \CheckSum{337}
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amsgen.ins b/macros/latex-dev/required/amsmath/amsgen.ins
new file mode 100644
index 0000000000..8c5683cb5a
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsgen.ins
@@ -0,0 +1,50 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amsgen.sty}{\from{amsgen.dtx}{}}
+}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/amsmath/amsgen.pdf b/macros/latex-dev/required/amsmath/amsgen.pdf
new file mode 100644
index 0000000000..9078999dc0
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsgen.pdf
diff --git a/macros/latex-dev/required/amsmath/amsldoc.pdf b/macros/latex-dev/required/amsmath/amsldoc.pdf
new file mode 100644
index 0000000000..decc68fe74
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsldoc.pdf
diff --git a/macros/latex-dev/required/amsmath/amsldoc.tex b/macros/latex-dev/required/amsmath/amsldoc.tex
new file mode 100644
index 0000000000..9e08f029f5
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsldoc.tex
@@ -0,0 +1,2770 @@
+%
+% Copyright (C) 1995, 2000, 2013 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+\documentclass[leqno,titlepage,openany]{amsldoc}[1999/12/13]
+
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+
+\ifx\UndEfiNed\url
+  \ClassError{amsldoc}{%
+    This version of amsldoc.tex must be processed\MessageBreak
+    with a newer version of amsldoc.cls (2.02 or later).}{}
+\fi
+
+\renewcommand\bibname{References}
+
+%    Definitions that should be moved to amsldoc.cls
+%    when it is next updated
+\makeatletter
+\let\cleardouble@page\cleardoublepage
+\AtBeginDocument{%
+  \ifx\cleardouble@page\cleardoublepage
+    \def\cleardoublepage{\clearpage{\pagestyle{empty}\cleardouble@page}}
+  \fi
+}
+
+% #1 is empty or one of class, environment, option, package
+% could use different font in each case
+\makeatletter
+\def\@category@index#1#2{%
+    \autoindex{%
+        #2\actualchar\string\index#1font{#2}%
+        \ifx\@nil#1\@nil\else\space#1\fi
+    }%
+}
+
+\let\indexpackagefont\textsf
+\let\indexclassfont\textsf
+\let\indexoptionfont\texttt
+\let\indexenvironmentfont\texttt
+\let\indexfont\texttt
+\makeatother
+%    For a package that won't be indexed, i.e. amsmath
+\newcommand{\nipkg}{\textsf}
+\def\tikz/{Ti\textit{k}Z}
+%    End definitions for amsldoc.cls
+
+\title{User's Guide for the \nipkg{amsmath} Package (Version~2.1)}
+\author{American Mathematical Society, \LaTeX3 Project}
+\date{1999-12-13 (revised 2002-02-25, 2016-11-14, 2018-04-05)}
+\makeatletter
+\def\@thanks{\bigskip\MaintainedByLaTeXTeam{amslatex}}
+\makeatother
+
+%    Use the amsmath package and amscd package in order to print
+%    examples.
+\usepackage{amsmath}
+\usepackage{amscd}
+
+\usepackage{imakeidx}
+%    Need alternate coding for vertical bar to get it into index.
+%    Based on \qcbang and \cnbang in amsldoc.cls, refined by David Carlisle.
+%    Give it a sort field that will be at the end of the symbols;
+%    must avoid " and | which have special meanings.
+\DeclareRobustCommand{\qcvert}{\qc\|\index{{z1}@{\ntt\char'174}}}
+\DeclareRobustCommand{\cnvert}{%
+  \ncn{\|}\index{{z0}@{\ntt\bslchar\char'174}}}
+%    Need alternate index sort field for bang to allow & to sort first
+\DeclareRobustCommand{\altcnbang}{%
+  \ncn{\!}\index{"!b@{\ntt\bslchar\qcbang}}}
+\DeclareRobustCommand{\cnamp}{%
+  \index{"!a@\texttt{\&}}}
+
+\makeindex[intoc] % generate index data
+\providecommand{\see}[2]{\textit{see} #1}
+
+%    The amsldoc class includes a number of features useful for
+%    documentation about TeX, including:
+%
+%    ---Commands \tex/, \amstex/, \latex/, ... for uniform treatment
+%    of the various logos and easy handling of following spaces.
+%
+%    ---Commands for printing various common elements: \cn for command
+%    names, \fn for file names (including font-file names), \env for
+%    environments, \pkg and \cls for packages and classes, etc.
+
+%    Many of the command names used here are rather long and will
+%    contribute to poor linebreaking if we follow the \latex/ practice
+%    of not hyphenating anything set in tt font; instead we selectively
+%    allow some hyphenation.
+\allowtthyphens % defined in amsldoc.cls
+
+\hyphenation{ac-cent-ed-sym-bol add-to-counter add-to-length align-at
+  aligned-at allow-dis-play-breaks ams-art ams-cd ams-la-tex amsl-doc
+  ams-symb ams-tex ams-text ams-xtra bmatrix bold-sym-bol cen-ter-tags
+  eqn-ar-ray idots-int int-lim-its latex med-space neg-med-space
+  neg-thick-space neg-thin-space no-int-lim-its no-name-lim-its
+  over-left-arrow over-left-right-arrow over-right-arrow pmatrix
+  qed-sym-bol set-length side-set small-er tbinom the-equa-tion
+  thick-space thin-space un-der-left-arrow un-der-left-right-arrow
+  un-der-right-arrow use-pack-age var-inj-lim var-proj-lim vmatrix
+  xalign-at xx-align-at}
+
+%    Prepare for illustrating the \vec example
+\newcommand{\vect}[1]{\mathbf{#1}}
+
+\newcommand{\booktitle}[1]{\textit{#1}}
+\newcommand{\journalname}[1]{\textit{#1}}
+\newcommand{\seriesname}[1]{\textit{#1}}
+
+%    Command to insert and index a particular phrase. Doesn't work for
+%    certain kinds of special characters in the argument.
+\newcommand{\ii}[1]{#1\index{#1}}
+
+\newcommand{\vstrut}[1]{\vrule width0pt height#1\relax}
+
+%    An environment for presenting comprehensive address information:
+\newenvironment{infoaddress}{%
+  \par\topsep\medskipamount
+  \trivlist\centering
+  \item[]%
+  \begin{minipage}{.7\columnwidth}%
+  \raggedright
+}{%
+  \end{minipage}%
+  \endtrivlist
+}
+
+\newenvironment{eqxample}{%
+  \par\addvspace\medskipamount
+  \noindent\begin{minipage}{.5\columnwidth}%
+  \def\producing{\end{minipage}\begin{minipage}{.5\columnwidth}%
+    \hbox\bgroup\kern-.2pt\vrule width.2pt%
+      \vbox\bgroup\parindent0pt\relax
+%    The 3pt is to cancel the -\lineskip from \displ@y
+    \abovedisplayskip3pt \abovedisplayshortskip\abovedisplayskip
+    \belowdisplayskip0pt \belowdisplayshortskip\belowdisplayskip
+    \noindent}
+}{%
+  \par
+%    Ensure that a lonely \[\] structure doesn't take up width less than
+%    \hsize.
+  \hrule height0pt width\hsize
+  \egroup\vrule width.2pt\kern-.2pt\egroup
+  \end{minipage}%
+  \par\addvspace\medskipamount
+}
+
+%    Errors in output shouldn't be \texttt, and they may also be longer
+%    than one line, but they should be identified by the "errorbullet".
+%    (They were formerly labeled as aubsections.)
+\newenvironment{erroro}[1]{%
+  \par\addvspace\medskipamount
+  \noindent\hangindent\parindent
+  \hbox to\parindent{\errorbullet\hfil}\ignorespaces
+  #1\par\vspace{\smallskipamount}
+}{%
+  \par\addvspace\medskipamount
+}
+
+%    The chapters are so short, perhaps we shouldn't call them by the
+%    name `Chapter'. We make \chaptername read an argument in order to
+%    remove a following \space or "{} " (both possibilities are present
+%    in book.cls).
+
+\renewcommand{\chaptername}[1]{}
+\newcommand{\chapnum}[1]{\mdash #1\mdash }
+\makeatletter
+\def\@makechapterhead#1{%
+  \vspace{1.5\baselineskip}%
+  {\parindent \z@ \raggedright \reset@font
+    \ifnum \c@secnumdepth >\m@ne
+      \large\bfseries \chapnum{\thechapter}%
+      \par\nobreak
+      \vskip.5\baselineskip\relax
+    \fi
+    #1\par\nobreak
+    \vskip\baselineskip
+  }}
+\makeatother
+
+%    A command for ragged-right parbox in a tabular.
+\newcommand{\rp}{\let\PBS\\\raggedright\let\\\PBS}
+
+%    Non-indexed file name
+\newcommand{\nfn}[1]{\texttt{#1}}
+
+%    For the examples in the math spacing table.
+%%\newcommand{\lspx}{\mbox{\rule{5pt}{.6pt}\rule{.6pt}{6pt}}}
+%%\newcommand{\rspx}{\mbox{\rule[-1pt]{.6pt}{7pt}%
+%%  \rule[-1pt]{5pt}{.6pt}}}
+\newcommand{\lspx}{\mathord{\Rightarrow\mkern-1mu}}
+\newcommand{\rspx}{\mathord{\mkern-1mu\Leftarrow}}
+\newcommand{\spx}[1]{$\lspx #1\rspx$}
+
+%    For a list of characters representing document input.
+\newcommand{\clist}[1]{%
+  \mbox{\ntt\spaceskip.2em plus.1em \xspaceskip\spaceskip#1}}
+
+%    Fix weird \latex/ definition of rightmark.
+\makeatletter
+\def\rightmark{\expandafter\@rightmark\botmark{}{}}
+%    Also turn off section marks.
+\let\sectionmark\@gobble
+\renewcommand{\chaptermark}[1]{%
+  \uppercase{\markboth{\rhcn#1}{\rhcn#1}}}
+\newcommand{\rhcn}{\thechapter. }
+\makeatother
+
+%    Include down to \section but not \subsection, in toc:
+\setcounter{tocdepth}{1}
+
+%    Subheadings for the bibliography
+\newif\iffirstbibsubhead \firstbibsubheadtrue
+\newcommand{\bibsubhead}[1]{%
+  \iffirstbibsubhead \firstbibsubheadfalse
+  \else \addvspace{\medskipamount}
+  \fi
+  \item[]\hspace*{-\leftmargin}\textbf{#1}\par
+  \vspace{\smallskipamount}
+}
+
+\DeclareMathOperator{\ix}{ix}
+\DeclareMathOperator{\nul}{nul}
+\DeclareMathOperator{\End}{End}
+\DeclareMathOperator{\xxx}{xxx}
+
+\usepackage{hyperref}
+\hypersetup{pdfborder=0 0 0}
+\makeatletter
+\let\oldcs\cs
+\def\cs#1{\texorpdfstring{\oldcs{#1}}{\@backslashchar\@backslashchar#1}}
+\let\cn\cs
+\makeatother
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\frontmatter
+
+\maketitle
+
+\pagestyle{headings}
+\tableofcontents
+\cleardoublepage % for better page number placement
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mainmatter
+\chapter{Introduction}
+
+\index{amsmath@\texttt{amsmath} package|(}
+
+The \nipkg{amsmath} package is a \LaTeX{} package that provides
+miscellaneous enhancements for improving the information structure and
+printed output of documents that contain mathematical formulas. Readers
+unfamiliar with \LaTeX{} should refer to \cite{lamport}. If you have an
+up-to-date version of \LaTeX{}, the \nipkg{amsmath} package is normally
+provided along with it. Upgrading when a newer version of the
+\nipkg{amsmath} package is released can be done via
+\url{http://mirror.ctan.org/macros/latex/required/amsmath.zip}.
+
+This documentation describes the features of the \nipkg{amsmath} package
+and discusses how they are intended to be used. It also covers some
+ancillary packages:
+\begin{ctab}{lll}
+\pkg{amsbsy}& \pkg{amsopn}& \pkg{amsxtra}\\
+\pkg{amscd}& \pkg{amstext}\\
+\end{ctab}
+These all have something to do with the contents of math formulas. For
+information on extra math symbols and math fonts, see \cite{amsfonts}
+and \url{https://www.ams.org/tex/amsfonts.html}. For documentation of the
+\pkg{amsthm} package or AMS document classes (\cls{amsart},
+\cls{amsbook}, etc.\@) see \cite{amsthdoc} or \cite{amshandbk} and
+\url{https://www.ams.org/tex/author-info.html}.
+
+If you are a long-time \latex/ user and have lots of mathematics in what
+you write, then you may recognize solutions for some familiar problems
+in this list of \nipkg{amsmath} features:
+\begin{itemize}
+
+\item A convenient way to define new `operator name' commands analogous
+to \cn{sin} and \cn{lim}, including proper side spacing and automatic
+selection of the correct font style and size (even when used in
+sub- or superscripts).
+
+\item Multiple substitutes for the \env{eqnarray} environment to make
+various kinds of equation arrangements easier to write.
+
+\item Equation numbers automatically adjust up or down to avoid
+overprinting on the equation contents (unlike \env{eqnarray}).
+
+\item Spacing around equals signs matches the normal spacing in the
+\env{equation} environment (unlike \env{eqnarray}).
+
+\item A way to produce multiline subscripts as are often used with
+summation or product symbols.
+
+\item An easy way to substitute a variant equation number for a given
+equation instead of the automatically supplied number.
+
+\item An easy way to produce subordinate equation numbers of the form
+(1.3a) (1.3b) (1.3c) for selected groups of equations.
+
+\end{itemize}
+
+The \nipkg{amsmath} package is distributed together with some small
+auxiliary packages:
+\begin{description}
+\item[\nipkg{amsmath}] Primary package, provides various features for
+  displayed equations and other mathematical constructs.
+
+\item[\pkg{amstext}] Provides a \cn{text} command for
+  typesetting a fragment of text inside a display.
+
+\item[\pkg{amsopn}] Provides \cn{DeclareMathOperator} for defining new
+  `operator names' like \cn{sin} and \cn{lim}.
+
+\item[\pkg{amsbsy}] For backward compatibility this package continues
+to exist but use of the newer \pkg{bm} package that comes with \LaTeX{}
+is recommended instead.
+
+\item[\pkg{amscd}] Provides a \env{CD} environment for simple
+  commutative diagrams (no support for diagonal arrows).
+
+\item[\pkg{amsxtra}] Provides certain odds and ends such as
+  \cn{fracwithdelims} and \cn{accentedsymbol}, for compatibility with
+  documents created using version 1.1.
+
+\end{description}
+
+The \nipkg{amsmath} package incorporates \pkg{amstext}, \pkg{amsopn}, and
+\pkg{amsbsy}. The features of \pkg{amscd} and \pkg{amsxtra}, however,
+are available only by invoking those packages separately.
+
+The independent \pkg{mathtools} package \cite{mt} provides some
+enhancements to \nipkg{amsmath}; \pkg{mathtools} loads \nipkg{amsmath}
+automatically, so there is no need to separately load \nipkg{amsmath}
+if \pkg{mathtools} is used.  Some \pkg{mathtools} facilities
+will be noted below as appropriate.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Options for the \nipkg{amsmath} package}\label{options}
+
+The \nipkg{amsmath} package has the following options:
+\index{options!amsmath@\texttt{amsmath} package options|(}
+\begin{description}
+
+\item[\opt{centertags}] (default) For an equation containing a
+\env{split} environment, place equation
+numbers\index{equationn@equation numbers!vertical placement}
+vertically centered on the total height of the equation.
+
+\item[\opt{tbtags}] `Top-or-bottom tags': For an equation containing
+a \env{split} environment, place equation
+numbers\index{equationn@equation numbers!vertical placement} level with the last
+(resp.\ first) line, if numbers are on the right (resp.\ left).
+
+\item[\opt{sumlimits}] (default) Place the subscripts and
+superscripts\index{subscripts and superscripts!placement}\relax
+\index{limits|see{subscripts and superscripts}} of summation symbols
+above and below, in displayed equations. This option also affects other
+symbols of the same type\mdash $\prod$, $\coprod$, $\bigotimes$,
+$\bigoplus$, and so forth\mdash but excluding integrals (see below).
+
+\item[\opt{nosumlimits}] Always place the subscripts and superscripts of
+summation-type symbols to the side, even in displayed equations.
+
+\item[\opt{intlimits}] Like \opt{sumlimits}, but for
+integral\index{integrals!placement of limits} symbols.
+
+\item[\opt{nointlimits}] (default) Opposite of \opt{intlimits}.
+
+\item[\opt{namelimits}] (default) Like \opt{sumlimits}, but for certain
+`operator names' such as $\det$, $\inf$, $\lim$, $\max$, $\min$, that
+traditionally have subscripts%
+\index{subscripts and superscripts!placement} placed underneath when
+they occur in a displayed equation.
+
+\item[\opt{nonamelimits}] Opposite of \opt{namelimits}.
+
+\end{description}
+
+\goodbreak
+
+\begin{description}
+\item[\opt{alignedleftspaceyes}]
+\item[\opt{alignedleftspaceno}]
+\item[\opt{alignedleftspaceyesifneg}]
+\end{description}
+
+To use one of these package options, put the option name in the optional
+argument of the \cn{usepackage} command\mdash e.g.,
+\verb"\usepackage[intlimits]{amsmath}".
+For AMS document classes and any other classes that preload \nipkg{amsmath}
+desired options must be specified with the \cn{documentclass}\mdash
+e.g.,\\
+\verb+\documentclass[intlimits,tbtags,reqno]{amsart}+.
+
+The \nipkg{amsmath} package also recognizes the following options which
+are normally selected (implicitly or explicitly) through the
+\cn{documentclass} command, and thus need not be repeated in the option
+list of the \cn{usepackage}|{amsmath}| statement.
+\begin{description}
+
+\item[\opt{leqno}] Place equation numbers on the left.%
+\index{equationn@equation numbers!left or right placement}
+
+\item[\opt{reqno}] Place equation numbers on the right.
+
+\item[\opt{fleqn}] Position equations at a fixed indent from the left
+margin rather than centered in the text column.%
+\index{displayed equations!centering}
+
+\end{description}
+
+Three options have been added to control the space to the left of
+\env{aligned} and \env{gathered} environments. Prior to the 2017 release
+a thin space was added to the left but not the right of these constructs.
+This appears to have been an accidental feature of the implementation and
+was typically corrected by prefixing the environments with \altcnbang.
+
+The new default behavior is aimed to ensure that the environments do
+not have a thin space added in most cases, and that existing documents
+using |\!\begin{aligned}| continue to work as before.
+
+\begin{description}
+\item[\opt{alignedleftspaceyes}] Always add \cn{\,} to the left of \env{aligned} and \env{gathered}.
+\item[\opt{alignedleftspaceno}] Never add \cn{\,} to the left of \env{aligned} and \env{gathered}.
+\item[\opt{alignedleftspaceyesifneg}] Only add \cn{\,} if the environment is prefixed by negative space. (New default behavior.)
+\end{description}
+
+\index{options!amsmath@\texttt{amsmath} package options|)}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Displayed equations}
+
+\section{Introduction}
+The \nipkg{amsmath} package provides a number of additional displayed
+equation structures\index{displayed equations}%
+\index{equations|see{displayed equations}} beyond the ones
+provided in basic \latex/. The augmented set includes:
+\begin{verbatim}
+  equation     equation*     align       align*
+  gather       gather*       alignat     alignat*
+  multline     multline*     flalign     flalign*
+  split
+\end{verbatim}
+(Although the standard \env{eqnarray} environment remains available,
+it is better to use \env{align} or \env{equation}+\env{split} instead.
+Within \env{eqnarray}, spacing\index{horizontal spacing} around signs
+of relation is not the preferred mathematical spacing, and is
+inconsistent with that spacing as it appears in other environments.
+Long lines in this environment may result in misplaced or overprinted
+equation numbers. This environment also does not support the use of
+\cn{qed} or \cn{qedhere} as provided by theorem packages.)
+
+Except for \env{split}, each environment has both starred and unstarred
+forms, where the unstarred forms have automatic numbering using
+\latex/'s \env{equation} counter. You can suppress the number on any
+particular line by putting \cn{notag} before the end of that line;
+\cn{notag} should not be used outside a display environment as it will
+mess up the numbering.  You can also
+override\index{equationn@equation numbers!overriding} a number with a tag
+of your own using \cn{tag}|{|\<label>|}|, where \<label> means arbitrary
+text such as |$*$| or |ii| used to \qq{number} the equation.
+A tag can reference a different tagged display by use of
+|\tag{\ref{|\<label>|}|\<modifier>|}| where \<modifier> is optional.
+If you are using \pkg{hyperref}, use \cn{ref*};
+use of the starred form of \cn{ref} prevents a reference to a modified
+tag containing a nested link from linking to the original display.
+
+There is also a
+\cn{tag*} command that causes the text you supply to be typeset
+literally, without adding parentheses around it. \cn{tag} and \cn{tag*}
+can also be used within the unnumbered versions of all the \nipkg{amsmath}
+alignment structures. Some examples of the use of \cn{tag} may be found
+in the sample files \fn{testmath.tex} and \fn{subeqn.tex} provided with
+the \nipkg{amsmath} package.
+
+The \env{split} environment is a special subordinate form that is used
+only \emph{inside} one of the others. It cannot be used inside
+\env{multline}, however. \env{split} supports only one alignment (|&|)
+column; if more are needed, \env{aligned} or \env{alignedat} should be
+used. The width of a \env{split} structure is the full line width.
+
+In the structures that do alignment (\env{split}, \env{align} and
+variants), relation symbols have an |&| before them but not
+after\mdash unlike \env{eqnarray}. Putting the |&| after the
+relation symbol will interfere with the normal spacing; it has to go
+before.
+
+In all multiline environments, lines are divided by \cn{\\}.  The \cn{\\}
+should \emph{not} be used to end the last line.  Using it there will
+result in unwanted extra vertical space following the display.
+
+In \emph{all} math environments (inline or display), blank lines
+(equivalent to \cn{par}) are not permitted, and will result in an error.
+
+\begin{table}[p]
+\caption[]{Comparison of displayed equation environments (vertical lines
+indicating nominal margins)}\label{displays}
+\renewcommand{\theequation}{\arabic{equation}}
+\begin{eqxample}
+\begin{verbatim}
+\begin{equation*}
+a=b
+\end{equation*}
+\end{verbatim}
+\producing
+\begin{equation*}
+a=b
+\end{equation*}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{equation}
+a=b
+\end{equation}
+\end{verbatim}
+\producing
+\begin{equation}
+a=b
+\end{equation}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{equation}\label{xx}
+\begin{split}
+a& =b+c-d\\
+ & \quad +e-f\\
+ & =g+h\\
+ & =i
+\end{split}
+\end{equation}
+\end{verbatim}
+\producing
+\begin{equation}\label{xx}
+\begin{split}
+a& =b+c-d\\
+ & \quad +e-f\\
+ & =g+h\\
+ & =i
+\end{split}
+\end{equation}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{multline}
+a+b+c+d+e+f\\
++i+j+k+l+m+n
+\end{multline}
+\end{verbatim}
+\producing
+\begin{multline}
+a+b+c+d+e+f\\
++i+j+k+l+m+n
+\end{multline}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{gather}
+a_1=b_1+c_1\\
+a_2=b_2+c_2-d_2+e_2
+\end{gather}
+\end{verbatim}
+\producing
+\begin{gather}
+a_1=b_1+c_1\\
+a_2=b_2+c_2-d_2+e_2
+\end{gather}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{align}
+a_1& =b_1+c_1\\
+a_2& =b_2+c_2-d_2+e_2
+\end{align}
+\end{verbatim}
+\producing
+\begin{align}
+a_1& =b_1+c_1\\
+a_2& =b_2+c_2-d_2+e_2
+\end{align}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{align}
+a_{11}& =b_{11}&
+  a_{12}& =b_{12}\\
+a_{21}& =b_{21}&
+  a_{22}& =b_{22}+c_{22}
+\end{align}
+\end{verbatim}
+\producing
+\begin{align}
+a_{11}& =b_{11}&
+  a_{12}& =b_{12}\\
+a_{21}& =b_{21}&
+  a_{22}& =b_{22}+c_{22}
+\end{align}
+\end{eqxample}
+
+\begin{eqxample}
+\begin{verbatim}
+\begin{flalign*}
+a_{11} + b_{11}& = c_{11}&
+  a_{12}& =b_{12}\\
+b_{21}& = c_{21}&
+  a_{22}& =b_{22}+c_{22}
+\end{flalign*}
+\end{verbatim}
+\producing
+\begin{flalign*}
+a_{11} + b_{11}& = c_{11}&
+  a_{12}& =b_{12}\\
+b_{21}& = c_{21}&
+  a_{22}& =b_{22}+c_{22}
+\end{flalign*}
+\end{eqxample}
+\end{table}
+
+%% ------------------------------------------------------------------ %%
+\enlargethispage{1\baselineskip}
+
+\section{Single equations}
+
+The \env{equation} environment is for a single equation with an
+automatically generated number. The \env{equation*} environment is the
+same except for omitting the number.%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\footnote{Basic \latex/ doesn't provide an \env{equation*} environment,
+but rather a functionally equivalent environment named
+\env{displaymath}.}
+The wrapper \verb+\[ ... \]+ is equivalent to \env{equation*}.%
+\index{[@\verb+\[ ... \]+}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Split equations without alignment}
+
+The \env{multline} environment is a variation of the \env{equation}
+environment used for equations that don't fit on a single line. The
+first line of a \env{multline} will be at the left margin and the last
+line at the right margin, except for an indention on both sides in the
+amount of \cn{multlinegap}. Any additional lines in between will be
+centered independently within the display width (unless the \opt{fleqn}
+option is in effect).%
+\index{options!behavior of particular options}
+
+Like \env{equation}, \env{multline} has only a single equation number
+(thus, none of the individual lines should be marked with \cn{notag}).
+The equation number is placed on the last line (\opt{reqno} option) or
+first line (\opt{leqno} option); vertical centering as for \env{split}
+is not supported by \env{multline}.%
+\index{options!behavior of particular options}
+
+It's possible to force one of the middle lines to the left or right with
+commands \cn{shoveleft}, \cn{shoveright}. These commands take the entire
+line as an argument, up to but not including the final \cn{\\}; for
+example
+\begin{multline}
+\framebox[.65\columnwidth]{A}\\
+\framebox[.5\columnwidth]{B}\\
+\shoveright{\framebox[.55\columnwidth]{C}}\\
+\framebox[.65\columnwidth]{D}
+\end{multline}
+\begin{verbatim}
+\begin{multline}
+\framebox[.65\columnwidth]{A}\\
+\framebox[.5\columnwidth]{B}\\
+\shoveright{\framebox[.55\columnwidth]{C}}\\
+\framebox[.65\columnwidth]{D}
+\end{multline}
+\end{verbatim}
+
+The value of \cn{multlinegap} can be changed with the usual \latex/
+commands \cn{setlength} or \cn{addtolength}.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Split equations with alignment}
+
+Like \env{multline}, the \env{split} environment is for \emph{single}
+equations that are too long to fit on one line and hence must be split
+into multiple lines.  Unlike \env{multline}, however, the \env{split}
+environment provides for alignment among the split lines, using |&| to
+mark alignment points. Unlike the other \nipkg{amsmath} equation
+structures, the \env{split} environment provides no numbering, because
+it is intended to be used \emph{only inside some other displayed
+  equation structure}, usually an \env{equation}, \env{align}, or
+\env{gather} environment, which provides the numbering. For example:
+\begin{equation}\label{e:barwq}\begin{split}
+H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
+  \sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+  \Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
+  \kern-2em % adjust equation body to the right [mjd,13-Nov-1994]
+\end{split}\end{equation}
+
+\begin{verbatim}
+\begin{equation}\label{e:barwq}\begin{split}
+H_c&=\frac{1}{2n} \sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
+  \sum_{l _1+\dots+ l _p=l}\prod^p_{i=1} \binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+  \Bigl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\Bigr].
+\end{split}\end{equation}
+\end{verbatim}
+
+The \env{split} structure should constitute the entire body of the
+enclosing structure, apart from commands like \cn{label} that produce no
+visible material.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Equation groups without alignment}
+
+The \env{gather} environment is used for a group of consecutive
+equations when there is no alignment desired among them; each one is
+centered separately within the text width (see Table~\ref{displays}).
+Equations inside \env{gather} are separated by a \cn{\\} command.
+Any equation in a \env{gather} may consist of a \verb'\begin{split}'
+  \dots\ \verb'\end{split}' structure\mdash for example:
+\begin{verbatim}
+\begin{gather}
+  first equation\\
+  \begin{split}
+    second & equation\\
+           & on two lines
+  \end{split}
+  \\
+  third equation
+\end{gather}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Equation groups with mutual alignment}
+
+The \env{align} environment is used for two or more equations when
+vertical alignment is desired; usually binary relations such as equal
+signs are aligned (see Table~\ref{displays}).
+
+To have several equation columns side-by-side, use extra ampersands
+to separate the columns:
+\begin{align}
+x&=y       & X&=Y       & a&=b+c\\
+x'&=y'     & X'&=Y'     & a'&=b\\
+x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b
+\end{align}
+%
+\begin{verbatim}
+\begin{align}
+x&=y       & X&=Y       & a&=b+c\\
+x'&=y'     & X'&=Y'     & a'&=b\\
+x+x'&=y+y' & X+X'&=Y+Y' & a'b&=c'b
+\end{align}
+\end{verbatim}
+Line-by-line annotations on an equation can be done by judicious
+application of \cn{text} inside an \env{align} environment:
+\begin{align}
+x& = y_1-y_2+y_3-y_5+y_8-\dots
+                    && \text{by \eqref{eq:C}}\\
+ & = y'\circ y^*    && \text{by \eqref{eq:D}}\\
+ & = y(0) y'        && \text {by Axiom 1.}
+\end{align}
+%
+\begin{verbatim}
+\begin{align}
+x& = y_1-y_2+y_3-y_5+y_8-\dots
+                    && \text{by \eqref{eq:C}}\\
+ & = y'\circ y^*    && \text{by \eqref{eq:D}}\\
+ & = y(0) y'        && \text {by Axiom 1.}
+\end{align}
+\end{verbatim}
+A variant environment \env{alignat} allows the horizontal space between
+equations to be explicitly specified. This environment takes one argument,
+the number of \qq{equation columns} (the number of pairs of right-left
+aligned columns; the argument is the number of pairs): count the maximum
+number of \verb'&'s in any row, add~1 and divide by~2.
+\begin{alignat}{2}
+x& = y_1-y_2+y_3-y_5+y_8-\dots
+                  &\quad& \text{by \eqref{eq:C}}\\
+ & = y'\circ y^*  && \text{by \eqref{eq:D}}\\
+ & = y(0) y'      && \text {by Axiom 1.}
+\end{alignat}
+%
+\begin{verbatim}
+\begin{alignat}{2}
+x& = y_1-y_2+y_3-y_5+y_8-\dots
+                  &\quad& \text{by \eqref{eq:C}}\\
+ & = y'\circ y^*  && \text{by \eqref{eq:D}}\\
+ & = y(0) y'      && \text {by Axiom 1.}
+\end{alignat}
+\end{verbatim}
+The environment \env{flalign} (``full length alignment'') stretches the
+space between the equation columns to the maximum possible width, leaving
+only enough space at the margin for the equation number, if present.
+\begin{flalign}
+x&=y       & X&=Y\\
+x'&=y'     & X'&=Y'\\
+x+x'&=y+y' & X+X'&=Y+Y'
+\end{flalign}
+%
+\begin{verbatim}
+\begin{flalign}
+x&=y       & X&=Y\\
+x'&=y'     & X'&=Y'\\
+x+x'&=y+y' & X+X'&=Y+Y'
+\end{flalign}
+\end{verbatim}
+%
+\begin{flalign*}
+x&=y       & X&=Y\\
+x'&=y'     & X'&=Y'\\
+x+x'&=y+y' & X+X'&=Y+Y'
+\end{flalign*}
+%
+\begin{verbatim}
+\begin{flalign*}
+x&=y       & X&=Y\\
+x'&=y'     & X'&=Y'\\
+x+x'&=y+y' & X+X'&=Y+Y'
+\end{flalign*}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Alignment building blocks}
+
+Like \env{equation}, the multi-equation environments \env{gather},
+\env{align}, and \env{alignat} are designed to produce a structure
+whose width is the full line width. This means, for example, that one
+cannot readily add parentheses around the entire structure. But
+variants\index{ed env@\texttt{-ed} environments|(}
+\env{gathered}, \env{aligned}, and \env{alignedat} are provided whose
+total width is the actual width of the contents; thus they can be used
+as a component in a containing expression. E.g.,
+\begin{equation*}
+\left.\begin{aligned}
+  B'&=-\partial\times E,\\
+  E'&=\partial\times B - 4\pi j,
+\end{aligned}
+\right\}
+\qquad \text{Maxwell's equations}
+\end{equation*}
+\begin{verbatim}
+\begin{equation*}
+\left.\begin{aligned}
+  B'&=-\partial\times E,\\
+  E'&=\partial\times B - 4\pi j,
+\end{aligned}
+\right\}
+\qquad \text{Maxwell's equations}
+\end{equation*}
+\end{verbatim}
+Like the \env{array} environment, these \texttt{-ed} variants also take
+an optional\index{options!positioning of \texttt{-ed} environments}
+|[t]|\index{t option@\texttt{t} (top) option},
+|[b]|\index{b option@\texttt{b} (bottom) option} or the default
+|[c]|\index{c option@\texttt{c} (center) option}
+argument to specify vertical
+positioning.  For maximum interoperability, do not insert a
+space\index{options!space before \texttt{[}}
+or line break\index{line break} before the option.  See
+also the note on page~\pageref{breaknote} regarding page breaking
+within the \texttt{-ed} environments.
+
+\qq{Cases} constructions like the following are common in
+mathematics:
+\begin{equation}\label{eq:C}
+P_{r-j}=
+  \begin{cases}
+    0&  \text{if $r-j$ is odd},\\
+    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
+  \end{cases}
+\end{equation}
+and in the \nipkg{amsmath} package there is a \env{cases} environment to
+make them easy to write:
+\begin{verbatim}
+P_{r-j}=\begin{cases}
+    0&  \text{if $r-j$ is odd},\\
+    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
+  \end{cases}
+\end{verbatim}
+Notice the use of \cn{text} (cf.~\secref{text}) and the nested math
+formulas. \env{cases} is set in \cn{textstyle}. If \cn{displaystyle}
+is wanted, it must be requested explicitly; \pkg{mathtools} provides
+a \env{dcases} environment for this purpose.
+
+The |-ed|\index{ed env@\texttt{-ed} environments|)} and \env{cases}
+environments must appear within an enclosing math environment, which can
+be either in text, between |$...$|, or in any of the display environments.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Adjusting tag placement}
+
+Placing equation numbers can be a rather complex problem in multiline
+displays. The environments of the \nipkg{amsmath} package try hard to
+avoid overprinting an equation number on the equation contents, if
+necessary moving the number down or up to a separate line. Difficulties
+in accurately calculating the profile of an equation can occasionally
+result in number movement that doesn't look right.
+A \cn{raisetag} command is provided to adjust the vertical position of the
+current equation number, if it has been shifted away from its normal
+position. To move a particular number up by six points, write
+|\raisetag{6pt}|. (At the end of a display, this also shifts up the
+text following the display.)
+This kind of adjustment is fine tuning like line
+breaks and page breaks, and should therefore be left undone until your
+document is nearly finalized, or you may end up redoing the fine tuning
+several times to keep up with changing document contents.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Vertical spacing and page breaks in multiline displays}
+
+You can use the \cn{\\}|[|\<dimension>|]|%
+\index{options!extra vertical space after \cn{\\}}
+command to get extra vertical
+space between lines in all the \nipkg{amsmath} displayed equation
+environments, as is usual in \latex/. Do not type a space between the%
+\index{options!space before \texttt{[}}
+\cn{\\} and the following |[|; \emph{only} for display environments
+defined by \nipkg{amsmath} the space is interpreted to mean that the
+bracketed material is part of the document content.
+
+When the \nipkg{amsmath} package is
+in use \ii{page breaks} between equation lines are normally disallowed;
+the philosophy is that page breaks in such material should receive
+individual attention from the author. To get an individual page break
+inside a particular displayed equation, a \cn{displaybreak} command is
+provided. \cn{displaybreak} is best placed immediately before the
+\cn{\\} where it is to take effect.  Like \latex/'s \cn{pagebreak},
+\cn{displaybreak} takes an optional argument%
+\index{options!behavior of particular options} between 0 and 4 denoting
+the desirability of the pagebreak. |\displaybreak[0]| means \qq{it is
+  permissible to break here} without encouraging a break;
+\cn{displaybreak} with no optional argument is the same as
+|\displaybreak[4]| and forces a break.
+
+If you prefer a strategy of letting page breaks fall where they may,
+even in the middle of a multiline equation, then you might put
+\cn{allowdisplaybreaks}\texttt{[1]} in the preamble of your document. An
+optional argument\index{options!behavior of particular options}
+1\ndash 4 can be used for finer control: |[1]| means
+allow page breaks, but avoid them as much as possible; values of 2,3,4
+mean increasing permissiveness. When display breaks are enabled with
+\cn{allowdisplaybreaks}, the \cn{\\*} command can be used to prohibit a
+pagebreak after a given line, as usual.
+
+\begin{bfseries}
+Note:\label{breaknote} Certain equation environments wrap their contents
+in an unbreakable box, with the consequence that neither \cn{displaybreak}
+nor \cn{allowdisplaybreaks} will have any effect on them. These include
+\env{split}, \env{aligned}, \env{gathered}, and \env{alignedat}.
+\end{bfseries}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Interrupting a display}
+
+The command \cn{intertext} is used for a short interjection of one or
+two lines of text\index{text fragments inside math} in the middle of a
+multiple-line display structure (see also the \cn{text} command in
+\secref{text}). Its salient feature is preservation of the alignment,
+which would not happen if you simply ended the display and then started
+it up again afterwards. \cn{intertext} may only appear right after a
+\cn{\\} or \cn{\\*} command. Notice the position of the word \qq{and} in
+this example.
+\begin{align}
+  A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\
+  A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\
+\intertext{and}
+  A_3&=\mathcal{N}(\lambda;\omega).
+\end{align}
+\begin{verbatim}
+\begin{align}
+  A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\
+  A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\
+\intertext{and}
+  A_3&=\mathcal{N}(\lambda;\omega).
+\end{align}
+\end{verbatim}
+
+The \pkg{mathtools} package provides a command \cn{shortintertext} that
+is intended for use when the interjected text is only a few words; it uses
+less vertical space than \cn{intertext}. This
+is most effective when equation numbers are on the right.%
+\index{equationn@equation numbers!left or right placement}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Equation numbering}
+
+\subsection{Numbering hierarchy}
+In \latex/ if you wanted to have equations numbered within
+sections\mdash that is, have
+equation numbers (1.1), (1.2), \dots, (2.1), (2.2),
+\dots, in sections 1, 2, and so forth\mdash you could redefine
+\cn{theequation} as suggested in the \latex/ manual \cite[\S6.3, \S
+C.8.4]{lamport}:
+\begin{verbatim}
+\renewcommand{\theequation}{\thesection.\arabic{equation}}
+\end{verbatim}
+
+This works pretty well, except that the equation counter won't be reset
+to zero at the beginning of a new section or chapter, unless you do it
+yourself using \cn{setcounter}. To make this a little more convenient,
+the \nipkg{amsmath} package provides a 
+command\index{equationn@equation numbers!hierarchy} \cn{numberwithin}.
+To have equation numbering tied to section numbering, with automatic
+reset of the equation counter, write
+\begin{verbatim}
+\numberwithin{equation}{section}
+\end{verbatim}
+As its name implies, the \cn{numberwithin} command can be applied to
+any counter, not just the \texttt{equation} counter.
+
+\subsection{Cross references to equation numbers}
+
+To make cross-references to equations easier, an \cn{eqref}
+command\index{equationn@equation numbers!cross-references} is provided. This
+automatically supplies the parentheses around the equation number. I.e.,
+if \verb'\ref{abc}' produces 3.2 then \verb'\eqref{abc}' produces
+(3.2). The parentheses around an \cn{eqref} equation number will be
+set in upright type regardless of type style of the context.
+
+\subsection{Subordinate numbering sequences}
+
+The \nipkg{amsmath} package provides also a wrapper environment,
+\env{subequations}\index{equationn@equation numbers!subordinate numbering}, to make it
+easy to number equations in a particular \cn{align} or similar group with
+a subordinate numbering scheme. For example
+\begin{verbatim}
+\begin{subequations}
+...
+\end{subequations}
+\end{verbatim}
+causes all numbered equations within that part of the document to be
+numbered (4.9a) (4.9b) (4.9c) \dots, if the preceding numbered
+equation was (4.8). A \cn{label} command immediately after
+\verb/\begin{subequations}/ will produce a \cn{ref} of the parent
+number 4.9, not 4.9a. The counters used by the subequations
+environment are \verb/parentequation/ and \verb/equation/ and
+\cn{addtocounter}, \cn{setcounter}, \cn{value}, etc., can be applied
+as usual to those counter names. To get anything other than lowercase
+letters for the subordinate numbers, use standard \latex/ methods for
+changing numbering style \cite[\S6.3, \S C.8.4]{lamport}. For example,
+redefining \cn{theequation} as follows will produce roman numerals.
+\begin{verbatim}
+\begin{subequations}
+\renewcommand{\theequation}{\theparentequation \roman{equation}}
+...
+\end{verbatim}
+
+\subsection{Numbering style}
+
+The default equation number is set in \cn{normalfont}.  This means that
+in bold section headings, bold is suppressed; a workaround for this is
+to use \verb+(\ref{+\ldots\verb+})+ rather than \verb+\eqref{+\ldots\verb+}+.
+
+If smaller type is specified for a numbered display, the size of the
+equation number will also be small.  The default size can be ensured
+throughout a document by applying this patch in the preamble:
+\begin{verbatim}
+\makeatletter
+\renewcommand{\maketag@@@}[1]{\hbox{\m@th\normalsize\normalfont#1}}%
+\makeatother
+\end{verbatim}
+(This modification may be included in a future version of
+\nipkg{amsmath}.)
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Miscellaneous mathematical features}
+
+\section{Matrices}\label{ss:matrix}
+
+The \nipkg{amsmath} package provides some environments for
+matrices\index{matrices} beyond the basic \env{array} environment of
+\latex/. The \env{pmatrix}, \env{bmatrix}, \env{Bmatrix}, \env{vmatrix}
+and \env{Vmatrix} have (respectively) $(\,)$, $[\,]$, $\lbrace\,\rbrace$,
+$\lvert\,\rvert$, and $\lVert\,\rVert$ delimiters\index{delimiters}
+built in. For naming consistency there is a
+\env{matrix} environment sans delimiters. This is not entirely redundant
+with the \env{array} environment; the matrix environments all use more
+economical horizontal spacing than the rather prodigal spacing of the
+\env{array} environment. Also, unlike the \env{array} environment, you
+don't have to give column specifications for any of the matrix
+environments; by default you can have up to 10 centered columns.%
+\footnote{%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+More precisely: The maximum number of columns in a matrix is determined
+by the counter |MaxMatrixCols| (normal value = 10), which you can change
+if necessary using \latex/'s \cn{setcounter} or \cn{addtocounter}
+commands.%
+}\space%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+(If you need left or right alignment in a column or other special
+formats you may use \env{array}, or the \pkg{mathtools}
+package which provides \verb+*+ variants%
+\index{matrix@\indexenvironmentfont{matrix} environment!\verb+*+ variants}
+of these environments with
+an optional argument to specify left or right alignment.)
+
+To produce a small matrix suitable for use in text, there is a
+\env{smallmatrix} environment (e.g.,
+\begin{math}
+\bigl( \begin{smallmatrix}
+  a&b\\ c&d
+\end{smallmatrix} \bigr)
+\end{math})
+that comes closer to fitting within a single text line than a normal
+matrix. Delimiters\index{delimiters} must be provided. (The
+\pkg{mathtools} package provides |p|,|b|,|B|,|v|,|V| versions of
+\env{smallmatrix},%
+\index{smallmatrix@\indexenvironmentfont{smallmatrix} environment!variant delimiters}
+as well as |*| variants%
+\index{smallmatrix@\indexenvironmentfont{smallmatrix} environment!\verb+*+ variants}
+as described above.)
+The above example was produced by
+\begin{verbatim}
+\bigl( \begin{smallmatrix}
+  a&b\\ c&d
+\end{smallmatrix} \bigr)
+\end{verbatim}
+
+\cn{hdotsfor}|{|\<number>|}| produces a row of dots in a
+matrix\index{matrices!ellipsis dots}\index{ellipsis dots!in
+matrices}\index{dots|see{ellipsis dots}} spanning the given number of
+columns. For example,
+\begin{center}
+\begin{minipage}{.3\columnwidth}
+\noindent$\begin{matrix} a&b&c&d\\
+e&\hdotsfor{3} \end{matrix}$
+\end{minipage}%
+\qquad
+\begin{minipage}{.45\columnwidth}
+\begin{verbatim}
+\begin{matrix} a&b&c&d\\
+e&\hdotsfor{3} \end{matrix}
+\end{verbatim}
+\end{minipage}%
+\end{center}
+
+The spacing of the dots can be varied through use of a square-bracket
+option,\index{options!behavior of particular options}
+for example, |\hdotsfor[1.5]{3}|.  The number in square brackets
+will be used as a multiplier (i.e., the normal value is 1.0).
+\begin{equation}\label{eq:D}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix},
+\end{equation}
+\begin{verbatim}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Math spacing commands}
+
+The \nipkg{amsmath} package slightly extends the set of math
+spacing\index{horizontal spacing} commands, as shown below.
+Both the spelled-out and abbreviated forms of these commands are robust,
+and they can also be used outside of math.
+\begin{ctab}{lll|lll}
+Abbrev.& Spelled out& Example & Abbrev.& Spelled out& Example\\
+\hline
+\vstrut{2.5ex}
+& no space& \spx{}& & no space & \spx{}\\
+\cn{\,}& \cn{thinspace}& \spx{\,}&
+  \altcnbang& \cn{negthinspace}& \spx{\!}\\
+\cn{\:}& \cn{medspace}& \spx{\:}&
+  & \cn{negmedspace}& \spx{\negmedspace}\\
+\cn{\;}& \cn{thickspace}& \spx{\;}&
+  & \cn{negthickspace}& \spx{\negthickspace}\\
+& \cn{quad}& \spx{\quad}\\
+& \cn{qquad}& \spx{\qquad}
+\end{ctab}
+For the greatest possible control over math spacing, use \cn{mspace}
+and `math units'. One math unit, or |mu|, is equal to 1/18 em. Thus to
+get a negative \cn{quad} you could write |\mspace{-18.0mu}|.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Dots}
+
+For preferred placement of ellipsis dots (raised or on-line) in various
+contexts there is no general consensus. It may therefore be considered a
+matter of taste. By using the semantically oriented commands
+\begin{itemize}
+\item \cn{dotsc} for \qq{dots with commas}
+\item \cn{dotsb} for \qq{dots with binary operators/relations}
+\item \cn{dotsm} for \qq{multiplication dots}
+\item \cn{dotsi} for \qq{dots with integrals}
+\item \cn{dotso} for \qq{other dots} (none of the above)
+\end{itemize}
+instead of \cn{ldots} and \cn{cdots}, you make it possible for your
+document to be adapted to different conventions on the fly, in case (for
+example) you have to submit it to a publisher who insists on following
+house tradition in this respect. The default treatment for the various
+kinds follows American Mathematical Society conventions:
+\begin{center}
+\begin{tabular}{@{}l@{}l@{}}
+\begin{minipage}[t]{.54\textwidth}
+\begin{verbatim}
+Then we have the series $A_1, A_2,
+\dotsc$, the regional sum $A_1
++A_2 +\dotsb $, the orthogonal
+product $A_1 A_2 \dotsm $, and
+the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\].
+\end{verbatim}
+\end{minipage}
+&
+\begin{minipage}[t]{.45\textwidth}
+\noindent
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi.\]
+\end{minipage}
+\end{tabular}
+\end{center}
+For most situations, the undifferentiated \cn{dots} can be used, and
+\nipkg{amsmath} will output the most suitable form based on the
+immediate context; if an inappropriate form results, it can be corrected
+after examining the output.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Nonbreaking dashes}
+
+A command \cn{nobreakdash} is provided to suppress the possibility of a
+line break\index{line break|(} after the following hyphen or dash. For
+example, if you write `pages 1\ndash 9' as |pages 1\nobreakdash--9|
+then a line break will never occur between the dash and the 9. You can
+also use \cn{nobreakdash} to prevent undesirable hyphenations in
+combinations like |$p$-adic|. For frequent use, it's advisable to make
+abbreviations, e.g.,
+\begin{verbatim}
+\newcommand{\p}{$p$\nobreakdash}% for "\p-adic"
+\newcommand{\Ndash}{\nobreakdash--}% for "pages 1\Ndash 9"
+%    For "\n dimensional" ("n-dimensional"):
+\newcommand{\n}[1]{$n$\nobreakdash-\hspace{0pt}}
+\end{verbatim}
+The last example shows how to prohibit a line break\index{line break|)}
+after the hyphen but allow normal hyphenation in the following
+word. (It suffices to add a zero-width space after the hyphen.)
+
+%% ------------------------------------------------------------------ %%
+
+\section{Accents in math}
+
+In ordinary \LaTeX{} the placement of the second accent in doubled math
+accents is often poor. With the \nipkg{amsmath} package you
+will get improved placement of the second accent:
+$\hat{\hat{A}}$ (\cn{hat}|{\hat{A}}|).
+
+The commands \cn{dddot} and \cn{ddddot} are available to produce triple
+and quadruple dot accents in addition to the \cn{dot} and \cn{ddot}
+accents already available in \latex/.
+
+To get a superscripted hat or tilde character, load the \pkg{amsxtra}
+package and use \cn{sphat} or \cn{sptilde}. Usage is \verb'A\sphat'
+(note the absence of the \verb'^' character).
+
+
+To place an arbitrary symbol in math accent position, or to get under
+accents, see the \pkg{accents} package by Javier Bezos. (\nipkg{amsmath}
+must be loaded before \pkg{accents}.)
+
+%% ------------------------------------------------------------------ %%
+
+\section{Roots}
+
+In ordinary \latex/ the placement of root indices is sometimes not so
+good: $\sqrt[\beta]{k}$ (|\sqrt||[\beta]{k}|).  In the
+\nipkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
+the position of the root:%
+\index{options!adjust positioning}
+\begin{verbatim}
+  \sqrt[\leftroot{-2}\uproot{2}\beta]{k}
+\end{verbatim}
+will move the beta up and to the right:
+$\sqrt[\leftroot{-2}\uproot{2}\beta]{k}$. The negative argument used
+with \cn{leftroot} moves the $\beta$ to the right. The units are a small
+amount that is a useful size for such adjustments.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Boxed formulas}
+
+The command \cn{boxed} puts a box around its
+argument, like \cn{fbox} except that the contents are in math mode:
+\begin{equation}
+\boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
+\end{equation}
+\begin{verbatim}
+  \boxed{\eta \leq C(\delta(\eta) +\Lambda_M(0,\delta))}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Over and under arrows}
+
+Basic \latex/ provides \cn{overrightarrow} and \cn{overleftarrow}
+commands. Some additional over and under arrow commands are provided
+by the \nipkg{amsmath} package to extend the set:
+
+\begin{tabbing}
+\qquad\=\ncn{overleftrightarrow}\qquad\=\kill
+\> \cn{overleftarrow}    \> \cn{underleftarrow} \+\\
+   \cn{overrightarrow}    \> \cn{underrightarrow} \\
+   \cn{overleftrightarrow}\> \cn{underleftrightarrow}
+\end{tabbing}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Extensible arrows}
+
+\cn{xleftarrow} and \cn{xrightarrow} produce
+arrows\index{arrows!extensible} that extend automatically to accommodate
+unusually wide subscripts or superscripts. These commands take one
+optional argument\index{options!behavior of particular options}
+(the subscript) and one mandatory argument (the
+superscript, possibly empty):
+\begin{equation}
+A\xleftarrow{n+\mu-1}B \xrightarrow[T]{n\pm i-1}C
+\end{equation}
+\begin{verbatim}
+  \xleftarrow{n+\mu-1}\quad \xrightarrow[T]{n\pm i-1}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Affixing symbols to other symbols}
+
+\latex/ provides \cn{stackrel} for placing a
+superscript\index{subscripts and superscripts} above a binary relation.
+In the \nipkg{amsmath} package there are somewhat more general commands,
+\cn{overset} and \cn{underset}, that can be used to place one symbol
+above or below another symbol, whether it's a relation or something
+else. The input |\overset{*}{X}| will place a superscript-size $*$ above
+the $X$: $\overset{*}{X}$; \cn{underset} is the analog for adding a
+symbol underneath.
+
+See also the description of \cn{sideset} in \secref{sideset}.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Fractions and related constructions}
+
+\subsection{The \cn{frac}, \cn{dfrac}, and \cn{tfrac} commands}
+
+The \cn{frac} command, which is in the basic command set of
+\latex/,\index{fractions|(} takes two arguments\mdash numerator and
+denominator\mdash and typesets them in normal fraction form. The
+\nipkg{amsmath} package provides also \cn{dfrac} and \cn{tfrac} as
+convenient abbreviations for |{\displaystyle\frac| |...| |}|
+and\indexcs{textstyle}\relax
+\indexcs{displaystyle} |{\textstyle\frac| |...| |}|.
+\begin{equation}
+\frac{1}{k}\log_2 c(f)\quad\tfrac{1}{k}\log_2 c(f)\quad
+\sqrt{\frac{1}{k}\log_2 c(f)}\quad\sqrt{\dfrac{1}{k}\log_2 c(f)}
+\end{equation}
+\begin{verbatim}
+\begin{equation}
+\frac{1}{k}\log_2 c(f)\;\tfrac{1}{k}\log_2 c(f)\;
+\sqrt{\frac{1}{k}\log_2 c(f)}\;\sqrt{\dfrac{1}{k}\log_2 c(f)}
+\end{equation}
+\end{verbatim}
+
+\subsection{The \cn{binom}, \cn{dbinom}, and \cn{tbinom} commands}
+
+For binomial expressions\index{binomials} such as $\binom{n}{k}$
+\nipkg{amsmath} has \cn{binom}, \cn{dbinom} and \cn{tbinom}:
+\begin{equation}
+2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
+\end{equation}
+\begin{verbatim}
+2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}
+\end{verbatim}
+
+\subsection{The \cn{genfrac} command}
+
+The capabilities of \cn{frac}, \cn{binom}, and their variants are
+subsumed by a generalized fraction command \cn{genfrac} with six
+arguments. The last two correspond to \cn{frac}'s numerator and
+denominator; the first two are optional delimiters\index{delimiters} (as
+seen in \cn{binom}); the third is a line thickness override (\cn{binom}
+uses this to set the fraction line thickness to 0\mdash i.e., invisible);
+and the fourth argument is a mathstyle override: integer values 0\ndash 3
+select respectively \cn{displaystyle}, \cn{textstyle}, \cn{scriptstyle},
+and \cn{scriptscriptstyle}. If the third argument is left empty, the line
+thickness defaults to `normal'.
+
+\begin{center}\begin{minipage}{.85\columnwidth}
+\raggedright \normalfont\ttfamily \exhyphenpenalty10000
+\newcommand{\ma}[1]{%
+  \string{{\normalfont\itshape#1}\string}\penalty9999 \ignorespaces}
+\string\genfrac \ma{left-delim} \ma{right-delim} \ma{thickness}
+\ma{mathstyle} \ma{numerator} \ma{denominator}
+\end{minipage}\end{center}
+To illustrate, here is how \cn{frac}, \cn{tfrac}, and
+\cn{binom} might be defined.
+\begin{verbatim}
+\newcommand{\frac}[2]{\genfrac{}{}{}{}{#1}{#2}}
+\newcommand{\tfrac}[2]{\genfrac{}{}{}{1}{#1}{#2}}
+\newcommand{\binom}[2]{\genfrac{(}{)}{0pt}{}{#1}{#2}}
+\end{verbatim}
+If you find yourself repeatedly using \cn{genfrac} throughout a document
+for a particular notation, you will do yourself a favor (and your
+publisher) if you define a meaningfully-named abbreviation for that
+notation, along the lines of \cn{frac} and \cn{binom}.
+
+The primitive generalized fraction commands \cs{over}, \cs{overwithdelims},
+\cs{atop}, \cs{atopwithdelims}, \cs{above}, \cs{abovewithdelims} produce
+warning  messages if used with the \nipkg{amsmath} package, for reasons
+discussed in \fn{technote.tex}.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Continued fractions}
+
+The continued fraction\index{continued fractions}
+\begin{equation}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+  \cfrac{1}{\sqrt{2}+\cdots
+}}}
+\end{equation}
+can be obtained by typing
+{\samepage
+\begin{verbatim}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+  \cfrac{1}{\sqrt{2}+\dotsb
+}}}
+\end{verbatim}
+}% End of \samepage
+This produces better-looking results than straightforward use of
+\cn{frac}. Left or right placement of any of the numerators is
+accomplished by using \cn{cfrac}|[l]| or \cn{cfrac}|[r]| instead of
+\cn{cfrac}.\index{options!adjust positioning}%
+\index{fractions|)}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Smash options}
+
+The command \cn{smash} is used to typeset a subformula with an
+effective height and depth of zero, which is sometimes
+useful in adjusting the subformula's position with respect to adjacent
+symbols. With the \nipkg{amsmath} package \cn{smash} has optional
+arguments\index{options!behavior of particular options}
+|[t]|\index{t option@\texttt{t} (top) option} and
+|[b]|\index{b option@\texttt{b} (bottom) option} because occasionally it is
+advantageous to be able to \qq{smash} only the top or only the bottom
+of something while retaining the natural depth or height. For example,
+when adjacent radical symbols are unevenly sized or positioned because
+of differences in the height and depth of their contents, \cn{smash}
+can be employed to make them more consistent. Compare
+$\sqrt{x}+\sqrt{y}+\sqrt{z}$ and $\sqrt{x}+\sqrt{\smash[b]{y}}+\sqrt{z}$,
+where the latter was produced by
+\verb"$\sqrt{x}" \verb"+"
+\verb"\sqrt{"\5\verb"\smash[b]{y}}" \verb"+" \verb"\sqrt{z}$".
+
+%% ------------------------------------------------------------------ %%
+
+\section{Delimiters}
+
+\index{delimiters|(}
+
+\subsection{Delimiter sizes}\label{bigdel}
+
+The automatic delimiter sizing done by \cn{left} and \cn{right} has two
+limitations: First, it is applied mechanically to produce delimiters
+large enough to encompass the largest contained item, and second, the
+range of sizes is not even approximately continuous but has fairly large
+quantum jumps. This means that a math fragment that is infinitesimally
+too large for a given delimiter size will get the next larger size, a
+jump of 3pt or so in normal-sized text. There are two or three
+situations where the delimiter size is commonly adjusted, using a set of
+commands that have `big' in their names.%
+\index{delimiters!fixed size|(}
+\begin{ctab}{l|llllll}
+Delimiter&
+  text& \ncn{left}& \ncn{bigl}& \ncn{Bigl}& \ncn{biggl}& \ncn{Biggl}\\
+size&
+  size& \ncn{right}& \ncn{bigr}& \ncn{Bigr}& \ncn{biggr}& \ncn{Biggr}\\
+\hline
+Result\vstrut{5ex}&
+  $\displaystyle(b)(\frac{c}{d})$&
+  $\displaystyle\left(b\right)\left(\frac{c}{d}\right)$&
+  $\displaystyle\bigl(b\bigr)\bigl(\frac{c}{d}\bigr)$&
+  $\displaystyle\Bigl(b\Bigr)\Bigl(\frac{c}{d}\Bigr)$&
+  $\displaystyle\biggl(b\biggr)\biggl(\frac{c}{d}\biggr)$&
+  $\displaystyle\Biggl(b\Biggr)\Biggl(\frac{c}{d}\Biggr)$
+\end{ctab}
+The first kind of situation is a cumulative operator with limits above
+and below. With \cn{left} and \cn{right} the delimiters usually turn out
+larger than necessary, and using the |Big| or |bigg|
+sizes\index{big@\cn{big}, \cn{Big}, \cn{bigg}, \dots\ delimiters}
+instead gives better results:
+\begin{equation*}
+\left[\sum_i a_i\left\lvert\sum_j x_{ij}\right\rvert^p\right]^{1/p}
+\quad\text{versus}\quad
+\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
+\end{equation*}
+\begin{verbatim}
+\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
+\end{verbatim}
+The second kind of situation is clustered pairs of delimiters where
+\cn{left} and \cn{right} make them all the same size (because that is
+adequate to cover the encompassed material) but what you really want
+is to make some of the delimiters slightly larger to make the nesting
+easier to see.
+\begin{equation*}
+\left((a_1 b_1) - (a_2 b_2)\right)
+\left((a_2 b_1) + (a_1 b_2)\right)
+\quad\text{versus}\quad
+\bigl((a_1 b_1) - (a_2 b_2)\bigr)
+\bigl((a_2 b_1) + (a_1 b_2)\bigr)
+\end{equation*}
+\begin{verbatim}
+\left((a_1 b_1) - (a_2 b_2)\right)
+\left((a_2 b_1) + (a_1 b_2)\right)
+\quad\text{versus}\quad
+\bigl((a_1 b_1) - (a_2 b_2)\bigr)
+\bigl((a_2 b_1) + (a_1 b_2)\bigr)
+\end{verbatim}
+The third kind of situation is a slightly oversize object in running
+text, such as $\left\lvert\frac{b'}{d'}\right\rvert$ where the
+delimiters produced by \cn{left} and \cn{right} cause too much line
+spreading. In that case \ncn{bigl} and \ncn{bigr}\index{big@\cn{big},
+\cn{Big}, \cn{bigg}, \dots\ delimiters} can be used to produce
+delimiters that are slightly larger than the base size but still able to
+fit within the normal line spacing:
+$\bigl\lvert\frac{b'}{d'}\bigr\rvert$.
+
+In ordinary \latex/ \ncn{big}, \ncn{bigg}, \ncn{Big}, and \ncn{Bigg}
+delimiters aren't scaled properly over the full range of \latex/ font
+sizes.  With the \nipkg{amsmath} package they are.%
+\index{delimiters!fixed size|)}
+
+\subsection{Vertical bar notations}
+
+The \nipkg{amsmath} package provides commands \cn{lvert}, \cn{rvert},
+\cn{lVert}, \cn{rVert} (compare \cn{langle}, \cn{rangle}) to address the
+%problem of overloading for the vert bar character \qc{\|}. This
+problem of overloading for the vert bar character \qcvert. This
+character is currently used in \latex/ documents to represent a wide
+variety of mathematical objects: the `divides' relation in a
+number-theory expression like $p\vert q$, or the absolute-value
+operation $\lvert z\rvert$, or the `such that' condition in set
+notation, or the `evaluated at' notation $f_\zeta(t)\bigr\rvert_{t=0}$.
+The multiplicity of uses in itself is not so bad; what is bad, however,
+is that fact that not all of the uses take the same typographical
+treatment, and that the complex discriminatory powers of a knowledgeable
+reader cannot be replicated in computer processing of mathematical
+documents. It is recommended therefore that there should be a one-to-one
+correspondence in any given document between the vert bar character
+%\qc{\|} and a selected mathematical notation, and similarly for the
+\qcvert\ and a selected mathematical notation, and similarly for the
+%double-bar command \ncn{\|}\index{"|@\verb"*+"\"|+}. This immediately
+double-bar command \cnvert. This immediately
+rules out the use of \qc{|}
+%and \ncn{\|}\index{"|@\verb"*+"\"|+} for delimiters, because left and right
+and \cnvert\ for delimiters, because left and right
+delimiters are distinct usages that do not relate in the same way to
+adjacent symbols; recommended practice is therefore to define suitable
+commands in the document preamble for any paired-delimiter use of vert
+bar symbols:
+\begin{verbatim}
+\providecommand{\abs}[1]{\lvert#1\rvert}
+\providecommand{\norm}[1]{\lVert#1\rVert}
+\end{verbatim}
+whereupon the document would contain |\abs{z}| to produce $\lvert
+z\rvert$ and |\norm{v}| to produce $\lVert v\rVert$.
+The \pkg{mathools} provides the command \cn{DeclarePairedDelimiter}
+for defining |\abs|-like macros with scaling delimiters.
+\index{delimiters|)}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Operator names}
+
+\section{Defining new operator names}\label{s:opname}
+
+Math functions\index{operator names}\relax \index{function
+names|see{operator names}} such as $\log$, $\sin$, and $\lim$ are
+traditionally typeset in roman type to make them visually more distinct
+from one-letter math variables, which are set in math italic. The more
+common ones have predefined names, \cn{log}, \cn{sin}, \cn{lim}, and so
+forth, but new ones come up all the time in mathematical papers, so the
+\nipkg{amsmath} package provides a general mechanism for defining new
+`operator names'. To define a math function \ncn{xxx} to work like
+\cn{sin}, you write
+\begin{verbatim}
+\DeclareMathOperator{\xxx}{xxx}
+\end{verbatim}
+whereupon ensuing uses of \ncn{xxx} will produce {\upshape xxx} in the
+proper font and automatically add proper spacing\index{horizontal
+spacing!around operator names} on either side when necessary, so that you
+get $A\xxx B$ instead of $A\mathrm{xxx}B$. In the second argument of
+\cn{DeclareMathOperator} (the name text), a pseudo-text mode prevails:
+the hyphen character \qc{\-} will print as a text hyphen rather than a
+minus sign and an asterisk \qc{\*} will print as a raised text asterisk
+instead of a centered math star. (Compare
+\textit{a}-\textit{b}*\textit{c} and $a-b*c$.) But otherwise the name
+text is printed in math mode, so that you can use, e.g., subscripts and
+superscripts there.
+
+%%%%xxx%%%\enlargethispage{1\baselineskip}
+If the new operator should have subscripts and superscripts placed in
+`limits' position above and below as with $\lim$, $\sup$, or $\max$, use
+the \qc{\*} form of the \cn{DeclareMathOperator} command:
+\begin{verbatim}
+\DeclareMathOperator*{\Lim}{Lim}
+\end{verbatim}
+See also the discussion of subscript placement in
+Section~\ref{subplace}.
+
+\goodbreak
+
+The following operator names are predefined:
+
+\vspace{-1\baselineskip}
+\begin{ctab}{@{}rlrlrlrl}
+\cn{arccos}& $\arccos$ &\cn{deg}& $\deg$ &      \cn{lg}& $\lg$ &        \cn{projlim}& $\projlim$\\
+\cn{arcsin}& $\arcsin$ &\cn{det}& $\det$ &      \cn{lim}& $\lim$ &      \cn{sec}& $\sec$\\
+\cn{arctan}& $\arctan$ &\cn{dim}& $\dim$ &      \cn{liminf}& $\liminf$ &\cn{sin}& $\sin$\\
+\cn{arg}& $\arg$ &      \cn{exp}& $\exp$ &      \cn{limsup}& $\limsup$ &\cn{sinh}& $\sinh$\\
+\cn{cos}& $\cos$ &      \cn{gcd}& $\gcd$ &      \cn{ln}& $\ln$ &        \cn{sup}& $\sup$\\
+\cn{cosh}& $\cosh$ &    \cn{hom}& $\hom$ &      \cn{log}& $\log$ &      \cn{tan}& $\tan$\\
+\cn{cot}& $\cot$ &      \cn{inf}& $\inf$ &      \cn{max}& $\max$ &      \cn{tanh}& $\tanh$\\
+\cn{coth}& $\coth$ &    \cn{injlim}& $\injlim$ &\cn{min}& $\min$\\
+\cn{csc}& $\csc$ &      \cn{ker}& $\ker$ &      \cn{Pr}& $\Pr$
+\end{ctab}
+\par\nobreak
+\vspace{-1.2\baselineskip}
+\begin{ctab}{rlrl}
+\cn{varinjlim}&  $\displaystyle\varinjlim$&
+\cn{varliminf}&  $\displaystyle\varliminf$\\
+\cn{varprojlim}& $\displaystyle\varprojlim$&
+\cn{varlimsup}&  $\displaystyle\varlimsup$
+\end{ctab}
+
+There is also a command \cn{operatorname} such that using
+\begin{verbatim}
+\operatorname{abc}
+\end{verbatim}
+in a math formula is equivalent to a use of \ncn{abc} defined by
+\cn{DeclareMathOperator}. This may be occasionally useful for
+constructing more complex notation or other purposes. (Use the variant
+\cn{operatorname*} to get limits.)
+
+%% ------------------------------------------------------------------ %%
+
+\section{\cn{mod} and its relatives}
+
+Commands \cn{mod}, \cn{bmod}, \cn{pmod}, \cn{pod} are provided to deal
+with the special spacing conventions of \qq{mod} notation. \cn{bmod} and
+\cn{pmod} are available in \latex/, but with the \nipkg{amsmath} package
+the spacing of \cn{pmod} will adjust to a smaller value if it's used in
+a non-display-mode formula. \cn{mod} and \cn{pod} are variants of
+\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses,
+whereas \cn{pod} omits the \qq{mod} and retains the parentheses.
+\begin{equation}
+\gcd(n,m\bmod n);\quad x\equiv y\pmod b;
+\quad x\equiv y\mod c;\quad x\equiv y\pod d
+\end{equation}
+\begin{verbatim}
+\gcd(n,m\bmod n);\quad x\equiv y\pmod b;
+\quad x\equiv y\mod c;\quad x\equiv y\pod d
+\end{verbatim}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\enlargethispage{1\baselineskip}
+
+\chapter{The \cn{text} command}\label{text}
+
+The main use of the command \cn{text} is for words or
+phrases\index{text fragments inside math} in a display. It is very
+similar to the \latex/ command \cn{mbox} in its effects, but has a
+couple of advantages. If you want a word or phrase of text in a
+subscript, you can type |..._{\textrm{word or phrase}}|, which is slightly
+easier than the \cn{mbox} equivalent: |..._{\mbox{\rmfamily\scriptsize| |word|
+|or| |phrase}}|. Note that the standard \cn{textrm} command will use the
+\nipkg{amsmath} \cn{text} definition, but ensure the \verb+\rmfamily+
+font is used.
+\begin{equation}
+f_{[x_{i-1},x_i]} \text{ is monotonic,}
+\quad i = 1,\dots,c+1
+\end{equation}
+\begin{verbatim}
+f_{[x_{i-1},x_i]} \text{ is monotonic,}
+\quad i = 1,\dots,c+1
+\end{verbatim}
+
+The font used for \cn{text} is the same as that of the surrounding
+environment; i.e., within a theorem, the contents of \cn{text} will
+be set in italic.
+
+If a math expression is included in a \cn{text} string, it must be
+explicitly marked as math (|$...$|).
+\[
+\partial_s f(x) = \frac{\partial}{\partial x_0} f(x)\quad
+  \text{for $x= x_0 + I x_1$.}
+\]
+\begin{verbatim}
+\partial_s f(x) = \frac{\partial}{\partial x_0} f(x)\quad
+  \text{for $x= x_0 + I x_1$.}
+\end{verbatim}
+
+Function names should \emph{not} be entered as \cn{text}.  Instead,
+use \cn{mathrm} or \cn{DeclareMathOperator} as appropriate.  These are
+fixed entities that should not change depending on outside content
+(such as appearing within a theorem that is set in italic), and in the
+case of declared operators, proper spacing\index{horizontal
+spacing!around operator names} is applied automatically.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Integrals and sums}
+
+\section{Multiline subscripts and superscripts}
+
+The \cn{substack} command can be used to produce a multiline subscript
+or superscript:\index{subscripts and superscripts!multiline}\relax
+\index{superscripts|see{subscripts and superscripts}} for example
+\begin{ctab}{ll}
+\begin{minipage}[t]{.6\columnwidth}
+\begin{verbatim}
+\sum_{\substack{
+         0\le i\le m\\
+         0<j<n}}
+  P(i,j)
+\end{verbatim}
+\end{minipage}
+&
+$\displaystyle
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)$
+\end{ctab}
+A slightly more generalized form is the \env{subarray} environment which
+allows you to specify that each line should be left-aligned instead of
+centered, as here:
+\begin{ctab}{ll}
+\begin{minipage}[t]{.6\columnwidth}
+\begin{verbatim}
+\sum_{\begin{subarray}{l}
+        i\in\Lambda\\ 0<j<n
+      \end{subarray}}
+ P(i,j)
+\end{verbatim}
+\end{minipage}
+&
+$\displaystyle
+  \sum_{\begin{subarray}{l}
+        i\in \Lambda\\ 0<j<n
+      \end{subarray}}
+ P(i,j)$
+\end{ctab}
+
+%% ------------------------------------------------------------------ %%
+
+\section{The \cn{sideset} command}\label{sideset}
+
+There's also a command called \cn{sideset}, for a rather special
+purpose: putting symbols at the subscript and
+superscript\index{subscripts and superscripts!on sums} corners of a
+large operator symbol such as $\sum$ or $\prod$. \emph{Note: this
+command is not designed to be applied to anything other than sum-class
+symbols.} The prime
+example is the case when you want to put a prime on a sum symbol. If
+there are no limits above or below the sum, you could just use
+\cn{nolimits}: here's
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+|\sum\nolimits' E_n| in display mode:
+\begin{equation}
+\sum\nolimits' E_n
+\end{equation}
+If, however, you want not only the prime but also something below or
+above the sum symbol, it's not so easy\mdash indeed, without
+\cn{sideset}, it would be downright difficult. With \cn{sideset}, you
+can write
+\begin{ctab}{ll}
+\begin{minipage}[t]{.6\columnwidth}
+\begin{verbatim}
+\sideset{}{'}
+  \sum_{n<k,\;\text{$n$ odd}} nE_n
+\end{verbatim}
+\end{minipage}
+&$\displaystyle
+\sideset{}{'}\sum_{n<k,\;\text{$n$ odd}} nE_n
+$
+\end{ctab}
+The extra pair of empty braces is explained by the fact that
+\cn{sideset} has the capability of putting an extra symbol or symbols at
+each corner of a large operator; to put an asterisk at each corner of a
+product symbol, you would type
+\begin{ctab}{ll}
+\begin{minipage}[t]{.6\columnwidth}
+\begin{verbatim}
+\sideset{_*^*}{_*^*}\prod
+\end{verbatim}
+\end{minipage}
+&$\displaystyle
+\sideset{_*^*}{_*^*}\prod
+$
+\end{ctab}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Placement of subscripts and limits}\label{subplace}
+
+The default positioning for subscripts depends on the
+base symbol involved. The default for sum-class symbols is
+`displaylimits' positioning: When a sum-class symbol appears
+in a displayed formula, subscript and superscript are placed in `limits'
+position above and below, but in an inline formula, they are placed to
+the side, to avoid unsightly and wasteful spreading of the
+surrounding text lines.
+The default for integral-class symbols is to have sub- and
+superscripts always to the side, even in displayed formulas.
+(See the discussion of the \opt{intlimits} and related
+options\index{options!behavior of particular options} in
+Section~\ref{options}.)
+
+Operator names such as $\sin$ or $\lim$ may have either `displaylimits'
+or `limits' positioning depending on how they were defined. The standard
+operator names are defined according to normal mathematical usage.
+
+The commands \cn{limits} and \cn{nolimits} can be used to override the
+normal behavior of a base symbol:
+\begin{equation*}
+\sum\nolimits_X,\qquad \iint\limits_{A},
+\qquad\varliminf\nolimits_{n\to \infty}
+\end{equation*}
+To define a command whose subscripts follow the
+same `displaylimits' behavior as \cn{sum}, put
+\cn{displaylimits} at the tail end of the definition. When multiple
+instances of \cn{limits}, \cn{nolimits}, or \cn{displaylimits} occur
+consecutively, the last one takes precedence.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Multiple integral signs}
+
+\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral
+signs\index{integrals!multiple} with the spacing between them nicely
+adjusted, in both text and display style. \cn{idotsint} is an extension
+of the same idea that gives two integral signs with dots between them.
+\begin{gather}
+\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A
+f(x,y,z)\,dx\,dy\,dz\\
+\iiiint\limits_A
+f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k)
+\end{gather}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Commutative diagrams}\label{s:commdiag}
+\index{commutative diagrams}
+
+Some commutative diagram commands like the ones in \amstex/ are
+available as a separate package, \pkg{amscd}. For complex commutative
+diagrams authors will need to turn to more comprehensive packages like
+\tikz/\index{TikZ@\tikz/ package} (in particular, \pkg{tikz-cd})
+or \xypic/\index{XY-pic@\xypic/ package},
+but for simple diagrams without diagonal
+arrows\index{arrows!in commutative diagrams} the \pkg{amscd} commands
+may be more convenient. Here is one example.
+\begin{equation*}
+\begin{CD}
+S^{\mathcal{W}_\Lambda}\otimes T   @>j>>   T\\
+@VVV                                    @VV{\End P}V\\
+(S\otimes T)/I                  @=      (Z\otimes T)/J
+\end{CD}
+\end{equation*}
+\begin{verbatim}
+\begin{CD}
+S^{\mathcal{W}_\Lambda}\otimes T   @>j>>   T\\
+@VVV                                    @VV{\End P}V\\
+(S\otimes T)/I                  @=      (Z\otimes T)/J
+\end{CD}
+\end{verbatim}
+In the \env{CD} environment the commands |@>>>|,
+|@<<<|, |@VVV|, and |@AAA| give respectively right, left, down, and up
+arrows. For the horizontal arrows, material between the first and second
+|>| or |<| symbols will be typeset as a superscript, and material
+between the second and third will be typeset as a subscript. Similarly,
+material between the first and second or second and third |A|s or |V|s
+of vertical arrows will be typeset as left or right \qq{sidescripts}.
+The commands |@=| and \verb'@|' give horizontal and vertical double lines.
+A \qq{null arrow} command |@.| can be used instead of a visible arrow
+to fill out an array where needed.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Using math fonts}
+
+\section{Introduction}
+
+For more comprehensive information on font use in \latex/, see the
+\latex/ font guide (\fn{fntguide.tex}) or \booktitle{The \latex/
+Companion} \cite{tlc2}. The basic set of math font commands\index{math
+fonts}\relax \index{math symbols|see{math fonts}} in \latex/ includes
+\cn{mathbf}, \cn{mathrm}, \cn{mathcal}, \cn{mathsf}, \cn{mathtt},
+\cn{mathit}. Additional math alphabet commands such as
+\cn{mathbb} for blackboard bold, \cn{mathfrak} for Fraktur, and
+\cn{mathscr} for Euler script are available through the packages
+\pkg{amsfonts} and \pkg{euscript} (distributed separately).
+
+%% ------------------------------------------------------------------ %%
+\enlargethispage{1\baselineskip}
+
+\section{Recommended use of math font commands}
+
+If you find yourself employing math font commands frequently in your
+document, you might wish that they had shorter names, such as \ncn{mb}
+instead of \cn{mathbf}. Of course, there is nothing to keep you from
+providing such abbreviations for yourself by suitable \cn{newcommand}
+statements. But for \latex/ to provide shorter names would actually be a
+disservice to authors, as that would obscure a much better alternative:
+defining custom command names derived from the names of the underlying
+mathematical objects, rather than from the names of the fonts used to
+distinguish the objects. For example, if you are using bold to indicate
+vectors, then you will be better served in the long run if you define a
+`vector' command instead of a `math-bold' command:
+\begin{verbatim}
+  \newcommand{\vect}[1]{\mathbf{#1}}
+\end{verbatim}
+you can write |\vect{a} + \vect{b}| to produce $\vect{a} +
+\vect{b}$.
+If you decide several months down the road that you want to use the bold
+font for some other purpose, and mark vectors by a small over-arrow
+instead, then you can put the change into effect merely by changing the
+definition of \ncn{vect}; otherwise you would have to replace all
+occurrences of \cn{mathbf} throughout your document, perhaps even
+needing to inspect each one to see whether it is indeed
+an instance of a vector.
+
+It can also be useful to assign distinct
+command names for different letters of a particular font:
+\begin{verbatim}
+\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}% or use amsfonts package
+\DeclareMathSymbol{\C}{\mathalpha}{AMSb}{"43}
+\DeclareMathSymbol{\R}{\mathalpha}{AMSb}{"52}
+\end{verbatim}
+These statements would define the commands \cn{C} and \cn{R} to produce
+blackboard-bold letters from the `AMSb' math symbols font. If you refer
+often to the\break complex numbers or real numbers in your document, you
+might find this method more convenient than (let's say) defining a
+\ncn{field} command and writing\break |\field{C}|, |\field{R}|. But for
+maximum flexibility and control, define such a \ncn{field} command and
+then define \ncn{C} and \ncn{R} in terms of that
+command:\indexcs{mathbb}
+\begin{verbatim}
+\usepackage{amsfonts}% to get the \mathbb alphabet
+\newcommand{\field}[1]{\mathbb{#1}}
+\newcommand{\C}{\field{C}}
+\newcommand{\R}{\field{R}}
+\end{verbatim}
+
+%% ------------------------------------------------------------------ %%
+\enlargethispage{3\baselineskip}
+
+\section{Bold math symbols}
+
+The \cn{mathbf} command is commonly used to obtain bold Latin letters in
+math, but for most other kinds of math symbols it has no effect, or its
+effects depend unreliably on the set of math fonts that are in use. For
+example, writing
+\begin{verbatim}
+\Delta \mathbf{\Delta}\mathbf{+}\delta \mathbf{\delta}
+\end{verbatim}
+produces $\Delta \mathbf{\Delta}\mathbf{+}\delta
+\mathbf{\delta}$; the \cn{mathbf} has no effect on the plus
+sign or the small delta.
+% should be paragraph break; avoid overfull box on next line
+The \nipkg{amsmath} package therefore provides two additional commands,
+\cn{boldsymbol} and \cn{pmb}, that can be applied to other kinds of math
+symbols. \cn{boldsymbol} can be used for a math symbol that remains
+unaffected by \cn{mathbf} if (and only if) your current math font set
+includes a bold version of that symbol. \cn{pmb} can be used as a last
+resort for any math symbols that do not have a true bold version
+provided by your set of math fonts; \qq{pmb} stands for \qq{poor man's
+bold} and the command works by typesetting multiple copies of the symbol
+with slight offsets. The quality of the output is inferior, especially
+for symbols that contain any hairline strokes. When the standard default set of
+\latex/ math fonts are in use (Computer Modern), the only symbols that
+are likely to require \cn{pmb} are large operator symbols like \cn{sum},
+extended delimiter\index{delimiters} symbols, or the extra math symbols
+provided by the \pkg{amssymb} package \cite{amsfonts}.
+
+The following formula shows some of the results that are possible:
+\begin{verbatim}
+A_\infty + \pi A_0
+\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+  \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}}
+\end{verbatim}
+\begin{equation*}
+A_\infty + \pi A_0
+\sim \mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+  \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\sim\pmb{A}_{\pmb{\infty}} \pmb{+}\pmb{\pi} \pmb{A}_{\pmb{0}}
+\end{equation*}
+If you want to use only the \cn{boldsymbol} command without loading the
+whole \nipkg{amsmath} package, the \pkg{bm} package is recommended (this
+is a standard \latex/ package, not an AMS package; you probably have it
+already if you have a 1997 or newer version of \latex/).
+
+%% ------------------------------------------------------------------ %%
+
+\section{Italic Greek letters}
+
+For italic versions of the capital Greek letters, the following commands
+are provided:
+\begin{ctab}{rlrl}
+\cn{varGamma}& $\varGamma$& \cn{varSigma}& $\varSigma$\\
+\cn{varDelta}& $\varDelta$& \cn{varUpsilon}& $\varUpsilon$\\
+\cn{varTheta}& $\varTheta$& \cn{varPhi}& $\varPhi$\\
+\cn{varLambda}& $\varLambda$& \cn{varPsi}& $\varPsi$\\
+\cn{varXi}& $\varXi$& \cn{varOmega}& $\varOmega$\\
+\cn{varPi}& $\varPi$
+\end{ctab}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Error messages and output problems}
+
+\section{General remarks}
+
+This is a supplement to Chapter~8 of the \latex/ manual \cite{lamport}
+(first edition: Chapter~6). Appendix~B of the
+\textit{Companion}~\cite{tlc2} lists all \latex/ errors including those
+for \nipkg{amsmath} with likely causes for each.  For the reader's
+convenience, the set of error messages discussed here overlaps
+somewhat with the set in those references,
+but please be aware that we don't provide exhaustive coverage here.
+The error messages are arranged in alphabetical order, disregarding
+unimportant text such as |! LaTeX Error:| at the beginning, and
+nonalphabetical characters such as \qc{\\}. Where examples are given, we
+show also the help messages that appear on screen when you respond to an
+error message prompt by entering |h|.
+
+Remember that the important error message is the first for a given line.
+When running in nonstop mode, errors accumulate, and the first error
+may create a further error condition from which it is impossible to
+recover.  In such a situation processing will stop after 100~errors,
+so the reporting of genuine errors may not be complete, and it may be
+impossible to determine which reported errors are genuine and which
+are not.
+
+A final section discusses some output errors, i.e., instances where
+the printed document has something wrong but there was no \latex/
+error during typesetting.
+
+%% ------------------------------------------------------------------ %%
+%% **********
+\enlargethispage{-2\baselineskip}
+
+\section{Error messages}
+
+\begin{error}{\begin{split} won't work here.}
+\errexa
+\begin{verbatim}
+! Package amsmath Error: \begin{split} won't work here.
+ ...
+
+l.8 \begin{split}
+
+? h
+\Did you forget a preceding \begin{equation}?
+If not, perhaps the `aligned' environment is what you want.
+?
+\end{verbatim}
+\errexpl
+The \env{split} environment does not construct a stand-alone displayed
+equation; it needs to be used within some other environment such as
+\env{equation} or \env{gather}.
+
+\end{error}
+
+\begin{error}{Erroneous nesting of equation structures}
+\errexa
+\begin{verbatim}
+! Package amsmath Error: Erroneous nesting of equation structures;
+(amsmath)                trying to recover with `aligned'.
+
+See the amsmath package documentation for explanation.
+Type  H <return>  for immediate help.
+ ...
+
+l.260 \end{alignat*}
+                    \end{equation*}
+\end{verbatim}
+\errexpl
+The structures \env{align}, \env{alignat}, etc., are designed
+for top-level use and for the most part cannot be nested inside some
+other displayed equation structure. The chief exception is that
+\env{align} and most of its variants can be used inside the
+\env{gather} environment.
+\end{error}
+
+\begin{error}{Extra & on this line}
+\errexa
+\begin{verbatim}
+! Package amsmath Error: Extra & on this line.
+
+See the amsmath package documentation for explanation.
+Type  H <return>  for immediate help.
+ ...
+
+l.9 \end{alignat}
+
+? h
+\An extra & here is so disastrous that you should probably exit
+ and fix things up.
+?
+\end{verbatim}
+\errexpl
+In an \env{alignat} structure the number of alignment points per line
+is dictated by the numeric argument given after |\begin{alignat}|.
+If you use more alignment points in a line it is assumed that you
+accidentally left out a newline command \cn{\\} and the above error is
+issued.
+\end{error}
+
+%% **********
+\enlargethispage{1.5\baselineskip}
+
+\begin{error}{Font OMX/cmex/m/n/7=cmex7 not loadable ...}
+\errexa
+\begin{verbatim}
+! Font OMX/cmex/m/n/7=cmex7 not loadable: Metric (TFM) file not found.
+<to be read again>
+                   relax
+l.8 $a
+      b+b^2$
+? h
+I wasn't able to read the size data for this font,
+so I will ignore the font specification.
+[Wizards can fix TFM files using TFtoPL/PLtoTF.]
+You might try inserting a different font spec;
+e.g., type `I\font<same font id>=<substitute font name>'.
+?
+\end{verbatim}
+\errexpl
+Certain extra sizes of some Computer Modern fonts that were formerly
+available mainly through the AMSFonts\index{amsfont@AMSFonts collection}
+distribution are considered part of standard \latex/ (as of June 1994):
+\fn{cmex7}\ndash \texttt{9}, \fn{cmmib5}\ndash \texttt{9}, and
+\fn{cmbsy5}\ndash \texttt{9}. If these extra sizes are missing on your
+system, you should try first to get them from the source where you
+obtained \latex/. If that fails, you could try getting the fonts from
+CTAN (e.g., in the form of Metafont\index{Metafont source files} source
+files, directory \nfn{/tex-archive/fonts/latex/mf}, or in PostScript
+Type 1 format, directory
+\nfn{/tex-archive/fonts/cm/ps-type1/bakoma}\index{BaKoMa fonts}\relax
+\index{PostScript fonts}).
+
+If the font name begins with \fn{cmex}, there is a special option%
+\index{options!behavior of particular options}
+\opt{cmex10} for the \nipkg{amsmath} package that provides a temporary
+workaround. I.e., change the \cn{usepackage} to
+\begin{verbatim}
+\usepackage[cmex10]{amsmath}
+\end{verbatim}
+This will force the use of the 10-point size of the \fn{cmex} font in
+all cases. Depending on the contents of your document this may be
+adequate.
+\end{error}
+
+\enlargethispage{1\baselineskip}
+\begin{error}{Improper argument for math accent}
+\errexa
+\begin{verbatim}
+! Package amsmath Error: Improper argument for math accent:
+(amsmath)                Extra braces must be added to
+(amsmath)                prevent wrong output.
+
+See the amsmath package documentation for explanation.
+Type  H <return>  for immediate help.
+ ...
+
+l.415 \tilde k_{\lambda_j} = P_{\tilde \mathcal
+                                               {M}}
+?
+\end{verbatim}
+\errexpl
+Non-simple arguments for any \LaTeX{} command should be enclosed in
+braces. In this example extra braces are needed as follows:
+\begin{verbatim}
+... P_{\tilde{\mathcal{M}}}
+\end{verbatim}
+\end{error}
+
+\begin{error}{Math formula deleted: Insufficient extension fonts}
+\errexa
+\begin{verbatim}
+! Math formula deleted: Insufficient extension fonts.
+l.8 $ab+b^2$
+
+?
+\end{verbatim}
+\errexpl
+This usually follows a previous error |Font ... not loadable|; see the
+discussion of that error (above) for solutions.
+\end{error}
+
+\enlargethispage{1\baselineskip}
+\begin{error}{Missing number, treated as zero}
+\errexa
+\begin{verbatim}
+! Missing number, treated as zero.
+<to be read again>
+                   a
+l.100 \end{alignat}
+
+? h
+A number should have been here; I inserted `0'.
+(If you can't figure out why I needed to see a number,
+look up `weird error' in the index to The TeXbook.)
+
+?
+\end{verbatim}
+\errexpl
+There are many possibilities that can lead to this error. However, one
+possibility that is relevant for the \nipkg{amsmath} package is that you
+forgot to give the number argument of an \env{alignat} environment, as
+in:
+\begin{verbatim}
+\begin{alignat}
+ a&  =b&    c& =d\\
+a'& =b'&   c'& =d'
+\end{alignat}
+\end{verbatim}
+where the first line should read instead
+\begin{verbatim}
+\begin{alignat}{2}
+\end{verbatim}
+
+Another possibility is that you have a left bracket character |[|
+following a line break\index{line break} command \cn{\\} in a multiline
+construction such as \env{array}, \env{tabular}, or \env{eqnarray}.
+This will be interpreted by \latex/ as the beginning of an `additional
+vertical space request \cite[\S C.1.6]{lamport}, even if it occurs on the
+following line and is intended to be part of the contents. For example,
+\begin{verbatim}
+\begin{array}{c}
+a+b\\
+[f,g]\\
+m+n
+\end{array}
+\end{verbatim}
+To prevent the error message in such a case, you can
+add braces as discussed in the \latex/ manual \cite[\S C.1.1]{lamport}:
+\begin{verbatim}
+\begin{array}{c}
+a+b\\
+{[f,g]}\\
+m+n
+\end{array}
+\end{verbatim}
+or precede the bracketed expression by \cn{relax}.
+\end{error}
+
+\goodbreak
+
+\begin{error}{Missing \right. inserted}
+\errexa
+\begin{verbatim}
+! Missing \right. inserted.
+<inserted text>
+                \right .
+l.10 \end{multline}
+
+? h
+I've inserted something that you may have forgotten.
+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+\end{verbatim}
+\errexpl
+This error typically arises when you try to insert a
+line break\index{line break} or |&|\cnamp\ between a
+\cn{left}-\cn{right} pair of delimiters\index{delimiters} in any
+multiline environment, including \env{split}.
+\begin{verbatim}
+\begin{multline}
+AAA\left(BBB\\
+  CCC\right)
+\end{multline}
+\end{verbatim}
+There are two possible solutions: (1)~instead of using \cn{left} and
+\cn{right}, use `big' delimiters\index{delimiters!fixed size} of fixed
+size (\cn{bigl} \cn{bigr} \cn{biggl} \cn{biggr} \dots; see
+\secref{bigdel}); or (2)~use null delimiters\index{delimiters!null} to
+break up the \cn{left}-\cn{right} pair into parts for each line (or cell):
+\begin{verbatim}
+AAA\left(BBB\right.\\
+  \left.CCC\right)
+\end{verbatim}
+The latter solution may result in mismatched
+delimiter\index{delimiters!mismatched sizes} sizes;
+ensuring that they match requires using \cn{vphantom} in the segment
+that has the smaller delimiter (or possibly \cn{smash} in the segment
+that has the larger delimiter). In the argument of \cn{vphantom} put a
+copy of the tallest element that occurs in the other segment, e.g.,
+\begin{verbatim}
+xxx \left(\int_t yyy\right.\\
+  \left.\vphantom{\int_t} zzz ... \right)
+\end{verbatim}
+\end{error}
+
+\goodbreak
+
+\begingroup
+\lccode`M=`M
+\lccode`@=`\}
+\lowercase{\endgroup
+\begin{error}{Missing @ inserted}}
+
+\errexa
+\begin{verbatim}
+! Missing } inserted.
+<inserted text>
+                \right .
+l.10 \end{multline}
+
+? h
+I've inserted something that you may have forgotten.
+(See the <inserted text> above.)
+With luck, this will get me unwedged. But if you
+really didn't forget anything, try typing `2' now; then
+my insertion and my current dilemma will both disappear.
+\end{verbatim}
+\errexpl
+This error is often the result of using \verb+$+ within a multiline
+display environment.  Remove such \verb+$+ signs (except when they
+appear within \verb+\text{...}+).
+\end{error}
+
+\begin{error}{Old form `\pmatrix' should be \begin{pmatrix}.}
+\errexa
+\begin{verbatim}
+! Package amsmath Error: Old form `\pmatrix' should be
+                         \begin{pmatrix}.
+
+See the amsmath package documentation for explanation.
+Type  H <return>  for immediate help.
+ ...
+
+\pmatrix ->\left (\matrix@check \pmatrix
+                                         \env@matrix
+l.16 \pmatrix
+             {a&b\cr c&d\cr}
+? h
+`\pmatrix{...}' is old Plain-TeX syntax whose use is
+ill-advised in LaTeX.
+?
+\end{verbatim}
+\errexpl
+When the \nipkg{amsmath} package is used, the old forms of \cn{pmatrix},
+\cn{matrix}, and \cn{cases} cannot be used any longer because of naming
+conflicts. Their syntax did not conform with standard \LaTeX{} syntax
+in any case.
+\end{error}
+
+\enlargethispage{2\baselineskip}
+\begin{error}{Paragraph ended before \xxx was complete}
+\errexa
+\begin{verbatim}
+Runaway argument?
+
+! Paragraph ended before \multline was complete.
+<to be read again>
+                   \par
+l.100
+
+? h
+I suspect you've forgotten a `}', causing me to apply this
+control sequence to too much text. How can we recover?
+My plan is to forget the whole thing and hope for the best.
+?
+\end{verbatim}
+\errexpl
+This might be produced by a blank line between the |\begin| and |\end|.
+Another possibility is a misspelling in the |\end{multline}| command,
+e.g.,
+\begin{verbatim}
+\begin{multline}
+...
+\end{multiline}
+\end{verbatim}
+or by using abbreviations for certain environments, such as |\bal| and
+|\eal| for |\begin{align}| and |\end{align}|:
+\begin{verbatim}
+\bal
+...
+\eal
+\end{verbatim}
+For technical reasons that kind of abbreviation does not work with
+the more complex displayed equation environments of the \nipkg{amsmath} package
+(\env{gather}, \env{align}, \env{split}, etc.; cf.\ \fn{technote.tex}).
+\end{error}
+
+\begin{error}{Runaway argument?}
+See the discussion for the error message
+\texttt{Paragraph ended before \ncn{xxx} was complete}.
+\end{error}
+
+\begin{error}{Unknown option `xxx' for package `yyy'}
+\errexa
+\begin{verbatim}
+! LaTeX Error: Unknown option `intlim' for package `amsmath'.
+...
+? h
+The option `intlim' was not declared in package `amsmath', perhaps you
+misspelled its name. Try typing  <return>  to proceed.
+?
+\end{verbatim}
+\errexpl
+This means that you misspelled the option\index{options!unknown}
+name, or the package simply does not have an option that you expected
+it to have. Consult the documentation for the given package.
+\end{error}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Warning messages}
+
+\begin{error}{Cannot use `split' here}
+\errexa
+\begin{verbatim}
+Package amsmath Warning: Cannot use `split' here;
+(amsmath)                trying to recover with `aligned'
+\end{verbatim}
+\errexpl The \env{split} environment is designed to serve as the entire
+body of an equation, or an entire line of an \env{align} or \env{gather}
+environment. There cannot be any printed material before or
+after it within the same enclosing structure:
+\begin{verbatim}
+\begin{equation}
+\left\{ % <-- Not allowed
+\begin{split}
+...
+\end{split}
+\right. % <-- Not allowed
+\end{equation}
+\end{verbatim}
+\end{error}
+
+\begin{error}{Foreign command \over [or \atop or \above]}
+\errexa
+\begin{verbatim}
+Package amsmath Warning: Foreign command \over; \frac or \genfrac
+(amsmath)                should be used instead.
+\end{verbatim}
+\errexpl The primitive generalized fraction commands of \tex/\mdash
+\cs{over}, \cs{atop}, \cs{above}\mdash are deprecated when the
+\nipkg{amsmath} package is used because their syntax is foreign to \latex/
+and \nipkg{amsmath} provides native \latex/ equivalents. See
+\fn{technote.tex} for further information.
+\end{error}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Wrong output}
+
+\begin{erroro}{Section numbers 0.1, 5.1, 8.1 instead of 1, 2, 3}
+%
+This most likely means that you have the arguments for \cn{numberwithin}
+in reverse order:
+\begin{verbatim}
+\numberwithin{section}{equation}
+\end{verbatim}
+That means `print the section number as \textit{equation
+number}.\textit{section number} and reset to 1 every time an equation
+occurs' when what you probably wanted was the inverse
+\begin{verbatim}
+\numberwithin{equation}{section}
+\end{verbatim}
+\end{erroro}
+
+\begin{erroro}{The \cn{numberwithin} command had no effect on equation
+  numbers}
+%
+Are you looking at the first section in your document? Check the section
+numbers elsewhere to see if the problem is the one described in the
+previous item.
+\end{erroro}
+
+\begin{erroro}{Bracketed material disappears at the beginning of
+  \env{aligned} or \env{gathered}}
+%
+For most multiline equation environments, \nipkg{amsmath} disables the
+\latex/ convention to recognize a [bracketed] expression as an option%
+\index{ed env@\texttt{-ed} environments}%
+\index{options!positioning of \texttt{-ed} environments}%
+\index{options!space before \texttt{[}}
+when it occurs at the beginning of an environment or immediately
+following \cn{\\}, provided a space intervenes.  This fails at the
+beginning of \env{aligned} and \env{gathered}, and is a bug.  Insert
+\cn{relax} before the opening brace to restore the desired result.
+\end{erroro}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\chapter{Additional information}
+
+\section{Compatibility with other packages}
+
+Several packages have already been mentioned as providing facilities
+lacking in \nipkg{amsmath}.
+
+\begin{itemize}
+\item \pkg{bm} is recommended for specifying bold math symbols.
+\item \pkg{mathtools} provides enhancements to some \nipkg{amsmath}
+  environments as well as additional compatible features, such as
+  \env{rcases} (similar to \env{cases} but with the brace on the
+  right-hand side), \env{multlined} (a subsidiary environment
+  comparable to \env{multline}), and \cn{shortintertext} (more
+  compact spacing than \cn{intertext}).  If \pkg{mathtools} is used,
+  \nipkg{amsmath} is loaded automatically, so it is not necessary
+  to load it separately.
+\item \pkg{unicode-math} provides commands for (most?)\ math symbols
+  in Unicode.
+%\item \pkg{empheq}
+\end{itemize}
+
+These packages have known problems when used with \nipkg{amsmath}.
+\begin{itemize}
+\item \pkg{lineno} may omit numbers before display environments.
+\item \pkg{breqn} redefines a number of commands from other packages,
+  so is best loaded after \nipkg{amsmath} and other packages with math
+  facilities.\\ \pkg{breqn} is not yet totally stable, and a number of
+  bugs have been reported via \texttt{tex.stackexchange} \cite{tex-sx}.
+\item \pkg{wasysym}, \pkg{mathabx} and perhaps other font packages also
+  define multiple integrals\index{integrals!multiple} using the same
+  names as \nipkg{amsmath}.
+\end{itemize}
+
+%% ------------------------------------------------------------------ %%
+
+\section{Converting existing documents}
+
+\subsection{Converting from plain \LaTeX{}}
+
+A \LaTeX{} document will typically continue to work the same in most
+respects if \verb'\usepackage{amsmath}' is added in the document
+preamble. By default, however, the \nipkg{amsmath} package suppresses page
+breaks inside multiple-line displayed equation structures such as
+\env{eqnarray}, \env{align}, and \env{gather}. To continue allowing page
+breaks inside \env{eqnarray} after switching to \nipkg{amsmath}, you will
+need to add the following line in your document preamble:
+\begin{verbatim}
+\allowdisplaybreaks[1]
+\end{verbatim}
+To ensure normal spacing around relation symbols, you might also want to
+change \env{eqnarray} to \env{align}, \env{multline}, or
+\env{equation}\slash\env{split} as appropriate.
+
+Most of the other differences in \nipkg{amsmath} usage can be considered
+optional refinements, e.g., using
+\begin{verbatim}
+\DeclareMathOperator{\Hom}{Hom}
+\end{verbatim}
+instead of \verb'\newcommand{\Hom}{\mbox{Hom}}'.
+
+\subsection{Converting from \texorpdfstring{\amslatex/}{amslatex} 1.1}
+See \fn{diffs-m.txt}.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Technical notes}
+The file \fn{technote.tex} contains some remarks on miscellaneous
+technical questions that are less likely to be of general interest.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Getting help}
+
+The \nipkg{amsmath} collection of packages is maintained by the \latex/
+team \cite{ltx-team}.  Bugs should be reported using the instructions
+at \url{https://www.latex-project.org/bugs/}.
+Please be careful not to confuse \nipkg{amsmath} with the AMS document
+classes (\cls{amsart}, \cls{amsbook}, and \cls{amsproc}), which
+automatically incorporate \nipkg{amsmath}; bugs in the classes should
+be reported directly to AMS, by email to \mail{tech-support@ams.org}.
+
+%Questions or comments regarding \nipkg{amsmath} and related packages
+%should be sent to:
+%\begin{infoaddress}
+%American Mathematical Society\\
+%Technical Support\\
+%Electronic Products and Services\\
+%P. O. Box 6248\\
+%Providence, RI 02940\\[3pt]
+%Phone: 800-321-4AMS (321-4267) \quad or \quad 401-455-4080\\
+%Internet: \mail{tech-support@ams.org}
+%\end{infoaddress}
+%If you are reporting a problem you should include
+%the following information to make proper investigation possible:
+%\begin{enumerate}
+%\item The source file where the problem occurred, preferably reduced
+%  to minimum size by removing any material that can be removed without
+%  affecting the observed problem.
+%\item A \latex/ log file showing the error message (if applicable) and
+%  the version numbers of the document class and option files being used.
+%\end{enumerate}
+
+The online forum\index{online Q\,\&\,A forum} \texttt{tex.stackexchange}
+\cite{tex-sx} is a good source of answers to common questions on usage.
+Look first in the archive to see if your question has already been asked
+and answered; if it has not, post your own question.
+
+There is an online discussion group called \fn{comp.text.tex} \cite{ctt}
+that is a fairly good source of information about \latex/ and \tex/ in
+general. This group, formerly a Unix newsgroup, predates
+\texttt{tex.stackexchange} by decades, and the archives can be a useful
+resource for historical investigation.
+
+%% ------------------------------------------------------------------ %%
+
+\section{Of possible interest}\label{a:possible-interest}
+Information about obtaining AMSFonts or other \tex/-related
+software from the AMS web server at \fn{www.ams.org}
+can be obtained by sending an email request to
+\mail{tech-support@ams.org}.  This software is also posted on
+CTAN\index{CTAN (Comprehensive \TeX\ Archive Network)} and included
+in distributions based on \TeX\,Live\index{TEX Live@\TeX\,Live}.
+
+The \tex/ Users Group\index{TeX Users@\tex/ Users Group} is a nonprofit
+organization that publishes a journal
+(\journalname{TUGboat}\index{TUGboat@\journalname{TUGboat}}), holds
+meetings, and serves as a clearinghouse for general information about
+\tex/ and \tex/-related software.
+\begin{infoaddress}
+\tex/ Users Group\\
+PO Box 2311\\
+Portland, OR 97208-2311\\
+USA\\[3pt]
+Phone: +1-503-223-9994\\
+Email: \mail{office@tug.org}
+\end{infoaddress}
+Membership in the \tex/ Users Group is a good way to support continued
+development of free \tex/-related software. There are also many local
+\tex/ user groups in other countries; information about contacting a
+local user group can be gotten from the \tex/ Users Group.
+
+\index{amsmath@\texttt{amsmath} package|)}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newpage
+
+\begin{thebibliography}{10}
+\addcontentsline{toc}{chapter}{\bibname}
+
+\raggedright
+
+\bibsubhead{References in print}
+
+\bibitem{mil} George Gr\"atzer, \booktitle{More Math into \latex/}, fifth ed.,
+Springer, New York, 2016.
+% Deal with a line breaking problem
+%\begin{raggedright}
+%\bibitem{mil} G. Gr\"{a}tzer,
+%\emph{Math into \LaTeX{}: An Introduction to \LaTeX{} and AMS-\LaTeX{}}
+%  \url{https://www.ams.org/cgi-bin/bookstore/bookpromo?fn=91&arg1=bookvideo&itmc=MLTEX},
+%Birkh\"{a}user, Boston, 1995.\par
+%\end{raggedright}
+
+\bibitem{kn} Donald E. Knuth, \booktitle{The \tex/book},
+Addison-Wesley, Reading, MA, 1984.
+
+\bibitem{lamport} Leslie Lamport, \booktitle{\latex/: A document preparation
+system}, 2nd revised ed., Addison-Wesley, Reading, MA, 1994.
+
+\bibitem{tlc2} Frank Mittelbach, Michel Goossens, et al.,
+\booktitle{The \latex/ companion}, second ed., Addison-Wesley, Reading,
+MA, 2004.  This is now also available as an ebook, in both English and
+German; see \url{https://www.latex-project.org/help/books/}.
+The front matter, including the full Table of Contents, can be viewed
+online, from a link on the same page.
+%Michel Goossens, Frank Mittelbach, and Alexander Samarin,
+%\booktitle{The \latex/ companion}, Addison-Wesley, Reading, MA, 1994.
+%  [\emph{Note: The 1994 edition is not a reliable guide for the
+%    \nipkg{amsmath} package unless you refer to the errata for Chapter
+%    8\mdash file \fn{compan.err}, distributed with \LaTeX{}.}]
+
+\bibitem{msf} Frank Mittelbach and Rainer Sch\"opf,
+\textit{The new font family selection\mdash user
+interface to standard \latex/}, \journalname{TUGboat} \textbf{11},
+no.~2 (June 1990), pp.~297\ndash 305.
+
+\bibitem{jt} Michael Spivak, \booktitle{The joy of \tex/}, 2nd revised ed.,
+Amer. Math. Soc., Providence, RI, 1990.
+
+\bibsubhead{Package documentation}
+
+\bibitem{amshandbk}\booktitle{AMS author handbook}, separate versions
+for journal articles, monographs and proceedings articles, Amer. Math.
+Soc., Providence, RI, 2017;
+\url{https://www.ams.org/publications/authors/tex/author-handbook}.
+
+\bibitem{amsfonts}\booktitle{AMSFonts version \textup{2.2d}\mdash user's guide},
+Amer. Math. Soc., Providence, RI, 2002; distributed
+with the AMSFonts package
+\url{http://mirror.ctan.org/tex-archive/fonts/amsfonts/doc/amsfndoc.pdf}.
+
+\bibitem{amsthdoc}\booktitle{Using the \pkg{amsthm} Package}, version 2.20.3,
+Amer. Math. Soc., Providence, RI, 2017;
+\url{http://mirror.ctan.org/tex-archive/macros/latex/required/amscls/doc/amsthdoc.pdf}.
+
+\bibitem{mt} Morten H{\o}gholm, Lars Madsen, \booktitle{The \pkg{mathtools}
+package}, 2018;
+\url{http://mirror.ctan.org/tex-archive/macros/latex/contrib/mathtools/mathtools.pdf}.
+
+\bibsubhead{Online resources}
+
+\bibitem{ltx-team} The \latex/ Project, \url{https://www.latex-project.org}.
+
+\bibitem{ctt} Online discussion group \texttt{comp.text.tex},
+\url{https://groups.google.com/forum/\#!forum/comp.text.tex}.
+
+\bibitem{tex-sx} Online question and answer forum \texttt{tex.stackexchange},
+\url{https://tex.stackexchange.com}.
+
+\end{thebibliography}
+
+\printindex
+
+\end{document}
diff --git a/macros/latex-dev/required/amsmath/amsmath.dtx b/macros/latex-dev/required/amsmath/amsmath.dtx
new file mode 100644
index 0000000000..8671694b70
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsmath.dtx
@@ -0,0 +1,6383 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 2000, 2013 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\raggedbottom
+\let\savedarg\arg
+\usepackage{amsmath}
+\let\arg\savedarg
+\GetFileInfo{amsmath.sty}
+\begin{document}
+\title{The \pkg{amsmath} package}
+\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes\and
+  David M. Jones\and David Carlisle}
+\date{Version \fileversion, \filedate}
+\providecommand{\histnote}{}
+\renewenvironment{histnote}{%
+  \trivlist\item[\hspace{\labelsep}\bfseries Historical Note:]%
+}{%
+  \endtrivlist
+}
+\DocInput{amsmath.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%
+%    A \latex/ package named \pkg{amstex} was created in 1988--1989 by
+%    adapting \fn{amstex.tex} for use within \latex/. The \pkg{amsmath}
+%    package is the successor of the \pkg{amstex} package. It was
+%    substantially overhauled to integrate it with \latex/2e, which
+%    arrived on the scene in 1994. It provides more or less the same
+%    features, but there are quite a few organizational differences as
+%    well as some new features and bug fixes. For example, the
+%    \pkg{amstex} package automatically loaded the \pkg{amsfonts}
+%    package, but the \pkg{amsmath} package does not. At the present
+%    time (November 1999) user-level documentation of the commands
+%    provided here is found in the AMSmath Users' Guide,
+%    \fn{amsldoc.tex}.
+%
+% \StopEventually{}
+%
+%    Standard file identification.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must be December 1994 or later
+%    \end{macrocode}
+%
+%    Providing a rollback to earlier version(s)
+%    \begin{macrocode}
+\providecommand\DeclareRelease[3]{}
+\providecommand\DeclareCurrentRelease[2]{}
+%
+\DeclareRelease{}{2018-12-01}{amsmath-2018-12-01.sty}
+\DeclareCurrentRelease{}{2019-04-01}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ProvidesPackage{amsmath}[2019/04/01 v2.17c AMS math features]
+%    \end{macrocode}
+%
+% \section{Catcode defenses}
+%
+%    Some packages change the catcode of characters that are essential
+%    in low-level \tex/ syntax. Any package that does so does not
+%    qualify as a PWWO package (\qq{Plays Well With Others}) because it
+%    can cause other packages to fail if they are loaded later. \LaTeX{}
+%    is partly to blame for this because it fails to provide adequate
+%    built-in safeguards in the package loading mechanisms. In the
+%    absence of such safeguards, we will provide them here.
+%    \begin{macrocode}
+\edef\@temp{\catcode 96=\number\catcode 96 }
+\catcode\string `\`=12
+\def\do#1{\catcode\number`#1=\number\catcode`#1}
+\edef\@temp{%
+  \noexpand\AtEndOfPackage{%
+    \@temp
+    \do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.%
+    \do\/\do\<\do\=\do\>\do\[\do\]\do\^\do\_\relax
+  }%
+}
+\@temp
+\def\do#1{\catcode\number`#1=12 }
+\do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.
+\do\/\do\<\do\=\do\>\do\[\do\]
+\catcode`\^=7 \catcode`\_=8
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Declare some options}
+%
+%    Handling of limits on integrals, sums, operatornames.
+%    \begin{macrocode}
+\DeclareOption{intlimits}{\let\ilimits@\displaylimits}
+\DeclareOption{nointlimits}{\let\ilimits@\nolimits}
+\DeclareOption{sumlimits}{\let\slimits@\displaylimits}
+\DeclareOption{nosumlimits}{\let\slimits@\nolimits}
+\DeclareOption{namelimits}{\PassOptionsToPackage{namelimits}{amsopn}}
+\DeclareOption{nonamelimits}{%
+  \PassOptionsToPackage{nonamelimits}{amsopn}}
+%    \end{macrocode}
+%
+%    The following two switches might have been defined already by the
+%    documentclass, but it doesn't hurt to re-execute the \cs{newif}'s.
+%    \begin{macrocode}
+\newif\ifctagsplit@
+\newif\iftagsleft@
+%    \end{macrocode}
+%    Right or left placement of equation numbers.
+%    \begin{macrocode}
+\DeclareOption{leqno}{\tagsleft@true}
+\DeclareOption{reqno}{\tagsleft@false}
+\DeclareOption{centertags}{\ctagsplit@true}
+\DeclareOption{tbtags}{\ctagsplit@false}
+%    \end{macrocode}
+%
+%    The \opt{cmex10} option is an escape hatch for people who don't
+%    happen to have sizes 7--9 of the \fn{cmex} fonts available to them
+%    yet. (Strictly speaking they are considered part of a minimum
+%    \latex/ distribution now, i.e., all \LaTeXe{} users should have
+%    them, without needing to get the AMSFonts distrib.)
+%    \begin{macrocode}
+\DeclareOption{cmex10}{%
+  \ifnum\cmex@opt=\@ne \def\cmex@opt{0}%
+  \else \def\cmex@opt{10}\fi
+}
+%    \end{macrocode}
+%    To help things work out better with various package loading orders
+%    of \pkg{amsmath} and \pkg{amsfonts}, we establish a variable to
+%    communicate the status of the cmex font definition. If the
+%    \pkg{amsfonts} package was loaded first this variable might be
+%    already defined, in which case we want to preserve its value.
+%    \begin{macrocode}
+\@ifundefined{cmex@opt}{\def\cmex@opt{7}}{}
+%    \end{macrocode}
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Flush-left equations [DMJ]}
+%
+%    The left margin of math enviroments is controlled by
+%    \cs{@mathmargin}.  This can be set to \cs{@centering} to
+%    implement the default behaviour, i.e., centered equations, and to
+%    something else to implement the flushleft style.
+%
+%    In theory, all that's needed to activate the flushleft mode
+%    in the AMS document classes is something like this:
+% \begin{verbatim}
+% \DeclareOption{fleqn}{%
+%   \AtBeginDocument{\@mathmargin30pt\relax}%
+% }
+% \end{verbatim}
+%    (In fact, unless the document class wants to specify the
+%    \cs{@mathmargin}, it doesn't need to do anything with the
+%    \opt{fleqn} option.)
+%    \begin{macrocode}
+\newif\if@fleqn
+%
+\newskip\@mathmargin
+\@mathmargin\@centering
+%
+\DeclareOption{fleqn}{%
+    \@fleqntrue
+    \@mathmargin = -1sp
+    \let\mathindent=\@mathmargin
+    \AtBeginDocument{%
+        \ifdim\@mathmargin= -1sp
+            \@mathmargin\leftmargini minus\leftmargini
+        \fi
+    }%
+}
+%    \end{macrocode}
+%
+%    DMJ: This ensures that \cs{@mathmargin} is given some sort of
+%    sensible default if the class doesn't specify one, while still
+%    allowing a user to override the default value in their document
+%    preamble.  (Incidentally, I'm initializing \cs{@mathmargin} to
+%    \cs{leftmargini} for compatibility with \fn{fleqn.clo}, but I'm
+%    not at all convinced that's the right thing to do.)
+%
+%    The next question is what happens when amsmath is used with
+%    one of the standard classes.  Unfortunately, \latex/ implements
+%    \opt{fleqn} somewhat clumsily; instead of paramaterizing the
+%    definitions of the math structures (as I've attempted to do
+%    here), \fn{fleqn.clo} declares a dimen \cn{mathindent} that is
+%    much like my \cs{@mathmargin} and then redefines \cn\[, \cn\],
+%    \cn{equation}, and \cn{eqnarray}.  This means that things could
+%    get rather messy in 2.09 compatibility mode, since \fn{fleqn.clo}
+%    might be loaded after \fn{amsmath.sty}, which could cause a real
+%    mess.
+%
+%    [mjd,1999/07/07]: Let \cs{mathindent} = \cs{@mathmargin} as
+%    envisioned by DMJ. Compatibility-mode documents will all use the
+%    \pkg{amstex} package, not \pkg{amsmath}. There is a remote chance
+%    of a problem if someone makes an assignment to \cs{mathindent} in a
+%    way that implicitly assumes it is a dimen register (inasmuch as it
+%    has now become a skip register), and the string ``plus'' follows in
+%    the input stream, but if someone's document croaks in that way, I
+%    think they will just have to bite the bullet and fix it. The
+%    alternative is to penalize a lot of other users with a known
+%    handicap.
+%
+% \section{Spacing around \cn{aligned} and \cn{gathered}}
+%
+%    [dpc, 2016] Option to control the space to the left of aligned and gathered.
+%
+%   Previously \cn{aligned} and \cn{gathered} inserted a thin space on
+%   their left but not their right, there is no good reason for this
+%   that anyone can remember, it has just always been that way
+%   inherited from amstex. The usual advice to authors has been to use
+%   |\!\begin{aligned}| to get better spacing.
+%
+% Here introduce:
+%
+% \opt{alignedleftspaceyes} to keep the behaviour of adding this space.
+%
+% \opt{alignedleftspaceno} to disable adding this space.
+%
+% \opt{alignedleftspaceyesifneg} the new default behaviour, do not add
+% the space unless the environment is preceded by a negative skip or
+% kern, so that |\!\begin{aligned}| works as before.
+%
+% \changes{v2.16a}{2016/11/05}{New options to control aligned spacing}
+%    \begin{macrocode}
+\DeclareOption{alignedleftspaceyes}{\def\alignedspace@left{\null\,}}
+\DeclareOption{alignedleftspaceno}{\def\alignedspace@left{\null}}
+\DeclareOption{alignedleftspaceyesifneg}{%
+\def\alignedspace@left{%
+  \edef\@tempa{\expandafter\@car\the\lastskip\@nil}%
+  \if-\@tempa\null\,%
+  \else
+    \edef\@tempa{\expandafter\@car\the\lastkern\@nil}%
+    \if-\@tempa\null\,%
+    \else\null
+    \fi
+  \fi}%
+}
+%    \end{macrocode}
+%
+%
+%    \begin{macrocode}
+\DeclareOption{?}{}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ExecuteOptions{%
+  nointlimits,sumlimits,namelimits,centertags,alignedleftspaceyesifneg}
+%    \end{macrocode}
+%    The \cs{par} after \cs{ProcessOptions} is to ensure the correct
+%    line number on screen if an error occurs during option processing;
+%    otherwise the lookahead for a \qc{\*} option would result in \tex/
+%    showing the following line instead.
+%    \begin{macrocode}
+\ProcessOptions\par
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\@ifpackagewith{amsmath}{?}{%
+  \typeout{^^J%
+Documentation for the amsmath package is found in amsldoc.dvi^^J%
+(or .pdf or .tex).^^J%
+^^J%
+See also https://www.ams.org/tex/amslatex.html.^^J%
+^^J%
+Note: Using the first edition of The LaTeX Companion (1994) without^^J%
+errata as a guide for amsmath use is not recommended.^^J%
+  }%
+}{%
+  \typeout{%
+For additional information on amsmath, use the \lq ?\rq\space option.%
+  }%
+}
+%    \end{macrocode}
+%
+%    Processing to handle the \opt{cmex10} option is a little tricky
+%    because of different possible loading orders for \pkg{amsmath} and
+%    \pkg{amsfonts}. The package \pkg{amsmath} sets the \cs{cmex@opt}
+%    flag to 7 or 10, and the package \pkg{amsfonts} sets the flag to 1
+%    or 0.
+%    \begin{macrocode}
+\ifnum\cmex@opt=7 \relax
+  \DeclareFontShape{OMX}{cmex}{m}{n}{%
+    <-8>cmex7<8>cmex8<9>cmex9%
+    <10><10.95><12><14.4><17.28><20.74><24.88>cmex10%
+  }{}%
+  \expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
+\else
+  \ifnum\cmex@opt=\z@ % need to override cmex7 fontdef from amsfonts
+%    \end{macrocode}
+%    Force reloading of the OMX/cmex font definition file.
+%    \begin{macrocode}
+    \begingroup
+    \fontencoding{OMX}\fontfamily{cmex}%
+    \expandafter\let\csname OMX+cmex\endcsname\relax
+    \try@load@fontshape
+    \endgroup
+%    \end{macrocode}
+%    The \fn{cmex10} font gets special preload handling in the building
+%    of the \latex/ format file, need an extra bit here to work around
+%    that.
+%    \begin{macrocode}
+    \expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
+    \def\cmex@opt{10}%
+  \fi
+\fi
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Call some other packages}
+%
+%    The \pkg{amstext} package provides the \cn{text} command. The
+%    \pkg{amsbsy} package provides \cn{boldsymbol} and \cn{pmb}. (Since
+%    1997 it is usually better to use the \pkg{bm} package instead; but
+%    I think we have to keep \pkg{amsbsy} here for backward
+%    compatibility [mjd,1999/11/19].) The \pkg{amsopn} package provides
+%    \cn{DeclareMathOperator}.
+%    \begin{macrocode}
+\RequirePackage{amstext}[1995/01/25]
+\RequirePackage{amsbsy}[1995/01/20]
+\RequirePackage{amsopn}[1995/01/20]
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Miscellaneous}
+%
+%  \begin{macro}{\ams@newcommand}
+%    Where \pkg{stix} and \pkg{amsmath} define the same control
+%    sequences, we want to avoid inadvertently overriding \pkg{stix}'s
+%    definitions.  If \pkg{stix} is loaded before \pkg{amsmath}, the
+%    following conditional takes care of the problem.  There is
+%    similar code in the \pkg{stix} package in case \pkg{amsmath} is
+%    loaded first.
+%    \begin{macrocode}
+\@ifpackageloaded{stix}{%
+    \let\ams@newcommand\providecommand
+    \let\ams@renewcommand\providecommand
+    \let\ams@def\providecommand
+    \let\ams@DeclareRobustCommand\providecommand
+}{%
+    \let\ams@newcommand\newcommand
+    \let\ams@renewcommand\renewcommand
+    \let\ams@def\def
+    \let\ams@DeclareRobustCommand\DeclareRobustCommand
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\@amsmath@err}
+%    Defining this error function saves main mem.
+%    \begin{macrocode}
+\def\@amsmath@err{\PackageError{amsmath}}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\AmS}
+%    The \cs{AmS} prefix can be used to construct the combination
+%    |\AmS-\LaTeX|.
+%    \begin{macrocode}
+\providecommand{\AmS}{{\protect\AmSfont
+  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
+%    \end{macrocode}
+%    In \cn{AmSfont} we call cmsy directly in lieu of trying to access
+%    it through the math fonts setup (e.g. |\the\textfont2|) because
+%    math fonts can't be relied on to be properly set up if we are not
+%    inside a math formula. This means that if this command is used in a
+%    document where CM fonts are not wanted, then a font substitution
+%    will need to be declared, e.g.:
+% \begin{verbatim}
+% \DeclareFontShape{OMS}{cmsy}{m}{n}{ <-> sub * xxx/m/n }{}
+% \end{verbatim}
+%    where |xxx| is some alternate font family.
+%    Taking the first letter of \cs{f@series} will produce |b| or |m|
+%    for the most common values (|b,bx,m|). It may produce nonsense for
+%    more unusual values of \cs{f@series}, so for safety's sake we have
+%    an additional \cs{if} test. We want to avoid setting the series to
+%    |bx| because in a standard \latex/ installation the combination
+%    |cmsy/bx/n| does not have a font definition, and the user
+%    would get a font substitution warning on screen.
+%    \begin{macrocode}
+\newcommand{\AmSfont}{%
+  \usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\@mathmeasure}
+%    The function |\@mathmeasure| takes three arguments; the third arg
+%    is typeset as a math formula in an hbox, using arg |#2| as the
+%    mathstyle, and the result is left in the box named by the first
+%    arg. It is assumed that we are already in math mode, so we can turn
+%    off |\everymath| (in particular, |\check@mathfonts|).
+%
+%    As of 2018/12 release we don't turn off |\evermath| as this
+%    optimization can be harmful.
+% \changes{v2.17b}{2018/12/01}{Don't drop \cs{frozen@everymath}}
+%    \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined  % kernel is < 2018/12
+\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
+    \m@th$#2#3$}}
+\else
+\def\@mathmeasure#1#2#3{\setbox#1\hbox{%
+  \m@th$#2#3$}}
+\fi
+%    \end{macrocode}
+%  \end{macro}
+%
+%    The \cs{inf@bad} constant is for testing overfull boxes.
+%    \begin{macrocode}
+\@ifundefined{inf@bad}{%
+  \newcount\inf@bad \inf@bad=1000000 \relax
+}{}
+%    \end{macrocode}
+%
+%\subsection{Math spacing commands}
+%
+%    \begin{macro}{\tmspace}
+%    \begin{macro}{\,}
+%    \begin{macro}{\thinspace}
+%    \begin{macro}{\!}
+%    \begin{macro}{\negthinspace}
+%    \begin{macro}{\:}
+%    \begin{macro}{\medspace}
+%    \begin{macro}{\negmedspace}
+%    \begin{macro}{\;}
+%    \begin{macro}{\thickspace}
+%    \begin{macro}{\negthickspace}
+%    Here we fill in some gaps in the set of spacing commands, and make them
+%    all work equally well in or out of math.
+%    We want all these commands to be robust but declaring them all with
+%    \cs{DeclareRobustCommand} uses up an control sequence name per
+%    command; to avoid this, we define a common command \cs{tmspace}
+%    (text-or-math space) which carries the robustness burden for all of
+%    them. The standard \cs{relax} before the \cs{ifmmode} is not
+%    necessary because of the \cs{protect} added by
+%    \cs{DeclareRobustCommand}.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{thinspace} and
+%   friends if necessary (github/49)}
+%    \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\DeclareRobustCommand{\tmspace}[3]{%
+  \ifmmode\mskip#1#2\else\kern#1#3\fi\relax}
+\else
+\DeclareRobustCommand{\tmspace}[3]{%
+  \ifmmode\mskip#1#2\else\leavevmode@ifvmode\kern#1#3\fi\relax}
+\fi
+\renewcommand{\,}{\tmspace+\thinmuskip{.1667em}}
+\let\thinspace\,
+\renewcommand{\!}{\tmspace-\thinmuskip{.1667em}}
+\let\negthinspace\!
+\renewcommand{\:}{\tmspace+\medmuskip{.2222em}}
+\let\medspace\:
+\newcommand{\negmedspace}{\tmspace-\medmuskip{.2222em}}
+\renewcommand{\;}{\tmspace+\thickmuskip{.2777em}}
+\let\thickspace\;
+\newcommand{\negthickspace}{\tmspace-\thickmuskip{.2777em}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\mspace}
+%    And while we're at it, why don't we provide an equivalent of
+%    \cn{hspace} for math mode use. This allows use of |mu| units in
+%    (for example) constructing compound math symbols.
+%    \begin{macrocode}
+\newcommand{\mspace}[1]{\mskip#1\relax}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \subsection{Vertical bar symbols}
+%    \begin{macro}{\lvert}
+%    \begin{macro}{\rvert}
+%    \begin{macro}{\lVert}
+%    \begin{macro}{\rVert}
+%    Add left/right specific versions of \cn{vert}, \cn{Vert}. Don't
+%    assume the delimiter codes are the CM defaults.
+%    \begin{macrocode}
+\def\@tempa#1#2\@nil{%
+  \ifx\delimiter#1\@tempcnta#2\relax\else\@tempcnta\z@\fi
+}
+\@xp\@tempa\vert\@empty\@nil
+\ifnum\@tempcnta>\z@
+  \advance\@tempcnta "4000000
+  \xdef\lvert{\delimiter\number\@tempcnta\space }
+  \advance\@tempcnta "1000000
+  \xdef\rvert{\delimiter\number\@tempcnta\space }
+\else
+  \ifx\@@undefined\lvert
+    % Fall back to cmex encoding since we don't know what else to do.
+    \DeclareMathDelimiter{\lvert}
+      {\mathopen}{symbols}{"6A}{largesymbols}{"0C}
+    \DeclareMathDelimiter{\rvert}
+      {\mathclose}{symbols}{"6A}{largesymbols}{"0C}
+  \fi
+\fi
+\@xp\@tempa\Vert\@empty\@nil
+\ifnum\@tempcnta>\z@
+  \advance\@tempcnta "4000000
+  \xdef\lVert{\delimiter\number\@tempcnta\space }
+  \advance\@tempcnta "1000000
+  \xdef\rVert{\delimiter\number\@tempcnta\space }
+\else
+  \ifx\@@undefined\lVert
+    \DeclareMathDelimiter{\lVert}
+      {\mathopen}{symbols}{"6B}{largesymbols}{"0D}
+    \DeclareMathDelimiter{\rVert}
+      {\mathclose}{symbols}{"6B}{largesymbols}{"0D}
+  \fi
+\fi
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% \subsection{Fractions}
+%    Bury the generalized fraction primitives \cs{over}, \cs{atop},
+%    etc., because of their bizarre syntax, which is decidedly out of
+%    place in a \latex/ document.
+%    \begin{macrocode}
+\@saveprimitive\over\@@over
+\@saveprimitive\atop\@@atop
+\@saveprimitive\above\@@above
+\@saveprimitive\overwithdelims\@@overwithdelims
+\@saveprimitive\atopwithdelims\@@atopwithdelims
+\@saveprimitive\abovewithdelims\@@abovewithdelims
+%    \end{macrocode}
+%
+%    \begin{macro}{\primfrac}
+%    If someone insists on using \cs{over}, give a warning the first
+%    time and then resurrect the old definition. Laissez-faire policy.
+%    \begin{macrocode}
+\DeclareRobustCommand{\primfrac}[1]{%
+  \PackageWarning{amsmath}{%
+Foreign command \@backslashchar#1;\MessageBreak
+\protect\frac\space or \protect\genfrac\space should be used instead%
+\MessageBreak
+  }
+  \global\@xp\let\csname#1\@xp\endcsname\csname @@#1\endcsname
+  \csname#1\endcsname
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macrocode}
+\renewcommand{\over}{\primfrac{over}}
+\renewcommand{\atop}{\primfrac{atop}}
+\renewcommand{\above}{\primfrac{above}}
+\renewcommand{\overwithdelims}{\primfrac{overwithdelims}}
+\renewcommand{\atopwithdelims}{\primfrac{atopwithdelims}}
+\renewcommand{\abovewithdelims}{\primfrac{abovewithdelims}}
+%    \end{macrocode}
+%
+%    \cn{frac} calls \cn{@@over} directly instead of via \cn{genfrac}, for
+%    better speed because it is so common. \cn{tfrac} and \cn{dfrac} are
+%    abbreviations for some commonly needed mathstyle overrides. To
+%    conserve csnames we avoid making \cn{dfrac} and \cn{tfrac} robust
+%    (\cn{genfrac} is itself robust).
+%    \begin{macrocode}
+\DeclareRobustCommand{\frac}[2]{{\begingroup#1\endgroup\@@over#2}}
+\newcommand{\dfrac}{\genfrac{}{}{}0}
+\newcommand{\tfrac}{\genfrac{}{}{}1}
+%    \end{macrocode}
+%    The \cn{binom} command for binomial notation works like \cn{frac}
+%    and has similar variants. Note that we do not use \cs{z@} in
+%    \cn{dbinom} and \cn{tbinom} because they are not top-level robust
+%    like \cn{binom}, and so the \cs{z@} with the potentially
+%    problematic \qc{\@} character would become visible when writing one
+%    of those commands to a \fn{.toc} file.
+%    \begin{macrocode}
+\DeclareRobustCommand{\binom}{\genfrac()\z@{}}
+\newcommand{\dbinom}{\genfrac(){0pt}0}
+\newcommand{\tbinom}{\genfrac(){0pt}1}
+%    \end{macrocode}
+%
+%  \begin{macro}{\genfrac}
+% \changes{v2.16a}{2016/11/05}{New genfrac implementation for extended
+% TeXs}
+%    This command provides access to \tex/'s generalized fraction
+%    primitives. Args: \arg{1} left delim, \arg{2} right delim, \arg{3}
+%    line thickness, \arg{4} mathstyle override, \arg{5} numerator,
+%    \arg{6} denominator. But we only read the first four args at first,
+%    in order to give us a moment to select the proper generalized
+%    fraction primitive. Any of those four args could be empty, and when
+%    empty the obvious defaults are selected (no delimiters, default
+%    line thickness (normally .4pt), and no mathstyle override).
+%
+%    the |withdelims| primitives do not work in xetex with OpenType
+%    fonts, and the relevant font dimen parameters are often not set
+%    in luatex as theer are no matching values in the OpenType Math
+%    table, so here we use variants that use the font parameters if
+%    they are set, but scale using |\left\right| rather than the
+%    |withdelims| primitives.
+%
+%    \begin{macrocode}
+\ifx\directlua\@undefined
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ifx\XeTeXcharclass\@undefined
+%    \end{macrocode}
+% Classic version
+%    \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[4]{%
+  \def\@tempa{#1#2}%
+  \edef\@tempb{\@nx\@genfrac\@mathstyle{#4}%
+    \csname @@\ifx @#3@over\else above\fi
+    \ifx\@tempa\@empty \else withdelims\fi\endcsname}
+  \@tempb{#1#2#3}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\else   
+%    \end{macrocode}
+%     XeTeX version
+%    \begin{macrocode}
+\def\genfrac@rule#1#2#3#4{%
+\hbox{$\left#1\vcenter{\hrule \@width\z@
+                       \@height 
+                       \ifdim\fontdimen#2#3\tw@=\z@
+                       #4\fontdimen6#3\tw@
+                       \else
+                       \fontdimen#2#3\tw@
+                       \fi
+                      }\right.$}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\genfrac@choice#1#2{%
+\ifx @#2@\else
+%    \end{macrocode}
+% \changes{v2.17a}{2017/09/02}{move \cs{nulldelimiterspace} correction}
+%    \begin{macrocode}
+\ifx c#1\kern-\nulldelimiterspace\fi
+{\delimitershortfall\z@\delimiterfactor\@m
+ \mathsurround\z@\nulldelimiterspace\z@
+\mathchoice
+{\genfrac@rule{#2}{20}\textfont{2.39}}%
+{\genfrac@rule{#2}{21}\textfont{1}}%
+{\genfrac@rule{#2}{21}\scriptfont{1.45}}%
+{\genfrac@rule{#2}{21}\scriptscriptfont{1.35}}%
+}%
+\ifx o#1\kern-\nulldelimiterspace\fi
+\fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[6]{{%
+\@mathstyle{#4}%
+\genfrac@choice o{#1}%
+{\begingroup#5\endgroup\ifx @#3@\@@over\else\@@above\fi#3\relax#6}%
+\genfrac@choice c{#2}%
+}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\fi
+\else
+%    \end{macrocode}
+% LuaTeX version
+%    \begin{macrocode}
+\def\genfrac@rule#1#2#3{%
+\hbox{$\left#1\vcenter{\hrule \@width\z@
+                       \@height 
+                       \ifdim\Umathfractiondelsize#2=\z@
+                       #3\fontdimen6#3\tw@
+                       \else
+                       \Umathfractiondelsize#2%
+                       \fi
+                      }\right.$}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\genfrac@choice#1#2{%
+\ifx @#2@\else
+%    \end{macrocode}
+% \changes{v2.17a}{2017/09/02}{move \cs{nulldelimiterspace} correction}
+%    \begin{macrocode}
+\ifx c#1\kern-\nulldelimiterspace\fi
+{\delimitershortfall\z@\delimiterfactor\@m
+ \mathsurround\z@\nulldelimiterspace\z@
+\mathchoice
+{\genfrac@rule{#2}\displaystyle{2.39}}%
+{\genfrac@rule{#2}\textstyle{1}}%
+{\genfrac@rule{#2}\scriptstyle{1.45}}%
+{\genfrac@rule{#2}\scriptscriptstyle{1.35}}%
+}%
+\ifx o#1\kern-\nulldelimiterspace\fi
+\fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[6]{{%
+\@mathstyle{#4}%
+\genfrac@choice o{#1}%
+{\begingroup#5\endgroup\ifx @#3@\@@over\else\@@above\fi#3\relax#6}%
+\genfrac@choice c{#2}%
+}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+%
+% End of test for Lua\TeX/Xe\TeX.
+%
+%    \cs{@genfrac} takes the preceding arguments and reads the
+%    numerator and denominator. Note that there's no convenient way to
+%    make the numerator and denominator \emph{contents}
+%    displaystyle, through this interface.
+%
+%    Args: \arg{1} mathstyle, \arg{2} fraction primitive,
+%    \arg{3} delimiters and rule thickness,
+%    \arg{4} numerator, \arg{5} denominator.
+%    \begin{macrocode}
+\def\@genfrac#1#2#3#4#5{{#1{\begingroup#4\endgroup#2#3\relax#5}}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    Empty mathstyle arg: no change; 0 = displaystyle, 1 = textstyle, 2
+%    = scriptstyle, 3 = scriptscriptstyle.
+%    \begin{macrocode}
+\def\@mathstyle#1{%
+  \ifx\@empty#1\@empty\relax
+  \else\ifcase#1\displaystyle % case 0
+    \or\textstyle\or\scriptstyle\else\scriptscriptstyle\fi\fi}
+%    \end{macrocode}
+%
+% \subsection{Sums and Integrals}
+%    Default value for sum limits is \cs{displaylimits}, see option
+%    `nosumlimits'.
+%
+%    We redefine all the cumulative operator symbols to use
+%    \cs{slimits@} so that switching between \cs{displaylimits} and
+%    \cs{nolimits} can be controlled by package options. Also add
+%    \cs{DOTSB} for the benefit of the dots lookahead. But we'd better
+%    make sure \cn{coprod} and the others are simple mathchars; if not,
+%    the attempted changes will probably fail miserably.
+%
+% \changes{v2.15}{2016/02/20}{Accept \cs{Umathchar}}
+%    \begin{macrocode}
+\begingroup
+%    \end{macrocode}
+%    \begin{macrocode}
+\edef\@tempa{\string\mathchar"}
+\edef\@tempd{\string\Umathchar"}
+\def\@tempb#1"#2\@nil{#1"}
+\edef\@tempc{\expandafter\@tempb\meaning\coprod "\@nil}
+\ifx\@tempc\@tempd\let\@tempc\@tempa\fi
+%    \end{macrocode}
+%    \begin{macrocode}
+\ifx\@tempa\@tempc
+  \global\let\coprod@\coprod
+  \gdef\coprod{\DOTSB\coprod@\slimits@}
+  \global\let\bigvee@\bigvee
+  \gdef\bigvee{\DOTSB\bigvee@\slimits@}
+  \global\let\bigwedge@\bigwedge
+  \gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
+  \global\let\biguplus@\biguplus
+  \gdef\biguplus{\DOTSB\biguplus@\slimits@}
+  \global\let\bigcap@\bigcap
+  \gdef\bigcap{\DOTSB\bigcap@\slimits@}
+  \global\let\bigcup@\bigcup
+  \gdef\bigcup{\DOTSB\bigcup@\slimits@}
+  \global\let\prod@\prod
+  \gdef\prod{\DOTSB\prod@\slimits@}
+  \global\let\sum@\sum
+  \gdef\sum{\DOTSB\sum@\slimits@}
+  \global\let\bigotimes@\bigotimes
+  \gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
+  \global\let\bigoplus@\bigoplus
+  \gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
+  \global\let\bigodot@\bigodot
+  \gdef\bigodot{\DOTSB\bigodot@\slimits@}
+  \global\let\bigsqcup@\bigsqcup
+  \gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
+\fi
+\endgroup
+%    \end{macrocode}
+%
+% \subsection{Roots and radicals}
+%
+%    \begin{macro}{\root}
+%    This root stuff needs syntax work and implementation work. Surely
+%    something more compact can be done?? [mjd, 1994/09/05]
+%    \begin{macrocode}
+\newcommand{\leftroot}{\@amsmath@err{\Invalid@@\leftroot}\@eha}
+\newcommand{\uproot}{\@amsmath@err{\Invalid@@\uproot}\@eha}
+\newcount\uproot@
+\newcount\leftroot@
+\renewcommand{\root}{\relaxnext@
+  \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
+   \ifx\@let@token\leftroot\let\next@\nextiii@\else
+   \let\next@\plainroot@\fi\fi\next@}%
+  \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
+  \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
+   \DN@.{\FN@\nextv@}\fi\next@.}%
+  \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
+   \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
+  \def\nextvii@{\ifx\@let@token\@sptoken
+   \DN@. {\FN@\nextviii@}\else
+   \DN@.{\FN@\nextviii@}\fi\next@.}%
+  \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
+  \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
+\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
+ $\m@th\scriptscriptstyle{#1}$}%
+ \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
+ {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \changes{v2.0}{1999/06/17}{Normalize @@sqrt to sqrtsign}
+
+%    Name change from \cs{@@sqrt} to \cs{sqrtsign} happened in the
+%    1995/12/01 release of \latex/. If we were to assume that
+%    \cs{sqrtsign} is defined then someone with the 1995/06/01 release
+%    of \latex/ would have trouble using this package.
+%    \begin{macrocode}
+\@ifundefined{sqrtsign}{\let\sqrtsign\@@sqrt}{}
+\def\r@@t#1#2{\setboxz@h{$\m@th#1\sqrtsign{#2}$}%
+ \dimen@\ht\z@\advance\dimen@-\dp\z@
+ \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
+ \advance\dimen@ by1.667\wd\@ne
+ \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
+ \mkern-10mu\mkern\leftroot@ mu\boxz@}
+%    \end{macrocode}
+%
+% \subsection{Et cetera}
+%
+% \changes{v2.0}{1999/06/18}{Leave Greek cap letters unaltered}
+%
+%    Specific names for the variant italic cap Greek letters are not
+%    defined by \latex/. If no preceding package defined these, we will
+%    define them now.
+%    \begin{macrocode}
+\@ifundefined{varGamma}{%
+  \DeclareMathSymbol{\varGamma}{\mathord}{letters}{"00}
+  \DeclareMathSymbol{\varDelta}{\mathord}{letters}{"01}
+  \DeclareMathSymbol{\varTheta}{\mathord}{letters}{"02}
+  \DeclareMathSymbol{\varLambda}{\mathord}{letters}{"03}
+  \DeclareMathSymbol{\varXi}{\mathord}{letters}{"04}
+  \DeclareMathSymbol{\varPi}{\mathord}{letters}{"05}
+  \DeclareMathSymbol{\varSigma}{\mathord}{letters}{"06}
+  \DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{"07}
+  \DeclareMathSymbol{\varPhi}{\mathord}{letters}{"08}
+  \DeclareMathSymbol{\varPsi}{\mathord}{letters}{"09}
+  \DeclareMathSymbol{\varOmega}{\mathord}{letters}{"0A}
+}{}
+%    \end{macrocode}
+%
+%    \begin{macro}{\overline}
+%    \amstex/ redefines \cn{overline} as shown here, for reasons that
+%    are probably less important in \latex/: Make it read its argument
+%    as a macro argument rather than a ``math field'' (\emph{The
+%    \tex/book}, Chapter 26), to avoid problems when something that is
+%    apparently a single symbol is actually a non-simple macro (e.g.,
+%    \cn{dag}) \emph{and} is given as a single-token argument without
+%    enclosing braces.
+%    \begin{macrocode}
+\@saveprimitive\overline\@@overline
+\DeclareRobustCommand{\overline}[1]{\@@overline{#1}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\boxed}
+%    The \cs{boxed} command is specifically intended to put a box around
+%    an equation or piece of an equation. (Not including the equation
+%    number.) This isn't trivial for end-users to do it properly
+%    with \cs{fbox} so we provide a command for them.
+%    \begin{macrocode}
+\newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\implies}
+%    \begin{macro}{\impliedby}
+%    \begin{macrocode}
+\newcommand{\implies}{\DOTSB\;\Longrightarrow\;}
+\newcommand{\impliedby}{\DOTSB\;\Longleftarrow\;}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\And}
+%    \begin{macrocode}
+\def\And{\DOTSB\;\mathchar"3026 \;}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\nobreakdash}
+%    The command \cn{nobreakdash} is designed only for use before a
+%    hyphen or dash (|-|, |--|, or |---|).
+%    Setting the hyphen in a box and then unboxing it means that the
+%    normal penalty will not be added after it---and if the penalty is
+%    not there a break will not be taken (unless an explicit penalty
+%    or glue follows, thus the final \verb=\nobreak=).
+%    \begin{macrocode}
+\newcommand{\nobreakdash}{\leavevmode
+  \toks@\@emptytoks \def\@tempa##1{\toks@\@xp{\the\toks@-}\FN@\next@}%
+  \DN@{\ifx\@let@token-\@xp\@tempa
+       \else\setboxz@h{\the\toks@\nobreak}\unhbox\z@\fi}%
+  \FN@\next@
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\colon}
+%    \cs{colon} is for a colon in math that resembles a text colon:
+%    small space on the left, larger space on the right. The \qc{\:}
+%    character by itself is treated as a \cs{mathrel} i.e. large, equal
+%    spacing on both sides.
+%    \begin{macrocode}
+\renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript
+  \mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
+%    \end{macrocode}
+%    \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Ellipsis dots}
+%
+%    We can't use \cs{newif} for \cs{ifgtest@} because we want
+%    to include \cs{global} in the definitions of
+%    \cs{gtest@true} and \cs{gtest@false}.
+%    \begin{macrocode}
+\let\ifgtest@\iffalse                              % initial value
+\def\gtest@true{\global\let\ifgtest@\iftrue}
+\def\gtest@false{\global\let\ifgtest@\iffalse}
+\let\DOTSI\relax
+\let\DOTSB\relax
+\let\DOTSX\relax
+{\uccode`7=`\\ \uccode`8=`m \uccode`9=`a \uccode`0=`t \uccode`!=`h
+ \uppercase{%
+  \gdef\math@#1#2#3#4#5#6\math@{\gtest@false\ifx 7#1\ifx 8#2%
+  \ifx 9#3\ifx 0#4\ifx !#5\xdef\meaning@{#6}\gtest@true
+  \fi\fi\fi\fi\fi}}}
+{\uccode`7=`c \uccode`8=`h \uccode`9=`\"
+ \uppercase{\gdef\mathch@#1#2#3#4#5#6\mathch@{\gtest@false
+  \ifx 7#1\ifx 8#2\ifx 9#5\gtest@true\xdef\meaning@{9#6}\fi\fi\fi}}}
+%    \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Accept \cs{Umathchar}}
+%    \begin{macrocode}
+{\uccode`(=`U \uccode`)=`m
+ \uppercase{\gdef\Umathch@#1#2#3#4"#5"#6\Umathch@{\gtest@false
+  \ifx(#2\ifx)#3\gtest@true
+  \ifcase"#5 \or\or\gdef\thedots@{\dotsb@}\or\gdef\thedots@{\dotsb@}\fi
+  \fi\fi
+  }}}
+%    \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Decode the mathcode of character tokens for Unicode TeX}
+% For Unicode TeXs, if the next token is a character token look up the (U)mathcode. Do not do this for classic TeX for compatibility reasons.
+%    \begin{macrocode}
+\ifx\Umathcharnumdef\@undefined
+\gdef\thecharacter@#1\thecharacter@{}
+\else
+{\uccode`(=`t \uccode`)=`c
+ \uppercase{\gdef\thecharacter@#1#2#3#4#5\thecharacter@{%
+  \ifx(#1\ifx)#4%
+    \@xp\getmathcode@\meaning@\getmathcode@
+  \fi\fi
+}}}
+\def\getmathcode@#1 #2 #3#4\getmathcode@{%
+  \Umathcharnumdef\@tempa\Umathcodenum`#3\relax
+  \edef\meaning@{\meaning\@tempa}%
+  \@xp\Umathch@\meaning@\Umathch@
+}
+\fi
+%    \end{macrocode}
+%    \begin{macrocode}
+\newcount\classnum@
+\def\getmathch@#1.#2\getmathch@{\classnum@#1 \divide\classnum@4096
+ \ifcase\number\classnum@\or\or\gdef\thedots@{\dotsb@}\or
+ \gdef\thedots@{\dotsb@}\fi}
+{\uccode`4=`b \uccode`5=`i \uccode`6=`n
+ \uppercase{\gdef\mathbin@#1#2#3{\relaxnext@
+  \def\nextii@##1\mathbin@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+  \gtest@false\DN@##1\mathbin@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`4=`r \uccode`5=`e \uccode`6=`l
+ \uppercase{\gdef\mathrel@#1#2#3{\relaxnext@
+  \def\nextii@##1\mathrel@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\mathrel@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`5=`m \uccode`6=`a \uccode`7=`c
+ \uppercase{\gdef\macro@#1#2#3#4\macro@{\gtest@false
+  \ifx 5#1\ifx 6#2\ifx 7#3\gtest@true
+  \xdef\meaning@{\macro@@#4\macro@@}\fi\fi\fi}}}
+\def\macro@@#1->#2\macro@@{#2}
+\newcount\DOTSCASE@
+{\uccode`6=`\\ \uccode`7=`D \uccode`8=`O \uccode`9=`T \uccode`0=`S
+ \uppercase{\gdef\DOTS@#1#2#3#4#5{\gtest@false\DN@##1\DOTS@{}%
+  \ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\ifx 0#5\let\next@\DOTS@@
+  \fi\fi\fi\fi\fi
+  \next@}}}
+{\uccode`3=`B \uccode`4=`I \uccode`5=`X
+ \uppercase{\gdef\DOTS@@#1{\relaxnext@
+  \def\nextii@##1\DOTS@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+  \DN@{\FN@\nextii@}%
+  \ifx 3#1\global\DOTSCASE@\z@\else
+  \ifx 4#1\global\DOTSCASE@\@ne\else
+  \ifx 5#1\global\DOTSCASE@\tw@\else\DN@##1\DOTS@{}%
+  \fi\fi\fi\next@}}}
+{\uccode`5=`\\ \uccode`6=`n \uccode`7=`o \uccode`8=`t
+ \uppercase{\gdef\not@#1#2#3#4{\relaxnext@
+  \def\nextii@##1\not@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\not@{}%
+ \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\DN@{\FN@\nextii@}\fi\fi\fi
+ \fi\next@}}}
+%    \end{macrocode}
+% \changes{v2.15}{2016/02/20}{macro added to strip \cs{long} during tests}
+%    \begin{macrocode}
+{\uccode`9=`\l %
+ \uppercase{\gdef\striplong@#1#2#3\relax{%
+  \ifx9#2 \@xp\@xp\@xp\zap@to@space\fi}}}
+\def\zap@to@space#1 {}
+%    \end{macrocode}
+%    \begin{macrocode}
+\def\keybin@{\gtest@true
+ \ifx\@let@token+\else\ifx\@let@token=\else
+ \ifx\@let@token<\else\ifx\@let@token>\else
+ \ifx\@let@token-\else\ifx\@let@token*\else\ifx\@let@token:\else
+   \gtest@false\fi\fi\fi\fi\fi\fi\fi}
+%    \end{macrocode}
+%    Patch to ensure \cs{@ldots} is defined. (Name changed to
+%    \cn{mathellipsis} in Dec 94 release of \latex/.)
+%    \begin{macrocode}
+\@ifundefined{@ldots}{\def\@ldots{\mathellipsis}}{}
+%    \end{macrocode}
+%    \begin{macro}{\ldots}
+%    \begin{macro}{\dots}
+%    Reiterate the standard definition of \cs{ldots} to keep it from
+%    being clobbered by the redefinition of \cs{dots}.
+%    \begin{macrocode}
+\DeclareRobustCommand{\ldots}{%
+  \ifmmode \mathellipsis \else \textellipsis \fi
+}
+\DeclareRobustCommand{\dots}{%
+  \ifmmode \@xp\mdots@\else \@xp\textellipsis \fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macrocode}
+\def\tdots@{\leavevmode\unskip\relaxnext@
+ \DN@{$\m@th\@ldots\,
+   \ifx\@let@token,\,$\else\ifx\@let@token.\,$\else
+   \ifx\@let@token;\,$\else\ifx\@let@token:\,$\else
+   \ifx\@let@token?\,$\else\ifx\@let@token!\,$\else
+     $ \fi\fi\fi\fi\fi\fi}%
+  \ \FN@\next@}
+\def\mdots@{\FN@\mdots@@}
+%    \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Indent \cs{mdots@@} for readability and add additional tests}
+%    \begin{macrocode}
+\def\mdots@@{\gdef\thedots@{\dotso@}%
+ \ifx\@let@token\boldsymbol 
+   \gdef\thedots@\boldsymbol{\boldsymboldots@}%
+ \else
+   \ifx,\@let@token \gdef\thedots@{\dotsc}%
+   \else
+     \ifx\not\@let@token
+       \gdef\thedots@{\dotsb@}%
+     \else
+       \keybin@
+       \ifgtest@ % if \keybin@ test
+         \gdef\thedots@{\dotsb@}%
+       \else
+%    \end{macrocode}
+% \changes{v2.15d}{2016/06/28}{Add space token to prevent runaway argument error}
+%    \begin{macrocode}
+         \xdef\meaning@{\meaning\@let@token. .........}%
+%    \end{macrocode}
+% In previous versions \verb|\long| macros were not seen by the lokkahead.
+% That was bad as this file uses \verb|\(re)newcommand| for \verb|\implies| etc.
+%    \begin{macrocode}
+         \xdef\meaning@@{\@xp\striplong@\meaning@\relax\meaning@}%
+%    \end{macrocode}
+%    \begin{macrocode}
+         \@xp\math@\meaning@\math@
+         \ifgtest@ % if \mathxxx test
+           \@xp\mathch@\meaning@\mathch@
+           \ifgtest@ % if \mathchar
+             \@xp\getmathch@\meaning@\getmathch@
+           \fi % end if \mathchar
+         \else  % \not \mathxxx
+%    \end{macrocode}
+% Test for \verb|\Umathchar| added.
+%    \begin{macrocode}
+             \@xp\Umathch@\meaning@"0"\Umathch@
+             \ifgtest@ % if \Umathchar
+             \else % else not \Umathcar
+%    \end{macrocode}
+%    \begin{macrocode}
+           \@xp\macro@\meaning@@\macro@
+           \ifgtest@ % if macro test
+             \@xp\not@\meaning@\not@
+             \ifgtest@ % if macro starts \not test
+               \gdef\thedots@{\dotsb@}%
+             \else% else not \not
+               \@xp\DOTS@\meaning@\DOTS@
+               \ifgtest@ % \if DOTS
+                 \ifcase\number\DOTSCASE@ %ifcase dots
+                   \gdef\thedots@{\dotsb@}%
+                 \or\gdef\thedots@{\dotsi}\else
+                 \fi % endifcase dots
+               \else % not macro starts \DOTS
+                 \@xp\math@\meaning@\math@
+                 \ifgtest@ % \if macro starts \mathxxxx
+                   \@xp\mathbin@\meaning@\mathbin@
+                   \ifgtest@ % if macro starts \mathbin
+                     \gdef\thedots@{\dotsb@}%
+                   \else % not macro starting \mathbin
+                     \@xp\mathrel@\meaning@\mathrel@
+                     \ifgtest@ % if macro starts \mathrel
+                       \gdef\thedots@{\dotsb@}%
+                     \fi % endif macro starts \mathrel (no else)
+                   \fi % endif macro starts \mathbin
+                 \fi % endif macro starts with \mathxxx (no else)
+               \fi % endif macro starts \DOTS else
+             \fi % end macro  starting \not \ifgtest@ test (no else)
+%    \end{macrocode}
+% Additional test for a catcode 12 character.
+%    \begin{macrocode}
+             \else
+               \@xp\thecharacter@\meaning@\thecharacter@
+%    \end{macrocode}
+%    \begin{macrocode}
+             \fi % end macro \ifgtest@ test (no else)
+           \fi % end if \Umathchar test
+         \fi % end \math@   \ifgtest@ 
+       \fi % end \keybin@ \ifgtest@ test (no else)
+     \fi % end if \not (no else)
+   \fi % end if comma (no else)
+ \fi % end if boldsymbol (no else)
+ \thedots@}
+%    \end{macrocode}
+%
+%    The \qc{\=} character is necessary in the two \cs{let} assignments
+%    in \cs{boldsymboldots@}, because the symbol we are making
+%    bold might be an \qc{\=} sign.
+%    \begin{macrocode}
+\def\boldsymboldots@#1{%
+  \bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
+  \boldsymbol#1\bold@false}
+%    \end{macrocode}
+%
+%    The definition of \cs{@cdots} is merely the \fn{plain.tex}
+%    definition of \cs{cdots}.
+%    \begin{macrocode}
+\ams@def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
+\newcommand{\dotsi}{\!\@cdots}
+\let\dotsb@\@cdots
+%    \end{macrocode}
+%
+%    If any new right delimiters are defined, they would need to be
+%    added to the definition of \cs{rightdelim@} in order for \cn{dots}
+%    to work properly in all cases.
+%    \begin{macrocode}
+\def\rightdelim@{\gtest@true
+ \ifx\@let@token)\else
+ \ifx\@let@token]\else
+ \ifx\@let@token\rbrack\else
+ \ifx\@let@token\}\else
+ \ifx\@let@token\rbrace\else
+ \ifx\@let@token\rangle\else
+ \ifx\@let@token\rceil\else
+ \ifx\@let@token\rfloor\else
+ \ifx\@let@token\rgroup\else
+ \ifx\@let@token\rmoustache\else
+ \ifx\@let@token\right\else
+ \ifx\@let@token\bigr\else
+ \ifx\@let@token\biggr\else
+ \ifx\@let@token\Bigr\else
+ \ifx\@let@token\Biggr\else\gtest@false
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
+\def\extra@{%
+ \rightdelim@\ifgtest@
+ \else\ifx\@let@token$\gtest@true
+ \else\xdef\meaning@{\meaning\@let@token..........}%
+ \@xp\macro@\meaning@\macro@\ifgtest@
+ \@xp\DOTS@\meaning@\DOTS@
+ \ifgtest@
+ \ifnum\DOTSCASE@=\tw@\gtest@true\else\gtest@false
+ \fi\fi\fi\fi\fi}
+\newif\ifbold@
+\def\dotso@{\relaxnext@
+ \ifbold@
+  \let\@let@token\delayed@
+  \def\nextii@{\extra@\@ldots\ifgtest@\,\fi}%
+ \else
+  \def\nextii@{\DN@{\extra@\@ldots\ifgtest@\,\fi}\FN@\next@}%
+ \fi
+ \nextii@}
+%    \end{macrocode}
+%    Why not save some tokens? (space vs. time).
+%    \begin{macrocode}
+\def\extrap@#1{%
+ \DN@{#1\,}%
+ \ifx\@let@token,\else
+ \ifx\@let@token;\else
+ \ifx\@let@token.\else\extra@
+ \ifgtest@\else
+ \let\next@#1\fi\fi\fi\fi\next@}
+%    \end{macrocode}
+%
+%    \begin{macro}{\cdots}
+%    \begin{macro}{\dotsb}
+%    \begin{macro}{\dotsm}
+%    \begin{macro}{\dotso}
+%    \begin{macro}{\dotsc}
+%    The \cn{cdots} command.
+%    \begin{macrocode}
+\ams@DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
+\let\dotsb\cdots
+\let\dotsm\cdots
+\DeclareRobustCommand{\dotso}{\relax
+  \ifmmode \DN@{\extrap@\@ldots}%
+  \else \let\next@\tdots@\fi
+  \FN@\next@}
+\DeclareRobustCommand{\dotsc}{%
+  \DN@{\ifx\@let@token;\@ldots\,%
+       \else \ifx\@let@token.\@ldots\,%
+       \else \extra@\@ldots \ifgtest@\,\fi
+       \fi\fi}%
+  \FN@\next@}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macro}{\longrightarrow}
+%    \begin{macro}{\Longrightarrow}
+%    \begin{macro}{\longleftarrow}
+%    \begin{macro}{\Longleftarrow}
+%    \begin{macro}{\longleftrightarrow}
+%    \begin{macro}{\Longleftrightarrow}
+%    \begin{macro}{\mapsto}
+%    \begin{macro}{\longmapsto}
+%    \begin{macro}{\hookrightarrow}
+%    \begin{macro}{\hookleftarrow}
+%    \begin{macro}{\iff}
+%    Various arrows.
+%    \begin{macrocode}
+\renewcommand{\longrightarrow}{%
+  \DOTSB\protect\relbar\protect\joinrel\rightarrow}
+\renewcommand{\Longrightarrow}{%
+  \DOTSB\protect\Relbar\protect\joinrel\Rightarrow}
+\renewcommand{\longleftarrow}{%
+  \DOTSB\leftarrow\protect\joinrel\protect\relbar}
+\renewcommand{\Longleftarrow}{%
+  \DOTSB\Leftarrow\protect\joinrel\protect\Relbar}
+\renewcommand{\longleftrightarrow}{\DOTSB\leftarrow\joinrel\rightarrow}
+\renewcommand{\Longleftrightarrow}{\DOTSB\Leftarrow\joinrel\Rightarrow}
+\renewcommand{\mapsto}{\DOTSB\mapstochar\rightarrow}
+\renewcommand{\longmapsto}{\DOTSB\mapstochar\longrightarrow}
+\renewcommand{\hookrightarrow}{\DOTSB\lhook\joinrel\rightarrow}
+\renewcommand{\hookleftarrow}{\DOTSB\leftarrow\joinrel\rhook}
+\renewcommand{\iff}{\DOTSB\;\Longleftrightarrow\;}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macro}{\doteq}
+%    The \cn{doteq} command formerly used \cs{buildrel}; we avoid that
+%    because it requires `\cn{over}' as part of its syntax. Use 0pt
+%    instead of \cs{z@} for robustitude.
+%    \begin{macrocode}
+\renewcommand{\doteq}{%
+  \DOTSB\mathrel{\mathop{\kern0pt =}\limits^{\textstyle.}}}
+%    \end{macrocode}
+%    \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Integral signs}
+%
+%    \begin{macro}{\if@display}
+%    The straightforward \cs{ifinner} test to see if the current math
+%    context is non-display, fails if, for instance, we are typesetting
+%    a multiline display within an \cs{halign}, with the pieces going
+%    into constructions like
+%    \begin{verbatim}
+%    $\displaystyle...$
+%    \end{verbatim}
+%    So we need a better test to find out if we are `in a display'. We
+%    therefore create \cs{if@display}.
+%
+%    \begin{macrocode}
+\newif\if@display
+\everydisplay\@xp{\the\everydisplay \@displaytrue}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\int}
+%    \begin{macro}{\oint}
+%    \begin{macro}{\iint}
+%    \begin{macro}{\iiint}
+%    \begin{macro}{\iiiint}
+%    \begin{macro}{\idotsint}
+%    Default value for integral limits is \cs{nolimits}, see the
+%    definition of the `nointlimits' option.
+%    \begin{macrocode}
+\renewcommand{\int}{\DOTSI\intop\ilimits@}
+\renewcommand{\oint}{\DOTSI\ointop\ilimits@}
+\def\intkern@{\mkern-6mu\mathchoice{\mkern-3mu}{}{}{}}
+\def\intdots@{\mathchoice{\@cdots}%
+ {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
+%
+\ams@newcommand{\iint}{\DOTSI\protect\MultiIntegral{2}}
+\ams@newcommand{\iiint}{\DOTSI\protect\MultiIntegral{3}}
+\ams@newcommand{\iiiint}{\DOTSI\protect\MultiIntegral{4}}
+\newcommand{\idotsint}{\DOTSI\protect\MultiIntegral{0}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\MultiIntegral}
+%    If the \cs{limits} option is applied, use \cs{mathop} and fudge
+%    the left-hand space a bit to make the subscript visually centered.
+%
+%    \verb'#1' is the multiplicity.
+%    \begin{macrocode}
+\newcommand{\MultiIntegral}[1]{%
+  \edef\ints@c{\noexpand\intop
+    \ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
+    \ifnum#1>\tw@\noexpand\intop\noexpand\intkern@\fi
+    \ifnum#1>\thr@@\noexpand\intop\noexpand\intkern@\fi
+    \noexpand\intop
+    \noexpand\ilimits@
+  }%
+  \futurelet\@let@token\ints@a
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macrocode}
+\def\ints@a{%
+  \ifx\limits\@let@token \ints@b
+  \else \ifx\displaylimits\@let@token \ints@b
+  \else\ifx\ilimits@\displaylimits \ints@b
+  \fi\fi\fi
+  \ints@c
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\ints@b{%
+  \mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
+  \mathop\bgroup
+    \mkern7mu\mathchoice{\mkern2mu}{}{}{}%
+    \let\ilimits@\egroup
+}%
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Size dependent definitions}
+%
+%    We now define all stuff which has to change whenever a new math
+%    size is to be activated. \latex/ provides a hook called
+%    |\every@math@size| to support such a need. All assignments in the
+%    |\every@math@size| hook that need to take outside effect should be
+%    global.
+%
+% \subsection{Struts for math}
+%
+%    The various kinds of struts could use some analysis and perhaps
+%    consolidation.
+%
+%    For example perhaps the \cn{bBigg} delimiters could use
+% \begin{verbatim}
+% 1.2\ht\strutbox (1.8, 2.4, 3.0)
+% \end{verbatim}
+%    instead of
+% \begin{verbatim}
+% 1.0\big@size (1.5, 2.0, 2.5)
+% \end{verbatim}
+%    since \cs{strut} is reset with every size change [mjd, 1994/10/07].
+%    But this change would introduce the possibility of changed line
+%    and page breaks in existing documents, so would need to be
+%    handled with care.
+%
+% \begin{macro}{\Mathstrut@}
+% \begin{macro}{\Mathstrutbox@}
+% \begin{macro}{\resetMathstrut@}
+%    Here comes the code for Spivak's |\Mathstrut@|.
+%    \begin{macrocode}
+\newbox\Mathstrutbox@
+\setbox\Mathstrutbox@=\hbox{}
+\def\Mathstrut@{\copy\Mathstrutbox@}
+%    \end{macrocode}
+%    The setting of the height and depth of the |\Mathstrutbox@| is done
+%    in the |\every@math@size| hook since it depends on the height of a
+%    paren. As \cs{every@math@size} is triggered by |$| after a font
+%    size change, we want to avoid using another math formula |$...$| to
+%    measure the math paren height; instead we go through the mathcode
+%    of the \qc{\(} character. We assume that the mathcode has a leading
+%    hex digit 4 indicating `open delimiter'; this allows us to make a
+%    relatively simple function to get the correct font and character
+%    position.
+%
+% \changes{v2.15}{2016/02/20}{Modify \cs{resetMathstrut@} for Unicode \TeX}
+% \changes{v2.15b}{2016/03/10}{Modify \cs{resetMathstrut@} for classic \TeX\ to preserve box 0}
+% Original code assuming |\mathcode| is kept for 8bit \TeX. Unicode \TeX{}
+% uses |\Umathcharnumdef| which works for xetex and luatex, which use
+% different forms for |\mathchardef|. (New luatex always reports
+% definitions using |\Umathchardef| syntax even if |\mathchardef| used.)
+%
+% The unicode version uses e-tex |\fontcharht| to avoid boxing which
+% could also be done for pdftex, but not done here.
+%    \begin{macrocode}
+\ifx\Umathcharnumdef\@undefined
+%    \end{macrocode}
+% Original code
+%    \begin{macrocode}
+\def\resetMathstrut@{%
+  \begingroup
+  \setbox\z@\hbox{%
+    \mathchardef\@tempa\mathcode`\(\relax
+    \def\@tempb##1"##2##3{\the\textfont"##3\char"}%
+    \expandafter\@tempb\meaning\@tempa \relax
+  }%
+ \edef\@tempa{%
+     \ht\Mathstrutbox@\the\ht\z@\relax
+     \dp\Mathstrutbox@\the\dp\z@\relax}%
+  \expandafter\endgroup\@tempa
+}
+\else
+%    \end{macrocode}
+% xetex/luatex version
+% \changes{v2.15a}{2016/03/03}{missing percent added}
+%    \begin{macrocode}
+\def\resetMathstrut@{%
+    \begingroup
+    \Umathcharnumdef\@tempa\Umathcodenum`\(\relax
+    \def\@tempb##1"##2"##3"##4\relax{%
+      \endgroup
+      \ht\Mathstrutbox@=\fontcharht\textfont"##3 "##4\relax
+      \dp\Mathstrutbox@=\fontchardp\textfont"##3 "##4\relax}%
+    \expandafter\@tempb\meaning\@tempa \relax
+}
+%    \end{macrocode}
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+%    These height and depth assignments are implicitly global.
+%    \begin{macrocode}
+\addto@hook\every@math@size{\resetMathstrut@}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\strut@}
+% \begin{macro}{\strutbox@}
+%    Next follows a special internal strut which is supposed to match
+%    the height and the depth of a normal |\strut| minus
+%    |\normallineskiplimit| according to M. Spivak.
+%
+%    This should really go into the definition of \cs{size@update}, and
+%    then the box reset could be local; but \cs{size@update} doesn't
+%    have any hook and is handled in such a way that it cannot even be
+%    changed except by changing \cs{set@fontsize}. So instead we put
+%    \cs{reset@strutbox@} into \cs{every@math@size} and make it global.
+%    Then because of some complications in the way \cs{glb@settings} and
+%    \cs{check@mathfonts} work, we have to re-invoke it at the beginning
+%    of every environment that might use \cs{strut@}. Fortunately this
+%    can be achieved (more or less) through the \cs{spread@equation}
+%    hook. [mjd,2000/03/10]
+%    \begin{macrocode}
+\newbox\strutbox@
+\def\strut@{\copy\strutbox@}
+\def\reset@strutbox@{%
+  \global\setbox\strutbox@\hbox{%
+    \lower.5\normallineskiplimit
+       \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
+\addto@hook\every@math@size{\reset@strutbox@}
+\AtBeginDocument{\reset@strutbox@}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Big delimiters}
+%
+%    We are now going to redefine the plain \tex/ commands \cn{big},
+%    \cn{bigl}, etc., to produce different results in different sizes.
+%    Actually we only have to define \cn{big}, \cn{Big}, etc., since
+%    they are used to construct the directional versions \cn{bigl},
+%    \cn{bigr}, and the rest.
+%
+% \begin{macro}{\big}
+% \begin{macro}{\Big}
+% \begin{macro}{\bigg}
+% \begin{macro}{\Bigg}
+%     To save token space we put everything into the common macro
+%    |\bBigg@|. The macros are now simply a call to |\bBigg@| with a
+%    factor to determine the correct height of the delimiter as an
+%    argument. This code should better go into a future version of
+%    the \latex/ kernel; the macro |\n@space| is then superfluous (since
+%    it is only used once) and should be removed to avoid wasting hash
+%    table space unnecessarily.
+%    \begin{macrocode}
+\renewcommand{\big}{\bBigg@\@ne}
+\renewcommand{\Big}{\bBigg@{1.5}}
+\renewcommand{\bigg}{\bBigg@\tw@}
+\renewcommand{\Bigg}{\bBigg@{2.5}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bBigg@}
+%    Now we tackle the macro which has to do the real work. It
+%    actually has two arguments, the factor and the wanted delimiter.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{bigl} and
+%   friends if necessary (github/49)}
+%    \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\def\bBigg@#1#2{%
+%    \end{macrocode}
+%    We start with an extra set of braces because we want
+%    constructions like |\def\bigl{\mathopen\big}| to work without the
+%    overhead of extra arguments.
+%    \begin{macrocode}
+  {\@mathmeasure\z@{\nulldelimiterspace\z@}%
+     {\left#2\vcenter to#1\big@size{}\right.}%
+   \box\z@}}
+\else
+\def\bBigg@#1#2{\leavevmode@ifvmode
+  {\@mathmeasure\z@{\nulldelimiterspace\z@}%
+     {\left#2\vcenter to#1\big@size{}\right.}%
+   \box\z@}}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\big@size}
+%    |\big@size| needs to be set to 1.2 times the height of a math
+%    paren. This height is already recorded in |\Mathstrutbox@|.
+%    \begin{macrocode}
+\addto@hook\every@math@size{%
+  \global\big@size 1.2\ht\Mathstrutbox@
+  \global\advance\big@size 1.2\dp\Mathstrutbox@ }
+\newdimen\big@size
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Math accents}
+%
+%    We want to change the leading digit of math accents to be
+%    \cs{accentclass@} so that it can vary according to certain internal
+%    purposes.
+%    \begin{macrocode}
+\def\accentclass@{7}
+\def\noaccents@{\def\accentclass@{0}}
+%    \end{macrocode}
+%
+%    There are a few \meta{math alphabet}s in the standard fonts where
+%    we have to change the extra macros because the standard definitions
+%    don't account for these accent problems. The first is for the
+%    \cs{mathit} command.
+%    \begin{macrocode}
+\DeclareFontEncoding{OML}{}{\noaccents@}
+%    \end{macrocode}
+%    The next one corrects the \cs{cal} alphabet.
+%    \begin{macrocode}
+\DeclareFontEncoding{OMS}{}{\noaccents@}
+%    \end{macrocode}
+%
+%    \begin{macro}{\dddot}
+%    \begin{macro}{\ddddot}
+%    Triple and quadruple dot accents.
+%    \begin{macrocode}
+\ams@newcommand{\dddot}[1]{%
+  {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+   \hbox{\normalfont ...}\vss}}}}
+\ams@newcommand{\ddddot}[1]{%
+  {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+   \hbox{\normalfont....}\vss}}}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%    The following code deals with support for compound accents.
+%    By redefining \cs{set@mathaccent} we ensure that
+%    \cn{DeclareMathAccent} will define accent commands to run our
+%    \cs{mathaccentV} function instead of the primitive \cs{mathaccent}.
+%    \begin{macrocode}
+\def\set@mathaccent#1#2#3#4{%
+  \xdef#2{\@nx\protect\@nx\mathaccentV
+    {\@xp\@gobble\string#2}\hexnumber@#1#4}%
+}
+%    \end{macrocode}
+%
+%    \begin{macro}{\hat}
+%    \begin{macro}{\check}
+%    \begin{macro}{\tilde}
+%    \begin{macro}{\acute}
+%    \begin{macro}{\grave}
+%    \begin{macro}{\dot}
+%    \begin{macro}{\ddot}
+%    \begin{macro}{\breve}
+%    \begin{macro}{\bar}
+%    \begin{macro}{\vec}
+%    \begin{macro}{\mathring}
+%    We redefine the standard math accent commands to
+%    call \cs{mathaccentV}, using the mathgroup/encoding-number
+%    information embedded in their previous definitions. If the
+%    definition of an accent command does not have the expected form, we
+%    leave the accent command alone, but give a warning. For widehat and
+%    widetilde, we need to avoid clobbering the definitions done by the
+%    \pkg{amsfonts} package. Arbitrating the contention between
+%    \pkg{amsmath} and \pkg{amsfonts} to allow doubling a widetilde
+%    accent looks tricky, so for the time being [mjd,1999/07/19] we just
+%    leave \cn{widehat} and \cn{widetilde} alone. As a result, if the
+%    \pkg{amsmath} package is loaded on top of a vanilla \latex/
+%    documentclass, everything runs through with no warnings. If a
+%    Lucida Math or other math fonts package is loaded in addition to
+%    \pkg{amsmath}, there are greater difficulties, but those are
+%    addressed elsewhere.
+%
+%
+% \changes{v2.15}{2016/02/20}{Detect \cs{Umathaccent} on package load}
+% Adjust the test made at package load to recognise
+% |\Umathaccent|. Although currently it is just used to give a
+% modified warning that the accents will not be redefined.
+%
+% Note that the engines behave quite differently here, luatex
+% even without these definitions using the OpenType accent set up by
+% unicode-math  stacks |\hat{hat{f}}| correctly but xetex acts like
+% classic tex and needs this adjustment. This difference is not
+% addressed here at all.
+%
+% This test is just at package loading and has no affect on the
+% definitions used in 8bit TeX.
+%    \begin{macrocode}
+%\def\@tempa#1{\@xp\@tempb\meaning#1\@nil#1}
+%    \end{macrocode}
+%    The extended definition below tests if the accent is already
+%    robust (as newer \LaTeX{} kernels do this by default) and if so
+%    picks up the robust definition. However, as of
+%    now it still redefines it to be non-robust.
+%    \begin{macrocode}
+\def\@tempa#1{%
+  \@ifundefined{\@xp\@gobble\string#1\space}%
+     {\@xp\@tempb\meaning#1\@nil#1}%
+     {\@xp\@xp\@xp\@tempb\@xp\meaning
+       \csname\@xp\@gobble\string#1\space\endcsname\@nil#1}%
+}
+\def\@tempb#1>#2#3 #4\@nil#5{%
+  \@xp\ifx\csname#3\endcsname\mathaccent
+    \@tempc#4?"7777\@nil#5%
+  \else
+  \@xp\ifx\csname#3\endcsname\Umathaccent
+    \@tempd#4\@nil#5%
+  \else
+    \PackageWarningNoLine{amsmath}{%
+      Unable to redefine math accent \string#5}%
+  \fi\fi}
+\def\@tempc#1"#2#3#4#5#6\@nil#7{%
+  \chardef\@tempd="#3\relax\set@mathaccent\@tempd{#7}{#2}{#4#5}}
+\def\@tempd#1\@nil#2{%
+    \PackageWarningNoLine{amsmath}{%
+      Unable to redefine \string\Umathaccent\space\string#2}%
+}
+%    \end{macrocode}
+%    \begin{macrocode}
+\@tempa{\hat}
+\@tempa{\check}
+\@tempa{\tilde}
+\@tempa{\acute}
+\@tempa{\grave}
+\@tempa{\dot}
+\@tempa{\ddot}
+\@tempa{\breve}
+\@tempa{\bar}
+\@tempa{\vec}
+\@ifundefined{mathring}{%
+  \DeclareMathAccent{\mathring}{\mathalpha}{operators}{"17}
+}{%
+  \@tempa{\mathring}
+}
+%%\@tempa\widetilde
+%%\@tempa\widehat
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    Regression testing of amsmath 2.0 showed that in some documents
+%    there occurred fragments of the form
+% \begin{verbatim}
+% \hat\mathcal{G}
+% \end{verbatim}
+%    This is not at all correct syntax for the argument of a \latex/
+%    command but it produced the intended result anyway because of the
+%    internal syntax of the \cs{mathaccent} primitive. With
+%    \cs{mathaccentV}, it will yield an error message. We therefore do a
+%    special check for such syntax problems in order to make the error
+%    message more informative. (dmj: ??????)
+%    \begin{macrocode}
+\newcommand{\acc@check}{}
+\newcommand{\acc@error}{}
+\def\acc@check{\@ifnextchar\@empty\relax\acc@error}
+%    \end{macrocode}
+%    We put most of the tokens in a separate macro so they do not get
+%    scanned unless they are actually needed.
+%    \begin{macrocode}
+\def\acc@error{%
+  \@amsmath@err{%
+    Improper argument for math accent:\MessageBreak
+    Extra braces must be added to prevent wrong output%
+  }\@ehc
+}
+%    \end{macrocode}
+%
+%    For \cs{mathaccentV} part of the processing is dependent on the
+%    depth of nesting of math accent commands. We introduce a dedicated
+%    counter for this instead of using chardef because we want to
+%    increment/decrement it during processing, and incrementing a
+%    chardef integer is more work.
+%    \begin{macrocode}
+\newcount\macc@depth
+%    \end{macrocode}
+%
+%    Provide this function in case it is not already available.
+%    \begin{macrocode}
+\long\def\@gobblethree#1#2#3{}
+%    \end{macrocode}
+%
+%    The \cs{mathaccentV} function first counts the number of nested
+%    math accents by setting the argument in a throw-away box. (This is
+%    not as risky as such an operation would normally be because the
+%    argument is generally either a simple math symbol or a nested math
+%    accent call with a simple math symbol at the bottom of the
+%    nesting.)
+%
+%    There are two benefits from counting the nesting levels first
+%    before doing anything else: (1) we can fall back to a simple
+%    \cs{mathaccent} call if the nesting depth is 1, and (2) if the
+%    nesting depth is greater than 1, we would like to be able to tell
+%    when we have reached the lowest level, because at that point we
+%    want to save the argument for later use and place an accent on top
+%    of a phantom copy.
+%
+%    When we have multiple accents, they will be placed on top of the
+%    invisible box, followed by some suitable kerns, then a visible copy
+%    of the nucleus. To see why, let us look at what goes wrong with a
+%    double application of the \cs{mathaccent} primitive. The standard
+%    definition of \cs{hat} is \verb'\mathaccent"705E', so
+%    \verb'\hat{\hat{F}}' expands to
+%\begin{verbatim}
+%\mathaccent"705E{\mathaccent"705E{F}}
+%\end{verbatim}
+%    The result of this operation is
+%\begin{verbatim}
+%\vbox(12.11111+0.0)x7.81946
+%.\hbox(6.94444+0.0)x0.0, shifted 1.40973
+%..\OT1/cmr/m/n/10 ^
+%.\kern-4.30554
+%.\vbox(9.47221+0.0)x7.81946
+%..\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%...\OT1/cmr/m/n/10 ^
+%..\kern-4.30554
+%..\hbox(6.83331+0.0)x7.81946
+%...\OML/cmm/m/it/10 F
+%\end{verbatim}
+%    \tex/ starts by constructing a vbox with the hat character on top
+%    of the F. Then it puts another hat character on top of the vbox;
+%    but without skew information, because that is only applied by
+%    \cs{mathaccent} when the base object is a simple symbol. So the
+%    first accent is skewed to the correct position but all later
+%    accents are not. By the way, the actual width of the F in the above
+%    example is less than 7.81946; the box in which it is packed was
+%    automatically lengthened by the width of the F's italic correction
+%    (without actually putting in a kern for it).
+%
+%    To get the second accent shifted farther to the right we
+%    artificially increase the width of the innermost box and add
+%    a compensating kern afterward. Furthermore, to get proper placement
+%    of a following subscript or superscript, we take the base symbol
+%    out, leaving a phantom in its place, and print it by itself
+%    following the kern. We then need to increase the kern amount to
+%    move the base character backward under the accents again.
+%    Here is what the results look like:
+%\begin{verbatim}
+%\vbox(12.11111+0.0)x9.48618
+%.\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%..\OT1/cmr/m/n/10 ^
+%.\kern-4.30554
+%.\vbox(9.47221+0.0)x9.48618
+%..\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%...\OT1/cmr/m/n/10 ^
+%..\kern-4.30554
+%..\hbox(6.83331+0.0)x9.48618
+%...\hbox(6.83331+0.0)x7.81946
+%...\kern 1.66672
+%\kern -9.48618
+%\OML/cmm/m/it/10 F
+%\end{verbatim}
+%
+%    Much of this implementation is based on code from the \pkg{accents}
+%    package of Javier Bezos. I added the test to revert to a simple
+%    \cs{mathaccent} when accents are not nested, and some other
+%    refinements to reduce the number of kerns used (to conserve box
+%    memory) and the number of cycles through \cs{mathchoice} (to make
+%    things run a little faster). It was all rather difficult and my
+%    first two attempts had serious bugs but I hope and believe that
+%    this version will do better. [mjd,2000/03/15]
+%
+%    The \qq{V} in \cs{mathaccentV} is just an indication that it takes
+%    five arguments. It is important that the name includes
+%    \texttt{mathaccent}, otherwise \cs{DeclareMathAccent} will balk at
+%    redefining one of our accent commands, for example when an
+%    alternative math font package is loaded.
+%    \begin{macrocode}
+\def\mathaccentV#1#2#3#4#5{%
+  \ifmmode
+    \gdef\macc@tmp{\macc@depth\@ne}%
+    \setbox\z@\hbox{%
+      \let\mathaccentV\macc@test
+      \let\use@mathgroup\@gobbletwo \let\select@group\@gobblethree
+      \frozen@everymath{}$#5$%
+    }%
+    \macc@tmp
+    \ifnum\macc@depth=\@ne
+      \global\let\macc@nucleus\@empty
+      \mathaccent"\accentclass@
+    \else
+      \@xp\macc@nested
+    \fi
+    #2#3#4{#5}%
+    \macc@nucleus
+  \else
+    \@xp\nonmatherr@\csname#1\endcsname
+  \fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\macc@test#1#2#3#4{\xdef\macc@tmp{\macc@tmp\advance\macc@depth\@ne}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\macc@group{-1}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\macc@nested#1#2#3#4{%
+  \begingroup
+  \let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar
+  \mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}%
+  \macc@set@skewchar\relax
+  \let\mathaccentV\macc@nested@a
+  \macc@nested@a\relax#1#2#3{#4}%
+  \endgroup
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\macc@palette\mathpalette
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\macc@nested@a#1#2#3#4#5{%
+%    \end{macrocode}
+%    This test saves some work that would otherwise be always repeated
+%    fourfold thanks to \cs{mathchoice}.
+%    \begin{macrocode}
+  \ifnum\macc@group=\mathgroup
+  \else \macc@set@skewchar\relax \edef\macc@group{\the\mathgroup}%
+  \fi
+  \mathchardef\macc@code "\accentclass@ #2#3#4\relax
+  \macc@palette\macc@a{#5}%
+}
+%    \end{macrocode}
+%
+%    The reason that \cs{macc@set@skewchar} takes an argument is so that
+%    it can serve as a direct substitute for \cs{math@egroup}, in
+%    addition to being used separately.
+%
+%    Setting a skewchar with this method works for symbols of variable
+%    mathgroup (class 7, letters and numbers) but not necessarily for
+%    special symbols like \cn{partial} or \cs{xi} whose mathgroup
+%    doesn't change; fortunately the most commonly used ones come from
+%    mathgroup one, which is the fall-back mathgroup for skewchar.
+%    \begin{macrocode}
+\def\macc@set@skewchar#1{%
+  \begingroup
+  \ifnum\mathgroup=\m@ne \let\@tempa\@ne
+  \else
+    \ifnum\skewchar\textfont\mathgroup=\m@ne \let\@tempa\@ne
+    \else \let\@tempa\mathgroup
+    \fi
+  \fi
+  \count@=\skewchar\textfont\@tempa
+  \advance\count@"7100
+  \edef\@tempa{\endgroup
+    \mathchardef\noexpand\macc@skewchar=\number\count@\relax}%
+  \@tempa
+  #1%
+}
+%    \end{macrocode}
+%
+%    Arg1 is math-style, arg2 is accent base object. We assume that math
+%    style doesn't change within the nested group of accents; this means
+%    we can set \cs{macc@style} only once and redefine \cs{macc@palette}
+%    to use it, in order to run \cs{mathchoice} only once instead of
+%    multiplying the calls exponentially as the nesting level increases.
+%    \begin{macrocode}
+\def\macc@a#1#2{%
+  \begingroup
+  \let\macc@style#1\relax
+  \def\macc@palette##1{##1\macc@style}%
+  \advance\macc@depth\m@ne
+  \ifnum\macc@depth=\z@
+    \gdef\macc@nucleus{#2}%
+%    \end{macrocode}
+%    Extra \cs{@empty} tokens are to prevent low-level \tex/ errors from
+%    the potential syntactic error that \cs{acc@check} checks for.
+%    \begin{macrocode}
+    \setbox\z@\hbox{$#1#2\@empty{}\macc@skewchar$}%
+    \setbox\tw@\hbox{$#1#2\@empty\macc@skewchar$}%
+    \dimen@\tw@\wd\tw@ \advance\dimen@-\tw@\wd\z@
+    \xdef\macc@kerna{\the\dimen@\relax}%
+    \setbox4\hbox{$#1#2\acc@check\@empty$}%
+    \global\setbox\@ne\hbox to\wd4{}%
+    \ht\@ne\ht4 \dp\@ne\dp4
+    \xdef\macc@kernb{\the\wd4\relax}%
+    \mathaccent\macc@code{\box\@ne\kern\macc@kerna}%
+  \else
+    \mathaccent\macc@code{\let\macc@adjust\@empty #1#2\@empty}%
+    \macc@adjust
+  \fi
+  \endgroup
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\macc@adjust{%
+  \dimen@\macc@kerna\advance\dimen@\macc@kernb
+  \kern-\dimen@
+}
+%    \end{macrocode}
+%
+%    The commands \cs{Hat}, \cs{Tilde}, \ldots, are supported as
+%    synonyms of \cs{hat}, \cs{tilde}, \ldots, for backward
+%    compatibility.
+%    \begin{macrocode}
+\def\Hat{\hat}
+\def\Check{\check}
+\def\Tilde{\tilde}
+\def\Acute{\acute}
+\def\Grave{\grave}
+\def\Dot{\dot}
+\def\Ddot{\ddot}
+\def\Breve{\breve}
+\def\Bar{\bar}
+\def\Vec{\vec}
+%    \end{macrocode}
+%
+%    This error message about math mode is used several times so we make
+%    an abbreviation for it.
+%    \begin{macrocode}
+\def\nonmatherr@#1{\@amsmath@err{\protect
+  #1 allowed only in math mode}\@ehd}
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Mods, continued fractions, etc.}
+%
+%    \begin{macro}{\bmod}
+%    \begin{macro}{\pmod}
+%    \begin{macro}{\pod}
+%    \begin{macro}{\mod}
+%    The commands \cn{bmod}, \cn{pmod}, \cn{pod}, \cn{mod} aren't
+%    currently robust. [mjd, 1994/09/05]
+%    \begin{macrocode}
+\renewcommand{\bmod}{\nonscript\mskip-\medmuskip\mkern5mu\mathbin
+  {\operator@font mod}\penalty900
+  \mkern5mu\nonscript\mskip-\medmuskip}
+\newcommand{\pod}[1]{\allowbreak
+  \if@display\mkern18mu\else\mkern8mu\fi(#1)}
+\renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}}
+\newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu
+  \else\mkern12mu\fi{\operator@font mod}\,\,#1}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\cfrac}
+%    Continued fractions. The optional arg l or r controls horizontal
+%    placement of the numerators. The |\kern-\nulldelimiterspace|
+%    is needed in the definition if we want the right-hand sides of the
+%    fraction rules to line up. The \cs{strut} keeps the numerator of
+%    a subsidiary cfrac from coming too close to the fraction rule above
+%    it.
+%    \begin{macrocode}
+\newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
+  \strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
+  \kern-\nulldelimiterspace}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\overset}
+%    \begin{macro}{\underset}
+%    \cn{overset} and \cn{underset} put symbols above, respectively
+%    below, a symbol that is not a \cs{mathop} and therefore does not
+%    naturally accept limits. \cs{binrel@@} uses information collected
+%    by \cs{binrel@} to make the resulting construction be of type
+%    mathrel or mathbin if the base symbol is either of those types.
+%    \begin{macrocode}
+\newcommand{\overset}[2]{\binrel@{#2}%
+  \binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newcommand{\underset}[2]{\binrel@{#2}%
+  \binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%
+%  \begin{macro}{\overunderset}
+%    This is the combination of the previous two commands which is
+%    something that is sometimes needed.
+% \changes{v2.17c}{FMi}{New command \cs{overunderset}}
+%    \begin{macrocode}
+\newcommand{\overunderset}[3]{\binrel@{#3}%
+  \binrel@@{\mathop{\kern\z@#3}\limits^{#1}_{#2}}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    \begin{macro}{\sideset}
+%    \cn{sideset} allows placing `adscript' symbols at the four
+%    corners of a \cs{mathop}, \emph{in addition to} limits. Left-side
+%    adscripts go into arg \arg{1}, in the form |_{...}^{...}|, and
+%    right-side adscripts go into arg \arg{2}.
+%
+%    As currently written [mjd, 1995/01/21] this is pretty haphazard.
+%    In order to really make it work properly in full generality we'd
+%    have to read and measure the top and bottom limits and use
+%    mathchoice to always get the right mathstyle for each piece,
+%    etc., etc.
+%    \begin{macrocode}
+\newcommand{\sideset}[3]{%
+  \@mathmeasure\z@\displaystyle{#3}%
+%    \end{macrocode}
+%    Use a global box assignment here since the depth override is
+%    implicitly global. Then move the constructed box to a local box
+%    register (2) to ensure it won't get destroyed during the next two
+%    mathmeasure statements. This precaution may be more extreme than
+%    necessary in practice.
+%    \begin{macrocode}
+  \global\setbox\@ne\vbox to\ht\z@{}\dp\@ne\dp\z@
+  \setbox\tw@\box\@ne
+  \@mathmeasure4\displaystyle{\copy\tw@#1}%
+  \@mathmeasure6\displaystyle{#3\nolimits#2}%
+  \dimen@-\wd6 \advance\dimen@\wd4 \advance\dimen@\wd\z@
+  \hbox to\dimen@{}\mathop{\kern-\dimen@\box4\box6}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \begin{macro}{\smash}
+%    We add to the \cn{smash} command an optional argument
+%    denoting the part of the formula to be smashed.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{smash}
+%   if necessary (github/49)}
+%    \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\renewcommand{\smash}[1][tb]{%
+  \def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
+  \edef\finsm@sh{\csname mb@#1\endcsname\z@\z@\box\z@}%
+  \ifmmode \@xp\mathpalette\@xp\mathsm@sh
+  \else \@xp\makesm@sh
+  \fi
+}
+\else
+\renewcommand{\smash}[1][tb]{%
+  \def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
+  \edef\finsm@sh{\csname mb@#1\endcsname\z@\z@ \leavevmode@ifvmode\box\z@}%
+  \ifmmode \@xp\mathpalette\@xp\mathsm@sh
+  \else \@xp\makesm@sh
+  \fi
+}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Extensible arrows}
+%
+%    The minus sign used in constructing these arrow fills is smashed so
+%    that superscripts above the arrows won't be too high. This
+%    primarily affects the \cn{xleftarrow} and \cn{xrightarrow} arrows.
+%
+%    \begin{macrocode}
+\mathchardef\std@minus\mathcode`\-\relax
+\mathchardef\std@equal\mathcode`\=\relax
+%    \end{macrocode}
+%    In case some alternative math fonts are loaded later:
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \mathchardef\std@minus\mathcode`\-\relax
+  \mathchardef\std@equal\mathcode`\=\relax
+}
+%    \end{macrocode}
+%
+%    \begin{macro}{\relbar}
+%    \begin{macro}{\Relbar}
+%    \begin{macrocode}
+\ams@def\relbar{\mathrel{\mathpalette\mathsm@sh\std@minus}}
+\ams@def\Relbar{\mathrel\std@equal}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macrocode}
+\def\arrowfill@#1#2#3#4{%
+  $\m@th\thickmuskip0mu\medmuskip\thickmuskip\thinmuskip\thickmuskip
+   \relax#4#1\mkern-7mu%
+   \cleaders\hbox{$#4\mkern-2mu#2\mkern-2mu$}\hfill
+   \mkern-7mu#3$%
+}
+\def\leftarrowfill@{\arrowfill@\leftarrow\relbar\relbar}
+\def\rightarrowfill@{\arrowfill@\relbar\relbar\rightarrow}
+\def\leftrightarrowfill@{\arrowfill@\leftarrow\relbar\rightarrow}
+\def\Leftarrowfill@{\arrowfill@\Leftarrow\Relbar\Relbar}
+\def\Rightarrowfill@{\arrowfill@\Relbar\Relbar\Rightarrow}
+\def\Leftrightarrowfill@{\arrowfill@\Leftarrow\Relbar\Rightarrow}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
+ \noalign{\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
+\ams@renewcommand{\overrightarrow}{%
+  \mathpalette{\overarrow@\rightarrowfill@}}
+\ams@renewcommand{\overleftarrow}{%
+  \mathpalette{\overarrow@\leftarrowfill@}}
+\ams@newcommand{\overleftrightarrow}{%
+  \mathpalette{\overarrow@\leftrightarrowfill@}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\underarrow@#1#2#3{%
+ \vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
+ \noalign{\nointerlineskip\kern1.3\ex@}#1#2\crcr}}}
+\ams@newcommand{\underrightarrow}{%
+  \mathpalette{\underarrow@\rightarrowfill@}}
+\ams@newcommand{\underleftarrow}{%
+  \mathpalette{\underarrow@\leftarrowfill@}}
+\ams@newcommand{\underleftrightarrow}{%
+  \mathpalette{\underarrow@\leftrightarrowfill@}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
+\def\ext@arrow#1#2#3#4#5#6#7{%
+  \mathrel{\mathop{%
+%    \end{macrocode}
+%    Measure the superscript and subscript.
+%    \begin{macrocode}
+    \setbox\z@\hbox{#5\displaystyle}%
+    \setbox\tw@\vbox{\m@th
+      \hbox{$\scriptstyle\mkern#3mu{#6}\mkern#4mu$}%
+      \hbox{$\scriptstyle\mkern#3mu{#7}\mkern#4mu$}%
+      \copy\z@
+    }%
+    \hbox to\wd\tw@{\unhbox\z@}}%
+%    \end{macrocode}
+%    We don't want to place an empty subscript since that will produce
+%    too much blank space below the arrow.
+%    \begin{macrocode}
+  \limits
+    \@ifnotempty{#7}{^{\if0#1\else\mkern#1mu\fi
+                       #7\if0#2\else\mkern#2mu\fi}}%
+    \@ifnotempty{#6}{_{\if0#1\else\mkern#1mu\fi
+                       #6\if0#2\else\mkern#2mu\fi}}}%
+}
+%    \end{macrocode}
+%
+%    Some extensible arrows to serve as mathrels and taking
+%    sub/superscripts. These commands are robust because they take an
+%    optional argument.
+%    \begin{macrocode}
+\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
+\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}}
+%    \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Array-related environments}
+% \subsection{Remarks}
+%
+%    Because these environments can be nested within the equation
+%    structures that allow \cn{tag}, there is some cross-influence in
+%    the internal workings of the \cn{\\} command.
+%
+% \subsection{The \env{subarray} environment and \cn{substack} command}
+%
+%    The \cn{substack} command can be used to set subscripts
+%    and superscripts that consist of several lines. Usage:
+% \begin{verbatim}
+% X_{\substack{a=1\\b=2}}
+% \end{verbatim}
+%
+% \changes{v2.0}{1999/06/17}{Removed environment definitions: Sb, Sp}
+%
+% \begin{environment}{subarray}
+%    The \env{subarray} environment makes a small-size array suitable
+%    for use in a subscript or superscript. At the moment the supported
+%    arguments are not the full possibilities of \env{array} but only
+%    |c| or |l| for centered or left-aligned. And only one column.
+%    \begin{macrocode}
+\newenvironment{subarray}[1]{%
+%    \end{macrocode}
+%    Note: The predecessors of \env{subarray} (\env{Sb} and \env{Sp},
+%    inherited from \amstex/) used \cs{vbox} instead of \cs{vcenter}.
+%    But when a multiline subscript is placed in \cs{limits} position
+%    \cs{vcenter} is no worse than \cs{vbox}, and when it is placed
+%    in the \cs{nolimits} position (e.g., for an integral), \cs{vcenter}
+%    provides clearly better positioning than \cs{vbox}.
+%    \begin{macrocode}
+  \vcenter\bgroup
+%    \end{macrocode}
+%    Use \cs{Let@} to set the proper meaning of the \cn{\\} and \cn{\\*}
+%    commands. And restore the meaning of \cs{math@cr@@@} to \cs{cr}
+%    (see above) in case \env{subarray} is used inside one of the more
+%    complicated alignment macros where the meaning of \cs{math@cr@@@}
+%    is different. Similarly, call \cs{default@tag} to ensure that a
+%    line break here doesn't get an equation number!
+%    \begin{macrocode}
+  \Let@ \restore@math@cr \default@tag
+%    \end{macrocode}
+%    Set the line spacing to be the same as \cs{atop} (when \cs{atop}
+%    occurs in \cs{textstyle} or smaller), cf \textit{The \tex/book},
+%    Appendix G.
+%    \begin{macrocode}
+  \baselineskip\fontdimen10 \scriptfont\tw@
+  \advance\baselineskip\fontdimen12 \scriptfont\tw@
+  \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
+  \lineskiplimit\lineskip
+%    \end{macrocode}
+%    Start the \cs{vbox} \cs{halign} structure that encloses the
+%    contents. Notice that we never get \cs{scriptscriptstyle}. That
+%    would require a \cs{mathchoice} (ugh).
+%    \begin{macrocode}
+  \ialign\bgroup\ifx c#1\hfil\fi
+    $\m@th\scriptstyle##$\hfil\crcr
+}{%
+  \crcr\egroup\egroup
+}
+%    \end{macrocode}
+% \end{environment}
+%
+% \begin{macro}{\substack}
+%    The \cn{substack} command is just an abbreviation for the
+%    most common use of \env{subarray}.
+%    \begin{macrocode}
+\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Matrices}
+%
+% \begin{environment}{smallmatrix}
+%    \env{smallmatrix} is again an alignment, this time in a centered
+%    box. The opening incantations are basically the same as those in
+%    \cs{multilimits@}, followed by the alignment itself. A remark:
+%    the baselineskip (|9\ex@|) used in \amstex/ is too large for
+%    use in text with the usual baselineskip of $12$ or $13$ points; we
+%    change it here to |6\ex@| and also adjust the \cs{lineskip}
+%    and \cs{lineskiplimit} slightly to compensate. (MJD)
+%    \begin{macrocode}
+\newenvironment{smallmatrix}{\null\,\vcenter\bgroup
+  \Let@\restore@math@cr\default@tag
+  \baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
+  \ialign\bgroup\hfil$\m@th\scriptstyle##$\hfil&&\thickspace\hfil
+  $\m@th\scriptstyle##$\hfil\crcr
+}{%
+  \crcr\egroup\egroup\,%
+}
+%    \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{matrix}
+%    The \env{matrix} environment is just an \env{array} that provides
+%    up to ten centered columns, so that users don't have to give the
+%    col-spec argument explicitly---unless they want some of the columns
+%    noncentered, that is. The maximum number of columns is actually not
+%    fixed at ten but given by the counter |MatrixCols|, and can
+%    therefore be increased by changing that counter.
+%
+%    The extra space of \cn{arraycolsep} that \env{array} adds on each
+%    side is a waste so we remove it here (perhaps we should instead
+%    remove it from \env{array} in general, but that's a harder task).
+%
+%    TODO: Think about re-implementing \cn{matrix} to get rid of the
+%    \cs{c@MatrixCols} limit and have hard-wired preamble that doesn't
+%    have to be rebuilt each time.
+%
+%    We must use \cn{renewenvironment} for \env{matrix} and
+%    \env{pmatrix} because \latex/ doesn't kill the definitions found in
+%    \fn{plain.tex}, even though it probably should because of their
+%    foreign syntax.
+%    \begin{macrocode}
+\renewenvironment{matrix}{%
+  \matrix@check\matrix\env@matrix
+}{%
+  \endarray \hskip -\arraycolsep
+}
+%    \end{macrocode}
+% \end{environment}
+%
+%  \begin{macro}{\env@matrix}
+%
+%    \begin{macrocode}
+\def\env@matrix{\hskip -\arraycolsep
+  \let\@ifnextchar\new@ifnextchar
+  \array{*\c@MaxMatrixCols c}}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\c@MaxMatrixCols}
+%    \begin{macrocode}
+\newcount\c@MaxMatrixCols \c@MaxMatrixCols=10
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\matrix@check}
+%    For various reasons, authors sometimes use the Plain \TeX{} form of
+%    \cn{matrix} or \cn{pmatrix} in \LaTeX{} documents. If they later
+%    add an invocation of the \pkg{amsmath} package to their document,
+%    the Plain \TeX{} syntax would lead to rather unintelligible error
+%    messages. The \cs{matrix@check} function does some checking to
+%    forestall that problem.
+%    \begin{macrocode}
+\def\matrix@check#1{%
+  \@xp\ifx\csname\@currenvir\endcsname#1%
+  \else\matrix@error#1%
+%    \end{macrocode}
+%    This error recovery is not that good but is better than the
+%    infinite loop that can result from calling \cs{array} without a
+%    matching \cs{endarray}. (The array setup leaves \cs{par} empty.)
+%    \begin{macrocode}
+    \@xp\@gobble
+  \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\matrix@error}
+%
+%    \begin{macrocode}
+\def\matrix@error#1{%
+  \@amsmath@err{%
+Old form `\string#1' should be \string\begin{\@xp\@gobble\string#1}%
+  }{%
+`\string#1{...}' is old Plain-TeX syntax whose use is
+ill-advised in LaTeX.%
+  }%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    \begin{macrocode}
+\renewenvironment{pmatrix}{%
+  \left(%
+  \matrix@check\pmatrix\env@matrix
+}{
+  \endmatrix\right)%
+}
+\newenvironment{bmatrix}{\left[\env@matrix}{\endmatrix\right]}
+\newenvironment{Bmatrix}{%
+  \left\lbrace\env@matrix
+}{%
+  \endmatrix\right\rbrace
+}
+\newenvironment{vmatrix}{\left\lvert\env@matrix}{\endmatrix\right\rvert}
+\newenvironment{Vmatrix}{\left\lVert\env@matrix}{\endmatrix\right\rVert}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\hdots\@ldots
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newcommand{\hdotsfor}[1]{%
+  \ifx[#1\@xp\shdots@for\else\hdots@for\@ne{#1}\fi}
+\newmuskip\dotsspace@
+\def\shdots@for#1]{\hdots@for{#1}}
+\def\hdots@for#1#2{\multicolumn{#2}c%
+  {\m@th\dotsspace@1.5mu\mkern-#1\dotsspace@
+   \xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
+           \hfill
+   \mkern-#1\dotsspace@}%
+   }
+%    \end{macrocode}
+%
+% \begin{environment}{cases}
+%    The easiest way to produce the \env{cases} environment is to base
+%    it on the \env{array} environment. We must use
+%    \cn{renewenvironment} to override the definition of \cn{cases} that
+%    \latex/ (unwisely) leaves in place from \fn{plain.tex}.
+%    \begin{macrocode}
+\renewenvironment{cases}{%
+  \matrix@check\cases\env@cases
+}{%
+  \endarray\right.%
+}
+\def\env@cases{%
+  \let\@ifnextchar\new@ifnextchar
+  \left\lbrace
+  \def\arraystretch{1.2}%
+  \array{@{}l@{\quad}l@{}}%
+}
+%    \end{macrocode}
+% \end{environment}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Equation sub-numbering}
+%
+%    \begin{macrocode}
+\newcounter{parentequation}% Counter for ``parent equation''.
+%    \end{macrocode}
+%
+%    We can't assume \cs{ignorespacesafterend} is defined since it was
+%    not there in the earliest releases of \latex/ 2e. And we need to
+%    include the \cs{global} for the same reason.
+%    \begin{macrocode}
+\@ifundefined{ignorespacesafterend}{%
+  \def\ignorespacesafterend{\global\@ignoretrue}%
+}{}
+%    \end{macrocode}
+%
+%    \begin{environment}{subequations}
+%    \begin{macrocode}
+\newenvironment{subequations}{%
+%    \end{macrocode}
+%    Before sending down the `equation' counter to the subordinate
+%    level, add 1 using standard \cn{refstepcounter}.
+%    \begin{macrocode}
+  \refstepcounter{equation}%
+%    \end{macrocode}
+%    Define \cn{theparentequation} equivalent to current
+%    \cn{theequation}. \cn{edef} is necessary to expand the current
+%    value of the equation counter. This might in rare cases cause
+%    something to blow up, in which case the user needs to add
+%    \cn{protect}.
+%    \begin{macrocode}
+  \protected@edef\theparentequation{\theequation}%
+  \setcounter{parentequation}{\value{equation}}%
+%    \end{macrocode}
+%    And set the equation counter to 0, so that the normal incrementing
+%    processes in the various equation environments will produce the
+%    desired results.
+%    \begin{macrocode}
+  \setcounter{equation}{0}%
+  \def\theequation{\theparentequation\alph{equation}}%
+  \ignorespaces
+}{%
+  \setcounter{equation}{\value{parentequation}}%
+  \ignorespacesafterend
+}
+%    \end{macrocode}
+%    \end{environment}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Equation numbering}
+%
+%    In the multiline equation environments provided here, the task
+%    of equation numbering is linked to the task of line breaking
+%    in the sense that it is the \cn{\\} command that marks where an
+%    equation number for the current line will be processed and added to
+%    the page.
+%
+%    \begin{macro}{\numberwithin}
+%    Provide a convenient way to specify that equations should be
+%    numbered within sections.
+%    \begin{macrocode}
+\newcommand{\numberwithin}[3][\arabic]{%
+  \@ifundefined{c@#2}{\@nocounterr{#2}}{%
+    \@ifundefined{c@#3}{\@nocnterr{#3}}{%
+      \@addtoreset{#2}{#3}%
+      \@xp\xdef\csname the#2\endcsname{%
+        \@xp\@nx\csname the#3\endcsname .\@nx#1{#2}}}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\eqref}
+%    To make references to equation numbers easier, we provide
+%    \cn{eqref}.  We almost don't need \cn{textup}, except that
+%    \cs{tagform@} doesn't supply the italic correction.
+%    \begin{macrocode}
+\newcommand{\eqref}[1]{\textup{\tagform@{\ref{#1}}}}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \subsection{Preliminary macros}
+%
+%    The following macros implement the \latex/ syntax for the
+%    \cn{\\} command, i.e. the possibility to add an asterisk to
+%    inhibit a page break, or an optional argument to denote additional
+%    vertical space. They are modelled more or less after the
+%    corresponding macros for \latex/'s \env{eqnarray} and \env{array}
+%    environments.
+%
+%    [We can perhaps use the eqnarray mechanism if we change it so that
+%    it also uses \cs{openup}.]
+%
+% \begin{macro}{\dspbrk@lvl}
+%    We begin by defining the \cs{dspbrk@lvl} counter. This counter
+%    records the desirability of a break after the current row, as a
+%    number between $0$ and $4$. Its default value is $-1$ meaning that
+%    no explicit \cn{displaybreak} command was given, and the default
+%    \cs{interdisplaylinepenalty} is to be used.
+%    \begin{macrocode}
+\newcount\dspbrk@lvl
+\dspbrk@lvl=-1
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\interdisplaylinepenalty}
+%    We set the \cs{interdisplaylinepenalty} to $10000$.
+%    \begin{macrocode}
+\interdisplaylinepenalty\@M
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\allowdisplaybreaks}
+%    The \cn{allowdisplaybreaks} command. Since this is intended for use
+%    outside displayed formulas (typically in the preamble), it does not
+%    need to use \cs{new@ifnextchar}.
+%    \begin{macrocode}
+\newcommand{\allowdisplaybreaks}[1][4]{%
+  \interdisplaylinepenalty\getdsp@pen{#1}\relax
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\getdsp@pen}
+%    Modelled after \latex/'s \cs{@getpen}.  We use higher numbers
+%    than would normally be provided by \cs{@lowpenalty},
+%    \cs{@medpenalty}, and \cs{@highpenalty}, since display
+%    breaks are almost always less desirable.
+%    \begin{macrocode}
+\def\getdsp@pen#1{%
+  \ifcase #1\@M \or 9999 \or 6999 \or 2999 \or \z@\fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\displaybreak}
+% \begin{macro}{\dspbrk@}
+% \begin{macro}{\dspbrk@context}
+% \begin{macro}{\nogood@displaybreak}
+%    For breaks in a certain row of a alignment.
+%    \begin{macrocode}
+\newcommand{\displaybreak}{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}
+\chardef\dspbrk@context=\sixt@@n
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\dspbrk@[#1]{%
+  \ifmeasuring@
+  \else
+    \ifcase\dspbrk@context % case 0 --- OK
+      \global\dspbrk@lvl #1\relax
+    \or                    % case 1 --- inside a box
+      \nogood@displaybreak
+    \else                  % other cases --- outside of a display
+      \@amsmath@err{\Invalid@@\displaybreak}\@eha
+    \fi
+  \fi
+}
+%    \end{macrocode}
+%
+%    This is the value of \cn{displaybreak} when it occurs inside some
+%    structure where it will not work.
+%    \begin{macrocode}
+\def\nogood@displaybreak{%
+  \@amsmath@err{\protect
+\displaybreak\space cannot be applied here}%
+{One of the enclosing environments creates an
+  unbreakable box\MessageBreak
+(e.g., split, aligned, gathered, ...).}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\math@cr}
+%    The macro \cs{math@cr} ends a row inside one of the equation
+%    environments, i.e., this is the internal name of the \cn{\\}
+%    commands in these environments. As usual for this kind of macro
+%    inside of alignments we insert a special brace into \tex/'s input
+%    stream. The initial \cs{relax} is needed to trigger entry into the
+%    \textit{u} template of the current column if the author ended the
+%    current row with an empty column (i.e., the mathcr was immediately
+%    preceded by an ampersand).
+%    \begin{macrocode}
+\def\math@cr{\relax\iffalse{\fi\ifnum0=`}\fi
+%    \end{macrocode}
+%    The first step is now to check whether an asterisk follows.
+%    \cs{@eqpen} is used to hold the penalty value to be put on
+%    the vertical list.
+%    Then we call up \cs{math@cr@} which performs the next step.
+%    If an asterisk is read page breaking is inhibited.
+%    \begin{macrocode}
+  \@ifstar{\global\@eqpen\@M\math@cr@}%
+%    \end{macrocode}
+%    Otherwise we have to check the \cs{dspbrk@lvl} value.
+%    \begin{macrocode}
+          {\global\@eqpen
+             \ifnum\dspbrk@lvl <\z@ \interdisplaylinepenalty
+              \else -\@getpen\dspbrk@lvl \fi
+           \math@cr@}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@}
+%    The purpose of \cs{math@cr@} is to check whether an optional
+%    argument follows.  If not it provides \cs{z@} as default
+%    value.
+%    \begin{macrocode}
+\def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@}
+%    \cs{math@cr@@} closes the special brace opened in
+%    \cs{math@cr}, and calls \cs{math@cr@@@} which is supposed
+%    the `real' row ending command.  The meaning of this macro depends
+%    on the environment in which it is used.
+%    \begin{macrocode}
+\def\math@cr@@[#1]{\ifnum0=`{\fi \iffalse}\fi\math@cr@@@
+%    \end{macrocode}
+%    Finally we put the additional space onto the vertical list.
+%    \begin{macrocode}
+  \noalign{\vskip#1\relax}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Let@}
+%    \cs{Let@} is called by all environments where \cn{\\}
+%    ends a row of an alignment.
+%    \begin{macrocode}
+\def\Let@{\let\\\math@cr}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\restore@math@cr}
+%    We mentioned already that the exact meaning of \cs{math@cr@@@}
+%    depends on the current environment.  Since it is often a simple
+%    \cs{cr} we provide \cs{restore@math@cr} to reset it.
+%    \begin{macrocode}
+\def\restore@math@cr{\def\math@cr@@@{\cr}}
+%    \end{macrocode}
+%    This is also the default case.
+%    \begin{macrocode}
+\restore@math@cr
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\intertext}
+% \begin{macro}{\intertext@}
+%    The \cn{intertext} command is used for inserting text between the
+%    rows of an alignment. It might better be done as an environment,
+%    but the \cs{begingroup} from \cn{begin} would cause the
+%    \cs{noalign} to fail.
+%    \begin{macrocode}
+\newcommand{\intertext}{\@amsmath@err{\Invalid@@\intertext}\@eha}
+%    \end{macrocode}
+%    \cs{intertext@} is called by all environments that allow the use of
+%    the \cn{intertext} command.
+%    \begin{macrocode}
+\def\intertext@{%
+  \def\intertext##1{%
+%    \end{macrocode}
+%    If current mode is not vmode, the most likely reason is that the
+%    writer forgot the \cn{\\} that is supposed to precede
+%    \cn{intertext}. All right, then, let's try adding it our ownself.
+%    But, to be slightly careful: \cn{\\} does a futurelet, and it's
+%    slightly dangerous to allow a letted token to barge around loose in
+%    our internal code when it has been let to a conditional token
+%    like \cs{fi}. So let's interpose something in front of the \cs{fi}
+%    for the futurelet to take instead. (And careful again: it has to be
+%    something evanescent, not (e.g.) \cs{relax} which would cause the
+%    next halign cell to fire up and keep \cs{noalign} from working.)
+%    \begin{macrocode}
+    \ifvmode\else\\\@empty\fi
+    \noalign{%
+      \penalty\postdisplaypenalty\vskip\belowdisplayskip
+      \vbox{\normalbaselines
+%    \end{macrocode}
+%    We need to do something extra if the outside environment is a list
+%    environment. I don't see offhand an elegant way to test ``are we
+%    inside any list environment'' that is both easy and reliable (for
+%    example, checking for zero \cs{@totalleftmargin} wouldn't catch the
+%    case where \cs{@totalleftmargin} is zero but \cs{linewidth} is less
+%    than \cs{columnwidth}), so it seems to me checking \cs{linewidth}
+%    is the best practical solution.
+% \changes{v2.15c}{2016/05/23}{\cs{ignorespaces} at the start of the argument}
+%    \begin{macrocode}
+        \ifdim\linewidth=\columnwidth
+        \else \parshape\@ne \@totalleftmargin \linewidth
+        \fi
+        \noindent\ignorespaces##1\par}%
+      \penalty\predisplaypenalty\vskip\abovedisplayskip%
+    }%
+}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Implementing tags and labels}
+%
+%    In this section we describe some of the macros needed to make the
+%    \cn{tag} command work in various places. We start by defining a
+%    help text to be used when a \cn{tag} command is used somewhere
+%    it should not appear.
+%
+% \begin{macro}{\tag@help}
+%    This is the default error help text provided when \cn{tag}
+%    generates an error message.
+%    Note that \cs{newhelp} generates a control sequence name
+%    from the string given as its argument so that a leading
+%    backslash is provided automatically.
+%    \begin{macrocode}
+\newhelp\tag@help
+  {tag cannot be used at this point.\space
+   If you don't understand why^^Jyou should consult
+   the documentation.^^JBut don't worry: just continue, and I'll
+   forget what happened.}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\gobble@tag}
+%    This macro is to be used when \cn{tag} should silently
+%    skip its argument.
+%    It is made to handle the \qc{\*}-form of \cn{tag} as well.
+%    \begin{macrocode}
+\def\gobble@tag{\@ifstar\@gobble\@gobble}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\invalid@tag}
+%    \cs{invalid@tag} is a macro that should be used whenever
+%    \cn{tag} appears in an illegal place.
+%    It sets up \cs{tag@help} (as defined above) as help message,
+%    prints its argument as error message, and skips \cn{tag}'s
+%    argument.
+%    \begin{macrocode}
+\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\dft@tag}
+% \begin{macro}{\default@tag}
+%    \cs{dft@tag} provides a convenient way to disallow the
+%    use of \cn{tag} at certain points.
+%    One simply has to write
+%    \begin{verbatim}
+%\let\tag\dft@tag
+%    \end{verbatim}
+%    and the \cn{tag} command will produce an error message,
+%    with a suitable error help text, and discard its argument.
+%    \begin{macrocode}
+\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
+%    \end{macrocode}
+%    Since this is used several times we provide an abbreviation for
+%    it.
+%    \begin{macrocode}
+\def\default@tag{\let\tag\dft@tag}
+%    \end{macrocode}
+%    Since this is also the default, i.e.\ the \cn{tag} command
+%    should not be used except in special places, we issue a
+%    \cs{default@tag} command.
+%    \begin{macrocode}
+\default@tag
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    Now that we have taken care of the case that \cn{tag} is not
+%    allowed we will provide some macros to process tags appropriately.
+%    As the user documentation states, a \cn{tag} command (without
+%    the asterisk typesets its argument according to the document
+%    styles' conventions, whereas a \cn{tag*} command typesets its
+%    argument exactly as given. We define therefore the following
+%    interface:
+%
+% \begin{macro}{\maketag@@}
+% \begin{macro}{\maketag@@@}
+% \begin{macro}{\tagform@}
+%    \cn{tag} is supposed to call \cs{maketag@@} which checks
+%    whether an asterisk follows. If this is the case it calls up
+%    \cs{maketag@@@} which sets its argument `as is'. Otherwise
+%    \cs{tagform@} is called to do the job. (This macro is to be
+%    defined appropriately by the document style.)
+%    \begin{macrocode}
+\def\maketag@@{\@ifstar\maketag@@@\tagform@}
+%    \end{macrocode}
+%    We define \cs{maketag@@@} to use the normal font of the document
+%    text (since this is the usual practice for numbering of document
+%    elements) and to put a box around the tag. Furthermore we use
+%    \cs{m@th} for exceptional cases where the tag involves a
+%    superscript or some such math. (Probably from an explicit use of
+%    \cs{tag*} rather than from the automatic numbering.)
+%    \begin{macrocode}
+\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
+%    \end{macrocode}
+%    We use the following default definition for \cs{tagform@}
+%    that puts only parentheses around the tag.
+%    \begin{macrocode}
+\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip\@@italiccorr)}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%    We need to insinuate \cs{tagform@} into \cs{@eqnnum} in case
+%    \env{eqnarray} is used (probably in a document that was originally
+%    written without use of the \pkg{amsmath} package).
+%    \begin{macrocode}
+\iftagsleft@
+  \def\@eqnnum{\hbox to1sp{}\rlap{\normalfont\normalcolor
+    \hskip -\displaywidth\tagform@\theequation}}
+\else
+  \def\@eqnnum{{\normalfont\normalcolor \tagform@\theequation}}
+\fi
+%    \end{macrocode}
+%
+% \begin{macro}{\thetag}
+%    Sometimes one needs to set a literal tag according to the rules of
+%    the document style. To achieve this we provide the \cn{thetag}
+%    command. It typesets its argument by calling \cs{tagform@} on
+%    it.
+%    \begin{macrocode}
+\newcommand{\thetag}{\leavevmode\tagform@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\df@tag}
+% \begin{macro}{\make@df@tag}
+% \begin{macro}{\make@df@tag@@}
+% \begin{macro}{\make@df@tag@@@}
+%    Sometimes it is necessary for a \cn{tag} command to store a tag
+%    in a safe place and to process it later, e.g., for a tag in a row
+%    of an alignment where the tag can only be typeset when the
+%    \cn{\\} at the end of the row was seen. Such a tag is stored in
+%    the macro \cs{df@tag} (for `deferred tag'). For this purpose we
+%    provide the \cs{make@df@tag} macro. It is built very similar to
+%    the \cs{maketag@@} macro above.
+%    \begin{macrocode}
+\let\df@tag\@empty
+\def\make@df@tag{\@ifstar\make@df@tag@@\make@df@tag@@@}
+%    \end{macrocode}
+%    \cs{make@df@tag} sets \cs{@currentlabel} and defines
+%    \cs{df@tag} appropriately.
+%
+%    To simplify the task of tracking \cs{tag} and \cs{label}
+%    commands inside math display environments, we defer \cs{label}
+%    commands until the tag is typeset, similar to the way that
+%    \cs{tag}s themselves are deferred.  This allows arbitrary
+%    placement of \cs{label} and \cs{tag} commands and also means we
+%    only increment the \cs{equation} counter when we really need to,
+%    thus avoiding the \cs{setb@ck} nonsense that used to be required.
+%
+%    \begin{macrocode}
+\def\make@df@tag@@#1{%
+  \gdef\df@tag{\maketag@@@{#1}\def\@currentlabel{#1}}}
+%    \end{macrocode}
+%    Autogenerated number:
+%    \begin{macrocode}
+\def\make@df@tag@@@#1{\gdef\df@tag{\tagform@{#1}%
+  \toks@\@xp{\p@equation{#1}}\edef\@currentlabel{\the\toks@}}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\ltx@label}
+%    \begin{macro}{\label@in@display}
+%    \begin{macro}{\df@label}
+%    Next, we store the default definition of \cs{label} in
+%    \cs{ltx@label} and then define a new version of \cs{label} for use
+%    in math display environments. \cs{label@in@display} merely issues a
+%    warning message if there is already a pending label (which will be
+%    discarded) and then stores the label in \cs{df@label}.
+%    \begin{macrocode}
+\let\ltx@label\label
+%
+\def\label@in@display{%
+    \ifx\df@label\@empty\else
+        \@amsmath@err{Multiple \string\label's:
+            label '\df@label' will be lost}\@eha
+    \fi
+    \gdef\df@label
+}
+%    \end{macrocode}
+%    In case there is an enumerate inside a minipage inside an equation,
+%    we need to reset \cn{label} to its normal value:
+%    \begin{macrocode}
+\toks@\@xp{\@arrayparboxrestore \let\label\ltx@label}%
+\edef\@arrayboxrestore{\the\toks@}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\df@label\@empty
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\make@display@tag}
+%    Now we define a macro to process \cs{tag} and \cs{label} commands
+%    in various display environments.  If the |@eqnsw| switch is set,
+%    then we should supply an equation number; otherwise, if the
+%    |@tag| switch is set, we should use the tag stored in
+%    \cs{df@tag}.  Finally, we process any pending \cs{label}s.
+%
+%    TODO: Arguably, \cs{make@display@tag} should issue a warning
+%    message if there is a \cs{label} but neither a tag nor an
+%    equation number.  Also, it would probably be worthwhile to
+%    explore whether \cs{iftag@} could be done away with and replaced
+%    by checks to see if \cs{df@tag} is empty or not.
+%    \begin{macrocode}
+\def\make@display@tag{%
+  \if@eqnsw \incr@eqnum \print@eqnum
+  \else \iftag@ \df@tag \global\let\df@tag\@empty \fi
+  \fi
+%    \end{macrocode}
+%    Need to check the \cs{ifmeasuring@} flag otherwise the \cs{write}
+%    node from \cn{label} might be discarded in a temp box and clearing
+%    \cs{df@label} will keep it from being reiterated on the real
+%    typesetting pass.
+%    \begin{macrocode}
+  \ifmeasuring@
+  \else
+    \ifx\df@label\@empty
+    \else
+      \@xp\ltx@label\@xp{\df@label}%
+      \global\let\df@label\@empty
+    \fi
+  \fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    Now we define the special versions of \cn{tag} used within the
+%    \env{align} environments.
+%
+% \begin{macro}{\tag@in@align}
+%    The \cn{tag} command may only appear once in a row of
+%    an alignment.  Therefore we first check the switch |tag@|
+%    that is set to false at the begin of every row.
+%    If this switch is true a \cn{tag} was already given in this
+%    row and we define \cs{next@} to expand to a call to
+%    \cs{invalid@tag}.
+%    \begin{macrocode}
+\def\tag@in@align{%
+    \relax
+    \iftag@
+        \DN@{\invalid@tag{Multiple \string\tag}}%
+    \else
+%    \end{macrocode}
+%    Otherwise we set the |tag@| switch.  But there is more to
+%    be done: we must also prevent the automatic generation of a
+%    tag.  Therefore we also reset the |@eqnsw|.
+%    \begin{macrocode}
+    \global\tag@true
+%    \end{macrocode}
+%    Changed to \cs{nonumber}, since that seems to be all that's
+%    required.---dmj, 1994/12/21
+%    \begin{macrocode}
+    \nonumber
+%    \end{macrocode}
+%    Within a row of an \env{align} environment the \cn{tag}
+%    command must not typeset the tag immediately since its
+%    position can be determined only later.
+%    Therefore we use the \cs{make@df@tag} macro defined
+%    earlier.
+%    Finally we call \cs{next@} to process the argument
+%    that follows.
+%    \begin{macrocode}
+        \let\next@\make@df@tag
+    \fi
+    \next@
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\raisetag}
+%    Usage: \cn{raisetag} \meta{dimen}
+%
+%    This will modify the vertical placement of the tag of the current
+%    equation by \meta{dimen}. Note that according to the current uses
+%    of \cs{raise@tag} in e.g., \cs{place@tag@gather}, no adjustment
+%    occurs if the tag falls in its normal position; i.e., \cn{raisetag}
+%    has no effect unless the tag has already been shifted off-line.
+%
+%    \begin{macrocode}
+\newcommand{\raisetag}[1]{\skip@#1\relax
+  \xdef\raise@tag{\vskip\iftagsleft@\else-\fi\the\skip@\relax}%
+}
+%    \end{macrocode}
+%    \cn{raise@tag} will be reemptied at the beginning of each equation,
+%    which might occur at a |\begin{xxx}| or \cn{\\}.
+%    \begin{macrocode}
+\let\raise@tag\@empty
+%    \end{macrocode}
+%    \end{macro}
+%
+% \begin{macro}{\notag}
+%    For consistency we provide \cn{notag}, equivalent to
+%    \cn{nonumber}. The alternative would have been to rename
+%    \cn{tag} as \cn{number} to go along with \cn{nonumber},
+%    but of course \cs{number} is a \tex/ primitive that should not
+%    be redefined.
+%    \begin{macrocode}
+\newcommand{\notag}{\nonumber}
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\nonumber}
+%    Need to add some additional code to \cn{nonumber} to deal with some
+%    complications related to nested environments.
+%    \begin{macrocode}
+\renewcommand{\nonumber}{%
+  \if@eqnsw
+    \ifx\incr@eqnum\@empty \addtocounter{equation}\m@ne \fi
+  \fi
+  \let\print@eqnum\@empty \let\incr@eqnum\@empty
+  \global\@eqnswfalse
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\print@eqnum{\tagform@\theequation}
+\def\incr@eqnum{\refstepcounter{equation}\let\incr@eqnum\@empty}
+%    \end{macrocode}
+%  \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Multiline equation environments}
+%
+% \subsection{Remarks}
+%
+%    In late 1994 David M. Jones did a thorough overhaul of these
+%    environments so that the number placement and a few other aspects
+%    are substantially improved over the original versions that were
+%    ported essentially unchanged from \fn{amstex.tex} in 1989. Most of
+%    the commentary in this section is DMJ's, and comments of any
+%    significance that I added are marked by my initials and date
+%    [mjd, 1995/01/11].
+%
+% \subsection{Preliminaries}
+%
+% \begin{macro}{\ifinalign@}
+% \begin{macro}{\ifingather@}
+%    We define two switches that are set to true in certain
+%    alignments: |inalign@| and |ingather@| inside of
+%    the \env{align} and \env{gather} environments.
+%    These switches are needed to control certain actions that
+%    depend on the surrounding conditions, more specifically:
+%    on the setting already done by the surrounding environments.
+%    \begin{macrocode}
+\newif\ifinalign@
+\newif\ifingather@
+%    \end{macrocode}
+% \begin{histnote}
+% Removed the \cs{ifinany@} test [mjd,1999/06/28] since it was mainly
+% used for the purpose now handled by \cs{spread@equation}.
+% \changes{v1.2g}{1999/06/28}{Removed ifinany@}
+% \end{histnote}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@arrayparboxrestore}
+%    Here we must reset a few additional parameters.
+%    \begin{macrocode}
+\@xp\def\@xp\@arrayparboxrestore\@xp{\@arrayparboxrestore
+  \ingather@false\inalign@false \default@tag
+  \let\spread@equation\@spread@equation
+  \let\reset@equation\@empty
+  \def\print@eqnum{\tagform@\theequation}%
+  \def\incr@eqnum{\refstepcounter{equation}\let\incr@eqnum\@empty}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iftag@}
+%    The switch |tag@| is set to false at the beginning of every
+%    row and set to true by a \cn{tag} command.
+%    This allows us to check whether there is more than one tag on
+%    a row.
+%    \begin{macrocode}
+\newif\iftag@
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ifst@rred}
+%    The switch |st@rred| is set to true by all starred
+%    environments
+%    and set to false by the unstarred versions.
+%    \begin{macrocode}
+\newif\ifst@rred
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ifmeasuring@}
+%    All display environments get typeset twice---once during a
+%    ``measuring'' phase and then again during a ``production'' phase;
+%    \cs{ifmeasuring@} will be used to determine which case we're in,
+%    so we can take appropriate action.
+%
+%    \begin{macrocode}
+\newif\ifmeasuring@
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\ifshifttag@}
+%    \cs{ifshifttag@} is used by \env{gather} to communicate between
+%    \cs{calc@shift@gather} and \cs{place@tag@gather} whether an
+%    equation tag should be shifted to a separate line.  It's also
+%    used by \env{multline}.
+%    \begin{macrocode}
+\newif\ifshifttag@
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\row@}
+%    \begin{macrocode}
+\newcount\row@
+%    \end{macrocode}
+%    \end{macro}
+%
+% \begin{macro}{\column@}
+%    The counter \cs{column@} is used by the alignment macros to
+%    keep track of the current column.
+%
+%    \begin{macrocode}
+\newcount\column@
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\column@plus}
+%    \cs{\column@plus} is a useful abbreviation.
+%    \begin{macrocode}
+\def\column@plus{%
+    \global\advance\column@\@ne
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    \begin{macro}{\maxfields@}
+%    \begin{macrocode}
+\newcount\maxfields@
+%    \end{macrocode}
+%    \end{macro}
+%
+%  \begin{macro}{\add@amp}
+%  \begin{macro}{\add@amps}
+%    \begin{macrocode}
+\def\add@amp#1{\if m#1&\@xp\add@amp\fi}
+\def\add@amps#1{%
+    \begingroup
+    \count@#1\advance\count@-\column@
+    \edef\@tempa{\endgroup
+      \@xp\add@amp\romannumeral\number\count@ 000q}%
+    \@tempa
+}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%
+% \begin{macro}{\andhelp@}
+%    The help text stored in \cs{andhelp@} is used for errors
+%    generated by too many \qc{\&} characters in a row.
+%    \begin{macrocode}
+\newhelp\andhelp@
+{An extra & here is so disastrous that you should probably exit^^J
+and fix things up.}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\eqnshift@}
+%    \cs{eqnshift@} is used by \env{align} and \env{gather} as the
+%    indentation of the lines of the environment from the left margin.
+%    \begin{macrocode}
+\newdimen\eqnshift@
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\alignsep@}
+%    \begin{macrocode}
+\newdimen\alignsep@
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\tagshift@}
+%    \begin{macrocode}
+\newdimen\tagshift@
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\mintagsep}
+%    \cs{mintagsep} is the minimum allowable separation between an
+%    equation and its tag.  We set it to half a quad in
+%    \cs{textfont}2, which is \tex/'s built-in value.
+%    \begin{macrocode}
+\newcommand{\mintagsep}{.5\fontdimen6\textfont\tw@}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\minalignsep}
+%    This should probably be a skip register [mjd,1999/06/18]
+%    \begin{macrocode}
+\newcommand{\minalignsep}{10pt}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\tagwidth@}
+%    \begin{macrocode}
+\newdimen\tagwidth@
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\totwidth@}
+%    \begin{macrocode}
+\newdimen\totwidth@
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lineht@}
+%    The dimen register \cs{lineht@} is used to keep track of the
+%    height (or depth, if tags are on the right) of a row in an
+%    alignment.
+%    \begin{macrocode}
+\newdimen\lineht@
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\tag@width}
+%    \begin{macro}{\savetaglength@}
+%    \begin{macro}{\shift@tag}
+%    \begin{macro}{\tag@shifts}
+%    \begin{macrocode}
+\def\tag@width#1{%
+    \ifcase\@xp#1\tag@lengths\fi
+}
+
+\def\savetaglength@{%
+    \begingroup
+        \let\or\relax
+        \xdef\tag@lengths{\tag@lengths\or \the\wdz@}%
+    \endgroup
+}
+
+\def\shift@tag#1{%
+    \ifcase\@xp#1\tag@shifts\fi\relax
+}
+
+\let\tag@shifts\@empty
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\saveshift@}
+%    \begin{macrocode}
+\def\saveshift@#1{%
+    \begingroup
+        \let\or\relax
+        \xdef\tag@shifts{\or#1\tag@shifts}%
+    \endgroup
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%  \begin{macro}{\spread@equation}
+%    This does the line-spacing adjustment that is normally wanted for
+%    displayed equations. We also call \cs{reset@strutbox@} here because
+%    otherwise a preceding font size change might leave \cs{strutbox@}
+%    with wrong contents. This is a less-than-ideal solution but
+%    probably good enough for now, until the situation can be
+%    overhauled.
+%    \begin{macrocode}
+\def\spread@equation{\reset@strutbox@
+  \openup\jot \let\spread@equation\@empty}
+\let\@spread@equation\spread@equation
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\displ@y}
+% \begin{macro}{\displ@y@}
+% \begin{macro}{\@display@init}
+%    \cs{displ@y} is from \fn{plain.tex}, with
+%    \cs{interdisplaylinepenalty} changed to \cs{@eqpen}. Also we
+%    transplanted most of its internal organs to \cs{@display@init} to
+%    support \cs{displ@y@} and other possibilities. Don't try to make
+%    sense of these naming conventions! They are a narrowly calculated
+%    mishmash of Knuth/Spivak/Lamport/Mittelbach precedents. The reason
+%    for not cleaning them up and forcing all names to a consistent
+%    scheme is that then in principle we'd have to do it everywhere else
+%    too. And we programmers are paranoid about the side effects of name
+%    changes.
+%    \begin{macrocode}
+\def\displ@y{\@display@init{}}
+\def\@display@init#1{%
+    \global\dt@ptrue \spread@equation
+    \everycr{%
+        \noalign{%
+            #1%
+            \ifdt@p
+                \global\dt@pfalse
+                \vskip-\lineskiplimit
+                \vskip\normallineskiplimit
+            \else
+                \penalty\@eqpen \global\dspbrk@lvl\m@ne
+            \fi
+        }%
+    }%
+}
+%    \end{macrocode}
+%    \cs{displ@y@} is nearly the same; it additionally sets the |tag@|
+%    switch and the \cs{column@} and \cs{dspbrk@lvl} counters to their
+%    default values. The argument is normally a bit of code to empty out
+%    \cs{raise@tag}, but in \env{multline} we don't want that to happen
+%    in \cs{everycr}.
+%    \begin{macrocode}
+\def\displ@y@{\@display@init{%
+  \global\column@\z@ \global\dspbrk@lvl\m@ne
+  \global\tag@false \global\let\raise@tag\@empty
+}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\black@}
+% \changes{v2.17a}{2017/09/02}{add fixed width box so overfull warning generated in centred environments in lists}
+%    This macro is made to produce an overfull box message and
+%    possibly (depending on the value of \cs{overfullrule})
+%    a rule in the margin if the total width of an alignment
+%    is larger than the value of \cs{displaywidth}.
+%    \begin{macrocode}
+\def\black@#1{%
+    \noalign{%
+        \ifdim#1>\displaywidth
+            \dimen@\prevdepth
+            \nointerlineskip
+            \vskip-\ht\strutbox@
+            \vskip-\dp\strutbox@
+            \vbox{\noindent\hbox to\displaywidth{\hbox to#1{\strut@\hfill}}}%
+            \prevdepth\dimen@
+        \fi
+    }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\savecounters@}
+%    \begin{macro}{\restorecounters@}
+%    These are used during the measuring phase of the various display
+%    math environments to save and restore the values of all \latex/
+%    counters. We make these local to a group, so nested environments
+%    works.
+%
+%    Changed \cn{stepcounter} to |\csname c@...\endcsname| to avoid
+%    overhead of ifundefined test [mjd, 1995/01/20].
+%    \begin{macrocode}
+\def\savecounters@{%
+    \begingroup
+        \def\@elt##1{%
+          \global\csname c@##1\endcsname\the\csname c@##1\endcsname}%
+        \xdef\@gtempa{%
+            \cl@@ckpt
+            \let\@nx\restorecounters@\@nx\@empty
+        }%
+    \endgroup
+    \let\restorecounters@\@gtempa
+}
+%
+\let\restorecounters@\@empty
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%    \begin{macro}{\savealignstate@}
+%    \begin{macro}{\restorealignstate@}
+%    These are used to save the values of various parameters that are
+%    shared by \env{align} and \env{gather} when the former is used
+%    inside the latter.
+%    \begin{macrocode}
+\def\savealignstate@{%
+    \begingroup
+        \let\or\relax
+        \xdef\@gtempa{%
+            \global\totwidth@\the\totwidth@
+            \global\row@\the\row@
+            \gdef\@nx\tag@lengths{\tag@lengths}%
+            \let\@nx\restorealignstate@\@nx\@empty
+        }%
+    \endgroup
+    \let\restorealignstate@\@gtempa
+}
+
+\let\restorealignstate@\@empty
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\savecolumn@}
+%  \begin{macro}{\restorecolumn@}
+%
+%    \begin{macrocode}
+\def\savecolumn@{%
+  \edef\restorecolumn@{%
+    \global\column@\number\column@
+    \let\@nx\restorecolumn@\@nx\@empty
+  }%
+}
+\let\restorecolumn@\@empty
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%
+% \subsection{Scanning the environment's body}
+%
+%    Several of the math alignment macros must scan their body twice:
+%    once to determine how wide the columns are and then to actually
+%    typeset them. This means that we must collect all text in this body
+%    before calling the environment macros.
+%
+%    \begin{macro}{\@envbody}
+%    We start by defining a token register to contain the body.
+%    \begin{macrocode}
+\newtoks\@envbody
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\addto@envbody}
+%    Then we define a macro to add something (i.e.\ its argument) to the
+%    token register \cs{@envbody}.
+%    \begin{macrocode}
+\def\addto@envbody#1{\global\@envbody\@xp{\the\@envbody#1}}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\collect@body}
+%    The macro \cs{collect@body} starts the scan for the |\end{...}|
+%    command of the current environment. It takes a macro name as
+%    argument. This macro is supposed to take the whole body of the
+%    environment as its argument. For example, |\begin{align}| would
+%    call |\collect@body\@align| if |@align#1{...}| is the macro that
+%    sets the alignment with body \arg{1}.
+%
+%    \begin{macrocode}
+\def\collect@body#1{%
+  \@envbody{\@xp#1\@xp{\the\@envbody}}%
+  \edef\process@envbody{\the\@envbody\@nx\end{\@currenvir}}%
+  \@envbody\@emptytoks \def\begin@stack{b}%
+%    \end{macrocode}
+%
+%    If we simply called \cs{collect@@body} directly,
+%    the error message for a \cn{par} token (usually from a blank line)
+%    would be
+% \begin{verbatim}
+% ! Paragraph ended before \collect@@body was complete.
+% \end{verbatim}
+%    But we use a little finesse to get a more intelligible error
+%    message:
+% \begin{verbatim}
+% ! Paragraph ended before \multline* was complete.
+% \end{verbatim}
+%    In order to avoid using up csnames unnecessarily we use the actual
+%    environment name as the name of the temporary function that is
+%    \cs{let} to \cs{collect@@body}; but then in order to preserve the
+%    theoretical possibility of nesting for environments that use
+%    \cs{collect@body} (not currently required by any \pkg{amsmath}
+%    environment [mjd,1999/06/23]), we do the \cs{let} inside a group.
+%    \begin{macrocode}
+  \begingroup
+  \@xp\let\csname\@currenvir\endcsname\collect@@body
+%    \end{macrocode}
+%    This small twist eliminates the need for \cs{expandafter}'s in
+%    \cs{collect@@body}.
+%    \begin{macrocode}
+  \edef\process@envbody{\@xp\@nx\csname\@currenvir\endcsname}%
+  \process@envbody
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\push@begins}
+%    When adding a piece of the current environment's contents to
+%    \cs{@envbody}, we scan it to check for additional \cn{begin}
+%    tokens, and add a `b' to the stack for any that we find.
+%    \begin{macrocode}
+\def\push@begins#1\begin#2{%
+  \ifx\end#2\else b\@xp\push@begins\fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\collect@@body}
+%    \cs{collect@@body} takes two arguments: the first will consist of
+%    all text up to the next \cn{end} command, the second will be the
+%    \cn{end} command's argument. If there are any extra \cn{begin}
+%    commands in the body text, a marker is pushed onto a stack by the
+%    \cs{push@begins} function. Empty state for this stack means that we
+%    have reached the \cn{end} that matches our original \cn{begin}.
+%    Otherwise we need to include the \cn{end} and its argument in the
+%    material that we are adding to our environment body accumulator.
+%
+% \begin{histnote}
+%    In a former implementation, the error messages resulting from a
+%    typo in the environment name were unsatisfactory, because it was
+%    matching of the environment name that was used to determine the end
+%    of our environment body, instead of counting begin-end pairs.
+%    Thanks to Lars Hellstr\"{o}m for a suggestion that led to this
+%    improvement. [mjd,1999/06/23]
+% \end{histnote}
+%    \begin{macrocode}
+\def\collect@@body#1\end#2{%
+  \edef\begin@stack{\push@begins#1\begin\end \@xp\@gobble\begin@stack}%
+  \ifx\@empty\begin@stack
+    \endgroup
+    \@checkend{#2}%
+    \addto@envbody{#1}%
+  \else
+    \addto@envbody{#1\end{#2}}%
+  \fi
+  \process@envbody % A little tricky! Note the grouping
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Simple aligning environments}
+%
+%  \begin{macro}{\math@cr@@@aligned}
+%    From tabskip we get an extra space of minalignsep after every
+%    second column; but when this falls at the right edge of the whole
+%    aligned structure, we need to cancel that space.
+%    \begin{macrocode}
+\def\math@cr@@@aligned{%
+  \ifodd\column@ \let\next@\@empty
+  \else \def\next@{&\kern-\alignsep@}%
+  \fi
+  \next@ \cr
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    \begin{macro}{\start@aligned}
+%    The \env{aligned} and \env{alignedat} environments are identical
+%    except that the latter takes a mandatory argument to specify the
+%    number of align structures, while the former allows any number of
+%    align structures automatically (the use of \env{alignedat} is
+%    deprecated).  So, they will be defined in terms of
+%    \cs{start@aligned}, which will take two arguments.  The first
+%    argument specifies the placement of the environments; it is
+%    either |c|, |t|, or |b|.  The second is the number of align
+%    structures; a value of~$-1$ means that an arbitrary number are
+%    allowed.
+%    \begin{macrocode}
+\newcommand{\start@aligned}[2]{%
+    \RIfM@\else
+        \nonmatherr@{\begin{\@currenvir}}%
+    \fi
+    \savecolumn@ % Assumption: called inside a group
+%    \end{macrocode}
+%    The \cs{null} here is to keep the \cs{,} glue from causing the
+%    invocation of the clause in \tex/'s built-in tag placement
+%    algorithm that can cause an equation to be shifted all the way over
+%    to the margin.
+%    \begin{macrocode}
+    \alignedspace@left
+    \if #1t\vtop \else \if#1b \vbox \else \vcenter \fi \fi \bgroup
+        \maxfields@#2\relax
+        \ifnum\maxfields@>\m@ne
+            \multiply\maxfields@\tw@
+%    \end{macrocode}
+%    Introduced new \cs{math@cr@@@} so we can provide standard error
+%    message for too many \qc{\&}'s in \env{alignedat}.
+%    \begin{macrocode}
+            \let\math@cr@@@\math@cr@@@alignedat
+            \alignsep@\z@skip
+        \else
+            \let\math@cr@@@\math@cr@@@aligned
+            \alignsep@\minalignsep
+        \fi
+%    \end{macrocode}
+%    Reset the meaning of \cn{\\}.
+%    \begin{macrocode}
+        \Let@ \chardef\dspbrk@context\@ne
+%    \end{macrocode}
+%    Restore the default definition of \cn{tag} (error message), in
+%    case \env{aligned} is used inside, e.g., a \env{gather}
+%    environment that accepts \cn{tag}.
+%    \begin{macrocode}
+        \default@tag
+        \spread@equation % no-op if already called
+%    \end{macrocode}
+%    Finally we start the alignment itself. For \env{aligned} we add
+%    \cs{minalignsep} after every second column to mimic the
+%    behavior of \env{align}. For \env{alignedat} the user has to
+%    specify interalign space explicitly.
+%    \begin{macrocode}
+        \global\column@\z@
+        \ialign\bgroup
+           &\column@plus
+            \hfil
+            \strut@
+            $\m@th\displaystyle{##}$%
+            \tabskip\z@skip
+           &\column@plus
+            $\m@th\displaystyle{{}##}$%
+            \hfil
+            \tabskip\alignsep@
+            \crcr
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\math@cr@@@alignedat}
+%    \cs{math@cr@@@alignedat} checks to make sure the user hasn't put in
+%    too many \qc{\&}s in \env{alignedat}.  Since \env{alignedat}
+%    doesn't use \cs{displ@y@}, we also reset \cs{column@} here.  Note
+%    than in \env{aligned}, \cs{column@} will increase without bound,
+%    since it never gets reset, but this is harmless.
+%    \begin{macrocode}
+\def\math@cr@@@alignedat{%
+    \ifnum\column@>\maxfields@
+        \begingroup
+          \measuring@false
+          \@amsmath@err{Extra & on this line}%
+            {\the\andhelp@}% "An extra & here is disastrous"
+        \endgroup
+    \fi
+    \global\column@\z@
+    \cr
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%  \begin{macro}{\alignsafe@testopt}
+%    Testing for an optional argument can be really, really tricky in
+%    certain complicated contexts. This we discovered by getting some
+%    bug reports for uses of \env{aligned}. So here is a safer
+%    form of \latex/'s \cs{@testopt} function.
+%    \begin{macrocode}
+\def\alignsafe@testopt#1#2{%
+  \relax\iffalse{\fi\ifnum`}=0\fi
+  \@ifnextchar[%
+    {\let\@let@token\relax \ifnum`{=\z@\fi\iffalse}\fi#1}%
+    {\let\@let@token\relax \ifnum`{=\z@\fi\iffalse}\fi#1[#2]}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{environment}{aligned}
+%    The \env{aligned} environment takes an optional argument that
+%    indicates its vertical position in relation to surrounding
+%    material: |t|, |c|, or |b| for top, center, or bottom.
+%    \begin{macrocode}
+\newenvironment{aligned}{%
+  \let\@testopt\alignsafe@testopt
+  \aligned@a
+}{%
+  \crcr\egroup
+  \restorecolumn@
+  \egroup
+}
+\newcommand{\aligned@a}[1][c]{\start@aligned{#1}\m@ne}
+%    \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{alignedat}
+%    To get a top or bottom positioned \env{alignedat} structure, you
+%    would write something like
+% \begin{verbatim}
+% \begin{alignedat}[t]{3}
+% \end{verbatim}
+%
+%    \begin{macrocode}
+\newenvironment{alignedat}{%
+  \let\@testopt\alignsafe@testopt
+  \alignedat@a
+}{%
+  \endaligned
+}
+\newcommand{\alignedat@a}[1][c]{\start@aligned{#1}}
+%    \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{gathered}
+%    The \env{gathered} environment is for several lines that are
+%    centered independently.
+%    \begin{macrocode}
+\newenvironment{gathered}[1][c]{%
+    \RIfM@\else
+        \nonmatherr@{\begin{gathered}}%
+    \fi
+    \alignedspace@left
+    \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi \bgroup
+        \Let@ \chardef\dspbrk@context\@ne \restore@math@cr
+        \spread@equation
+        \ialign\bgroup
+            \hfil\strut@$\m@th\displaystyle##$\hfil
+            \crcr
+}{%
+  \endaligned
+}
+%    \end{macrocode}
+% \end{environment}
+%
+%
+%    \subsection{The \env{gather} environment}
+%
+% \begin{macro}{\start@gather}
+%    \begin{macrocode}
+\def\start@gather#1{%
+    \RIfM@
+        \nomath@env
+        \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+    \else
+        $$%
+        #1%
+        \ifst@rred \else \global\@eqnswtrue \fi
+        \let\next@\gather@
+    \fi
+    \collect@body\next@
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{environment}{gather}
+%    \begin{environment}{gather*}
+%    \begin{macrocode}
+\newenvironment{gather}{%
+  \start@gather\st@rredfalse
+}{%
+  \math@cr \black@\totwidth@ \egroup
+  $$\ignorespacesafterend
+}
+
+\newenvironment{gather*}{%
+  \start@gather\st@rredtrue
+}{%
+  \endgather
+}
+%    \end{macrocode}
+%    \end{environment}
+%    \end{environment}
+%
+%    \begin{macro}{\gather@}
+%    \begin{macrocode}
+\def\gather@#1{%
+    \ingather@true \let\split\insplit@
+    \let\tag\tag@in@align \let\label\label@in@display
+    \chardef\dspbrk@context\z@
+    \intertext@ \displ@y@ \Let@
+    \let\math@cr@@@\math@cr@@@gather
+    \gmeasure@{#1}%
+    \global\shifttag@false
+    \tabskip\z@skip
+    \global\row@\@ne
+    \halign to\displaywidth\bgroup
+        \strut@
+        \setboxz@h{$\m@th\displaystyle{##}$}%
+        \calc@shift@gather
+        \set@gather@field
+        \tabskip\@centering
+       &\setboxz@h{\strut@{##}}%
+        \place@tag@gather
+        \tabskip \iftagsleft@ \gdisplaywidth@ \else \z@skip \span\fi
+        \crcr
+        #1%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\gmeasure@}
+%    \begin{macrocode}
+\def\gmeasure@#1{%
+    \begingroup
+        \measuring@true
+        \totwidth@\z@
+        \global\let\tag@lengths\@empty
+        \savecounters@
+        \setbox\@ne\vbox{%
+            \everycr{\noalign{\global\tag@false
+              \global\let\raise@tag\@empty \global\column@\z@}}%
+            \let\label\@gobble
+            \halign{%
+                \setboxz@h{$\m@th\displaystyle{##}$}%
+                \ifdim\wdz@>\totwidth@
+                    \global\totwidth@\wdz@
+                \fi
+               &\setboxz@h{\strut@{##}}%
+                \savetaglength@
+                \crcr
+                #1%
+                \math@cr@@@
+            }%
+        }%
+        \restorecounters@
+        \if@fleqn
+            \global\advance\totwidth@\@mathmargin
+        \fi
+        \iftagsleft@
+            \ifdim\totwidth@>\displaywidth
+                \global\let\gdisplaywidth@\totwidth@
+            \else
+                \global\let\gdisplaywidth@\displaywidth
+            \fi
+        \fi
+    \endgroup
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\math@cr@@@gather}
+%    Modified \cs{math@cr@@@gather} so that it always puts in the
+%    final field, which needs to be done under the new method for
+%    determining tag placement.  This is probably more efficient
+%    anyway.
+%
+%    \begin{macrocode}
+\def\math@cr@@@gather{%
+    \ifst@rred\nonumber\fi
+   &\relax
+    \make@display@tag
+    \ifst@rred\else\global\@eqnswtrue\fi
+%    \end{macrocode}
+%    We advance \cs{row@} here, rather than at the beginning of the
+%    preamble, because otherwise the \env{split} environment will
+%    cause \cs{row@} to be advanced twice instead of once.
+%    \begin{macrocode}
+    \global\advance\row@\@ne
+    \cr
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\calc@shift@gather}
+%    \cs{calc@shift@gather} has must make two decisions: (1) whether the
+%    equation tag for the current line should be put on a separate
+%    line and (2) what the distance between the equation and the
+%    equation tag should be.  We implement \tex/'s built-in
+%    tag-placement as well as possible, with one improvement: the
+%    minimum separation between tag and equation is now a
+%    user-settable parameter.
+%
+%    [1995/01/17] Added a check to make sure that the width of the tag
+%    on the current line is $>0$ before testing to see if tagwidth +
+%    linewidth + mintagsep $>$ displaywidth. Since an imbedded align
+%    shows up as line with width \cn{displaywidth}, and even lines
+%    without a tag get processed as if an empty tag were present, the
+%    result was that the empty tag assigned to the line containing the
+%    align was being shifted downwards, creating extra space after the
+%    align.
+%    \begin{macrocode}
+\def\calc@shift@gather{%
+    \dimen@\mintagsep\relax
+    \tagwidth@\tag@width\row@\relax
+%    \end{macrocode}
+%    If we're in \opt{fleqn} mode, there is no flexibility about
+%    placement of the equation, so all we can do is see if there's
+%    room for the tag in the given margin.
+%    \begin{macrocode}
+    \if@fleqn
+        \global\eqnshift@\@mathmargin
+        \ifdim\tagwidth@>\z@
+            \advance\dimen@\tagwidth@
+            \iftagsleft@
+                \ifdim\dimen@>\@mathmargin
+                    \global\shifttag@true
+                \fi
+            \else
+                \advance\dimen@\@mathmargin
+                \advance\dimen@\wdz@
+                \ifdim\dimen@>\displaywidth
+                   \global\shifttag@true
+                \fi
+            \fi
+        \fi
+    \else
+        \global\eqnshift@\displaywidth
+        \global\advance\eqnshift@-\wdz@
+        \ifdim\tagwidth@>\z@
+            \multiply\dimen@\tw@
+            \advance\dimen@\wdz@
+            \advance\dimen@\tagwidth@
+            \ifdim\dimen@>\displaywidth
+                \global\shifttag@true
+            \else
+                \ifdim\eqnshift@<4\tagwidth@
+                    \global\advance\eqnshift@-\tagwidth@
+                \fi
+            \fi
+        \fi
+        \global\divide\eqnshift@\tw@
+        \iftagsleft@
+            \global\eqnshift@-\eqnshift@
+            \global\advance\eqnshift@\displaywidth
+            \global\advance\eqnshift@-\wdz@
+        \fi
+        \ifdim\eqnshift@<\z@
+            \global\eqnshift@\z@
+        \fi
+    \fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\place@tag@gather}
+%    \begin{macro}{\set@gather@field}
+%    \begin{macrocode}
+\def\place@tag@gather{%
+    \iftagsleft@
+        \kern-\gdisplaywidth@
+        \ifshifttag@
+            \rlap{\vbox{%
+                \normalbaselines
+                \boxz@
+                \vbox to\lineht@{}%
+                \raise@tag
+            }}%
+            \global\shifttag@false
+        \else
+            \rlap{\boxz@}%
+        \fi
+    \else
+        \ifdim\totwidth@>\displaywidth
+            \dimen@\totwidth@
+            \advance\dimen@-\displaywidth
+            \kern-\dimen@
+        \fi
+        \ifshifttag@
+            \llap{\vtop{%
+                \raise@tag
+                \normalbaselines
+                \setbox\@ne\null
+                \dp\@ne\lineht@
+                \box\@ne
+                \boxz@
+            }}%
+            \global\shifttag@false
+        \else
+            \llap{\boxz@}%
+        \fi
+    \fi
+}
+%
+\def\set@gather@field{%
+    \iftagsleft@
+        \global\lineht@\ht\z@
+    \else
+        \global\lineht@\dp\z@
+    \fi
+    \kern\eqnshift@
+    \boxz@
+    \hfil
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%
+% \subsection{The \env{align} family of environments}
+%
+%    The \env{align}, \env{flalign}, \env{alignat}, \env{xalignat},
+%    and \env{xxalignat} environments are virtually
+%    identical, and thus will share much code.  We'll refer to the
+%    environments generically as ``\env{align}'' and will
+%    distinguish between them explicitly
+%    only when necessary.
+%
+% \begin{macro}{\ifxxat@}
+% \begin{macro}{\ifcheckat@}
+% \begin{macro}{\xatlevel@}
+%    The \cs{xatlevel@} macro will be used, informally speaking, to
+%    distinguish between the \env{alignat} and \env{xalignat}, and
+%    \env{xxalignat} environments.
+%
+%    \begin{macrocode}
+\newif\ifxxat@
+
+\newif\ifcheckat@
+
+\let\xatlevel@\@empty
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% \begin{macro}{\start@align}
+%    \cs{start@align} will be called by all of the \env{align}-like
+%    environments.  The first argument will be the \cs{xatlevel@},
+%    i.e., 0, 1, or~2; the second argument will be either
+%    \cs{st@rredtrue} or \cs{st@rredfalse}.  The third argument will
+%    be the number of aligned
+%    structures in the environment (either as supplied by the user, or
+%    $-1$ to indicate that checking shouldn't be done).  After
+%    performing the appropriate error detection and initialization,
+%    \cs{start@align} calls \cs{align@}.
+%
+%    Note that the \cs{equation} counter is no longer stepped at the
+%    beginning of these environments.
+%
+%    TODO: Implement \cs{shoveleft} and \cs{shoveright} for
+%    \env{align}.
+%    \begin{macrocode}
+\def\start@align#1#2#3{%
+    \let\xatlevel@#1% always \z@, \@ne, or \tw@
+    \maxfields@#3\relax
+    \ifnum\maxfields@>\m@ne
+        \checkat@true
+        \ifnum\xatlevel@=\tw@
+            \xxat@true
+        \fi
+        \multiply\maxfields@\tw@
+    \else
+        \checkat@false
+    \fi
+    \ifingather@
+        \iffalse{\fi\ifnum0=`}\fi
+        \DN@{\vcenter\bgroup\savealignstate@\align@#2}%
+    \else
+        \ifmmode
+          \if@display
+             \DN@{\align@recover}%
+          \else
+            \nomath@env
+            \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+          \fi
+        \else
+            $$%
+            \let\split\insplit@
+            \DN@{\align@#2}%
+        \fi
+    \fi
+    \collect@body\next@
+}
+%    \end{macrocode}
+%
+%    With version 1.2 of \pkg{amsmath}, it was possible to use
+%    \env{align*} and relatives in certain wrong contexts without
+%    getting an error, e.g.
+% \begin{verbatim}
+% \begin{equation*}
+% \begin{align*}
+% ...
+% \end{align*}
+% \end{equation*}
+% \end{verbatim}
+%
+%    For backward compatibility we therefore give only a warning for
+%    this condition instead of a full error, and try to recover using
+%    the \env{aligned} environment. The alignment of the material may be
+%    adversely affected but it will at least remain readable.
+%    \begin{macrocode}
+\def\align@recover#1#2#3{%
+  \endgroup
+  \@amsmath@err{%
+Erroneous nesting of equation structures;\MessageBreak
+trying to recover with `aligned'%
+  }\@ehc
+  \begin{aligned}\relax#1\end{aligned}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{environment}{align}
+%    \begin{environment}{align*}
+%    \begin{environment}{flalign}
+%    \begin{environment}{flalign*}
+%    \begin{environment}{alignat}
+%    \begin{environment}{alignat*}
+%    \begin{environment}{xalignat}
+%    \begin{environment}{xalignat*}
+%    \begin{environment}{xxalignat}
+%    The definitions of the various \env{align} environments are quite
+%    straight-forward.
+%
+%    \begin{macrocode}
+\newenvironment{alignat}{%
+  \start@align\z@\st@rredfalse
+}{%
+  \endalign
+}
+\newenvironment{alignat*}{%
+  \start@align\z@\st@rredtrue
+}{%
+  \endalign
+}
+\newenvironment{xalignat}{%
+  \start@align\@ne\st@rredfalse
+}{%
+  \endalign
+}
+\newenvironment{xalignat*}{%
+  \start@align\@ne\st@rredtrue
+}{%
+  \endalign
+}
+\newenvironment{xxalignat}{%
+  \start@align\tw@\st@rredtrue
+}{%
+  \endalign
+}
+\newenvironment{align}{%
+  \start@align\@ne\st@rredfalse\m@ne
+}{%
+  \math@cr \black@\totwidth@
+  \egroup
+  \ifingather@
+    \restorealignstate@
+    \egroup
+    \nonumber
+    \ifnum0=`{\fi\iffalse}\fi
+  \else
+    $$%
+  \fi
+  \ignorespacesafterend
+}
+\newenvironment{align*}{%
+  \start@align\@ne\st@rredtrue\m@ne
+}{%
+  \endalign
+}
+\newenvironment{flalign}{%
+  \start@align\tw@\st@rredfalse\m@ne
+}{%
+  \endalign
+}
+\newenvironment{flalign*}{%
+  \start@align\tw@\st@rredtrue\m@ne
+}{%
+  \endalign
+}
+%    \end{macrocode}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%    \end{environment}
+%
+%
+%  \begin{macro}{\align@}
+%    TODO: Some of these sets of initializations show up in multiple
+%    places.  It might be worth making an abbreviation for them.
+%
+%    \begin{macrocode}
+\def\align@#1#2{%
+    \inalign@true \intertext@ \Let@ \chardef\dspbrk@context\z@
+    \ifingather@\else\displ@y@\fi
+    \let\math@cr@@@\math@cr@@@align
+    \ifxxat@\else \let\tag\tag@in@align \fi
+    \let\label\label@in@display
+    #1% set st@r
+    \ifst@rred\else \global\@eqnswtrue \fi
+    \measure@{#2}%
+    \global\row@\z@
+    \tabskip\eqnshift@
+    \halign\bgroup
+        \span\align@preamble\crcr
+        #2%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\math@cr@@@align}
+%    \begin{macrocode}
+\def\math@cr@@@align{%
+  \ifst@rred\nonumber\fi
+  \if@eqnsw \global\tag@true \fi
+  \global\advance\row@\@ne
+  \add@amps\maxfields@
+  \omit
+  \kern-\alignsep@
+  \iftag@
+    \setboxz@h{\@lign\strut@{\make@display@tag}}%
+    \place@tag
+  \fi
+  \ifst@rred\else\global\@eqnswtrue\fi
+  \global\lineht@\z@
+  \cr
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\math@cr@@@align@measure}
+%    \begin{macrocode}
+\def\math@cr@@@align@measure{%
+   &\omit
+    \global\advance\row@\@ne
+    \ifst@rred\nonumber\fi
+    \if@eqnsw \global\tag@true \fi
+    \ifnum\column@>\maxfields@
+        \ifcheckat@
+            \begingroup
+              \measuring@false
+              \@amsmath@err{Extra & on this line}%
+                {\the\andhelp@}% "An extra & here is disastrous"
+            \endgroup
+        \else
+            \global\maxfields@\column@
+        \fi
+    \fi
+    \setboxz@h{\@lign\strut@{%
+        \if@eqnsw
+            \stepcounter{equation}%
+            \tagform@\theequation
+        \else
+            \iftag@\df@tag\fi
+        \fi
+    }}%
+    \savetaglength@
+    \ifst@rred\else\global\@eqnswtrue\fi
+    \cr
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\field@lengths}
+%    \begin{macro}{\savefieldlength@}
+%    \begin{macro}{\fieldlengths@}
+%    \begin{macrocode}
+\let\field@lengths\@empty
+
+\def\savefieldlength@{%
+    \begingroup
+        \let\or\relax
+        \xdef\field@lengths{%
+            \field@lengths
+            \ifnum\column@=0
+                \or
+            \else
+                ,%
+            \fi
+            \the\wdz@
+        }%
+    \endgroup
+}
+
+\def\fieldlengths@#1{%
+    \ifcase\@xp#1\field@lengths\fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%  \begin{macro}{\maxcolumn@widths}
+%    \cs{maxcolumn@widths} will be used to hold the widths of the
+%    fields of the \env{alignat} environment.  The widths will be
+%    separated by the token \cn{or}, making it easy to extract a given
+%    width using \cn{ifcase}.
+%    \begin{macrocode}
+\let\maxcolumn@widths\@empty
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\maxcol@width}
+% \cs{maxcol@width} $n$ = maximum width of $n$th column of the current
+%    \env{alignat} (i.e., the $n$th field of \cs{maxcolumn@widths}.)
+%    It expands to a \<dimen>, so it can be used as the right-hand
+%    side of a \<variable assignment> or \<arithmetic> statement.
+%    It's argument can be any \<number>, \<integer variable> or macro
+%    that expands to one of these.  [Check to make sure this is true.]
+%
+%    This is subtler than it looks.
+%    \begin{macrocode}
+\def\maxcol@width#1{%
+    \ifcase\@xp#1\maxcolumn@widths\fi\relax
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    Now comes the real fun.  A typical \env{align} environments looks
+%    something like this, where the vertical bars mark the edges of
+%    the fields of the underlying \cs{halign}:
+%    \[
+%    \makeatletter\tabskip\@centering\offinterlineskip
+%    \halign to\displaywidth{%^^A
+%       &$\strut$\vrule\hfil$\m@th\displaystyle{\@lign#}$\vrule
+%      \tabskip1pt&\vrule$\m@th\displaystyle{\@lign#}$\hfil\vrule
+%      \tabskip\@centering\cr
+%    \omit\small\hfil 1\hfil &\omit\small\hfil 2 &\omit\small\hfil
+%    3\hfil &\omit\small\hfil 4\hfil & \omit\small\hfil 5\hfil
+%    &\omit\small\hfil 6\hfil\cr
+%    \noalign{\vskip8pt\relax}
+%    V_i + q_i v_j & =v_i , &  X_i & = x_i - q_i x_j,
+%     &  U_i & = u_i,\qquad
+%      \hbox{for $i\ne j$;} %&\omit\hfill \llap{(3)}
+%    \cr
+%    V_j & = v_j, &  X_j & = x_j,
+%      &  U_j & = u_j + \sum_{i\ne j} q_i u_i. %&\omit\hfill \llap{(4)}
+%    \cr}
+%    \]
+%    Note that each align structure consists of two fields, with no
+%    space between them (a small space has been added here to
+%    highlight the boundaries).  Furthermore, the text inside the
+%    odd-numbered fields is flushright, while the text inside the
+%    even-numbered fields is flushleft.  The equation tags (shown on
+%    the right here) can be on either the right or the left.  If there
+%    is not room (in a sense to be defined shortly) for the tag on the
+%    same line as the equation, the tag will be shifted to a separate
+%    line.
+%
+%    Each environment also has a certain number of ``flexible
+%    spaces,'' meaning spaces whose width we are allowed to adjust to
+%    take up the amount of ``free space'' in the line, meaning the
+%    space not taken up by the equation tag and the fields of the
+%    underlying \cs{halign}.
+%
+%    The flexible spaces come in two flavors: interalign spaces and
+%    margin spaces.  If there are $n$ align structures ($n=3$ in the
+%    illustration above), there are $n-1$ interalign spaces, unless we
+%    are in an \env{alignat} environment, in which case there are no
+%    flexible interalign spaces.
+%
+%    The number of margin spaces is a little more complicated:
+%    Normally, there are two, but if we're in \opt{fleqn} mode, there
+%    is only one.  Furthermore, if we're in an \env{xxalignat} or
+%    \env{flalign} environment (corresponding to $\cs{xatlevel@} = 2$,
+%    then there are no flexible margin spaces.
+%
+%    Calculating the interalign and margin spaces is done in two
+%    stages.
+%
+%    First, the total amount of free space is divided uniformly among
+%    all the flexible spaces, without regard for the lengths of the tags
+%    on the various lines. For the non-\opt{fleqn} case, this
+%    corresponds to centering the align structures between the margins.
+%    Note that in \opt{fleqn} mode, the right margin is still allowed to
+%    be larger than \cs{@mathmargin}. This introduces an element of
+%    asymmetry into the appearance of the environment, but it has the
+%    advantage of leaving more space for equation tags in the right
+%    margin. If the right margin were constrained to be equal to the
+%    left margin in this case, tags would need to be shifted to a
+%    separate line more often than would be desirable.
+%
+%    Ordinarily, all flexible spaces will be given the same width.
+%    However, this is not invariably true, since the interalign spaces
+%    are constrained to be at least \cs{minalignsep} wide, while---in
+%    the absence of equation tags, at least---the margin spaces are
+%    allowed to shrink to zero.  As we shall see in a minute, if there
+%    are tags in the environment, then the margins are also bounded
+%    below by \cs{mintagsep}.
+%
+%    Next, we examine each line of the environment that has a tag to
+%    see if there is a gap of at least \cs{mintagsep} between the
+%    equation and its tag.  If there isn't, we attempt to center the
+%    equation between the tag and the opposite margin, leaving a gap
+%    of at least \cs{mintagsep} on either side, in order to preserve
+%    some symmetry, i.e., we want the equation to \emph{look} like
+%    it's centered between the margin and the tag, so we don't want
+%    the margin space to be less than the gap between the tag and the
+%    equation.  (Arguably, it would be better to allow the margin
+%    space to shrink to zero in this case in order to avoid shifting
+%    the tag to a separate line at any cost, but that would require
+%    all of our calculations to be a little more complicated and hence
+%    a little slower.)  Finally, if no values of the interalign spaces
+%    and the margins (with the constraints outlined above) will
+%    produce an acceptable distance between the equation and its tag,
+%    then the tag will be shifted to a separate line.
+%
+%  \begin{macro}{\measure@}
+%    \cs{measure@} collects the various bits of information that we'll
+%    need to perform the calculations outlined above, namely, the
+%    number of align structures in the environment, the natural
+%    lengths of the fields on each row, the maximum widths of each
+%    column, and the widths of the equation tags on each line.  It
+%    also calculates the number of flexible interalign and margin
+%    spaces and computes the initial values of the parameters
+%    \cs{eqnshift@} and \cs{alignsep@}, which correspond to the widths
+%    of the margins and the interalign spaces, respectively.
+%    \begin{macrocode}
+\def\measure@#1{%
+    \begingroup
+        \measuring@true
+        \global\eqnshift@\z@
+        \global\alignsep@\z@
+        \global\let\tag@lengths\@empty
+        \global\let\field@lengths\@empty
+        \savecounters@
+        \global\setbox0\vbox{%
+            \let\math@cr@@@\math@cr@@@align@measure
+            \everycr{\noalign{\global\tag@false
+              \global\let\raise@tag\@empty \global\column@\z@}}%
+            \let\label\@gobble
+            \global\row@\z@
+            \tabskip\z@
+            \halign{\span\align@preamble\crcr
+                #1%
+                \math@cr@@@
+                \global\column@\z@
+                \add@amps\maxfields@\cr
+            }%
+        }%
+        \restorecounters@
+%    \end{macrocode}
+%    It's convenient to have \cs{maxfields@} rounded up to the nearest
+%    even number, so that \cs{maxfields@} is precisely twice the
+%    number of align structures.
+%    \begin{macrocode}
+        \ifodd\maxfields@
+            \global\advance\maxfields@\@ne
+        \fi
+%    \end{macrocode}
+%    It doesn't make sense to have a single align structure in either
+%    \env{flalign} or \env{xxalignat}.  So, we check for that case now
+%    and, if necessary, switch to an \env{align} or \env{alignat}.
+%    Arguably, we should issue a warning message, but why bother?
+%    \begin{macrocode}
+        \ifnum\xatlevel@=\tw@
+            \ifnum\maxfields@<\thr@@
+                \let\xatlevel@\z@
+            \fi
+        \fi
+%    \end{macrocode}
+%    |\box0| now contains the lines of the \cs{halign}.  After the
+%    following maneuver, |\box1| will contain the last line of the
+%    \cs{halign}, which is what we're interested in.  (Incidentally,
+%    the penalty we're removing is the \cs{@eqpen} inserted by
+%    \cs{math@cr}.  Normally, this is \cs{interdisplaylinepenalty},
+%    unless the user has overridden that with a \cs{displaybreak}
+%    command.)
+%    \begin{macrocode}
+        \setbox\z@\vbox{%
+          \unvbox\z@ \unpenalty \global\setbox\@ne\lastbox
+        }%
+%    \end{macrocode}
+%    |\box1| begins with \cs{tabskip} glue and contains alternating
+%    \cs{hbox}es (the fields whose widths we're trying to get) and
+%    \cs{tabskip} glue [need better diagram]:
+%    \begin{verbatim}
+%    \hbox{\tabskip\hbox\tabskip...\hbox\tabskip}\end{verbatim}
+%    In fact, all the \cs{tabskip} glue will be 0pt, because all the
+%    \cs{tabskip}s in an \env{alignat} environment have a natural
+%    width of 0pt, and the \cs{halign} has been set in its natural
+%    width.
+%
+%    One nice result of this is that we can read \cs{totwidth@} off
+%    immediately, since it is just the width of |\box1|, plus
+%    \cs{@mathmargin} if we're in \opt{fleqn} mode.  (Actually, we
+%    also have to take \cs{minalignsep} into account, but we'll do
+%    that later):
+%    \begin{macrocode}
+        \global\totwidth@\wd\@ne
+        \if@fleqn \global\advance\totwidth@\@mathmargin \fi
+%    \end{macrocode}
+%    Now we initialize \cs{align@lengths} and start peeling the boxes
+%    off, one by one, and adding their widths to \cs{align@lengths}.
+%    We stop when we run out of boxes, i.e., when \cs{lastbox} returns
+%    a void box.  We're going to build a list using \cs{or} as a
+%    delimiter, so we want to disable it temporarily.
+%    \begin{macrocode}
+        \global\let\maxcolumn@widths\@empty
+        \begingroup
+          \let\or\relax
+          \loop
+            \global\setbox\@ne\hbox{%
+              \unhbox\@ne \unskip \global\setbox\thr@@\lastbox
+            }%
+          \ifhbox\thr@@
+           \xdef\maxcolumn@widths{ \or \the\wd\thr@@ \maxcolumn@widths}%
+          \repeat
+        \endgroup
+%    \end{macrocode}
+%    Now we calculate the number of flexible spaces and the initial
+%    values of \cs{eqnshift@} and \cs{alignsep@}.
+%    We start by calculating $\cs{displaywidth}-\cs{totwidth@}$,
+%    which gives us the total amount of ``free space'' in a row.
+%    \begin{macrocode}
+        \dimen@\displaywidth
+        \advance\dimen@-\totwidth@
+%    \end{macrocode}
+%    Next we calculate the number of columns of flexible spaces in the
+%    display, which depends on whether we're in \opt{fleqn} mode and
+%    in which particular environment we are in.
+%
+%    We use \cs{@tempcnta} to store the total number of flexible spaces
+%    in the align and \cs{@tempcntb} for the number of interalign
+%    spaces.
+%    \begin{macrocode}
+        \ifcase\xatlevel@
+%    \end{macrocode}
+%    In \env{alignat}, the interalign spaces are under user control,
+%    not ours.  So, we set \cs{alignsep@} and \cs{minalignsep} both
+%    equal to 0pt.  Later, when calculating a new value for
+%    \cs{alignsep@}, we will only save the new value if it is less
+%    than the current value of \cs{alignsep@} (i.e., \cs{alignsep@}
+%    will never increase).  Since the values we calculate will never
+%    be negative, this will ensure that \cs{alignsep@} remains zero in
+%    \env{alignat}.
+%    \begin{macrocode}
+            \global\alignsep@\z@
+            \let\minalignsep\z@
+            \@tempcntb\z@
+%    \end{macrocode}
+%    In \opt{fleqn} mode, the left margin---and hence the right margin
+%    in this case---is fixed.  Otherwise, we divide the free space
+%    equally between the two margins.
+%    \begin{macrocode}
+            \if@fleqn
+                \@tempcnta\@ne
+                \global\eqnshift@\@mathmargin
+            \else
+                \@tempcnta\tw@
+                \global\eqnshift@\dimen@
+                \global\divide\eqnshift@\@tempcnta
+            \fi
+        \or
+%    \end{macrocode}
+%    In an \env{align} or \env{xalignat} environment with $n$ aligned
+%    structures, there are $n-1$ interalign spaces and either 1 or~2
+%    flexible margins, depending on whether we're in \opt{fleqn} mode
+%    or not.
+%    \begin{macrocode}
+            \@tempcntb\maxfields@
+            \divide\@tempcntb\tw@
+            \@tempcnta\@tempcntb
+            \advance\@tempcntb\m@ne
+%    \end{macrocode}
+%    If we are in \opt{fleqn} mode, we fix the left margin and divide
+%    the free space equally among the interalign spaces and the right
+%    margin.
+%    \begin{macrocode}
+            \if@fleqn
+                \global\eqnshift@\@mathmargin
+                \global\alignsep@\dimen@
+                \global\divide\alignsep@\@tempcnta
+            \else
+%    \end{macrocode}
+%    Otherwise, we divide the free space equally among the interalign
+%    spaces and both margins.
+%    \begin{macrocode}
+                \global\advance\@tempcnta\@ne
+                \global\eqnshift@\dimen@
+                \global\divide\eqnshift@\@tempcnta
+                \global\alignsep@\eqnshift@
+            \fi
+        \or
+%    \end{macrocode}
+%    Finally, if we're in an \env{flalign} or \env{xxalignat}
+%    environment, there are no flexible margins and $n-1$ flexible
+%    interalign spaces.
+%    \begin{macrocode}
+            \@tempcntb\maxfields@
+            \divide\@tempcntb\tw@
+            \global\advance\@tempcntb\m@ne
+            \global\@tempcnta\@tempcntb
+            \global\eqnshift@\z@
+            \global\alignsep@\dimen@
+%    \end{macrocode}
+%    If we're in \opt{fleqn} mode, we need to add back the
+%    \cs{@mathmargin} that was removed when \cs{dimen@} was originally
+%    calculated above.
+%    \begin{macrocode}
+            \if@fleqn
+                \global\advance\alignsep@\@mathmargin\relax
+            \fi
+            \global\divide\alignsep@\@tempcntb
+        \fi
+%    \end{macrocode}
+%    Now we make sure \cs{alignsep@} isn't too small.
+%    \begin{macrocode}
+        \ifdim\alignsep@<\minalignsep\relax
+            \global\alignsep@\minalignsep\relax
+            \ifdim\eqnshift@>\z@
+                \if@fleqn\else
+                    \global\eqnshift@\displaywidth
+                    \global\advance\eqnshift@-\totwidth@
+                    \global\advance\eqnshift@-\@tempcntb\alignsep@
+                    \global\divide\eqnshift@\tw@
+                \fi
+            \fi
+        \fi
+        \ifdim\eqnshift@<\z@
+            \global\eqnshift@\z@
+        \fi
+        \calc@shift@align
+%    \end{macrocode}
+%    Next, we calculate the value of \cs{tagshift@}.  This is the glue
+%    that will be inserted in front of the equation tag to make sure
+%    it lines up flush against the appropriate margin.
+%    \begin{macrocode}
+        \global\tagshift@\totwidth@
+        \global\advance\tagshift@\@tempcntb\alignsep@
+        \if@fleqn
+            \ifnum\xatlevel@=\tw@
+                \global\advance\tagshift@-\@mathmargin\relax
+            \fi
+        \else
+            \global\advance\tagshift@\eqnshift@
+        \fi
+        \iftagsleft@ \else
+            \global\advance\tagshift@-\displaywidth
+        \fi
+%    \end{macrocode}
+%    Finally, we increase \cs{totwidth@} by an appropriate multiple of
+%    \cs{minalignsep}.  If the result is greater than
+%    \cs{displaywidth}, it means that at least one line in the
+%    \env{align} is overfull and we will issue an appropriate warning
+%    message (via \cs{bl@ck}) at the end of the environment.
+%    \begin{macrocode}
+        \dimen@\minalignsep\relax
+        \global\advance\totwidth@\@tempcntb\dimen@
+        \ifdim\totwidth@>\displaywidth
+            \global\let\displaywidth@\totwidth@
+        \else
+            \global\let\displaywidth@\displaywidth
+        \fi
+    \endgroup
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    The code for calculating the appropriate placement of equation
+%    tags in the \env{align} environments is quite complicated and
+%    varies wildly depending on the settings of the |tagsleft@| and
+%    |@fleqn| switches.  To minimize memory and hash space usage, we
+%    only define the variant appropriate for the current setting of
+%    those switches.
+%
+%    It would be worthwhile to examine this code more closely someday
+%    and see if it could be optimized any.
+%
+%    \paragraph{Tag placement when \cs{tagsleft@true},
+%    \cs{@fleqntrue}.}
+%
+%    We begin with the version of \cs{calc@shift@align} appropriate
+%    for flush-left equations with tags on the left.
+%
+%    \begin{macro}{\calc@shift@align}
+%    This is the simplest case.  Since the left margin is fixed, in
+%    general the only thing to do is check whether there is room for
+%    the tag in the left margin.  The only exception is that if
+%    $\cs{eqnshift@} = 0\,\mathrm{pt}$---meaning that we're in a
+%    \env{flalign} environment and this is the first line with a tag
+%    that we've encountered---then we set $\cs{eqnshift@} =
+%    \cs{@mathmargin}$ and recalculate \cs{alignsep@}.  This is done
+%    by \cs{x@calc@shift@lf}.
+%    \begin{macrocode}
+\iftagsleft@\if@fleqn
+    \def\calc@shift@align{%
+        \global\let\tag@shifts\@empty
+        \begingroup
+%    \end{macrocode}
+%    \cs{@tempdima} is initialized to $\cs{@mathmargin} -
+%    \cs{mintagsep}$, which yields the maximum size of a tag that will
+%    not be shifted to another line.
+%    \begin{macrocode}
+            \@tempdima\@mathmargin\relax
+            \advance\@tempdima-\mintagsep\relax
+%    \end{macrocode}
+%    Now we examine each row in turn.  If the width of the tag on the
+%    line is non-positive---meaning either that there is no tag or
+%    else that the user has forced it to have zero width---we mark the
+%    tag to remain unshifted.  Otherwise, we call \cs{x@calc@shift@lf}
+%    to determine whether any adjustments need to be made to
+%    \cs{eqnshift@} and \cs{alignsep@}.  Note the difference in
+%    treatment of zero-width tags between this code and \tex/'s
+%    built-in algorithm: here, a width of zero prohibits the tag from
+%    being shifted, while in \tex/'s built-in algorithm, a width of
+%    zero forces the tag to be shifted.
+%    \begin{macrocode}
+            \loop
+                \ifnum\row@>0
+                    \ifdim\tag@width\row@>\z@
+                        \x@calc@shift@lf
+                    \else
+                        \saveshift@0%
+                    \fi
+                    \advance\row@\m@ne
+            \repeat
+        \endgroup
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@calc@shift@lf}
+%    As mentioned above, \cs{x@calc@shift@lf} first checks to see if
+%    the current left margin is set to 0 and, if so, resets it to
+%    \cs{@mathmargin} and recalculates \cs{alignsep@}.  Next, it
+%    checks whether the length of the current tag exceeds the
+%    previously calculated limit and, if so, marks the tag to be
+%    shifted to a separate line.
+%    \begin{macrocode}
+    \def\x@calc@shift@lf{%
+        \ifdim\eqnshift@=\z@
+            \global\eqnshift@\@mathmargin\relax
+            \alignsep@\displaywidth
+            \advance\alignsep@-\totwidth@
+            \global\divide\alignsep@\@tempcntb
+            \ifdim\alignsep@<\minalignsep\relax
+                \global\alignsep@\minalignsep\relax
+            \fi
+        \fi
+        \ifdim\tag@width\row@>\@tempdima
+            \saveshift@1%
+        \else
+            \saveshift@0%
+        \fi
+    }
+\fi\fi
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \paragraph{Tag placement when \cs{tagsleft@false},
+%    \cs{@fleqntrue}.}
+%
+%    Next we consider the case when equations are flush-left, but tags
+%    are on the right.  This case is somewhat more complicated than
+%    the previous one, since we can adjust the right margin by varying
+%    the inter-align separatin. Thus, when a tag is found to be too
+%    close to its equation, we first attempt to decrease
+%    \cs{alignsep@} enough to move the equation off to an acceptable
+%    distance.  Only if that would require a value of \cs{alignsep@}
+%    less than \cs{minalignsep} do we move the tag to a separate line.
+%
+%    \begin{macro}{\calc@shift@align}
+%    This version of \cs{calc@shift@align} differs from the previous
+%    version only in calling \cs{x@calc@shift@rf} rather than
+%    \cs{x@calc@shift@lf}.
+%    \begin{macrocode}
+\iftagsleft@\else\if@fleqn
+    \def\calc@shift@align{%
+        \global\let\tag@shifts\@empty
+        \begingroup
+            \loop
+                \ifnum\row@>0
+                    \ifdim\tag@width\row@>\z@
+                        \x@calc@shift@rf
+                    \else
+                        \saveshift@0%
+                    \fi
+                    \advance\row@\m@ne
+            \repeat
+        \endgroup
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@calc@shift@rf}
+%    To start, we need to know two quantities: the number of align
+%    structures in the current row and the ``effective length'' of the
+%    row, defined as the distance from the left margin to the
+%    right edge of the text assuming that \cs{eqnshift@} and
+%    \cs{alignsep@} are both~0.  To get the number of align
+%    structures, we first count the number of columns by counting the
+%    number of entries in the \cs{fieldlengths@} for the current row.
+%    The effective length is calcuated by \cs{x@rcalc@width} and put
+%    in the temporary register \cs{@tempdimc}, using \cs{@tempdimb} as
+%    an auxiliary variable.
+%    \begin{macrocode}
+    \def\x@calc@shift@rf{%
+        \column@\z@
+        \@tempdimb\z@
+        \@tempdimc\z@
+        \edef\@tempb{\fieldlengths@\row@}%
+        \@for\@tempa:=\@tempb\do{%
+            \advance\column@\@ne
+            \x@rcalc@width
+        }%
+        \begingroup
+%    \end{macrocode}
+%    If there are $n$ columns in the current row, then there are
+%    $\lfloor (n+1)/2 \rfloor$ align structures and $\lfloor (n-1)/2
+%    \rfloor$ interalign spaces.
+%    \begin{macrocode}
+            \advance\column@\m@ne
+            \divide\column@\tw@
+%    \end{macrocode}
+%    If this is smaller than the maximum number of interalign spaces
+%    in the environment, then we need to reduce \cs{@tempcnta} (the
+%    total number of flexible spaces in the current line) by
+%    $\cs{@tempcntb} - \cs{column@}$ and reset \cs{@tempcntb} to
+%    \cs{column@}.
+%    \begin{macrocode}
+            \ifnum\@tempcntb>\column@
+                \advance\@tempcnta-\@tempcntb
+                \advance\@tempcnta\column@
+                \@tempcntb\column@
+            \fi
+%    \end{macrocode}
+%    Next, we add the width of the tag and the (fixed) left margin to
+%    the effective length calculated above.  This can be used to
+%    calculate how much ``free space'' there is in the current line
+%    and thus how much leeway we have to increase the amount of space
+%    between the tag and the equation.
+%    \begin{macrocode}
+            \tagwidth@\tag@width\row@\relax
+            \@tempdima\eqnshift@
+            \advance\@tempdima\@tempdimc\relax
+            \advance\@tempdima\tagwidth@
+%    \end{macrocode}
+%    The first thing to check is whether the tag should be shifted to
+%    a separate line.  To do this, we add the minimum interalign
+%    separation and the \cs{mintagsep} to the value of \cs{@tempdima}
+%    just calculated.  This yields the minimum acceptable length of
+%    the current line.  If that is greater than \cs{displaywidth}, we
+%    mark the tag to be calculated.  Otherwise, we mark the tag to be
+%    kept on the same line and then check to see if the \cs{alignsep@}
+%    needs to be reduced to make room for the tag.
+%    \begin{macrocode}
+            \dimen@\minalignsep\relax
+            \multiply\dimen@\@tempcntb
+            \advance\dimen@\mintagsep\relax
+            \advance\dimen@\@tempdima
+            \ifdim\dimen@>\displaywidth
+                \saveshift@1%
+            \else
+                \saveshift@0%
+%    \end{macrocode}
+%    Now we perform essentially the same calculation, but using the
+%    current value of \cs{alignsep@} instead of \cs{minalignsep}.
+%    This gives the current length of the line.  If this is greater
+%    than \cs{displaywidth}, we recalculate \cs{alignsep@} to make
+%    room for the tag.
+%    \begin{macrocode}
+                \dimen@\alignsep@\relax
+                \multiply\dimen@\@tempcntb
+                \advance\dimen@\@tempdima
+                \advance\dimen@\tagwidth@
+                \ifdim\dimen@>\displaywidth
+                    \dimen@\displaywidth
+                    \advance\dimen@-\@tempdima
+                    \ifnum\xatlevel@=\tw@
+                        \advance\dimen@-\mintagsep\relax
+                    \fi
+                    \divide\dimen@\@tempcnta
+                    \ifdim\dimen@<\minalignsep\relax
+                        \global\alignsep@\minalignsep\relax
+                    \else
+                        \global\alignsep@\dimen@
+                    \fi
+                \fi
+            \fi
+        \endgroup
+    }
+\fi\fi
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \paragraph{Tag placement when \cs{tagsleft@false},
+%    \cs{@fleqnfalse}.}
+%
+%    This is similar to the previous case, except for the added
+%    complication that both \cs{alignsep@} and \cs{eqnshift@} can
+%    vary, which makes the computations correspondingly more
+%    complicated.
+%
+%    \begin{macro}{\calc@shift@align}
+%    \begin{macrocode}
+\iftagsleft@\else\if@fleqn\else
+    \def\calc@shift@align{%
+        \global\let\tag@shifts\@empty
+        \begingroup
+            \loop
+                \ifnum\row@>0
+                    \ifdim\tag@width\row@>\z@
+                        \x@calc@shift@rc
+                    \else
+                        \saveshift@0%
+                    \fi
+                    \advance\row@\m@ne
+            \repeat
+        \endgroup
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@calc@shift@rc}
+%    \begin{macrocode}
+    \def\x@calc@shift@rc{%
+        \column@\z@
+        \@tempdimb\z@
+        \@tempdimc\z@
+        \edef\@tempb{\fieldlengths@\row@}%
+        \@for\@tempa:=\@tempb\do{%
+            \advance\column@\@ne
+            \x@rcalc@width
+        }%
+        \begingroup
+            \advance\column@\m@ne
+            \divide\column@\tw@
+            \ifnum\@tempcntb>\column@
+                \advance\@tempcnta-\@tempcntb
+                \advance\@tempcnta\column@
+                \@tempcntb\column@
+            \fi
+            \tagwidth@\tag@width\row@\relax
+            \@tempdima\@tempdimc
+            \advance\@tempdima\tagwidth@
+            \dimen@\minalignsep\relax
+            \multiply\dimen@\@tempcntb
+            \advance\dimen@\mintagsep\relax
+            \ifnum\xatlevel@=\tw@ \else
+                \advance\dimen@\mintagsep\relax
+            \fi
+            \advance\dimen@\@tempdima
+            \ifdim\dimen@>\displaywidth
+                \saveshift@1%
+            \else
+                \saveshift@0%
+                \dimen@\eqnshift@
+                \advance\dimen@\@tempdima
+                \advance\dimen@\@tempcntb\alignsep@
+                \advance\dimen@\tagwidth@
+                \ifdim\dimen@>\displaywidth
+                    \dimen@\displaywidth
+                    \advance\dimen@-\@tempdima
+                    \ifnum\xatlevel@=\tw@
+                        \advance\dimen@-\mintagsep\relax
+                    \fi
+                    \divide\dimen@\@tempcnta
+                    \ifdim\dimen@<\minalignsep\relax
+                        \global\alignsep@\minalignsep\relax
+                        \eqnshift@\displaywidth
+                        \advance\eqnshift@-\@tempdima
+                        \advance\eqnshift@-\@tempcntb\alignsep@
+                        \global\divide\eqnshift@\tw@
+                    \else
+                        \ifdim\dimen@<\eqnshift@
+                            \ifdim\dimen@<\z@
+                                \global\eqnshift@\z@
+                            \else
+                                \global\eqnshift@\dimen@
+                            \fi
+                        \fi
+                        \ifdim\dimen@<\alignsep@
+                            \global\alignsep@\dimen@
+                        \fi
+                    \fi
+                \fi
+            \fi
+        \endgroup
+    }
+\fi\fi
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@rcalc@width}
+%    \begin{macrocode}
+\iftagsleft@\else
+    \def\x@rcalc@width{%
+        \ifdim\@tempa > \z@
+            \advance\@tempdimc\@tempdimb
+            \ifodd\column@
+                \advance\@tempdimc\maxcol@width\column@
+                \@tempdimb\z@
+            \else
+                \advance\@tempdimc\@tempa\relax
+                \@tempdimb\maxcol@width\column@
+                \advance\@tempdimb-\@tempa\relax
+            \fi
+        \else
+            \advance\@tempdimb\maxcol@width\column@\relax
+        \fi
+    }
+\fi
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \paragraph{Tag placement when \cs{tagsleft@true},
+%    \cs{@fleqnfalse}.}
+%
+%    \begin{macro}{\calc@shift@align}
+%    \begin{macrocode}
+\iftagsleft@\if@fleqn\else
+    \def\calc@shift@align{%
+        \global\let\tag@shifts\@empty
+        \begingroup
+            \loop
+                \ifnum\row@>\z@
+                    \ifdim\tag@width\row@>\z@
+                        \x@calc@shift@lc
+                    \else
+                        \saveshift@0%
+                    \fi
+                    \advance\row@\m@ne
+            \repeat
+        \endgroup
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@calc@shift@lc}
+%    \begin{macrocode}
+    \def\x@calc@shift@lc{%
+        \column@\z@
+%    \end{macrocode}
+%    \cs{@tempdima} will (eventually) be set to the effective width of
+%    the current row, defined as the distance from the leftmost point
+%    of the current line to the end of the last field of the
+%    \cs{halign}, ignoring any intervening \cs{tabskip}s, plus the
+%    width of the current tag.  That is, it will be the width of the
+%    first non-empty field plus the sum of the maximum widths of all
+%    following fields, plus the tag width.
+%
+%    \cs{@tempdimb} will be the ``indentation'' of leftmost end of
+%    text, ignoring the \cs{tabskip} glue, i.e., it will be the sum of
+%    the maximum widths of any fields to the left of the first
+%    non-empty field, plus whatever empty space there is at the
+%    beginning of the first non-empty field.
+%    \begin{macrocode}
+        \@tempdima\z@ % ``width of equation''
+        \@tempdimb\z@ % ``indent of equation''
+        \edef\@tempb{\fieldlengths@\row@}%
+        \@for\@tempa:=\@tempb\do{%
+            \advance\column@\@ne
+            \x@lcalc@width
+        }%
+        \begingroup
+            \tagwidth@\tag@width\row@\relax
+%    \end{macrocode}
+%    \cs{@tempdima} is now easy to calculate, since it is just
+%    $\cs{totwidth@} - \cs{@tempdimb} + \cs{tagwidth@}$.
+%    \begin{macrocode}
+            \@tempdima\totwidth@
+            \advance\@tempdima-\@tempdimb
+            \advance\@tempdima\tagwidth@
+%    \end{macrocode}
+%    Next, we check to see whether there is room for both the equation
+%    and the tag on the same line, by calculating the minimum
+%    acceptable length of the current row and comparing that to
+%    \cs{displaywidth}.  Note that here we use \cs{@tempcntb}, i.e.,
+%    the number of interalign spaces after the first non-empty align
+%    structure.
+%    \begin{macrocode}
+            \dimen@\minalignsep\relax
+            \multiply\dimen@\@tempcntb
+            \advance\dimen@\mintagsep\relax
+            \ifnum\xatlevel@=\tw@ \else
+                \advance\dimen@\mintagsep\relax
+            \fi
+            \advance\dimen@\@tempdima
+%    \end{macrocode}
+%    If the minimum acceptable width of the current line is greater
+%    than \cs{displaywidth}, we mark the current tag to be shifted to
+%    a separate line.
+%    \begin{macrocode}
+            \ifdim\dimen@>\displaywidth
+                \saveshift@1%
+            \else
+%    \end{macrocode}
+%    Otherwise, the tag can stay on the same line as the equation, but
+%    we need to check whether it is too close to the equation.  So, we
+%    calculate the distance between the left margin and the left side
+%    of the equation, using the current values of \cs{eqnshift@} and
+%    \cs{alignsep@}.  Note that we use \cs{count@} here, not
+%    \cs{@tempcntb}, as above.
+%    \begin{macrocode}
+                \saveshift@0%
+                \dimen@\alignsep@
+                \multiply\dimen@\count@
+                \advance\dimen@\eqnshift@
+                \advance\dimen@\@tempdimb
+%    \end{macrocode}
+%    If the left margin is less than twice the tag width, we calculate
+%    new values of \cs{eqnshift@} and \cs{alignsep@} to move the
+%    equation further away from the tag.  In particular, we center the
+%    current line between its tag and the right margin.  Note that
+%    although we later will need to transform \cs{dimen@} into a value
+%    suitable for use as \cs{eqnshift@}, for the time being it is more
+%    useful to think of it as the space separating the tag from the
+%    equation.
+%    \begin{macrocode}
+                \ifdim\dimen@<2\tagwidth@
+                    \dimen@\displaywidth
+                    \advance\dimen@-\@tempdima
+                    \ifnum\xatlevel@=\tw@
+                        \advance\dimen@-\mintagsep\relax
+                    \fi
+%    \end{macrocode}
+%    In certain circumstances we will get a divide-by-zero error here
+%    unless we guard against it. Use of \cs{@tempcnta} is complicated,
+%    sometimes it is assigned globally, sometimes locally. Need to sort
+%    it out one of these days [mjd,2000/06/02].
+%    \begin{macrocode}
+                    \ifnum\@tempcnta>\z@
+                      \divide\dimen@\@tempcnta
+                    \else \dimen@\z@
+                    \fi
+%    \end{macrocode}
+%    As usual, we check to make sure we don't set \cs{alignsep@}
+%    smaller than \cs{minalignsep} and, in any case, that we don't
+%    replace \cs{alignsep@} by a larger value.
+%    \begin{macrocode}
+                    \ifdim\dimen@<\minalignsep\relax
+                        \global\alignsep@\minalignsep\relax
+                        \dimen@\displaywidth
+                        \advance\dimen@-\@tempdima
+                        \advance\dimen@-\@tempcntb\alignsep@
+                        \global\divide\dimen@\tw@
+                    \else
+                        \ifdim\dimen@<\alignsep@
+                            \global\alignsep@\dimen@
+                        \fi
+                    \fi
+%    \end{macrocode}
+%    Next, we calculate an appropriate value of \cs{eqnshift@},
+%    assuming that \cs{dimen@} is the desired separation between the
+%    tag and equation of the current line.  This means that we first
+%    need to adjust \cs{dimen@} if we're in an \env{flalign}
+%    environment.
+%    \begin{macrocode}
+                    \ifnum\xatlevel@=\tw@
+                        \dimen@\mintagsep\relax
+                    \fi
+%    \end{macrocode}
+%    Now we calculate the value of \cs{eqnshift@} needed to produce a
+%    separation of \cs{dimen@} between the equation tag and the
+%    beginning of the equation.  To do this, we need the following
+%    equation to hold:
+%    \[
+%       \cs{eqnshift@} + n\cs{alignsep@} + \cs{@tempdimb}
+%           = \cs{tagwidth@} + \cs{dimen@}
+%    \]
+%    where $n = \cs{count@}$ is the number of interalign spaces before
+%    the first non-empty field of the current line.
+%    \begin{macrocode}
+                    \advance\dimen@\tagwidth@
+                    \advance\dimen@-\@tempdimb
+                    \advance\dimen@-\count@\alignsep@
+%    \end{macrocode}
+%    The value of \cs{eqnshift@} just calculated is the minimum
+%    acceptable value; thus, we save it only if it is larger than the
+%    current value.
+%    \begin{macrocode}
+                    \ifdim\dimen@>\eqnshift@
+                        \global\eqnshift@\dimen@
+                    \fi
+                \fi
+            \fi
+        \endgroup
+    }
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{macro}{\x@lcalc@width}
+%    This macro calculates the ``indentation'' of the current row, as
+%    defined above under the description of \cs{x@calc@shift@lc}.
+%    This macro is called for each field of the current line, with
+%    \cs{@tempa} set to the width of the current field.  Ideally, the
+%    loop enclosing \cs{x@lcalc@width} would terminate as soon as
+%    \cs{@tempa} is non-zero, but that would be a bit tricky to
+%    arrange.  Instead, we use \cs{@tempdima} as a flag to signal when
+%    we've encountered the first non-empty field.
+%
+%    \begin{macrocode}
+    \def\x@lcalc@width{%
+        \ifdim\@tempdima = \z@
+%    \end{macrocode}
+%    If the current field is empty (i.e., $\cs{@tempa} =
+%    \mathrm{0\,pt}$, then we increment \cs{@tempdimb} by the width of
+%    the current field).  Otherwise, we set $\cs{@tempdima} =
+%    \mathrm{1\,pt}$ as a signal value and increment \cs{@tempdimb} by
+%    the width of whatever empty space there might be at the left of
+%    the current field.
+%    \begin{macrocode}
+            \ifdim\@tempa > \z@
+                \@tempdima\p@
+                \ifodd\column@
+                    \advance\@tempdimb \maxcol@width\column@
+                    \advance\@tempdimb-\@tempa
+                \fi
+%    \end{macrocode}
+%    In addition, we need to adjust the values of \cs{@tempcnta} and
+%    \cs{@tempcntb} to account for any empty align structures that
+%    might occur at the beginning of the current line.  More
+%    specifically, we first set \cs{count@} equal to the number of
+%    interalign spaces preceding the current field (namely, $\lfloor
+%    (\cs{\column@}-1)/2 \rfloor$), and then subtract \cs{count@} from
+%    both \cs{@tempcnta} and \cs{@tempcntb}.  The rationale is that
+%    for the purposes of adjusting the spacing between the tag and the
+%    equation, the only flexible interalign spaces are those after
+%    the first non-empty align structure, so we need to treat those
+%    different from the ones before the first non-empty align
+%    structure.
+%    \begin{macrocode}
+                \count@\column@
+                \advance\count@\m@ne
+                \divide\count@\tw@
+                \advance\@tempcnta-\count@
+                \advance\@tempcntb-\count@
+            \else
+                \advance\@tempdimb \maxcol@width\column@\relax
+            \fi
+        \fi
+    }
+\fi\fi
+%    \end{macrocode}
+%    \end{macro}
+%
+%  \begin{macro}{\place@tag}
+%    \cs{place@tag} takes care of the placment of tags in the
+%    \env{align} environments.
+%    \begin{macrocode}
+\def\place@tag{%
+    \iftagsleft@
+        \kern-\tagshift@
+        \if1\shift@tag\row@\relax
+            \rlap{\vbox{%
+                \normalbaselines
+                \boxz@
+                \vbox to\lineht@{}%
+                \raise@tag
+            }}%
+        \else
+            \rlap{\boxz@}%
+        \fi
+        \kern\displaywidth@
+    \else
+        \kern-\tagshift@
+        \if1\shift@tag\row@\relax
+%    \end{macrocode}
+%    Added depth to correct vertical spacing of shifted
+%    equation tags.---dmj, 1994/12/29
+%    \begin{macrocode}
+            \llap{\vtop{%
+                \raise@tag
+                \normalbaselines
+                \setbox\@ne\null
+                \dp\@ne\lineht@
+                \box\@ne
+                \boxz@
+            }}%
+        \else
+            \llap{\boxz@}%
+        \fi
+    \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\align@preamble}
+%    \begin{macrocode}
+\def\align@preamble{%
+   &\hfil
+    \strut@
+    \setboxz@h{\@lign$\m@th\displaystyle{##}$}%
+    \ifmeasuring@\savefieldlength@\fi
+    \set@field
+    \tabskip\z@skip
+   &\setboxz@h{\@lign$\m@th\displaystyle{{}##}$}%
+    \ifmeasuring@\savefieldlength@\fi
+    \set@field
+    \hfil
+    \tabskip\alignsep@
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\set@field}
+%    \cs{set@field} increments the column counter, tracks the value of
+%    \cs{lineht@} and finally inserts the box containing the contents
+%    of the current field.
+%    \begin{macrocode}
+\def\set@field{%
+    \column@plus
+    \iftagsleft@
+        \ifdim\ht\z@>\lineht@
+            \global\lineht@\ht\z@
+        \fi
+    \else
+        \ifdim\dp\z@>\lineht@
+            \global\lineht@\dp\z@
+        \fi
+    \fi
+    \boxz@
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+% \subsection {The \env{split} environment}
+%
+%    \begin{macro}{\split@err}
+%    A special error function for \env{split} to conserve main mem (at a
+%    cost of string pool/hash size.
+%    \begin{macrocode}
+\edef\split@err#1{%
+    \@nx\@amsmath@err{%
+        \string\begin{split} won't work here%
+    }{%
+        \@xp\@nx\csname
+  Did you forget a preceding \string\begin{equation}?^^J%
+  If not, perhaps the `aligned' environment is what
+  you want.\endcsname}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \begin{environment}{split}
+%    If the \env{split} environment occurs inside \env{align} or
+%    \env{gather}, it can make use of the enclosing halign; if it is
+%    called inside a simple equation, we add an implicit `gather'
+%    container.
+%
+%    \begin{macrocode}
+\newenvironment{split}{%
+  \if@display
+    \ifinner
+      \@xp\@xp\@xp\split@aligned
+    \else
+      \ifst@rred \else \global\@eqnswtrue \fi
+    \fi
+  \else \let\endsplit\@empty \@xp\collect@body\@xp\split@err
+  \fi
+  \collect@body\gather@split
+}{%
+      \crcr
+    \egroup
+  \egroup
+  \iftagsleft@ \@xp\lendsplit@ \else \@xp\rendsplit@ \fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\split@tag\relax % init
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\gather@split#1#2#3{%
+  \@xp\endgroup \reset@equation % math@cr will handle equation numbering
+  \iftag@
+     \toks@\@xp{\df@tag}%
+     \edef\split@tag{%
+       \gdef\@nx\df@tag{\the\toks@}%
+       \global\@nx\tag@true \@nx\nonumber
+     }%
+  \else \let\split@tag\@empty
+  \fi
+  \spread@equation
+%    \end{macrocode}
+%    The extra vcenter wrapper here is not really a good thing but
+%    without it there are compatibility problems with old documents that
+%    throw in some extra material between \verb'\begin{equation}' and
+%    \verb'\begin{split}' (for example, \verb'\hspace{-1pc}' or
+%    \verb'\left\{'). [mjd,1999/09/20]
+%    \begin{macrocode}
+  \vcenter\bgroup
+    \gather@{\split@tag  \begin{split}#1\end{split}}%
+    \def\endmathdisplay@a{%
+      \math@cr \black@ \totwidth@ \egroup
+      \egroup
+    }%
+}
+%    \end{macrocode}
+%
+%    \end{environment}
+%
+% \begin{macro}{\insplit@}
+%    \begin{macrocode}
+\def\insplit@{%
+  \global\setbox\z@\vbox\bgroup
+    \Let@ \chardef\dspbrk@context\@ne \restore@math@cr
+    \default@tag % disallow use of \tag here
+    \ialign\bgroup
+      \hfil
+      \strut@
+      $\m@th\displaystyle{##}$%
+     &$\m@th\displaystyle{{}##}$%
+      \hfill % Why not \hfil?---dmj, 1994/12/28
+      \crcr
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\rendsplit@}
+%    Moved the box maneuvers inside the \cs{ifinalign@}, since that is
+%    the only place they are needed.---dmj, 1994/12/28
+%
+%    TODO: Explore interaction of tag-placement algorithm with
+%    \env{split}.  Is there any way for \env{split} to pass the
+%    relevant information out to the enclosing \env{gather} or
+%    \env{align}?
+%    \begin{macrocode}
+\def\rendsplit@{%
+    \ifinalign@
+%    \end{macrocode}
+%    Changed |\box9| into a \cs{vtop} here for better spacing.
+%    \begin{macrocode}
+        \global\setbox9 \vtop{%
+            \unvcopy\z@
+            \global\setbox8 \lastbox
+            \unskip
+        }%
+        \setbox\@ne\hbox{%
+            \unhcopy8
+            \unskip
+            \global\setbox\tw@\lastbox
+            \unskip
+            \global\setbox\thr@@\lastbox
+        }%
+        \ifctagsplit@
+            \gdef\split@{%
+                \hbox to\wd\thr@@{}%
+               &\vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}%
+            }%
+        \else
+            \global\setbox7 \hbox{\unhbox\tw@\unskip}%
+%    \end{macrocode}
+%    Added \cs{add@amps} to make sure we put the last line of the
+%    \env{split} into the proper column of an \env{align} environment
+%    with multiple align structures.---dmj, 1994/12/28
+%
+%    Special care has to be taken in this case because the \env{split}
+%    turns into two lines of the \env{align} instead of just one.  So,
+%    we have to make sure that the first line produced by the
+%    \env{split} doesn't upset our bookkeeping, hence we call
+%    \cs{savetaglength@} to insert 0\,pt as the tag for this
+%    pseudo-line, and we advance the \cs{row@} counter and reset
+%    \cs{lineht@} afterwards.  It would be nice if we could just
+%    replace the \cs{crcr} by \cs{math@cr@@@}, but that would cause
+%    problems with the tag processing.
+%    \begin{macrocode}
+            \gdef\split@{%
+                \global\@tempcnta\column@
+               &\setboxz@h{}%
+                \savetaglength@
+                \global\advance\row@\@ne
+                \vbox{\moveleft\wd\thr@@\box9}%
+                \crcr
+                \noalign{\global\lineht@\z@}%
+                \add@amps\@tempcnta
+                \box\thr@@
+               &\box7
+            }%
+        \fi
+    \else
+        \ifctagsplit@
+            \gdef\split@{\vcenter{\boxz@}}%
+        \else
+%    \end{macrocode}
+%    Changed to just \cs{boxz@}, otherwise last line gets centered
+%    rather than aligned properly with respect to the rest of the
+%    lines.  But this means that we can't see inside of the last line
+%    to decide whether the tag needs to be moved.  Will have to think
+%    about this.---dmj, 1994/12/28
+%    \begin{macrocode}
+            \gdef\split@{%
+                \boxz@
+%                \box9
+%                \crcr
+%                \hbox{\box\thr@@\box7}%
+            }%
+        \fi
+    \fi
+    \aftergroup\split@
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lendsplit@}
+%    \begin{macrocode}
+\def\lendsplit@{%
+    \global\setbox9\vtop{\unvcopy\z@}%
+    \ifinalign@
+%    \end{macrocode}
+%    Moved following two boxes inside the \cs{ifinalign@}, since they
+%    are only used in that case.  In fact, if we just kept track of
+%    the width of the first column, we could dispense with this
+%    entirely.  Surely that would be more efficient than all these box
+%    copies.---dmj, 1994/12/28
+%    \begin{macrocode}
+        \setbox\@ne\vbox{%
+            \unvcopy\z@
+            \global\setbox8\lastbox
+        }%
+        \setbox\@ne\hbox{%
+            \unhcopy8%
+            \unskip
+            \setbox\tw@\lastbox
+            \unskip
+            \global\setbox\thr@@\lastbox
+        }%
+        \ifctagsplit@
+            \gdef\split@{%
+                \hbox to\wd\thr@@{}%
+               &\vcenter{\vbox{\moveleft\wd\thr@@\box9}}%
+            }%
+        \else
+            \gdef\split@{%
+                \hbox to\wd\thr@@{}%
+               &\vbox{\moveleft\wd\thr@@\box9}%
+            }%
+        \fi
+    \else
+        \ifctagsplit@
+            \gdef\split@{\vcenter{\box9}}%
+        \else
+            \gdef\split@{\box9}%
+        \fi
+    \fi
+    \aftergroup\split@
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    With \pkg{amsmath} 1.2 it was possible to put things like
+%    \verb'\left\{' between \verb'\begin{equation}' and
+%    \verb'\begin{split}' without getting any error message. For
+%    backward compatibility we try to avoid a fatal error in this case
+%    and instead attempt recovery with \env{aligned}.
+%    \begin{macrocode}
+\def\split@aligned#1#2{%
+   \iffalse{\fi\ifnum0=`}\fi
+   \collect@body\split@al@a}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\split@al@a#1#2#3{%
+  \split@warning
+  \endgroup
+%    \end{macrocode}
+%    If the \opt{fleqn} and \opt{tbtags} options are both in effect then
+%    we will need to add an optional argument on the \env{aligned}
+%    environment.
+%    \begin{macrocode}
+  \toks@{\begin{aligned}}%
+  \if@fleqn \split@al@tagcheck \fi
+%    \end{macrocode}
+%    The \cs{relax} here is to prevent \cs{@let@token} from being left
+%    equal to an ampersand if that happens to be the first thing in the body.
+%    \begin{macrocode}
+  \the\toks@\relax#1\end{aligned}%
+  \ifnum0=`{\fi\iffalse}\fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\split@al@tagcheck{%
+   \ifctagsplit@
+   \else
+     \iftagsleft@ \toks@\@xp{\the\toks@ [t]}%
+     \else \toks@\@xp{\the\toks@ [b]}%
+     \fi
+   \fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\split@warning{%
+  \PackageWarning{amsmath}{%
+Cannot use `split' here;\MessageBreak trying to recover with `aligned'}%
+}
+%    \end{macrocode}
+%
+% \subsection{The \env{multline} environment}
+%
+%    In the original \amstex/, \cn{multlinegap} is a macro with an
+%    argument that resets an internal dimension (one with an \qc{\@}
+%    character in its name). Here, to save control sequence names, we
+%    define \cn{multlinegap} to be the dimension itself and the
+%    documentation instructs users to use \cn{setlength} if they
+%    need to change it.
+% \begin{macro}{\multlinegap}
+% \begin{macro}{\multlinetaggap}
+%    Changed \cs{multlinegap} and \cs{multlinetaggap} to skip
+%    registers.  Also changed name to \cs{multlinetaggap} from
+%    \cs{multlinetaggap@}.
+%    \begin{macrocode}
+\newskip\multlinegap
+\multlinegap10pt
+\newskip\multlinetaggap
+\multlinetaggap10pt
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macro}{\start@multline}
+%    \begin{macrocode}
+\def\start@multline#1{%
+    \RIfM@
+        \nomath@env
+        \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+    \else
+        $$%
+        #1%
+        \ifst@rred
+            \nonumber
+        \else
+            \global\@eqnswtrue
+        \fi
+        \let\next@\multline@
+    \fi
+    \collect@body\next@
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \begin{environment}{multline}
+% \begin{environment}{multline*}
+%    \begin{macrocode}
+\newenvironment{multline}{%
+  \start@multline\st@rredfalse
+}{%
+  \iftagsleft@ \@xp\lendmultline@ \else \@xp\rendmultline@ \fi
+  \ignorespacesafterend
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newenvironment{multline*}{\start@multline\st@rredtrue}{\endmultline}
+%    \end{macrocode}
+% \end{environment}
+% \end{environment}
+%
+% \begin{macro}{\multline@}
+%    \begin{macrocode}
+\def\multline@#1{%
+    \Let@
+%    \end{macrocode}
+%
+%    For multline neither \cs{displ@y} no \cs{displ@y@} is quite right;
+%    we want to advance the row number and (I suppose?) the
+%    display-pagebreak level, but we only want to do tag-related stuff
+%    once before the first line, not repeat it for every line. (Recall
+%    that the arg of \cs{@display@init} goes into \cs{everycr}.)
+%    \begin{macrocode}
+    \@display@init{\global\advance\row@\@ne \global\dspbrk@lvl\m@ne}%
+    \chardef\dspbrk@context\z@
+    \restore@math@cr
+%    \end{macrocode}
+%    The \env{multline} environment is somewhat unusual, in that
+%    \cs{tag} and \cs{label} are enabled only during the measuring
+%    phase and disabled during the production phase.
+%    Here we disable \cs{tag} and \cs{label}; \cs{mmeasure@} will
+%    re-enable them temporarily.
+%    \begin{macrocode}
+    \let\tag\tag@in@align
+    \global\tag@false \global\let\raise@tag\@empty
+    \mmeasure@{#1}%
+    \let\tag\gobble@tag \let\label\@gobble
+    \tabskip \if@fleqn \@mathmargin \else \z@skip \fi
+    \totwidth@\displaywidth
+    \if@fleqn
+        \advance\totwidth@-\@mathmargin
+    \fi
+    \halign\bgroup
+        \hbox to\totwidth@{%
+%    \end{macrocode}
+%    In order to get the spacing of the last line right in fleqn
+%    mode, we need to play a little game here.  Normally the
+%    stretchability of the \cs{hskip} here will be suppressed by the
+%    \cs{hfil} at the end of the template, except inside the last line,
+%    when that \cs{hfil} will be removed by the \cs{hfilneg} in
+%    \cs{lendmultline@}.
+%    \begin{macrocode}
+            \if@fleqn
+                \hskip \@centering \relax
+            \else
+                \hfil
+            \fi
+            \strut@
+            $\m@th\displaystyle{}##\endmultline@math
+            \hfil
+        }%
+        \crcr
+%    \end{macrocode}
+%    In \opt{fleqn} mode, it's the \cs{tabskip} of \cs{@mathmargin}
+%    that needs to be removed in the first line, not the \cs{hfil} at
+%    the beginning of the template.
+%    \begin{macrocode}
+        \if@fleqn
+            \hskip-\@mathmargin
+            \def\multline@indent{\hskip\@mathmargin}% put it back
+        \else
+            \hfilneg
+            \def\multline@indent{\hskip\multlinegap}%
+        \fi
+        \iftagsleft@
+            \iftag@
+                \begingroup
+                    \ifshifttag@
+                        \rlap{\vbox{%
+                                \normalbaselines
+                                \hbox{%
+                                    \strut@
+                                    \make@display@tag
+                                }%
+                                \vbox to\lineht@{}%
+                                \raise@tag
+                        }}%
+%    \end{macrocode}
+%    If the equation tag doesn't fit on the same line with the first
+%    line of the display, we'll indent the first line by
+%    \cn{multlinegap}.  This is a change from \pkg{amstex}, where the
+%    first line would have been flush against the left margin in this
+%    case.  A corresponding change will be made in \cs{rendmultline@}.
+%    \begin{macrocode}
+                        \multline@indent
+                    \else
+                        \setbox\z@\hbox{\make@display@tag}%
+                        \dimen@\@mathmargin \advance\dimen@-\wd\z@
+                        \ifdim\dimen@<\multlinetaggap
+                          \dimen@\multlinetaggap
+                        \fi
+                        \box\z@ \hskip\dimen@\relax
+                    \fi
+                \endgroup
+            \else
+                \multline@indent
+            \fi
+        \else
+            \multline@indent
+        \fi
+    #1%
+}
+%    \end{macrocode}
+%
+%    An extra level of indirection for the closing \verb'$' in multline
+%    allows us to avoid getting an extra thinmuskip from a final
+%    mathpunct in the equation contents, when equation numbers are on
+%    the right. If we did not use this workaround, the sequence of
+%    elements for a final comma would be, e.g.,
+% \begin{verbatim}
+% ... ,<hskip><box containing equation number>
+% \end{verbatim}
+%    which is equivalent to a sequence \verb'<mathpunct><mathord>' as
+%    far as the automatic math spacing is concerned.
+%    \begin{macrocode}
+\def\endmultline@math{$}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lendmultline@}
+%    Bug fix: changed \cs{crcr} to \cs{math@cr} so that \cs{@eqpen}
+%    gets reset properly if \cs{displaybreak} is used on the
+%    penultimate line of an \env{align}.
+%    \begin{macrocode}
+\def\lendmultline@{%
+        \hfilneg
+        \hskip\multlinegap
+        \math@cr
+    \egroup
+    $$%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\rendmultline@}
+%    \begin{macrocode}
+\def\rendmultline@{%
+    \iftag@
+        $\let\endmultline@math\relax
+            \ifshifttag@
+                \hskip\multlinegap
+%    \end{macrocode}
+%    Added depth to correct vertical spacing of shifted equation
+%    tags.---dmj, 1994/12/29
+%    \begin{macrocode}
+                \llap{\vtop{%
+                    \raise@tag
+                    \normalbaselines
+                    \setbox\@ne\null
+                    \dp\@ne\lineht@
+                    \box\@ne
+                    \hbox{\strut@\make@display@tag}%
+                }}%
+            \else
+                \hskip\multlinetaggap
+                \make@display@tag
+            \fi
+    \else
+        \hskip\multlinegap
+    \fi
+    \hfilneg
+%    \end{macrocode}
+%    Use \cs{math@cr} rather than just \cs{crcr} so that \cs{@eqpen}
+%    gets reset properly if \cs{displaybreak} is used.
+%    \begin{macrocode}
+        \math@cr
+    \egroup$$%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mmeasure@}
+%    \begin{macrocode}
+\def\mmeasure@#1{%
+    \begingroup
+        \measuring@true
+%    \end{macrocode}
+%    We use \cs{begin/endgroup} rather than |{}| in this definition of
+%    \cn{label} because the latter would create an extra (wasteful of
+%    main mem) null box in the current math list. [mjd, 1995/01/17]
+%    \begin{macrocode}
+        \def\label##1{%
+          \begingroup\measuring@false\label@in@display{##1}\endgroup}%
+        \def\math@cr@@@{\cr}%
+        \let\shoveleft\@iden \let\shoveright\@iden
+        \savecounters@
+        \global\row@\z@
+        \setbox\@ne\vbox{%
+            \global\let\df@tag\@empty
+            \halign{%
+                \setboxz@h{\@lign$\m@th\displaystyle{}##$}%
+                \iftagsleft@
+                    \ifnum\row@=\@ne
+                        \global\totwidth@\wdz@
+                        \global\lineht@\ht\z@
+                    \fi
+                \else
+                    \global\totwidth@\wdz@
+                    \global\lineht@\dp\z@
+                \fi
+                \crcr
+                #1%
+                \crcr
+            }%
+        }%
+        \ifx\df@tag\@empty\else\global\tag@true\fi
+        \if@eqnsw\global\tag@true\fi
+        \iftag@
+            \setboxz@h{%
+                \if@eqnsw
+                    \stepcounter{equation}%
+                    \tagform@\theequation
+                \else
+                    \df@tag
+                \fi
+            }%
+            \global\tagwidth@\wdz@
+            \dimen@\totwidth@
+            \advance\dimen@\tagwidth@
+            \advance\dimen@\multlinetaggap
+            \iftagsleft@\else
+                \if@fleqn
+                    \advance\dimen@\@mathmargin
+                \fi
+            \fi
+            \ifdim\dimen@>\displaywidth
+                \global\shifttag@true
+            \else
+                \global\shifttag@false
+            \fi
+        \fi
+        \restorecounters@
+    \endgroup
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macro}{\shoveleft}
+%    \begin{macro}{\shoveright}
+%    \cs{shoveleft} and \cs{shoveright} need to do slightly different
+%    things depending on whether tags are on the left or the right and
+%    whether we're in \opt{fleqn} mode.  For compactness of code, we
+%    make the appropriate decisions at ``compile'' time rather than at
+%    load time.
+%
+%    TODO: Investigate making \cs{shoveright} behave ``properly''(?) if
+%    used on the first line of a \env{multline} and make \cs{shoveleft}
+%    behave properly if used on the last line of a \env{multline}. But
+%    in his \fn{amstex.doc} Spivak indicates those commands should never
+%    be used on a first or last line. Perhaps better to leave the
+%    question open unless/until real-life examples turn up.
+%    \begin{macrocode}
+\iftagsleft@
+    \def\shoveright#1{%
+        #1%
+        \hfilneg
+        \hskip\multlinegap
+    }
+\else
+    \def\shoveright#1{%
+        #1%
+        \hfilneg
+        \iftag@
+            \ifshifttag@
+                \hskip\multlinegap
+            \else
+                \hskip\tagwidth@
+                \hskip\multlinetaggap
+            \fi
+        \else
+            \hskip\multlinegap
+        \fi
+    }
+\fi
+
+\if@fleqn
+    \def\shoveleft#1{#1}%
+\else
+    \iftagsleft@
+        \def\shoveleft#1{%
+            \setboxz@h{$\m@th\displaystyle{}#1$}%
+            \setbox\@ne\hbox{$\m@th\displaystyle#1$}%
+            \hfilneg
+            \iftag@
+                \ifshifttag@
+                    \hskip\multlinegap
+                \else
+                    \hskip\tagwidth@
+                    \hskip\multlinetaggap
+                \fi
+            \else
+                \hskip\multlinegap
+            \fi
+            \hskip.5\wd\@ne
+            \hskip-.5\wdz@
+            #1%
+        }
+    \else
+        \def\shoveleft#1{%
+            \setboxz@h{$\m@th\displaystyle{}#1$}%
+            \setbox\@ne\hbox{$\m@th\displaystyle#1$}%
+            \hfilneg
+            \hskip\multlinegap
+            \hskip.5\wd\@ne
+            \hskip-.5\wdz@
+            #1%
+        }
+    \fi
+\fi
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%
+%    \subsection{The \env{equation} environment}
+%
+%    Rewritten from the ground up for version 2.0 to fix no-shrink and
+%    no-shortskips bugs [mjd,2000/01/06].
+%
+%    Standard \latex/ provides three environments for one-line equations:
+%    \cn{[}\cn{]}, \env{equation}, and \env{displaymath}. We add
+%    \env{equation*} as a synonym for \env{displaymath}.
+%    \begin{macrocode}
+\@saveprimitive\leqno\@@leqno
+\@saveprimitive\eqno\@@eqno
+\def\eqno{\@@eqno\let\eqno\relax\let\leqno\relax}
+\def\leqno{\@@leqno\let\leqno\relax\let\eqno\relax}
+%
+\let\veqno=\@@eqno
+\iftagsleft@ \let\veqno=\@@leqno \fi
+%    \end{macrocode}
+%
+%    Support for the \pkg{showkeys} package: provide no-op definitions
+%    for a couple of SK functions, if they are not already defined. Then
+%    we can just call them directly in our code without any extra fuss.
+%    If the \pkg{showkeys} package is loaded later, our trivial
+%    definitions will get overridden and everything works fine.
+%    \begin{macrocode}
+\@ifundefined{SK@@label}{%
+  \let\SK@@label\relax \let\SK@equationtrue\relax
+}{}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\reset@equation\@empty
+%    \end{macrocode}
+%
+%    Cf \cs{tag@in@align}. This is a bit of a mess though. Could use
+%    some work. [mjd,1999/12/21]
+%    \begin{macrocode}
+\let\alt@tag\@empty
+\def\tag@in@display#1#{\relax\tag@in@display@a{#1}}
+\def\tag@in@display@a#1#2{%
+  \iftag@
+    \invalid@tag{Multiple \string\tag}\relax
+  \else
+    \global\tag@true \nonumber \reset@equation \st@rredtrue
+    \if *\string#1%
+      \gdef\alt@tag{\def\SK@tagform@{#2\@gobble}%
+        \ifx\SK@@label\relax \let\tagform@\SK@tagform@ \fi
+      }%
+      \make@df@tag@@{#2}%
+    \else
+      \make@df@tag@@@{#2}%
+    \fi
+  \fi
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\restore@hfuzz\@empty
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\mathdisplay#1{%
+  \ifmmode \@badmath
+  \else
+    $$\def\@currenvir{#1}%
+%    \end{macrocode}
+%    Allow use of \cn{displaybreak}.
+%    \begin{macrocode}
+    \let\dspbrk@context\z@
+%    \end{macrocode}
+%    Although in some cases simpler label handling would seem to be
+%    sufficient, always using \cs{label@in@display} makes it easier to
+%    support the \pkg{showkeys} package.
+%    \begin{macrocode}
+    \let\tag\tag@in@display \let\label\label@in@display \SK@equationtrue
+    \global\let\df@label\@empty \global\let\df@tag\@empty
+    \global\tag@false
+    \let\mathdisplay@push\mathdisplay@@push
+    \let\mathdisplay@pop\mathdisplay@@pop
+    \if@fleqn
+%    \end{macrocode}
+%    Turn off overfull box messages temporarily\mdash otherwise there
+%    would be unwanted extra ones emitted during our measuring
+%    operations.
+%    \begin{macrocode}
+      \edef\restore@hfuzz{\hfuzz\the\hfuzz\relax}%
+      \hfuzz\maxdimen
+%    \end{macrocode}
+%    Initially set the equation body in a box of displaywidth. Then if
+%    the box is not overfull, as we find by checking \cs{badness}, we
+%    have acquired useful information for the subsequent processing.
+%    \begin{macrocode}
+      \setbox\z@\hbox to\displaywidth\bgroup
+        \let\split@warning\relax \restore@hfuzz
+        \everymath\@emptytoks \m@th $\displaystyle
+    \fi
+  \fi
+}
+%    \end{macrocode}
+%
+%    Arg 1 is not currently used. I thought it might come in handy for
+%    error messages.
+%    \begin{macrocode}
+\def\endmathdisplay#1{%
+  \ifmmode \else \@badmath \fi
+  \endmathdisplay@a
+  $$%
+%    \end{macrocode}
+%    I guess the following code means this structure is non-reentrant.
+%    But there is plenty of scope for tricky bugs here; suppressing them
+%    by brute force at least makes it possible to get things working
+%    correctly for normal use. [mjd,2000/01/06]
+%    \begin{macrocode}
+  \global\let\df@label\@empty \global\let\df@tag\@empty
+  \global\tag@false \global\let\alt@tag\@empty
+  \global\@eqnswfalse
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\endmathdisplay@a{%
+  \if@eqnsw \gdef\df@tag{\tagform@\theequation}\fi
+  \if@fleqn \@xp\endmathdisplay@fleqn
+  \else \ifx\df@tag\@empty \else \veqno \alt@tag \df@tag \fi
+    \ifx\df@label\@empty \else \@xp\ltx@label\@xp{\df@label}\fi
+  \fi
+  \ifnum\dspbrk@lvl>\m@ne
+    \postdisplaypenalty -\@getpen\dspbrk@lvl
+    \global\dspbrk@lvl\m@ne
+  \fi
+}
+%    \end{macrocode}
+%
+%    A boolean variable: Was that last box overfull or not? A value of 0
+%    means yes, it was overfull.
+%    \begin{macrocode}
+\let\too@wide\@ne
+%    \end{macrocode}
+%
+%    Special handling is needed for flush-left equations. We need to
+%    measure the equation body (found in box 0 after we close it with
+%    the \cs{egroup}). Then after a fairly normal test to see if it fits
+%    within the available space, we need to consider overlapping into
+%    the displayindent area if displayindent is nonzero (as in an
+%    indented list). If there is an equation number we may have to shift
+%    it by hand to a separate line when there is not enough room;
+%    we can no longer take advantage of the automatic shifting provided
+%    by the \cn{leqno}, \cn{eqno} primitives.
+%
+%    We initially add \cs{@mathmargin} glue at the end of box 0 to get
+%    an accurate overfull test. If \cs{@mathmargin} contains any shrink
+%    then we cannot reliably tell whether the box will be overfull or
+%    not simply by doing hand calculations from the actual width of the
+%    equation body. We have to actually set the box and find out what
+%    happens.
+%
+%    On the other hand if we put the \cs{@mathmargin} glue at the
+%    beginning of the box it's awkward to remove it afterwards. So we
+%    first put it in at the end and later we will move it to the
+%    beginning as needed.
+%
+%    \begin{macrocode}
+\def\endmathdisplay@fleqn{%
+  $\hfil\hskip\@mathmargin\egroup
+%    \end{macrocode}
+%    We need to save the information about whether box 0 was overfull in
+%    a variable, otherwise it will disappear in the next setbox
+%    operation. And we couldn't set the equation number box earlier than
+%    now, because the body of the equation might have contained a
+%    \cs{tag} command (well, it could have been done, but this way
+%    we can reuse the tag-handling code from elsewhere).
+%    \begin{macrocode}
+  \ifnum\badness<\inf@bad \let\too@wide\@ne \else \let\too@wide\z@ \fi
+  \ifx\@empty\df@tag
+  \else
+    \setbox4\hbox{\df@tag
+      \ifx\df@label\@empty \else \@xp\ltx@label\@xp{\df@label}\fi
+    }%
+  \fi
+  \csname emdf@%
+    \ifx\df@tag\@empty U\else \iftagsleft@ L\else R\fi\fi
+  \endcsname
+}
+%    \end{macrocode}
+%
+%    For an unnumbered flush-left equation we hope first that the
+%    the contents fit within displaywidth. If not we need to fall back
+%    on a more complicated reboxing operation.
+%    \begin{macrocode}
+\def\emdf@U{%
+  \restore@hfuzz
+  \ifodd\too@wide % not too wide: just need to swap the glue around
+    \hbox to\displaywidth{\hskip\@mathmargin\unhbox\z@\unskip}%
+  \else % M+B > displaywidth
+    \emdf@Ua
+  \fi
+}
+%    \end{macrocode}
+%
+%    Some notation: $M$ \cs{@mathmargin}, $B$ the width of the equation
+%    body, $I$ \cs{displayindent}, $D$ \cs{displaywidth}, $N$ the width
+%    of the equation number (aka the tag), $S$ \cs{mintagsep}, $C$
+%    \cs{columnwidth}. If $M+B > \mbox{displaywidth}$, and if we assume
+%    $M$ contains shrink, then the only solution left is to encroach
+%    into the displayindent space.
+%    \begin{macrocode}
+\def\emdf@Ua{%
+  \hbox to\columnwidth{%
+    \ifdim\displayindent>\z@
+      \hskip\displayindent minus\displayindent
+    \fi
+    \hskip\@mathmargin \unhbox\z@ \unskip
+  }%
+  \displayindent\z@ \displaywidth\columnwidth
+}
+%    \end{macrocode}
+%
+%    Find out first if the tag fits in ideal position. If so we can just
+%    plunk down box 2. Otherwise we need to do something more complicated.
+%    \begin{macrocode}
+\def\emdf@R{%
+  \setbox\tw@\hbox to\displaywidth{%
+    \hskip\@mathmargin \unhcopy\z@\unskip\hfil\hskip\mintagsep\copy4
+  }%
+  \restore@hfuzz
+  \ifnum\badness<\inf@bad \box\tw@ \else \emdf@Ra \fi
+}
+%    \end{macrocode}
+%
+%    We shift the equation number to line 2 if it does not fit within
+%    \cs{displaywidth}. Note that we do not first attempt to let the
+%    equation body shift leftward into the \cs{displayindent} space. If
+%    that is desired it will have to be done by hand by adding negative
+%    space at the beginning of the equation body. I don't expect this to
+%    arise very often in practice since most of the time
+%    \cs{displayindent} is zero anyway.
+%    \begin{macrocode}
+\def\emdf@Ra{%
+  \skip@\displayindent minus\displayindent
+  \displayindent\z@ \displaywidth\columnwidth
+  \spread@equation \everycr{}\tabskip\z@skip
+  \halign{\hbox to\displaywidth{##}\cr
+    \relax
+    \ifdim\skip@>\z@ \hskip\skip@ \fi
+    \hskip\@mathmargin\unhbox\z@\unskip\hfil\cr
+    \noalign{\raise@tag}%
+    \hfil\box4 \cr}%
+}
+%    \end{macrocode}
+%
+%    Find out first if the tag fits in ideal position. If so we can just
+%    plunk down box 2. Otherwise we need to do something more
+%    complicated.
+%    \begin{macrocode}
+\def\emdf@L{%
+%    \end{macrocode}
+%    Calculate the difference between $M$ and $N+S$. If the latter is
+%    greater, we don't want to add any extra glue between the number and
+%    the equation body. Otherwise the amount that we want to add is
+%    \verb'x minus x' where $x=M-(N+S)$. I.e., the distribution of
+%    spaces across the line is $N,S,x minus x,B,hfil$.
+%    \begin{macrocode}
+  \@tempdima\@mathmargin
+  \advance\@tempdima-\wd4 \advance\@tempdima-\mintagsep
+  \skip@\@tempdima minus\@tempdima
+  \setbox\tw@\hbox to\displaywidth{%
+    \copy4\hskip\mintagsep
+    \ifdim\skip@>\z@ \hskip\skip@\fi
+    \unhcopy\z@\unskip
+  }%
+  \restore@hfuzz
+  \ifnum\badness<\inf@bad \box\tw@ \else \emdf@La \fi
+}
+%    \end{macrocode}
+%
+%    If the equation body and equation number will not fit on the same
+%    line, we put the number on line 1 and the body on line 2, with the
+%    body positioned as for an unnumbered equation.
+%    \begin{macrocode}
+\def\emdf@La{%
+  \spread@equation \everycr{}\tabskip\z@skip
+  \halign{\hbox to\displaywidth{##}\cr
+    \box4 \hfil \cr
+    \noalign{\raise@tag}%
+    \hskip\@mathmargin\unhbox\z@\unskip\hfil\cr}%
+}
+%    \end{macrocode}
+%
+%    If someone has \verb'\[ \]' nested inside a minipage environment
+%    nested inside a numbered equation, the mathdisplay variables that
+%    are global will get out of whack unless we take extra care. So we
+%    make a stack and push all the variables before entering mathdisplay
+%    and pop them afterwards. But we can save a little work by not doing
+%    this at the top level, only at inner levels.
+%    \begin{macrocode}
+\newtoks\mathdisplay@stack
+\let\mathdisplay@push\@empty
+\def\mathdisplay@@push{%
+  \begingroup
+  \toks@\@xp{\df@label}\@temptokena\@xp{\df@tag}%
+  \toks8\@xp{\alt@tag}%
+  \edef\@tempa{%
+    \global\if@eqnsw\@nx\@eqnswtrue\else\@nx\@eqnswfalse\fi
+    \global\iftag@\@nx\tag@false\else\@nx\tag@true\fi
+    \gdef\@nx\df@label{\the\toks@}\gdef\@nx\df@tag{\the\@temptokena}%
+    \gdef\@nx\alt@tag{\the\toks8}%
+    \global\mathdisplay@stack{\the\mathdisplay@stack}%
+  }%
+  \global\mathdisplay@stack\@xp{\@tempa}
+  \endgroup
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\mathdisplay@pop\@empty
+\def\mathdisplay@@pop{\the\mathdisplay@stack}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\renewenvironment{equation}{%
+  \incr@eqnum
+  \mathdisplay@push
+  \st@rredfalse \global\@eqnswtrue
+  \mathdisplay{equation}%
+}{%
+  \endmathdisplay{equation}%
+  \mathdisplay@pop
+  \ignorespacesafterend
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newenvironment{equation*}{%
+  \mathdisplay@push
+  \st@rredtrue \global\@eqnswfalse
+  \mathdisplay{equation*}%
+}{%
+  \endmathdisplay{equation*}%
+  \mathdisplay@pop
+  \ignorespacesafterend
+}
+%    \end{macrocode}
+%
+%    Note: \latex/ defines the \env{displaymath} environment in
+%    terms of \cn{[} and \cn{]}.
+%    \begin{macrocode}
+\DeclareRobustCommand{\[}{\begin{equation*}}
+\DeclareRobustCommand{\]}{\end{equation*}}
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \section{Credits}
+%
+%    Much of the code for the \pkg{amsmath} package had its orgin in
+%    \fn{amstex.tex}, written by Michael Spivak. The initial work of
+%    porting \fn{amstex.tex} to \fn{amstex.sty} was done in 1988--1989
+%    by Frank Mittelbach and Rainer Sch\"opf. In 1994 David M. Jones
+%    added the support for the \opt{fleqn} option and did extensive
+%    improvements to the \env{align[at]} family of environments and to
+%    the equation number handling in general. Michael Downes at the AMS
+%    served as coordinator for the efforts of Mittelbach, Sch\"opf, and
+%    Jones, and has contributed various bug fixes and additional
+%    refinements over time.
+%
+%    Versions 1.0 and 1.1 of the package carried the name \pkg{amstex}
+%    instead of \pkg{amsmath}, to indicate its origins; the name was
+%    changed in 1994 to make it user-oriented rather than
+%    history-oriented.
+%
+\endinput
diff --git a/macros/latex-dev/required/amsmath/amsmath.ins b/macros/latex-dev/required/amsmath/amsmath.ins
new file mode 100644
index 0000000000..7a6a087359
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsmath.ins
@@ -0,0 +1,50 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999, 2000, 2013 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amsmath.sty}{\from{amsmath.dtx}{}}
+}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/amsmath/amsmath.pdf b/macros/latex-dev/required/amsmath/amsmath.pdf
new file mode 100644
index 0000000000..94a460afa4
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsmath.pdf
diff --git a/macros/latex-dev/required/amsmath/amsopn.dtx b/macros/latex-dev/required/amsmath/amsopn.dtx
new file mode 100644
index 0000000000..b7047377f3
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsopn.dtx
@@ -0,0 +1,263 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\let\savedarg\arg
+\usepackage{amsopn}
+\let\arg\savedarg
+\GetFileInfo{amsopn.sty}
+\begin{document}
+\title{The \pkg{amsopn} package}
+\author{Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amsopn.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%
+%    The \pkg{amsopn} package provides a command
+%    \cn{DeclareMathOperator} for defining new `math operator names'
+%    similar to the standard function names \cn{sin}, \cn{lim},
+%    \cn{max}, etc.
+%
+% \StopEventually{}
+%
+%    Standard file identification.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesPackage{amsopn}[2016/03/08 v2.02 operator names]
+%    \end{macrocode}
+%
+%    What \cs{nolimits@} does is keep a \cn{limits} typed by the user
+%    from having any effect. This is used for operatornames whose
+%    standard usage is never to have limits.
+%    \begin{macrocode}
+\def\nolimits@{\@ifnextchar\limits{\nolimits\@gobble}{\nolimits}}
+%    \end{macrocode}
+%
+%    In operator names, it is sometimes desired to have text-mode
+%    punctuation characters such as |*-/:'|.
+%    Because the body of an
+%    operator name is set in math mode, these few punctuation
+%    characters will not come out right (wrong symbol/and or wrong
+%    spacing). The purpose of \cs{newmcodes@} is to make them act like
+%    their normal text versions.
+%
+%    Where practical, we use decimal numbers to cut down main mem
+%    usage (\qc{\"} not needed).
+%    use |\Umathcodedefnum| with xetex and LuaTeX to avoid problems
+%    using |\mathcode| if |-| has already been defined using |\Umathcode|.
+% \changes{v2.02}{2016/03/08}{Unicode TeX version of \cs{newmcodes@}}
+%    \begin{macrocode}
+\begingroup \catcode`\"=12
+\ifx\Umathcode\@undefined
+\gdef\newmcodes@{\mathcode`\'39\mathcode`\*42\mathcode`\."613A%
+%    \end{macrocode}
+%    Define \cs{std@minus} for \cs{relbar} use; otherwise there are
+%    problems with arrows constructed with relbar.
+%    \begin{macrocode}
+  \ifnum\mathcode`\-=45 \else
+    \mathchardef\std@minus\mathcode`\-\relax
+  \fi
+  \mathcode`\-45\mathcode`\/47\mathcode`\:"603A\relax}
+%    \end{macrocode}
+%    \begin{macrocode}
+\else
+%    \end{macrocode}
+%    \begin{macrocode}
+\gdef\newmcodes@{\mathcode`\'39\mathcode`\*42\mathcode`\."613A%
+  \ifnum\Umathcodenum`\-=45 \else
+    \Umathcharnumdef\std@minus\Umathcodenum`\-\relax
+  \fi
+  \mathcode`\-45\mathcode`\/47\mathcode`\:"603A\relax}
+%    \end{macrocode}
+%    \begin{macrocode}
+\fi
+\endgroup
+%    \end{macrocode}
+%
+%    The command \cs{operatorname} prints its argument as a `math
+%    operator' like \cs{sin} or \cs{det}, with proper font and spacing.
+%    \begin{macrocode}
+\DeclareRobustCommand{\operatorname}{%
+  \@ifstar{\qopname\newmcodes@ m}%
+          {\qopname\newmcodes@ o}}%
+%    \end{macrocode}
+%    In the interior of the \cs{mathop} we need a null object (we choose
+%    a zero kern for minimum waste of main mem) in order to guard
+%    against the case where \arg{3} is a single letter; \tex/ will seize
+%    it and center it on the math axis if there is nothing else inside
+%    the \cs{mathop} atom.
+%    \begin{macrocode}
+\DeclareRobustCommand{\qopname}[3]{%
+  \mathop{#1\kern\z@\operator@font#3}%
+  \csname n#2limits@\endcsname}
+%    \end{macrocode}
+%
+%  \begin{macro}{\DeclareMathOperator}
+%    The command \cn{DeclareMathOperator} defines the first argument to
+%    be an operator name whose text is the second argument. The star
+%    form means that the operator name should take limits (like \cn{max}
+%    or \cn{lim}).
+%    \begin{macrocode}
+\newcommand{\DeclareMathOperator}{%
+  \@ifstar{\@declmathop m}{\@declmathop o}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    In the basic set of operator names (below) we did not use
+%    \cn{DeclareRobustCommand} because of the hash table cost. But we
+%    use it here to minimize the chances of trouble, since we are
+%    producing a user-defined command.
+%    \begin{macrocode}
+\long\def\@declmathop#1#2#3{%
+  \@ifdefinable{#2}{%
+    \DeclareRobustCommand{#2}{\qopname\newmcodes@#1{#3}}}}
+%
+\@onlypreamble\DeclareMathOperator
+\@onlypreamble\@declmathop
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\arccos{\qopname\relax o{arccos}}
+\def\arcsin{\qopname\relax o{arcsin}}
+\def\arctan{\qopname\relax o{arctan}}
+\def\arg{\qopname\relax o{arg}}
+\def\cos{\qopname\relax o{cos}}
+\def\cosh{\qopname\relax o{cosh}}
+\def\cot{\qopname\relax o{cot}}
+\def\coth{\qopname\relax o{coth}}
+\def\csc{\qopname\relax o{csc}}
+\def\deg{\qopname\relax o{deg}}
+\def\det{\qopname\relax m{det}}
+\def\dim{\qopname\relax o{dim}}
+\def\exp{\qopname\relax o{exp}}
+\def\gcd{\qopname\relax m{gcd}}
+\def\hom{\qopname\relax o{hom}}
+\def\inf{\qopname\relax m{inf}}
+\def\injlim{\qopname\relax m{inj\,lim}}
+\def\ker{\qopname\relax o{ker}}
+\def\lg{\qopname\relax o{lg}}
+\def\lim{\qopname\relax m{lim}}
+\def\liminf{\qopname\relax m{lim\,inf}}
+\def\limsup{\qopname\relax m{lim\,sup}}
+\def\ln{\qopname\relax o{ln}}
+\def\log{\qopname\relax o{log}}
+\def\max{\qopname\relax m{max}}
+\def\min{\qopname\relax m{min}}
+\def\Pr{\qopname\relax m{Pr}}
+\def\projlim{\qopname\relax m{proj\,lim}}
+\def\sec{\qopname\relax o{sec}}
+\def\sin{\qopname\relax o{sin}}
+\def\sinh{\qopname\relax o{sinh}}
+\def\sup{\qopname\relax m{sup}}
+\def\tan{\qopname\relax o{tan}}
+\def\tanh{\qopname\relax o{tanh}}
+%    \end{macrocode}
+%
+% \begin{macro}{\operator@font}
+% \begin{macro}{\operatorfont}
+%    This command is provided to allow the document styles to decide in
+%    which way math operators like `max' or `log' are typeset. The
+%    default is to set them in \meta{math group} zero of the current
+%    math version. The original name was \cs{operator@font}, retained
+%    for compatibility; the second name was added to make it
+%    more accessible so that users can call this font for use in special
+%    constructs that are not ordinary operator names but conceptually
+%    related.
+%    \begin{macrocode}
+\def\operator@font{\mathgroup\symoperators}
+\def\operatorfont{\operator@font}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    For backwards compatibility we keep this old command name for the
+%    time being:
+%    \begin{macrocode}
+\def\operatornamewithlimits{\operatorname*}
+%    \end{macrocode}
+%
+%    These macros use \cs{mathpalette}s so that they will change size
+%    in script and scriptscript styles, though it's hard to imagine they
+%    will ever be used there (the arrows, particularly, look bad in
+%    subscript sizes). Notice that the use of \cs{ex@} means that the
+%    vertical spacing may not be optimal in script and scriptscript
+%    sizes. Unfortunately \tex/ provides no easy way to do math mode
+%    vertical spacing that varies with current math style like mu units.
+%    \begin{macrocode}
+\def\varlim@#1#2{%
+  \vtop{\m@th\ialign{##\cr
+    \hfil$#1\operator@font lim$\hfil\cr
+    \noalign{\nointerlineskip\kern1.5\ex@}#2\cr
+    \noalign{\nointerlineskip\kern-\ex@}\cr}}%
+}
+\def\varinjlim{%
+  \mathop{\mathpalette\varlim@{\rightarrowfill@\textstyle}}\nmlimits@
+}
+\def\varprojlim{%
+  \mathop{\mathpalette\varlim@{\leftarrowfill@\textstyle}}\nmlimits@
+}
+\def\varliminf{\mathop{\mathpalette\varliminf@{}}\nmlimits@}
+\def\varliminf@#1{\@@underline{\vrule\@depth.2\ex@\@width\z@
+   \hbox{$#1\m@th\operator@font lim$}}}
+\def\varlimsup{\mathop{\mathpalette\varlimsup@{}}\nmlimits@}
+\def\varlimsup@#1{\@@overline{\hbox{$#1\m@th\operator@font lim$}}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\nmlimits@\displaylimits
+\DeclareOption{namelimits}{\let\nmlimits@\displaylimits}
+\DeclareOption{nonamelimits}{\let\nmlimits@\nolimits}
+\ProcessOptions\relax
+%    \end{macrocode}
+%
+%    If we don't load the \pkg{amsgen} package then the use of \cs{ex@}
+%    in \cs{varlim@} will lead to trouble.
+%    \begin{macrocode}
+\RequirePackage{amsgen}\relax
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \changes{v1.2a}{1995/02/20}{Fixed operatorname
+%   (shouldn't have same limits behavior as operatorname*)}
+%
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amsopn.ins b/macros/latex-dev/required/amsmath/amsopn.ins
new file mode 100644
index 0000000000..8c977446cc
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsopn.ins
@@ -0,0 +1,50 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amsopn.sty}{\from{amsopn.dtx}{}}
+}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/amsmath/amsopn.pdf b/macros/latex-dev/required/amsmath/amsopn.pdf
new file mode 100644
index 0000000000..f854a4246b
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsopn.pdf
diff --git a/macros/latex-dev/required/amsmath/amstex.sty b/macros/latex-dev/required/amsmath/amstex.sty
new file mode 100644
index 0000000000..edb57c1214
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amstex.sty
@@ -0,0 +1,2025 @@
+%
+% \iffalse meta-comment
+%
+% Copyright 1995, 1999 American Mathematical Society.
+% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%    This file was generated from version 1.2beta of amstex.dtx and then
+%    underwent additional hand-editing.
+\if@compatibility \else \catcode`\%=9 \fi
+%\PackageError{amstex}{%
+%Package `amstex' is obsolete, substituting `amsmath'}{You
+%should use \string\usepackage{amsmath} instead. If
+%that does not give satisfactory results, rename your previous copy
+%of amstex.sty to amstex12beta.sty and call it with
+%\string\usepackage{amstex12beta}.}
+%\catcode`\%=14 \relax \input{amsmath.sty}\endinput
+%
+\ProvidesPackage{amstex}[1999/11/15 v1.2f AMS extra math features]
+\let\@amsfonts=T
+\DeclareOption{noamsfonts}{\let\@amsfonts=F}
+\DeclareOption{psamsfonts}{\let\@amsfonts=P}
+\DeclareOption{intlimits}{\let\ilimits@\displaylimits}
+\DeclareOption{nointlimits}{\let\ilimits@\nolimits}
+\DeclareOption{sumlimits}{\let\slimits@\displaylimits}
+\DeclareOption{nosumlimits}{\let\slimits@\nolimits}
+\DeclareOption{namelimits}{\let\nlimits@\displaylimits}
+\DeclareOption{nonamelimits}{\let\nlimits@\nolimits}
+\newif\ifctagsplit@
+\newif\iftagsleft@
+\DeclareOption{leqno}{\tagsleft@true}
+\DeclareOption{reqno}{\tagsleft@false}
+\DeclareOption{centertags}{\ctagsplit@true}
+\DeclareOption{tbtags}{\ctagsplit@false}
+\newif\if@fleqn
+\newskip\@mathmargin
+\@mathmargin\@centering
+\DeclareOption{fleqn}{%
+    \@fleqntrue
+    \@mathmargin\m@ne sp
+    \AtBeginDocument{%
+        \ifdim\@mathmargin=\m@ne sp
+            \@mathmargin\leftmargini
+        \fi
+    }%
+}
+\DeclareOption{righttag}{\tagsleft@false}
+\DeclareOption{ctagsplt}{\ctagsplit@true}
+\DeclareOption{intlim}{\let\ilimits@\displaylimits}
+\DeclareOption{nosumlim}{\let\slimits@\nolimits}
+\DeclareOption{nonamelm}{\let\nlimits@\nolimits}
+\ExecuteOptions{nointlimits,sumlimits,namelimits,centertags}
+\ProcessOptions
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% In this section \RequirePackage statements were replaced with the
+%% contents of the referenced files.
+%%%     filename        = "amsgen.dtx",
+%%%     version         = "1.2beta",
+%%%     date            = "1994/12/13",
+\providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
+  \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
+  \ifx\@tempa\@tempb \global\let#2#1%
+  \else
+    \edef\@tempb{\meaning#2}%
+    \ifx\@tempa\@tempb
+    \else
+      \@latex@error{Unable to properly define \string#2; primitive
+      \noexpand#1no longer primitive}\@eha
+    \fi
+  \fi
+  \endgroup}
+\let\@xp=\expandafter
+\let\@nx=\noexpand
+\newtoks\@emptytoks
+\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
+\def\@ifempty#1{\@xifempty#1@@..\@nil}
+\long\def\@xifempty#1#2@#3#4#5\@nil{%
+  \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
+\long\def\@ifnotempty#1{\@ifempty{#1}{}}
+\def\FN@{\futurelet\@let@token}
+\def\DN@{\def\next@}
+\def\RIfM@{\relax\ifmmode}
+\def\setboxz@h{\setbox\z@\hbox}
+\def\wdz@{\wd\z@}
+\def\boxz@{\box\z@}
+\def\relaxnext@{\let\@let@token\relax}
+\def\new@ifnextchar#1#2#3{%
+  \let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}\futurelet
+    \@tempc\new@ifnch}
+\def\new@ifnch{\ifx\@tempc \@tempe \let\@tempd\@tempa
+             \else\let\@tempd\@tempb\fi\@tempd}
+\def\new@ifstar#1#2{\new@ifnextchar *{\def\@tempa*{#1}\@tempa}{#2}}
+\@ifundefined{every@math@size}{%
+\let\every@math@size=\every@size
+\def\glb@settings{%
+     \expandafter\ifx\csname S@\f@size\endcsname\relax
+       \calculate@math@sizes
+     \fi
+     \csname S@\f@size\endcsname
+      \ifmath@fonts
+        \begingroup
+          \escapechar\m@ne
+          \csname mv@\math@version \endcsname
+          \globaldefs\@ne
+          \let \glb@currsize \f@size
+          \math@fonts
+        \endgroup
+        \the\every@math@size
+      \else
+      \fi
+}
+\def\set@fontsize#1#2#3{%
+    \@defaultunits\@tempdimb#2pt\relax\@nnil
+    \edef\f@size{\strip@pt\@tempdimb}%
+    \@defaultunits\@tempskipa#3pt\relax\@nnil
+    \edef\f@baselineskip{\the\@tempskipa}%
+    \edef\f@linespread{#1}%
+    \let\baselinestretch\f@linespread
+      \def\size@update{%
+        \baselineskip\f@baselineskip\relax
+        \baselineskip\f@linespread\baselineskip
+        \normalbaselineskip\baselineskip
+        \setbox\strutbox\hbox{%
+          \vrule\@height.7\baselineskip
+                \@depth.3\baselineskip
+                \@width\z@}%
+%%%     \the\every@size
+        \let\size@update\relax}%
+  }
+}{}% end \@ifundefined test
+\newdimen\ex@
+\addto@hook\every@math@size{\compute@ex@}
+\def\compute@ex@{%
+  \begingroup
+  \dimen@-\f@size\p@
+  \ifdim\dimen@<-20\p@
+    \global\ex@ 1.5\p@
+  \else
+    \advance\dimen@10\p@ \multiply\dimen@\tw@
+    \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%
+    \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
+    \advance\dimen@-\@m sp % fudge factor
+    \vfuzz\p@
+    \def\do{\ifdim\dimen@>\z@
+      \vfuzz=.97\vfuzz
+      \advance\dimen@ -\p@
+      \@xp\do \fi}%
+    \do
+    \dimen@\p@ \advance\dimen@-\vfuzz
+    \global\ex@\p@
+    \global\advance\ex@ \@tempa\dimen@
+  \fi
+  \endgroup
+}
+\def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
+\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
+  \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
+\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
+  \m@th$#2#3$}}
+\def\nomath@env{\PackageError{amstex}{%
+  \string\begin{\@currenvir} allowed only in paragraph mode%
+}\@ehb% "You've lost some text"
+}
+\def\Invalid@@{Invalid use of \string}
+\def\nonmatherr@#1{\PackageError{amsfonts}%
+    {\noexpand#1allowed only in math mode}\@ehd}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%     filename        = "amstext.dtx",
+%%%     version         = "1.2beta",
+%%%     date            = "1994/12/13",
+\DeclareRobustCommand{\text}{%
+  \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
+\let\nfss@text\text
+\def\text@#1{\mathchoice
+  {\textdef@\displaystyle\f@size{#1}}%
+  {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
+  {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
+  {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
+  \check@mathfonts
+}
+\def\textdef@#1#2#3{\hbox{{%
+                    \everymath{#1}%
+                    \let\f@size#2\selectfont
+                    #3}}}
+\newif\iffirstchoice@
+\firstchoice@true
+\def\stepcounter#1{%
+  \iffirstchoice@
+     \global\expandafter\advance\csname c@#1\endcsname \@ne
+     \begingroup
+         \let\@elt\@stpelt
+         \csname cl@#1\endcsname
+     \endgroup
+  \fi}
+\toks@{\iffirstchoice@\else\@xp\@gobblefour\fi\protect}
+\edef\GenericInfo{\the\toks@
+  \@xp\@nx\csname GenericInfo \endcsname}
+\edef\GenericWarning{\the\toks@
+  \@xp\@nx\csname GenericWarning \endcsname}
+\toks@{\iffirstchoice@\else
+  \@xp\@xp\@xp\@gobblefour
+  \@xp\@gobbletwo\fi\protect}
+\edef\GenericError{\the\toks@
+  \@xp\@nx\csname GenericError \endcsname}
+\def\label#1{\@bsphack\iffirstchoice@\if@filesw {\let\thepage\relax
+   \def\protect{\noexpand\noexpand\noexpand}%
+\xdef\@gtempa{\write\@auxout{\string
+      \newlabel{#1}{{\@currentlabel}{\thepage}}}}}\@gtempa
+   \if@nobreak \ifvmode\nobreak\fi\fi\fi\fi\@esphack}
+\begingroup \catcode`\"=12
+\gdef\mathhexbox#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
+\endgroup
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%     filename        = "amsfonts.dtx",
+%%%     version         = "1.2beta",
+%%%     date            = "1994/12/13",
+\newbox\Mathstrutbox@
+\setbox\Mathstrutbox@=\hbox{}
+\def\Mathstrut@{\copy\Mathstrutbox@}
+\addto@hook\every@math@size{\setbox\z@\hbox{\normalfont(}%
+  \ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@}
+\newbox\strutbox@
+\def\strut@{\copy\strutbox@}
+\addto@hook\every@math@size{%
+  \global\setbox\strutbox@\hbox{\lower.5\normallineskiplimit
+         \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
+\def\big{\bBigg@\@ne}
+\def\Big{\bBigg@{1.5}}
+\def\bigg{\bBigg@\tw@}
+\def\Bigg{\bBigg@{2.5}}
+\def\bBigg@#1#2{%
+   {%
+    \hbox{$\left#2\vcenter to#1\big@size{}\right.%
+           \n@space
+     $}}}
+\addto@hook\every@math@size{%
+  \global\big@size 1.2\ht\Mathstrutbox@
+  \global\advance\big@size 1.2\dp\Mathstrutbox@ }
+\newdimen\big@size
+%% msam, msbm, eufm fonts dealt with at end of file
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%     filename        = "amsbsy.dtx",
+%%%     version         = "1.2beta",
+%%%     date            = "1994/10/27",
+\DeclareRobustCommand{\boldsymbol}[1]{%
+  \begingroup
+  \let\@nomath\@gobble \mathversion{bold}%
+  \math@atom{#1}{%
+  \mathchoice%
+    {\hbox{$\m@th\displaystyle#1$}}%
+    {\hbox{$\m@th\textstyle#1$}}%
+    {\hbox{$\m@th\scriptstyle#1$}}%
+    {\hbox{$\m@th\scriptscriptstyle#1$}}}%
+  \endgroup}
+\def\math@atom#1#2{%
+   \binrel@{#1}\binrel@@{#2}}
+\DeclareRobustCommand{\pmb}{%
+  \ifmmode\else \expandafter\pmb@@\fi\mathpalette\pmb@}
+\def\pmb@@#1#2#3{\leavevmode\setboxz@h{#3}%
+   \dimen@-\wdz@
+   \kern-.5\ex@\copy\z@
+   \kern\dimen@\kern.25\ex@\raise.4\ex@\copy\z@
+   \kern\dimen@\kern.25\ex@\box\z@
+}
+\newdimen\pmbraise@
+\def\pmb@#1#2{\setbox8\hbox{$\m@th#1{#2}$}%
+  \setboxz@h{$\m@th#1\mkern.5mu$}\pmbraise@\wdz@
+  \binrel@{#2}%
+  \dimen@-\wd8 %
+  \binrel@@{%
+    \mkern-.8mu\copy8 %
+    \kern\dimen@\mkern.4mu\raise\pmbraise@\copy8 %
+    \kern\dimen@\mkern.4mu\box8 }%
+}
+\def\binrel@#1{\begingroup
+  \setboxz@h{\thinmuskip0mu
+    \medmuskip\m@ne mu\thickmuskip\@ne mu
+    \setbox\tw@\hbox{$#1\m@th$}\kern-\wd\tw@
+    ${}#1{}\m@th$}%
+  \edef\@tempa{\endgroup\let\noexpand\binrel@@
+    \ifdim\wdz@<\z@ \mathbin
+    \else\ifdim\wdz@>\z@ \mathrel
+    \else \relax\fi\fi}%
+  \@tempa
+}
+\let\binrel@@\relax
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\AmSTeX{\protect\AmS-\protect\TeX{}}
+\def\AmS{{\protect\AmSfont
+  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
+\def\AmSfont{%
+  \usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
+\def\prim@s{\prime\futurelet\@let@token\pr@m@s}
+\def\pr@m@s{%
+  \ifx\@let@token'\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
+\let\@prime=\prime
+\renewcommand{\prime}{{\kern\z@\@prime}}
+\DeclareRobustCommand{\mspace}[3]{%
+  \ifmmode\mskip#1#2\else\kern#1#3\fi\relax}
+\renewcommand{\,}{\mspace+\thinmuskip{.1667em}}
+\let\thinspace\,
+\renewcommand{\!}{\mspace-\thinmuskip{.1667em}}
+\let\negthinspace\!
+\renewcommand{\:}{\mspace+\medmuskip{.2222em}}
+\let\medspace\:
+\newcommand{\negmedspace}{\mspace-\medmuskip{.2222em}}
+\renewcommand{\;}{\mspace+\thickmuskip{.2777em}}
+\let\thickspace\;
+\newcommand{\negthickspace}{\mspace-\thickmuskip{.2777em}}
+\def\implies{\DOTSB\;\Longrightarrow\;}
+\def\impliedby{\DOTSB\;\Longleftarrow\;}
+\begingroup \catcode`\"=12 % in case activated by a preceding package
+\gdef\And{\DOTSB\;\mathchar"3026 \;}
+\gdef\lvert{\delimiter"426A30C }
+\gdef\rvert{\delimiter"526A30C }
+\gdef\lVert{\delimiter"426B30D }
+\gdef\rVert{\delimiter"526B30D }
+\endgroup % restore "
+\DeclareRobustCommand{\frac}{\new@ifnextchar[{\frfrac{}}{\frfrac{}[]}}
+\def\frfrac#1[#2]#3#4{\def\next@{#2}%
+  \ifx\next@\@empty \def\next@{#1{#3\over#4}}%
+  \else \def\next@{{#1{#3\above#2\relax#4}}}%
+  \fi
+  \next@}
+\def\dfrac{\protect\frfrac\displaystyle[]}
+\def\tfrac{\protect\frfrac\textstyle[]}
+\DeclareRobustCommand{\binom}{\frbinom{}}
+\def\frbinom#1#2#3{{#1{#2\atopwithdelims()#3}}}
+\def\dbinom{\protect\frbinom\displaystyle}
+\def\tbinom{\protect\frbinom\textstyle}
+\def\colon{\nobreak\mskip2mu\mathpunct{}\nonscript
+  \mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
+\begingroup \catcode`\"=12
+\DeclareMathSymbol{\coprod@}{\mathop}{largesymbols}{"60}
+\gdef\coprod{\DOTSB\coprod@\slimits@}
+\DeclareMathSymbol{\bigvee@}{\mathop}{largesymbols}{"57}
+\gdef\bigvee{\DOTSB\bigvee@\slimits@}
+\DeclareMathSymbol{\bigwedge@}{\mathop}{largesymbols}{"56}
+\gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
+\DeclareMathSymbol{\biguplus@}{\mathop}{largesymbols}{"55}
+\gdef\biguplus{\DOTSB\biguplus@\slimits@}
+\DeclareMathSymbol{\bigcap@}{\mathop}{largesymbols}{"54}
+\gdef\bigcap{\DOTSB\bigcap@\slimits@}
+\DeclareMathSymbol{\bigcup@}{\mathop}{largesymbols}{"53}
+\gdef\bigcup{\DOTSB\bigcup@\slimits@}
+\DeclareMathSymbol{\prod@}{\mathop}{largesymbols}{"51}
+\gdef\prod{\DOTSB\prod@\slimits@}
+\DeclareMathSymbol{\sum@}{\mathop}{largesymbols}{"50}
+\gdef\sum{\DOTSB\sum@\slimits@}
+\DeclareMathSymbol{\bigotimes@}{\mathop}{largesymbols}{"4E}
+\gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
+\DeclareMathSymbol{\bigoplus@}{\mathop}{largesymbols}{"4C}
+\gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
+\DeclareMathSymbol{\bigodot@}{\mathop}{largesymbols}{"4A}
+\gdef\bigodot{\DOTSB\bigodot@\slimits@}
+\DeclareMathSymbol{\bigsqcup@}{\mathop}{largesymbols}{"46}
+\gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
+\endgroup
+\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont ...}\vss}}}}
+\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont....}\vss}}}}
+\def~{\nobreakspace}
+\DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newif\if@display
+\everydisplay\expandafter{\the\everydisplay \@displaytrue}
+\def\int{\DOTSI\intop\ilimits@}
+\def\oint{\DOTSI\ointop\ilimits@}
+\def\intkern@{\mkern-6mu\mathchoice{\mkern-3mu}{}{}{}}
+\def\intdots@{\mathchoice{\@cdots}%
+ {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
+
+\def\iint{\DOTSI\protect\ints@\tw@}
+\def\iiint{\DOTSI\protect\ints@\thr@@}
+\def\iiiint{\DOTSI\protect\ints@{4}}
+\def\idotsint{\DOTSI\protect\ints@\z@}
+
+\def\ints@#1{%
+  \mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
+  \mathop{\mkern7mu\mathchoice{\mkern2mu}{}{}{}%
+    \intop\ifnum#1=\z@\intdots@
+    \else\intkern@\fi
+    \ifnum#1>\tw@\intop\intkern@\fi
+    \ifnum#1>\thr@@\intop\intkern@\fi
+    \intop
+  }\ilimits@
+}
+\def\nolimits@{%
+  \DN@{\nolimits\ifx\@let@token\limits\expandafter\@gobble\fi}%
+  \FN@\next@}
+\begingroup \catcode`\"=12
+\gdef\newmcodes@{\mathcode`\'39\mathcode`\*42\mathcode`\."613A%
+ \mathcode`\-45\mathcode`\/47\mathcode`\:"603A\relax}
+\endgroup
+\DeclareRobustCommand{\operatorname}{%
+  \@ifstar{\qopname\newmcodes@ n}%
+          {\qopname\newmcodes@{no}}}%
+\DeclareRobustCommand{\qopname}[3]{\mathop{#1\kern\z@\operator@font#3}%
+  \csname #2limits@\endcsname}
+\def\arccos{\qopname\relax{no}{arccos}}
+\def\arcsin{\qopname\relax{no}{arcsin}}
+\def\arctan{\qopname\relax{no}{arctan}}
+\def\arg{\qopname\relax{no}{arg}}
+\def\cos{\qopname\relax{no}{cos}}
+\def\cosh{\qopname\relax{no}{cosh}}
+\def\cot{\qopname\relax{no}{cot}}
+\def\coth{\qopname\relax{no}{coth}}
+\def\csc{\qopname\relax{no}{csc}}
+\def\deg{\qopname\relax{no}{deg}}
+\def\det{\qopname\relax n{det}}
+\def\dim{\qopname\relax{no}{dim}}
+\def\exp{\qopname\relax{no}{exp}}
+\def\gcd{\qopname\relax n{gcd}}
+\def\hom{\qopname\relax{no}{hom}}
+\def\inf{\qopname\relax n{inf}}
+\def\injlim{\qopname\relax n{inj\,lim}}
+\def\ker{\qopname\relax{no}{ker}}
+\def\lg{\qopname\relax{no}{lg}}
+\def\lim{\qopname\relax n{lim}}
+\def\liminf{\qopname\relax n{lim\,inf}}
+\def\limsup{\qopname\relax n{lim\,sup}}
+\def\ln{\qopname\relax{no}{ln}}
+\def\log{\qopname\relax{no}{log}}
+\def\max{\qopname\relax n{max}}
+\def\min{\qopname\relax n{min}}
+\def\Pr{\qopname\relax n{Pr}}
+\def\projlim{\qopname\relax n{proj\,lim}}
+\def\sec{\qopname\relax{no}{sec}}
+\def\sin{\qopname\relax{no}{sin}}
+\def\sinh{\qopname\relax{no}{sinh}}
+\def\sup{\qopname\relax n{sup}}
+\def\tan{\qopname\relax{no}{tan}}
+\def\tanh{\qopname\relax{no}{tanh}}
+\def\operator@font{\mathgroup\symoperators}
+\def\operatornamewithlimits{\operatorname*}
+\def\varlim@#1#2{\mathop{\vtop{\ialign{##\crcr
+ \hfil$#1\m@th\operator@font lim$\hfil\crcr
+ \noalign{\nointerlineskip\kern\ex@}#2#1\crcr
+ \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
+\def\varinjlim{\mathpalette\varlim@\rightarrowfill@}
+\def\varprojlim{\mathpalette\varlim@\leftarrowfill@}
+\def\varliminf{\mathpalette\varliminf@{}}
+\def\varliminf@#1{\mathop{\@@underline{\vrule\@depth.2\ex@\@width\z@
+   \hbox{$#1\m@th\operator@font lim$}}}}
+\def\varlimsup{\mathpalette\varlimsup@{}}
+\def\varlimsup@#1{\mathop{\@@overline
+  {\hbox{$#1\m@th\operator@font lim$}}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\numberwithin#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}{%
+  \@ifundefined{c@#2}{\@nocnterr{#2}}{%
+  \@addtoreset{#1}{#2}%
+  \toks@\expandafter\expandafter\expandafter{\csname the#1\endcsname}%
+  \expandafter\xdef\csname the#1\endcsname
+    {\expandafter\noexpand\csname the#2\endcsname
+     .\the\toks@}}}}
+\def\eqref#1{\textup{\tagform@{\ref{#1}}}}
+\def\bmod{\mskip-\medmuskip\mkern5mu\mathbin
+  {\operator@font mod}\penalty900
+  \mkern5mu\mskip-\medmuskip}
+\def\pod#1{\allowbreak\if@display\mkern18mu\else\mkern8mu\fi(#1)}
+\def\pmod#1{\pod{{\operator@font mod}\mkern6mu#1}}
+\def\mod#1{\allowbreak\if@display\mkern18mu
+  \else\mkern12mu\fi{\operator@font mod}\,\,#1}
+\newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
+  \strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
+  \kern-\nulldelimiterspace}
+\def\lcfrac{\cfrac[l]}
+\def\rcfrac{\cfrac[r]}
+\def\overset#1#2{\binrel@{#2}%
+  \binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
+\def\underset#1#2{\binrel@{#2}%
+  \binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
+\def\sideset#1#2#3{%
+  \setbox\z@\hbox{$\displaystyle{\vphantom{#3}}#1{#3}\m@th$}%
+  \setbox\tw@\hbox{$\displaystyle{#3}#2\m@th$}%
+  \hskip\wd\z@\hskip-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd\z@
+  {\vphantom{#3}}#1{#3}#2}}
+\renewcommand{\smash}[2][tb]{%
+  \def\smash@{#1}%
+  \ifmmode\expandafter\mathpalette\expandafter\mathsm@sh\else
+        \expandafter\makesm@sh\fi{#2}}
+\def\finsm@sh{\def\mb@t{\ht\z@\z@}\def\mb@b{\dp\z@\z@}%
+  \def\mb@tb{\mb@t\mb@b}%
+  {\csname mb@\smash@\endcsname}%
+  \leavevmode\boxz@}
+\def\rightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+  $#1\copy\z@\mkern-6mu\cleaders
+  \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+  \mkern-6mu\mathord\rightarrow$}
+\def\leftarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+  $#1\mathord\leftarrow\mkern-6mu\cleaders
+  \hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
+  \mkern-6mu\box\z@$}
+\def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
+  $#1\mathord\leftarrow\mkern-6mu\cleaders
+  \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+  \mkern-6mu\mathord\rightarrow$}
+\def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
+ \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
+\def\overrightarrow{\mathpalette{\overarrow@\rightarrowfill@}}
+\def\overleftarrow{\mathpalette{\overarrow@\leftarrowfill@}}
+\def\overleftrightarrow{\mathpalette{\overarrow@\leftrightarrowfill@}}
+\def\underarrow@#1#2#3{%
+ \vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
+ \noalign{\nointerlineskip\kern-.5\ex@}#1#2\crcr}}}
+\def\underrightarrow{\mathpalette{\underarrow@\rightarrowfill@}}
+\def\underleftarrow{\mathpalette{\underarrow@\leftarrowfill@}}
+\def\underleftrightarrow{\mathpalette{\underarrow@\leftrightarrowfill@}}
+\let\ifgtest@\iffalse                              % initial value
+\def\gtest@true{\global\let\ifgtest@\iftrue}
+\def\gtest@false{\global\let\ifgtest@\iffalse}
+\let\DOTSI\relax
+\let\DOTSB\relax
+\let\DOTSX\relax
+{\uccode`7=`\\ \uccode`8=`m \uccode`9=`a \uccode`0=`t \uccode`!=`h
+ \uppercase{%
+  \gdef\math@#1#2#3#4#5#6\math@{\gtest@false\ifx 7#1\ifx 8#2%
+  \ifx 9#3\ifx 0#4\ifx !#5\xdef\meaning@{#6}\gtest@true
+  \fi\fi\fi\fi\fi}}}
+{\uccode`7=`c \uccode`8=`h \uccode`9=`\"
+ \uppercase{\gdef\mathch@#1#2#3#4#5#6\mathch@{\gtest@false
+  \ifx 7#1\ifx 8#2\ifx 9#5\gtest@true\xdef\meaning@{9#6}\fi\fi\fi}}}
+\newcount\classnum@
+\def\getmathch@#1.#2\getmathch@{\classnum@#1 \divide\classnum@4096
+ \ifcase\number\classnum@\or\or\gdef\thedots@{\dotsb@}\or
+ \gdef\thedots@{\dotsb@}\fi}
+{\uccode`4=`b \uccode`5=`i \uccode`6=`n
+ \uppercase{\gdef\mathbin@#1#2#3{\relaxnext@
+  \def\nextii@##1\mathbin@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+  \gtest@false\DN@##1\mathbin@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`4=`r \uccode`5=`e \uccode`6=`l
+ \uppercase{\gdef\mathrel@#1#2#3{\relaxnext@
+  \def\nextii@##1\mathrel@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\mathrel@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`5=`m \uccode`6=`a \uccode`7=`c
+ \uppercase{\gdef\macro@#1#2#3#4\macro@{\gtest@false
+  \ifx 5#1\ifx 6#2\ifx 7#3\gtest@true
+  \xdef\meaning@{\macro@@#4\macro@@}\fi\fi\fi}}}
+\def\macro@@#1->#2\macro@@{#2}
+\newcount\DOTSCASE@
+{\uccode`6=`\\ \uccode`7=`D \uccode`8=`O \uccode`9=`T \uccode`0=`S
+ \uppercase{\gdef\DOTS@#1#2#3#4#5{\gtest@false\DN@##1\DOTS@{}%
+  \ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\ifx 0#5\let\next@\DOTS@@
+  \fi\fi\fi\fi\fi
+  \next@}}}
+{\uccode`3=`B \uccode`4=`I \uccode`5=`X
+ \uppercase{\gdef\DOTS@@#1{\relaxnext@
+  \def\nextii@##1\DOTS@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+  \DN@{\FN@\nextii@}%
+  \ifx 3#1\global\DOTSCASE@\z@\else
+  \ifx 4#1\global\DOTSCASE@\@ne\else
+  \ifx 5#1\global\DOTSCASE@\tw@\else\DN@##1\DOTS@{}%
+  \fi\fi\fi\next@}}}
+{\uccode`5=`\\ \uccode`6=`n \uccode`7=`o \uccode`8=`t
+ \uppercase{\gdef\not@#1#2#3#4{\relaxnext@
+  \def\nextii@##1\not@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\not@{}%
+ \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\DN@{\FN@\nextii@}\fi\fi\fi
+ \fi\next@}}}
+\def\keybin@{\gtest@true
+  \ifx\@let@token+\else\ifx\@let@token=\else\ifx\@let@token<%
+  \else\ifx\@let@token>\else\ifx\@let@token-\else\ifx\@let@token*%
+  \else\ifx\@let@token:\else\gtest@false\fi\fi\fi\fi\fi\fi\fi}
+\@ifundefined{@ldots}{\def\@ldots{\mathellipsis}}{}
+\DeclareRobustCommand{\dots}{\relax
+  \csname\ifmmode m\else t\fi dots@\endcsname}
+\def\tdots@{\leavevmode\unskip\relaxnext@
+ \DN@{$\m@th\@ldots\,
+   \ifx\@let@token,\,$\else\ifx\@let@token.\,$\else\ifx\@let@token;\,$%
+   \else\ifx\@let@token:\,$\else\ifx\@let@token?\,$%
+   \else\ifx\@let@token!\,$\else$ \fi\fi\fi\fi\fi\fi}%
+ \ \FN@\next@}
+\def\mdots@{\FN@\mdots@@}
+\def\mdots@@{\gdef\thedots@{\dotso@}%
+ \ifx\@let@token\boldsymbol\gdef\thedots@\boldsymbol{\boldsymboldots@}%
+ \else\ifx,\@let@token\gdef\thedots@{\dotsc}%
+ \else\ifx\not\@let@token\gdef\thedots@{\dotsb@}%
+ \else\keybin@
+ \ifgtest@\gdef\thedots@{\dotsb@}%
+ \else\xdef\meaning@{\meaning\@let@token..........}%
+  \xdef\meaning@@{\meaning@}%
+  \expandafter\math@\meaning@\math@
+  \ifgtest@
+   \expandafter\mathch@\meaning@\mathch@
+   \ifgtest@\expandafter\getmathch@\meaning@\getmathch@\fi
+  \else\expandafter\macro@\meaning@@\macro@
+  \ifgtest@
+   \expandafter\not@\meaning@\not@\ifgtest@\gdef\thedots@{\dotsb@}%
+  \else\expandafter\DOTS@\meaning@\DOTS@
+  \ifgtest@
+   \ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}%
+    \or\gdef\thedots@{\dotsi}\else\fi
+  \else\expandafter\math@\meaning@\math@
+  \ifgtest@\expandafter\mathbin@\meaning@\mathbin@
+  \ifgtest@\gdef\thedots@{\dotsb@}%
+  \else\expandafter\mathrel@\meaning@\mathrel@
+  \ifgtest@\gdef\thedots@{\dotsb@}%
+  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+ \thedots@}
+\def\boldsymboldots@#1{%
+ \bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
+ \boldsymbol#1\bold@false}
+\def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
+\def\dotsi{\!\@cdots}
+\let\dotsb@\@cdots
+\def\rightdelim@{\gtest@true
+ \ifx\@let@token)\else
+ \ifx\@let@token]\else
+ \ifx\@let@token\rbrack\else
+ \ifx\@let@token\}\else
+ \ifx\@let@token\rbrace\else
+ \ifx\@let@token\rangle\else
+ \ifx\@let@token\rceil\else
+ \ifx\@let@token\rfloor\else
+ \ifx\@let@token\rgroup\else
+ \ifx\@let@token\rmoustache\else
+ \ifx\@let@token\right\else
+ \ifx\@let@token\bigr\else
+ \ifx\@let@token\biggr\else
+ \ifx\@let@token\Bigr\else
+ \ifx\@let@token\Biggr\else\gtest@false
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
+\def\extra@{%
+ \rightdelim@\ifgtest@
+ \else\ifx\@let@token$\gtest@true
+ \else\xdef\meaning@{\meaning\@let@token..........}%
+ \expandafter\macro@\meaning@\macro@\ifgtest@
+ \expandafter\DOTS@\meaning@\DOTS@
+ \ifgtest@
+ \ifnum\DOTSCASE@=\tw@\gtest@true\else\gtest@false
+ \fi\fi\fi\fi\fi}
+\newif\ifbold@
+\def\dotso@{\relaxnext@
+ \ifbold@
+  \let\@let@token\delayed@
+  \def\nextii@{\extra@\@ldots\ifgtest@\,\fi}%
+ \else
+  \def\nextii@{\DN@{\extra@\@ldots\ifgtest@\,\fi}\FN@\next@}%
+ \fi
+ \nextii@}
+\def\extrap@#1{%
+ \DN@{#1\,}%
+ \ifx\@let@token,\else
+ \ifx\@let@token;\else
+ \ifx\@let@token.\else\extra@
+ \ifgtest@\else
+ \let\next@#1\fi\fi\fi\fi\next@}
+\DeclareRobustCommand{\ldots}{\relax
+  \ifmmode \DN@{\extrap@\@ldots}%
+  \else \let\next@\tdots@\fi
+  \FN@\next@}
+\DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
+\let\dotso\ldots
+\let\dotsb\cdots
+\let\dotsm\dotsb
+\DeclareRobustCommand{\dotsc}{%
+  \DN@{\ifx\@let@token;\@ldots\,%
+       \else \ifx\@let@token.\@ldots\,%
+       \else \extra@\@ldots \ifgtest@\,\fi
+       \fi\fi}%
+  \FN@\next@}
+\def\longrightarrow{\DOTSB\relbar\joinrel\rightarrow}
+\def\Longrightarrow{\DOTSB\Relbar\joinrel\Rightarrow}
+\def\longleftarrow{\DOTSB\leftarrow\joinrel\relbar}
+\def\Longleftarrow{\DOTSB\Leftarrow\joinrel\Relbar}
+\def\longleftrightarrow{\DOTSB\leftarrow\joinrel\rightarrow}
+\def\Longleftrightarrow{\DOTSB\Leftarrow\joinrel\Rightarrow}
+\def\mapsto{\DOTSB\mapstochar\rightarrow}
+\def\longmapsto{\DOTSB\mapstochar\longrightarrow}
+\def\hookrightarrow{\DOTSB\lhook\joinrel\rightarrow}
+\def\hookleftarrow{\DOTSB\leftarrow\joinrel\rhook}
+\def\doteq{\DOTSB\buildrel\textstyle.\over=}
+\def\iff{\DOTSB\;\Longleftrightarrow\;}
+\begingroup \catcode`\"=12
+\mathchardef\@tempa="7000
+\ifx\@tempa\Gamma
+  \DeclareMathSymbol{\Gamma}{\mathord}{operators}{"00}
+  \DeclareMathSymbol{\Delta}{\mathord}{operators}{"01}
+  \DeclareMathSymbol{\Theta}{\mathord}{operators}{"02}
+  \DeclareMathSymbol{\Lambda}{\mathord}{operators}{"03}
+  \DeclareMathSymbol{\Xi}{\mathord}{operators}{"04}
+  \DeclareMathSymbol{\Pi}{\mathord}{operators}{"05}
+  \DeclareMathSymbol{\Sigma}{\mathord}{operators}{"06}
+  \DeclareMathSymbol{\Upsilon}{\mathord}{operators}{"07}
+  \DeclareMathSymbol{\Phi}{\mathord}{operators}{"08}
+  \DeclareMathSymbol{\Psi}{\mathord}{operators}{"09}
+  \DeclareMathSymbol{\Omega}{\mathord}{operators}{"0A}
+  \DeclareMathSymbol{\varGamma}{\mathord}{letters}{"00}
+  \DeclareMathSymbol{\varDelta}{\mathord}{letters}{"01}
+  \DeclareMathSymbol{\varTheta}{\mathord}{letters}{"02}
+  \DeclareMathSymbol{\varLambda}{\mathord}{letters}{"03}
+  \DeclareMathSymbol{\varXi}{\mathord}{letters}{"04}
+  \DeclareMathSymbol{\varPi}{\mathord}{letters}{"05}
+  \DeclareMathSymbol{\varSigma}{\mathord}{letters}{"06}
+  \DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{"07}
+  \DeclareMathSymbol{\varPhi}{\mathord}{letters}{"08}
+  \DeclareMathSymbol{\varPsi}{\mathord}{letters}{"09}
+  \DeclareMathSymbol{\varOmega}{\mathord}{letters}{"0A}
+\fi
+\endgroup
+\def\accentclass@{7}
+\def\noaccents@{\def\accentclass@{0}}
+\DeclareFontEncoding{OML}{}{\noaccents@}
+\DeclareFontEncoding{OMS}{}{\noaccents@}
+\edef\@tempa#1#2{\def#1{\mathaccent\string"\noexpand\accentclass@#2 }}
+\@tempa\hat{05E}\@tempa\check{014}\@tempa\tilde{07E}\@tempa\acute{013}
+\@tempa\grave{012}\@tempa\dot{05F}\@tempa\ddot{07F}\@tempa\breve{015}
+\@tempa\bar{016}
+\newcount\skewcharcount@
+\newcount\familycount@
+\def\theskewchar@{\familycount@\@ne
+ \global\skewcharcount@\the\skewchar\textfont\@ne
+ \ifnum\mathgroup>\m@ne\ifnum\mathgroup<16
+  \global\familycount@\the\mathgroup\relax
+  \global\skewcharcount@\the\skewchar\textfont\the\mathgroup\relax\fi\fi
+ \ifnum\skewcharcount@>\m@ne
+  \ifnum\skewcharcount@<128
+  \multiply\familycount@256
+  \global\advance\skewcharcount@\familycount@
+  \global\advance\skewcharcount@28672
+  \mathchar\skewcharcount@\else
+  \global\skewcharcount@\m@ne\fi\else
+ \global\skewcharcount@\m@ne\fi}
+\newcount\pointcount@
+\def\getpoints@#1.#2\getpoints@{\pointcount@#1 }
+\newdimen\accentdimen@
+\newcount\accentmu@
+\def\dimentomu@{\multiply\accentdimen@ 100
+ \expandafter\getpoints@\the\accentdimen@\getpoints@
+ \multiply\pointcount@18
+ \divide\pointcount@\@m
+ \global\accentmu@\pointcount@}
+\def\mathaccent@#1#2{\ifnum\mathgroup=\m@ne\xdef\thefam@{1}\else
+ \xdef\thefam@{\the\mathgroup}\fi
+ \accentdimen@\z@
+ \setboxz@h{\unbracefonts@$\m@th\mathgroup\thefam@\relax#2$}%
+ \ifdim\accentdimen@=\z@\DN@{\mathaccent#1{#2}}%
+  \setbox\@ne\hbox{\unbracefonts@
+    $\m@th\mathgroup\thefam@\relax#2\theskewchar@$}
+  \setbox\tw@\hbox{$\m@th\ifnum\skewcharcount@=\m@ne\else
+   \mathchar\skewcharcount@\fi$}%
+  \global\accentdimen@\wd\@ne\global\advance\accentdimen@-\wdz@
+  \global\advance\accentdimen@-\wd\tw@
+  \global\multiply\accentdimen@\tw@
+  \dimentomu@\global\advance\accentmu@\@ne
+ \else\DN@{{\mathaccent#1{#2\mkern\accentmu@ mu}%
+    \mkern-\accentmu@ mu}{}}\fi
+ \next@}
+\def\unbracefonts@{\let\math@bgroup\@empty\let\math@egroup\@empty}
+\begingroup \catcode`\"=12
+\def\@tempa#1#2{\gdef#1{\RIfM@\DN@{\mathaccent@{"\accentclass@#2 }}%
+  \else\DN@{\nonmatherr@{#1}}\fi\next@}}
+\@tempa\Hat{05E}\@tempa\Check{014}\@tempa\Tilde{07E}\@tempa\Acute{013}
+\@tempa\Grave{012}\@tempa\Dot{05F}\@tempa\Ddot{07F}\@tempa\Breve{015}
+\@tempa\Bar{016}
+\gdef\Vec{\RIfM@\DN@{\mathaccent@{"017E }}\else
+ \DN@{\nonmatherr@\Vec}\fi\next@}
+\endgroup
+\begingroup \catcode`\"=12
+\gdef\@@sqrt#1{\radical"270370 {#1}}
+\endgroup
+\@saveprimitive\overline\@@overline
+\def\overline#1{\@@overline{#1}}
+\def\boxed#1{\fbox{\m@th$\displaystyle#1$}}
+\def\setb@ck{\iffirstchoice@\global\advance\c@equation\m@ne\fi}
+\newcount\dspbrk@lvl
+\dspbrk@lvl=-1
+\interdisplaylinepenalty\@M
+\def\allowdisplaybreaks{%
+  \new@ifnextchar[\allowdspbrks@{\allowdspbrks@[4]}}
+\def\allowdspbrks@[#1]{%
+  \interdisplaylinepenalty\getdsp@pen{#1}}
+\def\getdsp@pen#1{%
+  \ifcase #1\relax \@M
+    \or 9999
+    \or 6999
+    \or 2999
+    \or \z@\fi}
+\def\displaybreak{\PackageError{amstex}{\Invalid@@\displaybreak}\@eha}
+\def\displaybreak@{%
+  \def\displaybreak{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}}
+\def\dspbrk@[#1]{\global\dspbrk@lvl #1\relax}
+\def\math@cr{{\ifnum0=`}\fi
+  \new@ifstar{\global\@eqpen\@M\math@cr@}%
+          {\global\@eqpen
+             \ifnum\dspbrk@lvl <\z@ \interdisplaylinepenalty
+              \else -\@getpen\dspbrk@lvl \fi
+           \math@cr@}}
+\def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
+\def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@
+  \noalign{\vskip#1\relax}}
+\def\Let@{\let\\\math@cr}
+\def\restore@math@cr{\def\math@cr@@@{\cr}}
+\restore@math@cr
+\def\intertext{\PackageError{amstex}{\Invalid@@\intertext}\@eha}
+\def\intertext@{\def\intertext##1{\noalign{%
+  \penalty\postdisplaypenalty\vskip\belowdisplayskip
+  \vbox{\normalbaselines\noindent##1}%
+  \penalty\predisplaypenalty\vskip\abovedisplayskip}}}
+\newhelp\tag@help
+  {tag cannot be used at this point.\space
+   If you don't understand why^^Jyou should consult
+   the documentation.^^JBut don't worry: just continue, and I'll
+   forget what happened.}
+\def\gobble@tag{\new@ifstar\@gobble\@gobble}
+\def\invalid@tag#1{\PackageError{amstex}{#1}{\the\tag@help}\gobble@tag}
+\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
+\def\default@tag{\let\tag\dft@tag}
+\default@tag
+\def\maketag@@{\new@ifstar\maketag@@@\tagform@}
+\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
+\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip)}}
+\def\thetag{\leavevmode\tagform@}
+\def\make@df@tag{\new@ifstar\make@df@tag@@\make@df@tag@@@}
+\def\make@df@tag@@#1{%
+  \def\@currentlabel{#1}%
+  \gdef\df@tag{\maketag@@@{#1}}}
+\def\make@df@tag@@@#1{\@seteqlabel{#1}\gdef\df@tag{\tagform@{#1}}}
+\def\@seteqlabel#1{\toks@\@xp{\p@equation{#1}}%
+  \edef\@currentlabel{\the\toks@}}
+\def\notag{\nonumber}
+\iftagsleft@
+\def\@eqnnum{\hbox to1sp{}\rlap{\normalfont
+    \hskip -\displaywidth\tagform@\theequation}}
+\fi
+
+\let\@adjusttag\@empty
+
+\def\adjusttag#1{\skip@#1\relax\gdef\@adjusttag{#1}}
+
+\def\@movetag{%
+    \ifx\@adjusttag\@empty \else
+        \vskip\@adjusttag\relax
+        \global\let\@adjusttag\@empty
+    \fi
+}
+\def\multilimits@{\bgroup
+  \Let@
+  \restore@math@cr
+  \default@tag
+ \baselineskip\fontdimen10 \scriptfont\tw@
+ \advance\baselineskip\fontdimen12 \scriptfont\tw@
+ \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
+ \lineskiplimit\lineskip
+ \vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
+\def\Sb{_\multilimits@}
+\def\Sp{^\multilimits@}
+\def\endSb{\crcr\egroup\egroup\egroup}
+\let\endSp=\endSb
+\def\smallmatrix{\null\,\vcenter\bgroup
+ \Let@\restore@math@cr\default@tag
+ \baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
+ \ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil&&\thickspace\hfil
+ $\m@th\scriptstyle{##}$\hfil\crcr}
+\def\endsmallmatrix{\crcr\egroup\egroup\,}
+\newcount\c@MaxMatrixCols
+\c@MaxMatrixCols=10
+
+\def\matrix{\hskip -\arraycolsep\array{*\c@MaxMatrixCols c}}
+\def\endmatrix{\endarray \hskip -\arraycolsep}
+\@ifundefined{prepnext@tok}{%
+  \def\@array[#1]#2{%
+    \setbox\@arstrutbox\hbox{\vrule\@height\arraystretch\ht\strutbox
+       \@depth\arraystretch\dp\strutbox \@width\z@}%
+    \@mkpream{#2}\edef\@preamble{\ialign \noexpand\@halignto
+    \bgroup \tabskip\z@ \@arstrut \@preamble \tabskip\z@ \cr}%
+    \let\@startpbox\@@startpbox \let\@endpbox\@@endpbox
+    \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
+    \bgroup \let\par\@empty
+    \let\@sharp##\let\protect\relax
+    \lineskip\z@\baselineskip\z@\@preamble}%
+\begingroup \lccode`\~=`\@ \catcode`\~=\active % just to be sure!
+\lowercase{%
+\gdef\@xexpast#1*#2#3#4\@@{\begingroup
+  \def~{@}\edef\reserved@a{#1}\@tempcnta#2\relax
+  \ifnum\@tempcnta >\z@
+    \@whilenum\@tempcnta >\z@\do
+      {\edef\reserved@a{\reserved@a#3}\advance\@tempcnta \m@ne}%
+    \let\reserved@b\@xexpast
+  \else \let\reserved@b\@xexnoop\fi
+  \expandafter\reserved@b \reserved@a #4\@@
+  \expandafter\endgroup
+  \expandafter\def\expandafter\reserved@a\expandafter{\reserved@a}%
+  \let\@tempa\reserved@a
+}% End of \@xexpast
+}% End of \lowercase
+\endgroup
+}{}% End of \@ifundefined test.
+\def\pmatrix{\left(\matrix}
+\def\endpmatrix{\endmatrix\right)}
+\def\bmatrix{\left[\matrix}
+\def\endbmatrix{\endmatrix\right]}
+\def\vmatrix{\left|\matrix}
+\def\endvmatrix{\endmatrix\right|}
+\def\Vmatrix{\left\|\matrix}
+\def\endVmatrix{\endmatrix\right\|}
+\let\hdots\@ldots
+\def\hdotsfor#1{\if\noexpand#1[\expandafter\shdots@for\else
+                \hdots@for\@ne{#1}\fi}
+\newmuskip\dotsspace@
+\def\shdots@for#1]{\hdots@for{#1}}
+\def\hdots@for#1#2{\multicolumn{#2}c%
+  {\m@th\dotsspace@1.5mu\mkern-#1\dotsspace@
+   \xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
+           \hfill
+   \mkern-#1\dotsspace@}%
+   }
+\def\cases{\left\{\def\arraystretch{1.2}\hskip-\arraycolsep
+  \array{l@{\quad}l}}
+\def\endcases{\endarray\hskip-\arraycolsep\right.}
+\newif\ifinany@
+\newif\ifinalign@
+\newif\ifingather@
+\newcount\and@
+\newif\iftag@
+\newhelp\andhelp@
+{An extra & here is so disastrous that you should probably exit^^J
+and fix things up.}
+\newif\ifst@rred
+\newtoks\@envbody
+\def\addto@envbody#1{\@envbody\expandafter{\the\@envbody#1}}
+\def\collect@body#1{%
+  \@envbody{}%
+  \def\process@envbody{%
+    \expandafter#1\expandafter{\the\@envbody}}%
+  \expandafter\let\csname\@currenvir\endcsname\collect@@body
+  \csname\@currenvir\endcsname}
+\def\collect@@body#1\end#2{%
+  \def\@tempa{#2}%
+  \ifx\@tempa\@currenvir
+    \addto@envbody{#1}%
+    \expandafter\edef\csname\@currenvir\endcsname
+      {\noexpand\process@envbody\noexpand\end{\@tempa}}%
+  \else
+    \addto@envbody{#1\end{#2}}%
+  \fi
+  \csname\@currenvir\endcsname}
+\newenvironment{aligned}{%
+  \relax\ifmmode\else\nonmatherr@{\begin{aligned}}\fi
+  \null\,\new@ifnextchar[{\aligned@}{\aligned@[c]}%
+}{%
+  \crcr\egroup\egroup
+}
+\def\aligned@[#1]{%
+  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
+  \bgroup
+   \Let@\restore@math@cr
+   \default@tag
+   \ifinany@\else\openup\jot\fi
+   \ialign\bgroup\hfil\strut@$\m@th\displaystyle{##}$&%
+    $\m@th\displaystyle{{}##}$\hfil\crcr}
+\newtoks\hashtoks@
+\hashtoks@{#}
+\newcount\atcount@
+\def\doat@#1{\toks@{\hfil\strut@$\m@th
+  \displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
+  {{}\the\hashtoks@}$\hfil}%
+ \atcount@#1\relax\advance\atcount@\m@ne
+ \loop\ifnum\atcount@>\z@\toks@\expandafter{\the\toks@&\hfil$\m@th
+  \displaystyle{\the\hashtoks@}$&$\m@th
+  \displaystyle{{}\the\hashtoks@}$\hfil}\advance
+ \atcount@\m@ne\repeat
+ \xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
+\newenvironment{alignedat}[2][c]{%
+  \null\,%
+  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
+  \bgroup\doat@{#2}\Let@ \restore@math@cr\default@tag
+  \ifinany@\else\openup\jot\fi\ialign\bgroup\span\preamble@@\crcr
+}{%
+  \endaligned
+}
+\newenvironment{gathered}[1][c]{%
+  \relax\ifmmode\else\nonmatherr@{\begin{gathered}}\fi
+  \null\,%
+  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
+  \bgroup\Let@\restore@math@cr
+  \ifinany@\else\openup\jot\fi\ialign
+  \bgroup\hfil\strut@$\m@th\displaystyle##$\hfil\crcr
+}{%
+  \endaligned
+}
+\def\tag@in@align{\relax
+  \iftag@\DN@{\invalid@tag{Multiple \string\tag}}\else
+   \global\tag@true
+   \if@eqnsw\global\@eqnswfalse\fi
+   \let\next@\make@df@tag\fi
+  \next@}
+\def\math@cr@@@align{%
+  \if@eqnsw\global\tag@true\fi
+  \iftag@
+   \ifcase\and@
+    \DN@{&&}\else
+    \DN@{&}\fi\else
+    \let\next@\relax\fi
+  \next@
+  \relax
+  \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
+  \iftag@\df@tag\fi\fi
+  \global\@eqnswtrue\cr}
+\def\Tag@{\relax\iftag@\else\firstchoice@true
+  \PackageError{amstex}{%
+  Extra & on this line%
+  }{\the\andhelp@% "An extra & here is disastrous"
+}\fi}
+\newdimen\lwidth@
+\newdimen\rwidth@
+\newdimen\maxlwidth@
+\newdimen\maxrwidth@
+\newdimen\totwidth@
+\def\measure@#1{\lwidth@\z@\rwidth@\z@\maxlwidth@\z@\maxrwidth@\z@
+ \global\and@\z@
+ \setbox\@ne\vbox{%
+   \everycr{\noalign{\global\tag@false\global\and@\z@}}\Let@
+   \let\tag\gobble@tag
+   \let\notag\@empty \let\nonumber\@empty
+   \firstchoice@false
+    \halign{\setboxz@h{$\m@th\displaystyle{\@lign##}$}%
+     \global\lwidth@\wdz@
+     \ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi
+     \global\advance\and@\@ne
+     &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
+     \global\rwidth@\wdz@
+     \ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi
+     \global\advance\and@\@ne
+     &\Tag@\@gobble{##}\crcr#1\crcr}}%
+ \totwidth@\maxlwidth@\advance\totwidth@\maxrwidth@}
+\def\displ@y{\global\dt@ptrue\openup\jot\m@th
+  \everycr{\noalign{\ifdt@p \global\dt@pfalse
+      \vskip-\lineskiplimit \vskip\normallineskiplimit
+      \else \penalty\@eqpen \fi}}}
+\def\displ@y@{\global\dt@ptrue\openup\jot
+  \everycr{\noalign{\global\tag@false
+                   \global\and@\z@
+                   \global\dspbrk@lvl\m@ne
+                   \ifdt@p\global\dt@pfalse
+      \vskip-\lineskiplimit\vskip\normallineskiplimit\else
+      \penalty\@eqpen\fi}}}
+\def\black@#1{\noalign{\ifdim#1>\displaywidth
+ \dimen@\prevdepth\nointerlineskip
+ \vskip-\ht\strutbox@\vskip-\dp\strutbox@
+ \vbox{\noindent\hbox to#1{\strut@\hfill}}%
+ \prevdepth\dimen@
+ \fi}}
+\def\align{\ifingather@
+  {\ifnum0=`}\fi
+  \DN@{\@nameuse{align (in \string\gather)}}%
+  \else \ifmmode\nomath@env
+    \DN@{\let\endalign\relax\@gobble}\else
+  $$\stepcounter{equation}%
+  \st@rredfalse\let\next@\align@\fi\fi
+ \collect@body\next@}
+\@namedef{align*}{\ifingather@
+  {\ifnum0=`}\fi
+  \DN@{\@nameuse{align* (in \string\gather)}}\else
+   \ifmmode\nomath@env
+    \DN@{\@namedef{endalign*}{}\@gobble}\else
+   $$\st@rredtrue
+  \let\next@\align@\fi\fi
+ \collect@body\next@}
+\newdimen\lineht@
+\def\align@{\inalign@true\inany@true
+ \displaybreak@\intertext@
+ \let\math@cr@@@\math@cr@@@align
+ \let\tag\tag@in@align
+ \global\and@\z@\global\dspbrk@lvl\m@ne
+ \iftagsleft@\DN@{\@nameuse{align }}\else
+  \DN@{\@nameuse{align \space}}\fi\next@}
+\@namedef{align }#1{%
+    \measure@{#1}%
+    \global\and@\z@
+    \global\dspbrk@lvl\m@ne
+    \if@fleqn %%*F
+        \advance\totwidth@\@mathmargin %%*F
+    \fi %%*F
+    \ifdim\totwidth@>\displaywidth
+        \let\displaywidth@\totwidth@
+    \else
+        \let\displaywidth@\displaywidth
+    \fi
+    \ifingather@
+        \everycr{%
+            \noalign{%
+                \global\and@\z@
+                \global\dspbrk@lvl\m@ne
+            }%
+        }%
+    \else
+        \displ@y@
+    \fi
+    \Let@
+    \ifst@rred\else\@seteqlabel\theequation\fi
+    \tabskip\@mathmargin %%*F
+    \dimen@\displaywidth %%*F
+    \if@fleqn %%*F
+        \ifingather@ %%*F
+            \tabskip\z@skip %%*F
+            \advance\dimen@-\@mathmargin %%*F
+        \fi %%*F
+    \fi %%*F
+    \halign to\dimen@\bgroup %%*F
+        \ifst@rred\nonumber\fi
+        \hfil
+        \strut@
+        \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
+        \global\lwidth@\wdz@
+        \global\lineht@\ht\z@
+        \boxz@
+        \global\advance\and@\@ne
+        \tabskip\z@skip
+       &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
+        \global\rwidth@\wdz@
+        \ifdim\ht\z@>\lineht@
+            \global\lineht@\ht\z@
+        \fi
+        \boxz@
+        \hfil
+        \global\advance\and@\@ne
+        \tabskip\@centering
+       &\kern-\displaywidth@
+        \setboxz@h{\@lign\strut@{##}}%
+        \if@fleqn %%*F
+            \dimen@\@mathmargin %%*F
+            \advance\dimen@\maxlwidth@ %%*F
+            \advance\dimen@-\lwidth@ %%*F
+        \else %%*F
+            \dimen@\displaywidth
+            \advance\dimen@-\totwidth@
+            \divide\dimen@\tw@
+            \advance\dimen@\maxlwidth@
+            \advance\dimen@-\lwidth@
+        \fi %%*F
+        \ifdim\dimen@<\tw@\wdz@
+            \rlap{\vbox{\normalbaselines\boxz@\vbox to\lineht@{}}}%
+        \else
+            \rlap{\boxz@}%
+        \fi
+        \tabskip\displaywidth@
+        \crcr
+        #1%
+}
+\@namedef{align \space}#1{%
+    \measure@{#1}%
+    \if@fleqn %%*F
+        \advance\totwidth@\@mathmargin %%*F
+    \fi %%*F
+    \global\and@\z@
+    \global\dspbrk@lvl\m@ne
+    \ifingather@
+        \everycr{\noalign{\global\and@\z@\global\dspbrk@lvl\m@ne}}%
+    \else
+        \displ@y@
+    \fi
+    \Let@
+    \ifst@rred\else\@seteqlabel\theequation\fi
+    \tabskip\@mathmargin %%*F
+    \dimen@\displaywidth %%*F
+    \if@fleqn %%*
+        \ifingather@ %%*F
+            \tabskip\z@skip %%*F
+            \advance\dimen@-\@mathmargin %%*F
+        \fi %%*F
+    \fi %%*F
+     \halign to\dimen@\bgroup %%*F
+        \ifst@rred\nonumber\fi
+        \hfil
+        \strut@
+        \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
+        \global\lwidth@\wdz@\boxz@
+        \global\advance\and@\@ne
+        \tabskip\z@skip
+       &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
+        \global\rwidth@\wdz@
+        \boxz@
+        \hfill
+        \global\advance\and@\@ne
+        \tabskip\@centering
+       &\setboxz@h{\@lign\strut@{##}}%
+        \dimen@\displaywidth
+        \advance\dimen@-\totwidth@
+        \divide\dimen@\tw@
+        \advance\dimen@\maxrwidth@
+        \advance\dimen@-\rwidth@
+        \ifdim\dimen@<\tw@\wdz@
+            \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T
+        \else
+            \llap{\boxz@}%
+        \fi
+        \tabskip\z@skip
+        \crcr#1%
+}
+\def\endalign{\math@cr@@@align
+  \black@\totwidth@
+  \egroup$$\global\@ignoretrue\setb@ck}
+
+\@namedef{endalign*}{\math@cr@@@align\black@\totwidth@
+  \egroup$$\global\@ignoretrue}
+\@namedef{align (in \string\gather)}{%
+  \ifst@rred\stepcounter{equation}\fi
+  \def\endalign{\@nameuse{endalign (in \string\gather)}\ifnum0=`{\fi}}%
+  \vcenter\bgroup\st@rredfalse
+    \collect@body\align@}
+\@namedef{endalign (in \string\gather)}{%
+  \math@cr@@@align\black@\totwidth@
+  \egroup\egroup
+  \ifst@rred\setb@ck\fi% this ifst@rred is set by the enclosing gather
+  \global\tag@false\global\@eqnswfalse}
+\@namedef{align* (in \string\gather)}{%
+  \@namedef{endalign*}{\@nameuse{endalign* (in \string\gather)}%
+                       \ifnum0=`{\fi}}%
+  \vcenter\bgroup\st@rredtrue
+    \collect@body\align@}
+\@namedef{endalign* (in \string\gather)}{%
+  \math@cr@@@align\black@\totwidth@\egroup\egroup
+  \global\tag@false\global\@eqnswfalse}
+\newif\ifxat@
+\def\alignat#1{%
+ \ifmmode\nomath@env\DN@{\let\endalignat\relax\@gobble}\else$$%
+ \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
+ \DN@{\@nameuse{alignat }#1}\fi
+ \collect@body\next@}
+\@namedef{alignat*}#1{%
+ \ifmmode\nomath@env\DN@{\@namedef{endalignat*}{}\@gobble}\else$$%
+ \st@rredtrue
+ \DN@{\@nameuse{alignat }#1}\fi
+ \collect@body\next@}
+\newif\ifmeasuring@
+\newbox\savealignat@
+\def\math@cr@@@alignat{%
+  \if@eqnsw\global\tag@true\fi
+  \iftag@
+   \multiply\count@\tw@
+   \xdef\next@{}\loop\ifnum\count@>\and@\xdef\next@{&\next@}%
+    \advance\count@\m@ne\repeat\else
+   \let\next@\relax\fi
+  \next@
+  \relax
+  \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
+  \iftag@\df@tag\fi\fi
+  \global\@eqnswtrue\cr}%
+\@namedef{alignat }#1#2{%
+    \inany@true
+    \xat@false
+    \let\tag\tag@in@align
+    \def\math@cr@@@{\count@#1\relax \math@cr@@@alignat}%
+    \displaybreak@
+    \intertext@
+    \displ@y@
+    \ifst@rred
+        \global\@eqnswfalse
+    \else
+        \global\@eqnswtrue
+    \fi
+    \measuring@true
+    \setbox\savealignat@\hbox{%
+        $\m@th\displaystyle\Let@
+        \attag@{#1}%
+        \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$%
+    }%
+    \measuring@false
+    \Let@
+    \attag@{#1}%
+    \tabskip\@mathmargin %%*F
+    \halign to\displaywidth\bgroup
+        \span\preamble@@\crcr
+        #2%
+}
+\def\endalignat{\math@cr@@@\black@{\wd\savealignat@}%
+     \egroup\setb@ck$$\global\@ignoretrue}
+\@namedef{endalignat*}{\math@cr@@@\black@{\wd\savealignat@}\egroup
+  $$\global\@ignoretrue}
+\def\xalignat#1{%
+ \ifmmode\nomath@env\DN@{\let\endxalignat\relax\@gobble}\else$$%
+ \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
+ \DN@{\@nameuse{xalignat }#1}\fi
+ \collect@body\next@}
+\@namedef{xalignat*}#1{%
+ \ifmmode\nomath@env\DN@{\@namedef{endxalignat*}{}\@gobble}\else$$%
+ \st@rredtrue
+ \DN@{\@nameuse{xalignat }#1}\fi
+ \collect@body\next@}
+\let\endxalignat=\endalignat
+
+\expandafter\let\csname endxalignat*\expandafter
+  \endcsname\csname endalignat*\endcsname
+\@namedef{xalignat }#1#2{%
+    \inany@true
+    \xat@true
+    \let\tag\tag@in@align
+    \def\math@cr@@@{\count@#1\relax\math@cr@@@alignat}%
+    \displaybreak@
+    \intertext@
+    \displ@y@
+    \measuring@true
+    \setbox\savealignat@\hbox{%
+        $\m@th\displaystyle\Let@
+        \attag@{#1}%
+        \vbox{%
+            \firstchoice@false
+            \halign{\span\preamble@@\crcr#2\crcr}%
+        }%
+        $%
+    }%
+    \measuring@false
+    \Let@
+    \attag@{#1}%
+    \tabskip\@mathmargin %%*F
+    \halign to\displaywidth\bgroup
+        \span\preamble@@\crcr#2%
+}
+\def\attag@#1{%
+ \let\TAG@\Tag@\let\Tag@0%
+ \ifmeasuring@\def\llap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
+  \def\rlap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}\else
+  \let\llap@\llap\let\rlap@\rlap\fi
+ \toks@{\hfil\strut@$\m@th\displaystyle{\@lign\the\hashtoks@}$%
+  \tabskip\z@skip
+  \global\advance\and@\@ne
+  &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil
+  \ifxat@\tabskip\@centering\fi\global\advance\and@\@ne}%
+ \iftagsleft@
+  \@temptokena{\tabskip\@centering&\Tag@\kern-\displaywidth
+   \rlap@{\@lign
+     \the\hashtoks@
+    }%
+   \global\advance\and@\@ne\tabskip\displaywidth}\else
+  \@temptokena{\tabskip\@centering&\Tag@\llap@{\@lign
+   \the\hashtoks@
+  }\global\advance\and@\@ne\tabskip\z@skip}\fi
+ \atcount@#1\relax\advance\atcount@\m@ne
+ \loop\ifnum\atcount@>\z@
+ \toks@\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\@lign
+  \the\hashtoks@}$\global\advance\and@\@ne
+  \tabskip\z@skip
+  &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil\ifxat@
+  \tabskip\@centering\fi\global\advance\and@\@ne}\advance\atcount@\m@ne
+ \repeat
+ \xdef\preamble@{\the\toks@\the\@temptokena}%
+ \xdef\preamble@@{\ifst@rred\noexpand\nonumber\fi\preamble@}%
+ \let\Tag@\TAG@}
+\def\xxalignat#1{%
+ \ifmmode\nomath@env\DN@{\let\endxxalignat\relax\@gobble}\else$$%
+ \DN@{\@nameuse{xxalignat }#1}\fi
+ \collect@body\next@}
+\@namedef{xxalignat }#1#2{\inany@true
+ \displaybreak@\intertext@
+ \displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
+ \xxattag@{#1}%
+ \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$}%
+ \Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth\bgroup
+  \span\preamble@@\crcr#2}
+\expandafter\let\expandafter\endxxalignat\csname endxalignat*\endcsname
+\def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
+ $\m@th\displaystyle{\the\hashtoks@}$&%
+ $\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\@centering&}%
+ \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
+ \toks@
+  \expandafter
+   {\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
+  \tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
+  \tabskip\@centering}\advance\atcount@\m@ne\repeat
+ \xdef\preamble@{\the\toks@\tabskip\z@skip}\xdef\preamble@@{\preamble@}}
+\newdimen\gwidth@
+\newdimen\gmaxwidth@
+\def\gmeasure@#1{\gwidth@\z@\gmaxwidth@\z@\setbox\@ne\vbox{\Let@
+ \firstchoice@false\let\tag\gobble@tag
+ \halign{\setboxz@h{$\m@th\displaystyle{##}$}\global\gwidth@\wdz@
+ \ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
+ &\@gobble{##}\crcr#1\crcr}}}
+\def\math@cr@@@gather{%
+  \if@eqnsw\global\tag@true\fi
+  \iftag@
+    \DN@{&\relax \if@eqnsw
+                    \tagform@\theequation \stepcounter{equation}%
+                 \else\iftag@\df@tag\fi\fi}%
+  \else
+    \expandafter\@gobble\fi
+  \next@
+  \global\@eqnswtrue\cr}
+\def\gather{%
+ \ifmmode\nomath@env\DN@{\let\endgather\relax\@gobble}\else $$%
+  \ingather@true\inany@true
+  \stepcounter{equation}%
+  \let\tag\tag@in@align\st@rredfalse
+  \displaybreak@\intertext@
+  \displ@y
+  \Let@\@seteqlabel\theequation
+  \let\math@cr@@@\math@cr@@@gather
+  \iftagsleft@\DN@{\@nameuse{gather }}\else
+   \DN@{\@nameuse{gather \space}}\fi\fi
+ \collect@body\next@}
+\@namedef{gather*}{%
+ \ifmmode\nomath@env\DN@{\@namedef{endgather*}{}\@gobble}\else $$%
+  \ingather@true\inany@true
+  \let\tag\tag@in@align\st@rredtrue
+  \displaybreak@\intertext@
+  \displ@y\Let@
+  \let\math@cr@@@\math@cr@@@gather
+  \iftagsleft@\DN@{\@nameuse{gather }}\else
+   \DN@{\@nameuse{gather \space}}\fi\fi
+ \collect@body\next@}
+\newdimen\glineht@
+\@namedef{gather \space}#1{%
+    \gmeasure@{#1}%
+    \if@fleqn %%*F
+        \advance\gmaxwidth@\@mathmargin %%*F
+    \fi %%*F
+    \global\dt@ptrue
+    \tabskip\@mathmargin %%*F
+    \halign to\displaywidth\bgroup
+        \ifst@rred\nonumber\else\global\@eqnswtrue\fi
+        \if@fleqn\else\hfil\fi %%*F
+        \strut@
+        \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
+        \global\gwidth@\wdz@\boxz@
+        \hfil
+        \tabskip\@centering %%*F
+       &\setboxz@h{\strut@{##}}%
+        \dimen@\displaywidth
+        \advance\dimen@-\gwidth@
+        \if@fleqn %%*F
+            \advance\dimen@-\@mathmargin %%*F
+        \else %%*F
+            \divide\dimen@\tw@ %%*B
+        \fi %%*F
+        \ifdim\dimen@<\tw@\wdz@ %%*
+            \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T %%*
+        \else
+            \llap{\boxz@}% %%*
+        \fi
+        \tabskip\z@skip
+        \crcr
+        #1%
+}
+\def\endgather{\math@cr
+  \black@\gmaxwidth@\egroup $$\setb@ck\global\@ignoretrue}
+
+\@namedef{endgather*}{\math@cr
+  \black@\gmaxwidth@\egroup $$\global\@ignoretrue}
+\@namedef{gather }#1{%
+    \gmeasure@{#1}%
+    \global\dt@ptrue
+    \if@fleqn %%*F
+        \advance\gmaxwidth@\@mathmargin %%*F
+    \fi %%*F
+    \ifdim\gmaxwidth@>\displaywidth
+        \let\gdisplaywidth@\gmaxwidth@
+    \else
+        \let\gdisplaywidth@\displaywidth
+    \fi
+    \tabskip\@mathmargin %%*F
+    \halign to\displaywidth\bgroup
+        \ifst@rred\nonumber\else\global\@eqnswtrue\fi
+        \if@fleqn\else\hfil\fi %%*F
+        \strut@
+        \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
+        \global\gwidth@\wdz@
+        \global\glineht@\ht\z@
+        \boxz@
+        \hfil
+        \tabskip\@centering %%*F
+       &\kern-\gdisplaywidth@
+        \setboxz@h{\strut@{##}}%
+        \if@fleqn %%*F
+            \dimen@\@mathmargin %%*F
+        \else %%*F
+            \dimen@\displaywidth
+            \advance\dimen@-\gwidth@
+            \divide\dimen@\tw@ %%*B
+        \fi %%*F
+        \ifdim\dimen@<\tw@\wdz@ %%*
+            \rlap{\vbox{\normalbaselines\boxz@\vbox to\glineht@{}}}% %%*
+        \else
+            \rlap{\boxz@}% %%*
+        \fi
+        \tabskip\gdisplaywidth@
+        \crcr
+        #1%
+}
+\def\split{%
+ \ifinany@\let\next@\insplit@\else
+  \DN@{\PackageError{amstex}{\string\begin{split} is not allowed
+    here.  Try the `aligned' environment.}\@ehb}\fi
+ \next@}
+\def\insplit@{\global\setbox\z@\vbox\bgroup
+  \Let@ \restore@math@cr \default@tag % disallow use of \tag here
+  \ialign\bgroup \hfil\strut@
+   $\m@th\displaystyle{##}$&$\m@th\displaystyle{{}##}$\hfill\crcr}
+\def\endsplit{\crcr\egroup\egroup
+ \iftagsleft@\expandafter\lendsplit@\else
+  \expandafter\rendsplit@\fi}
+\def\rendsplit@{\global\setbox9 \vbox
+ {\unvcopy\z@\global\setbox8 \lastbox\unskip}%
+ \setbox\@ne\hbox{\unhcopy8 \unskip\global\setbox\tw@\lastbox
+ \unskip\global\setbox\thr@@\lastbox}%
+ \global\setbox7 \hbox{\unhbox\tw@\unskip}%
+ \ifinalign@\ifctagsplit@
+  \gdef\split@{\hbox to\wd\thr@@{}&
+   \vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}}%
+ \else\gdef\split@{&\vbox{\moveleft\wd\thr@@\box9}\crcr
+  \box\thr@@&\box7}\fi
+ \else
+  \ifctagsplit@\gdef\split@{\vcenter{\boxz@}}\else
+  \gdef\split@{\box9\crcr\hbox{\box\thr@@\box7}}\fi
+ \fi
+ \aftergroup\split@}
+\def\lendsplit@{\global\setbox9\vtop{\unvcopy\z@}%
+ \setbox\@ne\vbox{\unvcopy\z@\global\setbox8\lastbox}%
+ \setbox\@ne\hbox{\unhcopy8\unskip\setbox\tw@\lastbox
+  \unskip\global\setbox\thr@@\lastbox}%
+ \ifinalign@\ifctagsplit@
+  \gdef\split@{\hbox to\wd\thr@@{}&
+  \vcenter{\vbox{\moveleft\wd\thr@@\box9}}}%
+  \else
+  \gdef\split@{\hbox to\wd\thr@@{}&\vbox{\moveleft\wd\thr@@\box9}}\fi
+ \else
+  \ifctagsplit@\gdef\split@{\vcenter{\box9}}\else
+  \gdef\split@{\box9}\fi
+ \fi\aftergroup\split@}
+\newdimen\multlinegap
+\multlinegap10pt
+\newdimen\multlinetaggap@
+\multlinetaggap@10pt
+\def\multline{%
+ \ifmmode\nomath@env\DN@{\let\endmultline\relax\@gobble}%
+ \else $$\DN@{\collect@body\multline@}\fi
+ \st@rredfalse\@eqnswtrue \@seteqlabel\theequation
+ \stepcounter{equation}\next@}
+\@namedef{multline*}{%
+ \ifmmode\nomath@env\DN@{\@namedef{endmultline*}{}\@gobble}%
+ \else $$\DN@{\collect@body\multline@}\fi
+ \st@rredtrue\@eqnswfalse \let\@currentlabel\@empty
+ \next@}
+\def\multline@{\inany@true\displaybreak@
+ \global\tag@false
+ \def\tag{\ifst@rred\else
+   \global\advance\c@equation\m@ne\fi\tag@in@align}%
+ \iftagsleft@
+  \expandafter\lmultline@@\else
+  \expandafter\rmultline@@\fi}
+\newdimen\mwidth@
+\def\rmmeasure@#1{%
+ \def\shoveleft##1{##1}\def\shoveright##1{##1}%
+ \setbox\@ne\vbox{\firstchoice@false\Let@\halign{\setboxz@h
+  {$\m@th\@lign\displaystyle{}##$}\global\mwidth@\wdz@
+  \crcr#1\crcr}}}
+\newdimen\mlineht@
+\newif\ifzerocr@
+\newif\ifonecr@
+\def\lmmeasure@#1{\global\zerocr@true\global\onecr@false
+ \everycr{\noalign{\ifonecr@\global\onecr@false\fi
+  \ifzerocr@\global\zerocr@false\global\onecr@true\fi}}%
+  \def\shoveleft##1{##1}\def\shoveright##1{##1}%
+ \setbox\@ne\vbox{\Let@\firstchoice@false\halign{\setboxz@h
+  {$\m@th\@lign\displaystyle{}##$}\ifonecr@\global\mwidth@\wdz@
+  \global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
+\newbox\mtagbox@
+\newdimen\ltwidth@
+\newdimen\rtwidth@
+\def\lmultline@@#1{%
+    \lmmeasure@{#1}%
+    \setbox\mtagbox@\hbox{%
+        \iftag@
+            \df@tag
+        \else
+            \if@eqnsw
+                \global\tag@true
+                \tagform@\theequation
+            \fi
+        \fi
+    }%
+    \dimen@\mwidth@
+    \advance\dimen@\wd\mtagbox@
+    \advance\dimen@\multlinetaggap@
+    \if@fleqn %%*F
+        \advance\dimen@\@mathmargin %%*F
+    \fi %%*F
+    \ifdim\dimen@>\displaywidth
+        \ltwidth@\z@
+    \else
+        \ltwidth@\wd\mtagbox@
+    \fi
+    \lmultline@@@#1
+}
+\def\lmultline@@@{%
+    \displ@y
+    \def\shoveright##1{##1\hfilneg\hskip\multlinegap}%
+    \if@fleqn %%*F
+        \def\shoveleft##1{##1}% %%*F
+    \else %%*F
+        \def\shoveleft##1{%
+                \setboxz@h{$\m@th\displaystyle{}##1$}%
+                \setbox\@ne\hbox{$\m@th\displaystyle##1$}%
+                \hfilneg
+                \iftag@
+                    \ifdim\ltwidth@>\z@
+                        \hskip\ltwidth@
+                        \hskip\multlinetaggap@
+                    \fi
+                \else
+                    \hskip\multlinegap
+                \fi
+                \hskip.5\wd\@ne
+                \hskip-.5\wdz@##1%
+        }%
+    \fi %%*F
+    \if@fleqn %%*F
+        \tabskip\@mathmargin %%*F
+    \else %%*F
+        \tabskip\z@skip %%*
+    \fi %%*F
+    \totwidth@\displaywidth %%*F
+    \if@fleqn %%*F
+        \advance\totwidth@-\@mathmargin %%*F
+    \fi %%*F
+    \halign\bgroup
+        \Let@
+        \let\tag\gobble@tag
+        \hbox to\totwidth@{% %%*F
+            \strut@$\m@th\displaystyle
+            \if@fleqn %%*F
+                \hskip 0pt plus 1000pt %%*F
+            \else %%*F
+                \hfil
+            \fi %%*F
+            {}##\hfil$%
+        }%
+        \crcr
+        \if@fleqn %%*F
+            \hskip-\@mathmargin %%*F
+        \else %%*F
+            \hfilneg
+        \fi %%*F
+        \iftag@
+            \ifdim\ltwidth@>\z@
+                \box\mtagbox@
+                \hskip\multlinetaggap@
+            \else
+                \rlap{%
+                    \vbox{%
+                        \normalbaselines
+                        \hbox{\strut@\box\mtagbox@}%
+                        \vbox to\mlineht@{}%
+                    }%
+                }%
+                \hskip\multlinegap %%*
+            \fi
+        \else
+            \hskip\multlinegap
+        \fi
+}
+\def\rmultline@@#1{%
+    \rmmeasure@{#1}%
+    \setbox\mtagbox@\hbox{%
+        \iftag@
+            \df@tag
+        \else
+            \if@eqnsw
+                \global\tag@true
+                \tagform@\theequation
+            \fi
+        \fi
+    }%
+    \dimen@\mwidth@
+    \advance\dimen@\wd\mtagbox@
+    \advance\dimen@\multlinetaggap@
+    \if@fleqn %%*F
+        \advance\dimen@\@mathmargin %%*F
+    \fi %%*F
+    \ifdim\dimen@>\displaywidth
+        \rtwidth@\z@
+    \else
+        \rtwidth@\wd\mtagbox@
+    \fi
+    \rmultline@@@#1
+}
+\def\rmultline@@@{%
+    \displ@y
+    \def\shoveright##1{%
+        ##1%
+        \hfilneg
+        \iftag@
+            \ifdim\rtwidth@>\z@
+                \hskip\rtwidth@
+                \hskip\multlinetaggap@
+            \fi
+        \else
+            \hskip\multlinegap
+        \fi
+    }%
+    \if@fleqn %%*F
+        \def\shoveleft##1{##1}% %%*F
+    \else %%*F
+        \def\shoveleft##1{%
+            \setboxz@h{$\m@th\displaystyle{}##1$}%
+            \setbox\@ne\hbox{$\m@th\displaystyle##1$}%
+            \hfilneg
+            \hskip\multlinegap
+            \hskip.5\wd\@ne
+            \hskip-.5\wdz@
+            ##1%
+        }%
+    \fi %%*F
+    \if@fleqn %%*F
+        \tabskip\@mathmargin %%*F
+    \else %%*F
+        \tabskip\z@skip %%*
+    \fi %%*F
+    \totwidth@\displaywidth %%*F
+    \if@fleqn %%*F
+        \advance\totwidth@-\@mathmargin %%*F
+    \fi %%*F
+    \halign\bgroup
+        \Let@
+        \let\tag\gobble@tag
+        \hbox to\totwidth@{%
+            \strut@$\m@th\displaystyle
+            \if@fleqn %%*F
+                \hskip 0pt plus 1000pt %%*F
+            \else %%*F
+                \hfil
+            \fi %%*F
+            {}##\hfil$%
+        }%
+        \crcr
+        \if@fleqn %%*F
+            \hskip-\@mathmargin %%*F
+        \else %%*F
+            \hfilneg
+        \fi %%*F
+        \hskip\multlinegap
+}
+\def\endmultline{\iftagsleft@\expandafter\lendmultline@\else
+  \expandafter\rendmultline@\fi\global\@ignoretrue}
+\expandafter\let\csname endmultline*\endcsname=\endmultline
+\def\lendmultline@{\hfilneg\hskip\multlinegap\crcr\egroup$$}
+\def\rendmultline@{%
+    \iftag@
+        \ifdim\rtwidth@>\z@
+            \hskip\multlinetaggap@
+            \box\mtagbox@
+        \else
+            \hskip\multlinegap %%*
+            \llap{%
+                \vtop{%
+                    \@movetag %%*T
+                    \normalbaselines\null\hbox{\strut@\box\mtagbox@}%
+                }%
+            }%
+        \fi
+    \else
+        \hskip\multlinegap
+    \fi
+    \hfilneg
+    \crcr
+    \egroup$$%
+}
+\expandafter\def
+ \expandafter\@arrayparboxrestore
+  \expandafter{\@arrayparboxrestore
+               \inany@false\ingather@false\inalign@false
+   \default@tag}
+\def\equation{\gather\def\\{\PackageError{amstex}{\Invalid@@\\}\@eha}}
+\def\endequation{\endgather}
+\newenvironment{equation*}{%
+  \equation
+}{%
+  \nonumber\endequation
+}
+\newcounter{parentequation}% Counter for ``parent equation''.
+\newenvironment{subequations}{%
+  \refstepcounter{equation}%
+  \begingroup % conservative approach
+  \let\protect\@nx
+  \edef\@tempa{\def\@nx\theparentequation{\theequation}}%
+  \@xp\endgroup\@tempa
+  \setcounter{parentequation}{\value{equation}}%
+  \setcounter{equation}{0}%
+  \def\theequation{\theparentequation\alph{equation}}%
+  \ignorespaces
+}{%
+  \setcounter{equation}{\value{parentequation}}%
+  \global\@ignoretrue
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
+\begingroup \catcode`\@=\active
+\gdef @{\Iat}
+\endgroup
+\DeclareRobustCommand{\Iat}{\FN@\at@}
+\def\at@{\let\next@\at@@
+ \ifcat\noexpand\@let@token a\else
+ \ifcat\noexpand\@let@token0\else
+ \ifcat\noexpand\@let@token\relax\else
+ \let\@let@token@\at@@@\fi\fi\fi\next@}
+\def\at@@#1{\expandafter
+  \@ifundefined{ @\string#1}%
+    {\DN@{\at@@@#1}}%
+    {\DN@{\csname\space @\string#1\endcsname}}%
+  \next@}%
+\def\at@@@{\PackageError{amstex}{\Invalid@@ @}%
+  {\the\athelp@}% "I'll assume you wanted @@"
+  \char64\relax}
+\newhelp\athelp@
+{Only certain combinations beginning with @ make sense to me.^^J%
+I'll assume you wanted @@ for a printed @.}
+\atdef@ @{{\atchar}}% to define @@
+\chardef\atchar=64
+\def\makeatother{\catcode64=\active}
+\def\@tempa#1#2#3#4#5#6{%
+  {#1}{#2}\ifnum0#6=0{13}\@xp\@gobblefour
+  \else{#3}\fi\@tempa{#4}{#5}{#6}}%
+\xdef\@currnamestack{\@xp\@tempa\@currnamestack{}{}{0}}
+{\def\@makeother{\noexpand\@makeother\noexpand}
+\xdef\@sanitize{\@sanitize\@makeother\@}}
+{\def\do{\noexpand\do\noexpand}
+\xdef\dospecials{\dospecials\do\@}}
+\atdef@,{\ifmmode\mskip.1\thinmuskip\else \nonmatherr@{@,}\fi}
+\atdef@!{\RIfM@\mskip-.1\thinmuskip\else \nonmatherr@{@!}\fi}
+
+\@ifpackageloaded{amscd}{%
+}{%
+\atdef@>#1>#2>{%
+  \global\bigaw@\minaw@
+  \setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%
+  \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
+  \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
+    \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
+   \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill@\displaystyle}}%
+     \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+}% end of @>>>
+\atdef@<#1<#2<{%
+  \global\bigaw@\minaw@
+  \setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%
+  \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
+  \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%
+    \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
+  \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill@\displaystyle}}%
+      \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+}% end of @<<<
+}% end of @ifpackageloaded
+\@ifundefined{minaw@}{\newdimen\minaw@}{}
+\minaw@11.111pt
+\@ifundefined{bigaw@}{\newdimen\bigaw@}{}
+\atdef@-{\let\next-%%
+  \DN@{\ifx\next-%%
+    \def\next-{\setbox\z@\hbox{-}\unhbox\z@\FN@\next@}%%
+    \expandafter\next \else\nobreak\fi}%%
+  \next@-}%%
+\def\leftroot{\PackageError{amstex}{\Invalid@@\leftroot}\@eha}
+\def\uproot{\PackageError{amstex}{\Invalid@@\uproot}\@eha}
+\newcount\uproot@
+\newcount\leftroot@
+\def\root{\relaxnext@
+  \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
+   \ifx\@let@token\leftroot\let\next@\nextiii@\else
+   \let\next@\plainroot@\fi\fi\next@}%
+  \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
+  \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
+   \DN@.{\FN@\nextv@}\fi\next@.}%
+  \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
+   \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
+  \def\nextvii@{\ifx\@let@token\@sptoken
+   \DN@. {\FN@\nextviii@}\else
+   \DN@.{\FN@\nextviii@}\fi\next@.}%
+  \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
+   \let\next@\plainroot@\fi\next@}%
+  \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
+  \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
+\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
+ $\m@th\scriptscriptstyle{#1}$}%
+ \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
+ {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
+\def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
+ \dimen@\ht\z@\advance\dimen@-\dp\z@
+ \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
+ \advance\dimen@ by1.667\wd\@ne
+ \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
+ \mkern-10mu\mkern\leftroot@ mu\boxz@}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Fragment from old amsfonts.sty to deal with msam, msbm, eufm fonts;
+%% omit if `noamsfonts' option was specified.
+\ifx F\@amsfonts \endinput \fi
+\DeclareSymbolFont{AMSa}{U}{msa}{m}{n}
+\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
+\ifx P\@amsfonts
+  \DeclareFontFamily{U}{msa}{}%
+  \DeclareFontShape{U}{msa}{m}{n}{<-6>msam5<6-8>msam7<8->msam10}{}%
+  \DeclareFontFamily{U}{msb}{}%
+  \DeclareFontShape{U}{msb}{m}{n}{<-6>msbm5<6-8>msbm7<8->msbm10}{}%
+  \DeclareFontFamily{U}{euf}{}%
+  \DeclareFontShape{U}{euf}{m}{n}{<-6>eufm5<6-8>eufm7<8->eufm10}{}%
+  \DeclareFontShape{U}{euf}{b}{n}{<-6>eufb5<6-8>eufb7<8->eufb10}{}%
+\fi
+\@ifundefined{yen}{%
+  \edef\yen{\noexpand\mathhexbox{\hexnumber@\symAMSa}55}
+}{}
+\@ifundefined{checkmark}{%
+  \edef\checkmark{\noexpand\mathhexbox{\hexnumber@\symAMSa}58}
+}{}
+\@ifundefined{circledR}{%
+  \edef\circledR{\noexpand\mathhexbox{\hexnumber@\symAMSa}72}
+}{}
+\@ifundefined{maltese}{%
+  \edef\maltese{\noexpand\mathhexbox{\hexnumber@\symAMSa}7A}
+}{}
+\begingroup \catcode`\"=12
+\DeclareMathDelimiter\ulcorner{\mathopen} {AMSa}{"70}{AMSa}{"70}
+\DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{"71}{AMSa}{"71}
+\DeclareMathDelimiter\llcorner{\mathopen} {AMSa}{"78}{AMSa}{"78}
+\DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{"79}{AMSa}{"79}
+\xdef\widehat#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
+  \noexpand\ifdim\noexpand\wdz@>\tw@ em%
+  \mathaccent"0\hexnumber@\symAMSb 5B{#1}%
+  \noexpand\else\mathaccent"0362{#1}\noexpand\fi}
+\xdef\widetilde#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
+  \noexpand\ifdim\noexpand\wdz@>\tw@ em%
+  \mathaccent"0\hexnumber@\symAMSb 5D{#1}%
+  \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
+\DeclareMathSymbol\dabar@{\mathord}{AMSa}{"39}
+\xdef\dashrightarrow{\mathrel{\dabar@\dabar@
+                              \mathchar"0\hexnumber@\symAMSa 4B}}%
+\xdef\dashleftarrow{\mathrel{\mathchar"0\hexnumber@\symAMSa 4C\dabar@
+                              \dabar@}}%
+\global\let\dasharrow\dashrightarrow
+\global\let\rightleftharpoons\undefined
+\DeclareMathSymbol\rightleftharpoons{\mathrel}{AMSa}{"0A}
+\global\let\angle\undefined
+\DeclareMathSymbol\angle            {\mathord}{AMSa}{"5C}
+\global\let\hbar\undefined
+\DeclareMathSymbol\hbar             {\mathord}{AMSb}{"7E}
+\global\let\sqsubset\undefined
+\DeclareMathSymbol\sqsubset         {\mathrel}{AMSa}{"40}
+\global\let\sqsupset\undefined
+\DeclareMathSymbol\sqsupset         {\mathrel}{AMSa}{"41}
+\global\let\mho\undefined
+\DeclareMathSymbol\mho              {\mathord}{AMSb}{"66}
+\DeclareMathSymbol\square           {\mathord}{AMSa}{"03}
+\DeclareMathSymbol\lozenge          {\mathord}{AMSa}{"06}
+\DeclareMathSymbol\vartriangleright {\mathrel}{AMSa}{"42}
+\DeclareMathSymbol\vartriangleleft  {\mathrel}{AMSa}{"43}
+\DeclareMathSymbol\trianglerighteq  {\mathrel}{AMSa}{"44}
+\DeclareMathSymbol\trianglelefteq   {\mathrel}{AMSa}{"45}
+\DeclareMathSymbol\rightsquigarrow  {\mathrel}{AMSa}{"20}
+\def\@tempa{\not@base\lhd}
+\ifx\lhd\@tempa
+ \global\let\lhd\vartriangleleft
+ \global\let\unlhd\trianglelefteq
+ \global\let\rhd\vartriangleright
+ \global\let\unrhd\trianglerighteq
+ \global\let\Box\square
+ \global\let\Diamond\lozenge
+ \global\let\leadsto\rightsquigarrow
+\xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F\mkern-13.8mu%
+  \mathchar"0\hexnumber@\symAMSb 6E}}
+\fi
+\endgroup
+\DeclareMathAlphabet\mathfrak{U}{euf}{m}{n}
+\SetMathAlphabet\mathfrak{bold}{U}{euf}{b}{n}
+\DeclareSymbolFontAlphabet{\mathbb}{AMSb}
+\DeclareFontEncodingDefaults{\relax}{\def\accentclass@{7}}
+\def\frak{\mathfrak}
+\def\Bbb{\mathbb}
+\def\bold{\mathbf}
+\begingroup \catcode`\"=12 \relax
+\gdef\newsymbol#1#2#3#4#5{%
+  \@ifdefinable#1{%
+     \edef\next@
+       {\ifcase #2 \or
+          \hexnumber@\symAMSa\or
+          \hexnumber@\symAMSb\fi}%
+     \ifx\next@\@empty
+       \PackageError{amsfonts}{\Invalid@@\newsymbol}\@ehd%
+     \else
+      \global\mathchardef#1"#3\next@#4#5
+     \fi}}
+\endgroup
+%%   Some odds and ends
+\def\sphat{^{\mathchoice{}{}%
+ {\,\,\smash[b]{\hbox{\lower4\ex@\hbox{$\m@th\widehat{\null}$}}}}%
+ {\,\smash[b]{\hbox{\lower3\ex@\hbox{$\m@th\hat{\null}$}}}}}}
+\def\spcheck{^\vee}
+\def\sptilde{^\sim}
+\def\spdot{^{\hbox{\raise\ex@\hbox{\normalfont .}}}}
+\def\spddot{^{\hbox{\raise\ex@\hbox{\normalfont ..}}}}
+\def\spdddot{^{\hbox{\raise\ex@\hbox{\normalfont...}}}}
+\def\spbreve{^{\!\smash[b]{\hbox{\lower4\ex@\hbox{\u{}}}}}}
+\def\fracwithdelims#1#2{\new@ifnextchar[{\fracwithdelims@#1#2}%
+  {\fracwithdelims@#1#2[\@empty]}}
+\def\fracwithdelims@#1#2[#3]#4#5{\relax
+  \ifx\@empty#3{#4\overwithdelims#1#2#5}\else
+  {#4\abovewithdelims#1#2#3\relax#5}\fi}
+\def\accentedsymbol#1#2{%
+  \expandafter\newbox
+    \csname\expandafter\@gobble\string#1@box\endcsname
+  \expandafter\setbox
+    \csname\expandafter\@gobble\string#1@box\endcsname
+      \hbox{$\m@th#2$}%
+  \newcommand{#1}{%
+    \expandafter\copy
+      \csname\expandafter\@gobble\string#1@box\endcsname{}}%
+}
+\def~{\nobreakspace}
+\DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
+%%
+%% End of file `amstex.sty'.
diff --git a/macros/latex-dev/required/amsmath/amstext.dtx b/macros/latex-dev/required/amsmath/amstext.dtx
new file mode 100644
index 0000000000..a4c9aeb5d9
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amstext.dtx
@@ -0,0 +1,302 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amstext}
+\GetFileInfo{amstext.sty}
+\begin{document}
+\title{The \pkg{amstext} package}
+\author{Frank Mittelbach \and Rainer Sch\"opf}
+\date{Version \fileversion, \filedate}
+\DocInput{amstext.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%
+%    This style file implements the \AmSTeX{} macro \cn{text} for use
+%    with the new font selection scheme.  The \cn{text} macro is a
+%    sophisticated command which allows the user to insert ``normal text''
+%    into math formulas without worrying about correct sizes in sub- or
+%    superscripts. It can also be used in ordinary text; there it
+%    produces an unbreakable unit similar to \cn{mbox}.
+%
+%    Here is an example demonstrating some of its features:
+% \[
+%^^A mathbin spacing is nonscript glue, disappears in superscript
+%    x^{2\,\times\,\text{size of $y$}}
+%    \leq
+%    z_{i_{\text{upper bound of the array}}}
+% \]
+%    This was produced by
+% \begin{verbatim}
+% \[
+%    x^{2\,\times\,\text{size of $y$}}
+%    \leq
+%    z_{i_{\text{upper bound of the array}}}
+% \]
+% \end{verbatim}
+%
+%    Additionally this style file redefines an internal \fn{plain.tex}
+%    macro called \cs{mathhexbox} so that commands like \cn{dag}
+%    or \cn{P} will change sizes if used in math subscripts.
+%
+% \StopEventually{}
+%    Package information.
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must be December 1994 or later
+\ProvidesPackage{amstext}[2000/06/29 v2.01 AMS text]
+%    \end{macrocode}
+%
+% \section{The implementation}
+%    We need a few tools from \fn{amsgen.sty}.
+%    \begin{macrocode}
+\RequirePackage{amsgen}
+%    \end{macrocode}
+%
+% \begin{macro}{\text}
+%    Now we come to the \cn{text} macro which is used to place
+%    ordinary text inside of math formulas. If it is used outside
+%    math it will produce an unbreakable unit of text.
+%    \begin{macrocode}
+\DeclareRobustCommand{\text}{%
+  \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
+%    \end{macrocode}
+%    At the present time (late 1994) the \latex/ internal function
+%    |\nfss@text| is used in |\ref|, in font commands like |\textbf|,
+%    and in a few text symbol definitions like |\$| and |\pounds|. By
+%    equating |\nfss@text| to |\text| we give it the ability of
+%    |\text| to change sizes properly if used in a subscript.
+%    \begin{macrocode}
+\let\nfss@text\text
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\text@}
+%    If \cn{text} is encountered inside math mode the macro
+%    \cs{text@} is called.  It has one mandatory argument, the text
+%    which should be produced.  Since we do not know in which math
+%    style we are currently in we call \cs{mathchoice} to tyeset
+%    our text in all four possible styles.
+%    \begin{macrocode}
+\def\text@#1{{\mathchoice
+%    \end{macrocode}
+%    To save token space we call a macro \cs{textdef@} which takes
+%    three arguments: the current math style, the corresponding size
+%    macro and the text to typeset possibly with some additional
+%    information for typesetting.
+%    \begin{macrocode}
+  {\textdef@\displaystyle\f@size{#1}}%
+%    \end{macrocode}
+%    The other three cases are similar except for the
+%    \cs{iffirstchoice} switch which we set to false. This is
+%    done to prevent \LaTeX{} macros like \cn{ref} or \cn{index}
+%    from writing their arguments more than once.
+%    \begin{macrocode}
+  {\textdef@\textstyle\f@size{\firstchoice@false #1}}%
+  {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
+  {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
+%    \end{macrocode}
+%    Here we need to check whether a math size-change occurred inside
+%    the argument of \cn{text}. If so, restore
+%    \begin{macrocode}
+  \check@mathfonts
+  }%
+}
+%    \end{macrocode}
+%    The macros \cs{f@size}, \cs{sf@size} and \cs{ssf@size} hold the
+%    sizes which should be used when we are loading a new font for use
+%    in \cs{textfont}, \cs{scriptfont} and \cs{scriptscriptfont}. There
+%    is some question whether we should use use \cs{tf@size} or
+%    \cs{f@size} for the main size, but since the primary purpose of the
+%    \cn{text} macro is to switch back to text within a display, it
+%    seems that \cs{f@size} is the better choice. (Indeed it could be
+%    said that the \cn{text} actually provides two different functions:
+%    one for escaping out of math mode in a display to print some words,
+%    and the other for handling math objects that are named by a
+%    fragment of text, when \cn{operatorname} isn't the right choice.
+%    For the latter \cs{tf@size} might be more correct but for the
+%    former \cs{f@size} is clearly better.)
+% \end{macro}
+%
+% \begin{macro}{\textdef@}
+%    To typeset the argument of \cn{text} correctly we have to make
+%    several actions. We start by placing everything inside an
+%    \cs{hbox}.  But this is not enough: we need one extra level of
+%    grouping.  These extra braces are necessary because of the new
+%    font selection scheme which might produce an \cs{aftergroup}
+%    to globally restore some font values after the current group. To
+%    prevent any damage by this mechanism we add the braces thereby
+%    bringing the token inserted by \cs{aftergroup} inside the
+%    \cs{hbox}.\footnote{The mechanism will not produce a second
+%    \cs{aftergroup}. For more details see the technical documentation
+%    for NFSS2.}
+%    \begin{macrocode}
+\def\textdef@#1#2#3{\hbox{{%
+%    \end{macrocode}
+%    Since text typeset inside an \cs{hbox} always stays in the size
+%    of the text surrounding the formula we have to adjust this for
+%    script and scriptscript sizes.  For any math formula inside this
+%    argument this will be achieved by setting \cs{everymath} to
+%    the first argument of \cs{textdef@} since this argument
+%    contains the math size in the current typeset case of
+%    \cs{mathchoice}.
+%    Since \latex/ also knows about \cn{parbox}es and the
+%    \env{minipage} environment it might be neccessary to adjust
+%    \cs{everydisplay} too but this has to be tested further.
+%    \begin{macrocode}
+                    \everymath{#1}%
+%    \end{macrocode}
+%    The next line of code changes locally (i.e.\ inside the current
+%    \cs{hbox}) the value of \cs{f@size}. This macro holds the
+%    size for typesetting ordinary text (e.g.\ loading or selecting a
+%    new font via \cs{selectfont}). By changing it to a smaller
+%    value a following \cs{selectfont} will switch to the wanted
+%    size.
+%    \begin{macrocode}
+                    \let\f@size#2\selectfont
+%    \end{macrocode}
+%    Now we simply call the third argument and close all open groups.
+%    \begin{macrocode}
+                    #3}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iffirstchoice@}
+%    Here is the switch that we use to decide if \cn{ref} etc.\
+%    should print its warnings.  The default is true since
+%    normally these warnings shouldn't be suppressed.
+%    \begin{macrocode}
+\newif\iffirstchoice@
+\firstchoice@true
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Re-definition of \latex/ macros to work with \cn{text}}
+%
+%    If a counter-changing command occurs inside the argument of
+%    \cn{text}, we don't want the counter to be changed four times
+%    because \cn{stepcounter} and \cn{addtocounter} have global effect.
+%    So we add the \cs{iffirstchoice@} test to make the counter
+%    operations execute only once.
+%
+% \begin{macro}{\stepcounter}
+%    Use \cs{def} rather than \cn{renewcommand*} because the star-form
+%    (for non-\cs{long} definitions) doesn't work with the June 1994
+%    release of \latex/.
+%    \begin{macrocode}
+\def\stepcounter#1{%
+  \iffirstchoice@
+     \addtocounter{#1}\@ne
+     \begingroup \let\@elt\@stpelt \csname cl@#1\endcsname \endgroup
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\addtocounter}
+%    \begin{macrocode}
+\def\addtocounter#1#2{%
+  \iffirstchoice@
+  \@ifundefined {c@#1}{\@nocounterr {#1}}%
+    {\global \advance \csname c@#1\endcsname #2\relax}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%    For \cn{ref}, \cn{pageref}, and indeed anything else that issues a
+%    warning or error, \cn{text} will produce four copies of the
+%    warning/error message. To suppress the last three copies, we change
+%    \cs{GenericInfo}, \cs{GenericWarning}, \cs{GenericError}.
+%    \begin{macrocode}
+\let\m@gobble\@empty
+\@xp\let\csname m@gobble4\endcsname\@gobblefour
+\long\@xp\def\csname m@gobble6\endcsname#1#2#3#4#5#6{}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\toks@{%
+  \csname m@gobble\iffirstchoice@\else 4\fi\endcsname
+  \protect}
+\edef\GenericInfo{\the\toks@
+  \@xp\@nx\csname GenericInfo \endcsname}
+%
+\edef\GenericWarning{\the\toks@
+  \@xp\@nx\csname GenericWarning \endcsname}
+%
+\toks@{%
+  \csname m@gobble\iffirstchoice@\else 6\fi\endcsname
+  \protect}
+\edef\GenericError{\the\toks@
+  \@xp\@nx\csname GenericError \endcsname}
+%    \end{macrocode}
+%
+%    At one time \cn{label}, \cs{@wrindex} and \cs{@wrglossary} were
+%    changed here too to use the \cs{iffirstchoice@} test but it seems
+%    that was a mistake because those are non-immediate writes.
+%    Something like
+% \begin{verbatim}
+% \text{something \index{foo}}
+% \end{verbatim}
+%    within a math formula would therefore \emph{lose the index term} if
+%    the surrounding context was not displaystyle. (Unlikely in
+%    practice, but not impossible.) [mjd,1994/12/09]
+%
+%\subsection{Applications of \cn{text}}
+%
+% \begin{macro}{\mathhexbox}
+%    We start with an re-definition of the \fn{plain.tex} macro
+%    \cs{mathhexbox}. (Although M. Spivak in \amstex/ uses the name
+%    \cs{mathhexbox@} for this purpose, I [FMi] don't see any reason
+%    to use a new name since the new definition is superior, has the
+%    same syntax and is used for the same purpose.)
+%    \begin{macrocode}
+\begingroup \catcode`\"=12
+\gdef\mathhexbox#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
+\endgroup
+%    \end{macrocode}
+%    This redefinition means that now symbols like \S, \P, \dag, \ldots,
+%    which are defined via \cs{mathhexbox} in \fn{plain.tex} or
+%    elsewhere now correctly change sizes if they are used in math mode.
+% \end{macro}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \CheckSum{129}
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amstext.ins b/macros/latex-dev/required/amsmath/amstext.ins
new file mode 100644
index 0000000000..84fcb0cb95
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amstext.ins
@@ -0,0 +1,51 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amstext.sty}{\from{amstext.dtx}{}}
+}
+
+\endbatchfile
+
diff --git a/macros/latex-dev/required/amsmath/amstext.pdf b/macros/latex-dev/required/amsmath/amstext.pdf
new file mode 100644
index 0000000000..a5c78d6737
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amstext.pdf
diff --git a/macros/latex-dev/required/amsmath/amsxtra.dtx b/macros/latex-dev/required/amsmath/amsxtra.dtx
new file mode 100644
index 0000000000..2165dde41a
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsxtra.dtx
@@ -0,0 +1,127 @@
+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% 
+% This work has the LPPL maintenance status `maintained'.
+% 
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amsxtra}
+\GetFileInfo{amsxtra.sty}
+\begin{document}
+\title{The \pkg{amsxtra} package}
+\author{American Mathematical Society\\Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amsxtra.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%    The \pkg{amsxtra} package contains a few rarely used commands that
+%    were present in version 1.1 of the \pkg{amstex} package:
+%    \cn{fracwithdelims}, {accentedsymbol}, \cn{sphat}, \cn{spcheck},
+%    \cn{sptilde}, \cn{spdot}, \cn{spddot}, \cn{spdddot}, \cn{spbreve}.
+%    If any of these commands were used in existing documents, the
+%    \pkg{amsxtra} package provides a way to get them. But for 99\% of
+%    documents using the \pkg{amstex} package these commands are just
+%    wasted overhead.
+%
+% \StopEventually{}
+%
+%    \begin{macrocode}
+\ProvidesPackage{amsxtra}[1999/11/15 v1.2c AMS extra commands]
+%    \end{macrocode}
+%    We need to ensure that either the \pkg{amstex} package or the
+%    \pkg{amsmath} package is loaded. This means we need something a
+%    little more complicated than \cn{RequirePackage}.
+%    \begin{macrocode}
+\@ifpackageloaded{amstex}{}{%
+  \RequirePackage{amsmath}[1996/10/01 v1.2]}
+%    \end{macrocode}
+%
+%    Superscripted accent characters.
+%    \begin{macrocode}
+\def\sphat{^{\mathchoice{}{}%
+ {\,\,\smash[b]{\hbox{\lower4\ex@\hbox{$\m@th\widehat{\null}$}}}}%
+ {\,\smash[b]{\hbox{\lower3\ex@\hbox{$\m@th\hat{\null}$}}}}}}
+\def\spcheck{^\vee}
+\def\sptilde{^\sim}
+\def\spdot{^{\hbox{\raise\ex@\hbox{\normalfont .}}}}
+\def\spddot{^{\hbox{\raise\ex@\hbox{\normalfont ..}}}}
+\def\spdddot{^{\hbox{\raise\ex@\hbox{\normalfont...}}}}
+\def\spbreve{^{\!\smash[b]{\hbox{\lower4\ex@\hbox{\u{}}}}}}
+%    \end{macrocode}
+%
+%    The \cn{fracwithdelims} command is skipped if the base package is
+%    \pkg{amsmath}; it is only needed if the base package is
+%    \pkg{amstex}.
+%    \begin{macrocode}
+\@ifpackageloaded{amstex}{%
+\def\fracwithdelims#1#2{\new@ifnextchar[{\fracwithdelims@#1#2}%
+  {\fracwithdelims@#1#2[\@empty]}}
+\def\fracwithdelims@#1#2[#3]#4#5{\relax
+  \ifx\@empty#3{#4\overwithdelims#1#2#5}\else
+  {#4\abovewithdelims#1#2#3\relax#5}\fi}
+}{}
+%    \end{macrocode}
+%
+%    Perhaps |\accentedsymbol| should use |\newsavebox|, but I don't
+%    know of any compelling reason at the moment.[mjd,5-Sep-1994]
+%    |\accentedsymbol| can only produce a single size of
+%    the given symbol, so you'd need two different versions for main
+%    size and subscript size.
+%    \begin{macrocode}
+\def\accentedsymbol#1#2{%
+  \expandafter\newbox
+    \csname\expandafter\@gobble\string#1@box\endcsname
+  \expandafter\setbox
+    \csname\expandafter\@gobble\string#1@box\endcsname
+      \hbox{$\m@th#2$}%
+  \newcommand{#1}{%
+    \expandafter\copy
+      \csname\expandafter\@gobble\string#1@box\endcsname{}}%
+}
+%    \end{macrocode}
+%
+%    Change the definition of \qc{\~} to automatically remove a
+%    preceding space as well as a following space, if present.
+%    \begin{macrocode}
+\def~{\nobreakspace}
+\DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
+%    \end{macrocode}
+%
+%    The usual \cs{endinput} to ensure that random garbage at the end of
+%    the file doesn't get copied by \fn{docstrip}.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%
+% \CheckSum{113}
+% \Finale
diff --git a/macros/latex-dev/required/amsmath/amsxtra.ins b/macros/latex-dev/required/amsmath/amsxtra.ins
new file mode 100644
index 0000000000..9e739c3d4b
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsxtra.ins
@@ -0,0 +1,51 @@
+%% 
+%% Copyright 2010 American Mathematical Society.
+%% Copyright 2016 LaTeX3 Project and American Mathematical Society.
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%   https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This work has the LPPL maintenance status `maintained'.
+%% 
+%% The Current Maintainer of this work is the LaTeX3 Project.
+%%
+%% ====================================================================
+
+\input docstrip
+
+\askforoverwritefalse
+
+\keepsilent
+
+\preamble
+
+Copyright 1995, 1999 American Mathematical Society.
+Copyright 2016 LaTeX3 Project and American Mathematical Society.
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+  https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX
+version 2005/12/01 or later.
+
+This work has the LPPL maintenance status `maintained'.
+
+The Current Maintainer of this work is the LaTeX3 project.
+
+\endpreamble
+
+\usedir{tex/latex/amsmath}
+
+\generate{
+    \file{amsxtra.sty}{\from{amsxtra.dtx}{}}
+}
+
+\endbatchfile
+
diff --git a/macros/latex-dev/required/amsmath/amsxtra.pdf b/macros/latex-dev/required/amsmath/amsxtra.pdf
new file mode 100644
index 0000000000..11cea1ef60
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/amsxtra.pdf
diff --git a/macros/latex-dev/required/amsmath/changes.txt b/macros/latex-dev/required/amsmath/changes.txt
new file mode 100644
index 0000000000..1b2d097dd5
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/changes.txt
@@ -0,0 +1,123 @@
+2019-02-06  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* amsmath.dtx (section{Mods, continued fractions, etc.}):
+	Command \overunderset added
+
+#########################
+# 2018-12-01 Release
+#########################
+
+2018-10-09  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* amsmath.dtx
+	Don't drop \frozen@everymath
+	Start LR-mode for \thinspace and friends if necessary (github/49)
+	Start LR-mode for \bigl and friends if necessary (github/49)
+	Start LR-mode for \smash if necessary (github/49)
+
+#########################
+# 2018-04-01 Release
+#########################
+
+2017-09-02  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: ensure that overfull alignments give warnings in more cases
+	https://tex.stackexchange.com/questions/141287/addmargin-enumerate-and-align-miss-an-overfull-hbox
+
+	* amsmath.dtx: move the nulldelimiterspace correction for closing
+	delimiters in \genfrac for extended TeXs to the line before
+	\nulldelimiterspace is locally set to 0pt.
+
+2017-04-14  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amscd.dtx: typo fix in ProvidesPackage line.
+
+2016-11-05 David Carlisle  <latex-bugs@latex-project.org>
+
+        * alignedleftspace[yes|no|yesifneg] package options
+	* New genfrac implementation for XeTeX and LuaTeX
+	* Delete obsolete install.txt file.
+
+2016-06-28  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: Add space to prevent runaway argument error with \dots \left...
+
+2016-05-26  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: ignore spaces at start of \intertext
+
+2016-03-10  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: Preserve box0 in \resetMathstrut@
+
+2016-03-08  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsopn.dtx: In xetex, and luatex, add version of \newmcodes@
+	that works even if - has a \Umathcode definition.
+
+2016-03-03  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: missing %
+
+2016-02-20  David Carlisle  <latex-bugs@latex-project.org>
+
+	* amsmath.dtx: update to support \Umathchardef and \long macros in \dots.
+
+2013-01-14 amsmath.dtx 2.14
+
+    * amsmath.sty 2.14
+      -- Minimal changes to make amsmath compatible with stix.sty.
+
+2000-07-18 amsmath.dtx 2.13
+    -- After the numbering patches in 2.11, \notag failed in certain
+       circumstances: introduce some more auxiliary functions to sort
+       things out, and redefine \nonumber.
+
+2000-06-29 amstext.dtx 2.01
+    -- Use \f@size instead of \tf@size because they are not
+       necessarily the same and the former is better for putting a few
+       words into a display.
+
+2000-06-06 amsmath.dtx 2.12
+    -- Fix transposed lines in 2.11 patch.
+
+2000-06-02 amsmath.dtx 2.11
+
+    * amsmath.sty 2.11
+      -- Prevent "Arithmetic overflow" error by guarding against
+         divide-by-zero in \x@calc@shift@lc (align environment).
+
+    * amsdtx.dtx
+      -- Moved to the amscls distribution.
+
+2000-05-25 amsmath.dtx 2.10
+    -- Clear up error message for \allowdisplaybreaks[0].
+    -- Make mathdisplay re-entrant by introducing mathdisplay@stack,
+       to clear up numbering problems in unusual circumstances such as
+       \[ \] nested inside minipage inside equation.
+
+2000-04-21 amsmath.dtx 2.09
+    -- Ensure good catcodes for " etc.
+
+2000-03-16 amsmath.dtx 2.08
+    -- Fixed erroneous tag placement on split with fleqn/tbtags options.
+
+2000-03-15 amsmath.dtx 2.07
+    -- Add \reset@strutbox@ to deal with the following bug: After
+       $...\mbox{\Huge $...$}...$, line spacing is wrong in a
+       following "gather" or other environment that uses \strut@.
+    -- Patch to fix bug with intlimits option: too much space in the
+       middle of \iint.
+    -- Overhaul math accents again to fix a couple of bugs reported by
+       Thimm.
+
+2000-03-10 amsmath.dtx 2.06
+    -- Change \MathAccent to \mathaccentV so \DeclareMathAccent won't
+       give an error when redefining an accent.
+
+2000-01-06 amsmath.dtx 2.05
+    -- Fixed incorrect placement of fleqn/reqno equation numbers
+       inside indented lists (displaywidth < columnwidth). Changed the
+       multline/fleqn/leqno indent to match mathmargin when possible
+       instead of always just using multlinetaggap.
+
diff --git a/macros/latex-dev/required/amsmath/diffs-m.txt b/macros/latex-dev/required/amsmath/diffs-m.txt
new file mode 100644
index 0000000000..af3a273f52
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/diffs-m.txt
@@ -0,0 +1,551 @@
+diffs-m.txt [1999/12/15] American Mathematical Society
+
+This is a synopsis of the principal differences between various versions
+of the amsmath package and its companion packages.
+
+A synopsis of changes in the "AMS-LaTeX" distribution is included at the
+end of this file. See also diffs-c.txt in the amslatex/classes area.
+
+Those upgrading from version 1.2 to version 2.0 will probably be
+interested in the question:
+
+  After I upgrade will anything fail in my pre-existing documents?
+
+Certain of the bug fixes have the potential to affect the output of
+existing documents in the following ways:
+
+---Vertical spacing for some displayed equations will change because
+"abovedisplayshortskip" is now applied when possible.
+
+---Incorrect horizontal spacing for certain math constructs will change,
+e.g., for \iint\nolimits or a subscript on a double-accented letter.
+
+---The default subscript placement in displayed formulas for \varinjlim,
+\varprojlim, \varliminf, \varlimsup is now below rather than to the
+side. To get the old behavior, add \nolimits---e.g.,
+\varliminf\nolimits_{...}.
+
+---Ellipsis dots in text (\ldots or \dots) will now behave the same as
+in standard LaTeX; the surrounding space may therefore change.
+
+During regression testing we found some errors cropping up in documents
+from incorrect usage that had not been caught with version 1.2. Although
+these errors are relatively rare, documents containing such usage will
+need to be corrected before they will run properly with version 2.0:
+
+---Use of two mutually exclusive display structures for the same
+display. In this example the outer \[ \] are redundant:
+
+      \[
+      \begin{align*}
+      ...
+      \end{align*}
+      \]
+
+---Inadequate argument markup for math accents:
+
+      \hat \mathcal{C}
+
+This should have been written with braces surrounding the argument of
+the \hat command: \hat{\mathcal{C}}.
+
+For documents where error messages crop up after the upgrade, there are
+various possible approaches, including:
+
+(a) Change instances of incorrect usage (if applicable).
+
+(b) Put a copy of amsmath.sty version 1.2 into the home directory of the
+document. Then it should continue to work the same as before.
+
+(c) Use the snapshot package in combination with a shell script to
+arrange that version 1.2 of amsmath is found instead of 2.0 when
+processing the document. See ftp://ftp.ams.org/pub/tex/snapshot.*. This
+approach requires a certain amount of technical knowledge.
+
+(d) Downgrade to version 1.2 again.
+
+========================================================================
+Changes in amsmath 2.0 [November 1999]
+
+---The AMS-LaTeX User's Guide (amsldoc.tex) has been turned into the
+   AMSmath User's Guide by moving the amsthm documentation into a
+   separate file (amsthdoc.tex) in the amslatex/classes area.
+
+---Restored normal use of "shortskip" spacing in single equations.
+
+[!! NOTE: This means that page breaks may change in existing documents.]
+
+---Restored normal use of available shrink around binary operators in
+   single equations.
+
+---Fixed poor subscript placement for double-accented letters. Math
+accent handling was reworked in the process in such a way that the
+capitalized forms of the math accent commands are no longer necessary.
+\hat{\hat{X}} will do proper alignment of the second accent. \Hat et
+cetera are retained for compabitility reasons. (Thanks to Javier Bezos
+for donating some code from his accents package.)
+
+[!! NOTE: Improper math accent use will now produce wrong output.]
+
+Suppose that we have \boldH defined in the preamble as
+\newcommand{\boldH}{\mathbf{H}}. Then the following examples illustrate
+recommended usage.
+
+     \hat{\mathbf{H}}    OK
+     \hat{\boldH}        OK
+     \hat\boldH          Works OK, but deprecated by the LaTeX book
+     \hat\mathbf{H}      Not OK! Output will be incorrect.
+
+Since the output will be wrong, amsmath gives an error message when the
+last variant is detected.
+
+---The following kinds of mixed structures worked by happenstance with
+   amsmath 1.2, although they should have produced an error message.
+   With amsmath 2.0 they will produce an error or warning message.
+
+   [!! NOTE: Potential error messages]
+
+    % Outer \[ \] is redundant
+
+    \[
+    \begin{align*}
+     ...
+    \end{align*}
+    \]
+
+    % Outer \begin{equation*} ... \end{equation*} is redundant
+
+    \begin{equation*}\begin{alignat*}{2}
+    ...
+    \end{alignat*}
+    \end{equation*}
+
+    % No printed material is allowed between \begin{equation} and
+    % \begin{split}:
+
+    \begin{equation*}\left \{
+    \begin{split}
+     ...
+    \end{split}\right .
+    \end{equation*}
+
+---diff12.tex is replaced by diffs-m.txt and diffs-c.txt, with the
+   latter moving to the amslatex/classes area.
+
+---Added an "?" option which gives some information about the available
+   documentation.
+
+---The amsmath definitions for matrix, pmatrix, and cases are
+   incompatible with the plain-TeX syntax for \pmatrix, \matrix, and
+   \cases, which are used occasionally by some authors in LaTeX
+   documents. In version 2.0 the error messages resulting from the
+   plain-TeX syntax have been made more intelligible.
+
+---If you need the boldsymbol facilities of the amsbsy package, use of
+   the "bm" (boldmath) package is recommended instead for new documents.
+   The amsbsy package is retained for compatibility with existing
+   documents. If you have a recent version of LaTeX (1998 or newer) you
+   already have the bm package; otherwise you may need to get it from
+   CTAN. (It is not an AMS package.)
+
+---\iint\nolimits: Fixed poor placement of subscript (also \iiint,
+\idotsint, etc).
+
+---\varinjlim, \varprojlim, \varliminf, \varlimsup: Default to
+\displaylimits instead of nolimits.
+
+---Fixed alignedat so that it doesn't take the first token of its
+   contents and try to interpret it as a number.
+
+---Leave text version of \dots and \ldots unchanged.
+
+---Changed \numberwithin so it no longer assumes previous definition of
+   \thesomething contained no prefixes.
+
+---\mathbf{\Gamma}: Leave cap Greek letters alone instead of converting
+   them from variable (fam 7) to fixed (fam 0). \mathbf{\gamma} still
+   fails---but that's a math font problem.
+
+---\mathindent is aliased to \@mathmargin so that when the fleqn option
+   is used, users can reset it as the LaTeX book advertises.
+
+---With the showkeys package: Corrected loss of marginal notes when
+labels occurred inside an align environment.
+
+---Carried over some tweaks (\bmod, \right/leftarrowfill) from the 1996
+   version of plain.tex.
+
+---Adjusted spacing of overarrow@ and underarrow@ to allow more room for
+   larger cmsy arrowheads.
+
+---Corrected spurious "overfull \hbox" warnings for \xrightarrow.
+
+---Corrected poor spacing for \xleftarrow.
+
+---Removed the \leavevmode in \smash which caused trouble for some
+   applications (e.g., the crop package) that expected the original
+   LaTeX definition.
+
+---Changed \def to \newcommand/\newenvironment where appropriate.
+
+---Use \sqrtsign instead of \@@sqrt (but include a backward
+   compatibility hack for the latter).
+
+---Left brace in \env{cases} environment would fail to work in
+   certain circumstances: Fix by using \lbrace instead of \{.
+
+---Use \ignorespacesafterend where applicable instead of
+   \global\@ignoretrue.
+
+---Protected commands in the definition of \theequation were
+   incorrectly expanded by the subequations environment when copying
+   the definition to \theparentequation: Fix by using \protected@edef.
+
+---Spurious extra space following punctuation at that end of a display:
+   In \math@cr, \math@cr@@, etc, use \iffalse{\fi instead of simply { to
+   keep an unwanted mathord atom from being added at the end of the
+   current math list; added \endmultline@math to work around a similar
+   sort of problem specific to the `multline' environment.
+
+---Various wrong results or no effect for \displaybreak inside "align",
+   "alignat", etc. Resetting \dspbrk@level in the \everycr of
+   \@display@init cleared most of these up.
+
+---Changed \displaybreak to issue an error message if enclosed in boxing
+   environment that will keep it from having any effect.
+
+---Turned off \displaybreak during the measuring phase of multline.
+
+---Fixed some numbering problems with multline and multline* and error
+   for use of \tag.
+
+---Use \@gtempa instead of \@tempa where assigned globally (standard
+   save stack precaution).
+
+---Save and restore \column@ to keep aligned from screwing up the column
+   counting of a parent align environment. Made \column@ assignments
+   uniformly global, except in a couple of places where the risk of side
+   effects seemed too great.
+
+---Error recovery for misspelled '\end{multline}' was not very helpful.
+   Improve \collect@body along lines suggested by Hellström.
+
+---Fixed up certain number placement problems with align
+
+---Add \alignsafe@testopt to work around a LaTeX bug: when a nested
+   alignment environment that takes an optional argument has an empty
+   first cell (i.e., begins with an &) LaTeX's optional argument
+   scanning screws up the alignment state.
+
+---Add `mathdisplay' environment (internal use) to correct several
+   problems of \[ \] and the `equation' environment arising from the
+   previous implementation as a degenerate case of `gather'.
+
+---It is possible now to use \eeq as an abbreviation for \end{equation}
+(one of the consequences of the preceding change). But still not \eal
+for \end{align} or certain other display structures.
+
+---Reorganize `split' internal calling sequence to go along with the use
+   of `mathdisplay' in \[ \] and `equation'.
+
+---Suppression of LaTeX error messages during measuring phase made
+   primitive TeX errors harder to understand; stop suppressing. (As a
+   result, users will sometimes get redundant error messages now.)
+   Remove obsolete Sb, Sp environments again.
+
+---The file amsintx.dtx was removed from the distribution pending
+   further development.
+
+---Remove the \ifinany@ switch, use \spread@equation instead to achieve
+   the same ends.
+
+---Remove unbracefonts@ function, no longer needed after changes in
+   math accent handling.
+
+---Got rid of the special trap for '^x that had been carried over from
+AMS-TeX.
+
+---Made \overline, \doteq, \longrightarrow, etc, robust.
+
+---Changed \relbar to use \std@minus---otherwise \underleftrightarrow
+works poorly in a \DeclareMathOperator definition.
+
+---Use \new@ifnextchar in matrix, pmatrix, cases so that \\<newline>[x]
+doesn't trigger an error.
+
+---Bug fix for nested use of \label inside minipage inside equation.
+
+---Add minalignsep after every second column in aligned, for consistency
+with align.
+
+========================================================================
+Changes in amsmath 1.2 [January 1995]
+
+---Name change; relation to the "amsfonts" package
+
+In version 1.1 of AMS-LaTeX, the name of this package was "amstex". The
+new name is "amsmath". The amstex package automatically invoked the
+amsfonts package as well; the amsmath package does not.
+
+---Adapted for LaTeX2e
+
+Old method of invocation:
+
+  \documentstyle[amstex]{article}% LaTeX 2.09
+
+New method of invocation:
+
+  \documentclass{article}
+  \usepackage{amsmath}
+
+---Handling of options intlim, nosumlim, nonamelm, righttag, ctagsplt
+
+Old usage:
+
+  \documentstyle[amstex,righttag,intlim]
+
+New usage:
+
+  \usepackage[reqno,intlimits]{amsmath}
+
+Several option names were changed (mainly, they are no longer restricted
+to eight characters):
+
+  intlim   -> intlimits
+  nosumlim -> nosumlimits
+  nonamelm -> nonamelimits
+  righttag -> reqno         [for consistency with "leqno"]
+  ctagsplt -> centertags
+
+---Character @ is no longer used as a special command prefix
+
+Certain commands in the amstex pkg started with "@" instead of "\". This
+special usage has been discontinued, except for the amscd package, and
+then only within the CD environment. Practically speaking, this means
+primarily that it is no longer necessary to use doubled @@ to get a
+single printed @ character (e.g., in e-mail addresses).
+
+---The @, and @! micro-spacing commands are no longer provided
+
+As a consequence of the @ character change, "@," and "@!" are no longer
+recognized spacing commands. An \mspace command is provided that can be
+used instead; see the AMSmath User's Guide.
+
+---Extensible arrow commands @>>> and @<<<
+
+The commands @>>> and @<<< are no longer available [except in the CD
+environment of the amscd package]; alternative commands \xleftarrow and
+\xrightarrow are provided by the amsmath package. The sub and
+superscripts are given through an optional resp. mandatory argument, for
+example
+
+  X\xleftarrow{b}Y                  % superscript "b" only
+  X\xrightarrow[\alpha]{\beta}Y     % sub alpha, sup beta
+
+---The command \bold has been superseded by the command \mathbf, as the
+latter is now the standard name provided by LaTeX for this purpose.
+
+---The commands \newsymbol, \frak, \Bbb are no longer available because
+the amsfonts package is not loaded by amsmath. In any case those
+commands now have new names---\frak -> \mathfrak, \Bbb -> \mathbb, etc.
+See the amsfonts documentation for further details.
+
+---The amsmath package provides \lvert and \rvert to use for vert-bar
+symbols when they act as delimiters (compare \langle, \rangle for
+angle-bracket delimiters). Commands \lVert and \rVert are likewise
+provided instead of \| for paired-delimiter use of the double-vert
+symbol. Use of | and \| for paired delimiters can lead to incorrect
+spacing in rare cases. Further discussion is found in the AMS-LaTeX
+user's guide (amsldoc.tex).
+
+---The ~ command is now left unchanged by amsmath; the change
+that makes it remove a redundant preceding or following space character
+is now done only by AMS documentclasses (in version 1.1 this was done by
+the amstex package).
+
+---The following rarely used commands are removed to the amsxtra
+package: \accentedsymbol, \sphat, \spcheck, \sptilde, \spdot, \spddot,
+\spdddot, \spbreve, \@))), \@(((.
+
+---The six generalized fraction commands \over, \overwithdelims, \atop,
+\atopwithdelims, \above, \abovewithdelims are deprecated and produce
+warning messages. Their functionality can be obtained through \frac,
+\binom, and \genfrac instead. See amsldoc.tex and technote.tex for
+further details.
+
+---The \fracwithdelims command is gone, as \genfrac provides
+equivalent functionality (and a little more).
+
+---The optional argument of \frac that allowed changing the thickness of
+the fraction line is gone. That functionality is now provided only
+through \genfrac: the need to change the line thickness is so rare in
+practice that it seems better not to burden the ubiquitous \frac command
+with the somewhat time-consuming look-ahead process required for an
+optional argument. I.e., this change will contribute in a small way to
+making your documents run faster.
+
+---The commands \lcfrac and \rcfrac for left or right alignment of
+continued fraction numerators are gone; they are replaced by an optional
+argument of the \cfrac command.
+
+---A new command \DeclareMathOperator is provided for defining new
+operator names:
+
+\DeclareMathOperator{\Tr}{Tr}
+\DeclareMathOperator*{\xlim}{x-lim}
+
+The * form makes the operator name produce limit-style sub and
+superscripts, like \max or \lim. This is now the preferred method,
+instead of using the old command \operatorname (which is, however,
+retained for now). The command \operatornamewithlimits has been renamed
+\operatorname*. These commands now can also be obtained through a
+separate package amsopn, so it's not necessary to load the entire
+amsmath package just to get that feature.
+
+---Environments "Sb", "Sp" retired.
+
+The environments Sb and Sp for multiline subscripts have been replaced
+by a single command \substack, used as follows:
+
+\sum_{\substack{first line\\second line}}
+
+This command can be used equally well in a subscript or superscript, and
+provides better vertical positioning (as compared to Sb, Sp) if a
+multiline subscript is placed on the side, as perhaps for an integral.
+There is also a slightly generalized alternative, an environment
+subarray that allows you to specify either centering or left alignment
+for the contents:
+
+\sum_{\begin{subarray}{l}first line\\second line\end{subarray}}
+
+---New command \nobreakdash
+
+A command \nobreakdash is provided to suppress the possibility of a
+linebreak after the following hyphen or dash. For example, if you write
+"$p$\nobreakdash-adic" then a linebreak will never be taken between the
+hyphen and the "adic".
+
+---The placement of equation numbers has been substantially improved for
+align, gather, and split. Numbers will now never overlap on top of the
+equation body (as far as we can ascertain), and they are much less
+likely to be shifted up or down unnecessarily when there is actually
+adequate space to leave the number in the normal place. In a few
+remaining cases, an equation number will be shifted unnecessarily
+because technical complications make accurate measurement of the
+available room too difficult; for those cases a \raisetag command is
+provided that allows you to manually adjust the vertical position of the
+equation number.
+
+---The [xx]align[at] family of environments has been thoroughly revised:
+now the xalignat environment is gone, as its function has been merged
+into the align environment (it's no longer necessary to specify how many
+side-by-side structures, as was required for xalignat, because align
+automatically handles any number of them). Similarly, the xxalignat
+environment has been replaced by an environment flalign that doesn't
+require you to specify how many side-by-side structures will be needed.
+Certain numbering problems (presence of an equation number when it
+should be absent, or vice versa) have also been cleared up.
+
+(Thanks to David M. Jones for his substantial [volunteer] work behind
+this change and the preceding one.)
+
+---The alignedat environment was changed to take two arguments rather
+than one: a mandatory argument (as formerly) specifying the number of
+align structures, and a new optional one specifying the placement of the
+environment (parallel to the optional argument of aligned). However,
+aligned is simpler to use, allowing any number of aligned structures
+automatically, and therefore the use of alignedat is deprecated.
+
+---The seldom-used command \oldnos is gone; if you need it, you should
+consult the LaTeX documentation on using fonts (e.g., fntguide.tex) to
+find out how to construct an equivalent command.
+
+---A new subequations environment causes all numbered equation
+environments within its scope to be numbered (4.9a) (4.9b) (4.9c) etc.,
+if the preceding numbered equation was 4.8. A \label command immediately
+after \begin{subequations} will produce a \ref of the parent number
+`4.9', not `4.9a'. The counters used by the subequations environment are
+parentequation and equation and standard uses of \addtocounter,
+\setcounter, etc., are possible with those counter names.
+
+---The amsmath package (unlike amstex) respects the setting provided by
+the documentclass for putting equation numbers on the right or the left.
+[Technical note: a documentclass that has leqno as the default should
+explicitly pass that option to the amsmath package with
+\PassOptionsToPackage in order for it to be effective.]
+
+---The fleqn option for left-aligned instead of centered equations is
+now supported (thanks to David M. Jones).
+
+************************************************************************
+The remainder of this file discusses some changes that do not directly
+pertain to the amsmath package but to the parent distribution known as
+"AMS-LaTeX".
+
+========================================================================
+Changes in AMS-LaTeX 2.0
+
+---The AMS-LaTeX User's Guide (amsldoc.tex) is split up into amsldoc.tex
+and amsthdoc.tex, with the latter moving into the "classes" area.
+
+---The file amslatex.faq was split into amsmath.faq and amsclass.faq.
+
+---The file amslatex.bug was done away with; most of the information was
+merged into diffs-m.txt, diffs-c.txt, amsmath.faq, and amsclass.faq.
+
+========================================================================
+Changes in AMS-LaTeX 1.2
+
+---Adapted for LaTeX2e
+
+AMS-LaTeX 1.0 and 1.1 were designed to work with LaTeX 2.09, which
+became obsolete in 1994 with the appearance of "LaTeX2e". AMS-LaTeX 1.2
+has been extensively adapted to take advantage of various features of
+LaTeX2e. It is no longer a separate TeX format---i.e., it does not need
+to be invoked by a separate "amslatex" command.
+
+---LaTeX 2.09 font commands (\bf, \it, etc)
+
+Pre-existing documents will for the most part continue to work fine
+without requiring any changes. However, depending on the installation
+options used for your copy of AMS-LaTeX 1.1 you may need to update the
+options list of the \documentstyle command by adding newlfont, for
+example:
+
+  \documentstyle[newlfont]{amsart}
+
+---The packages amsfonts, amssymb were moved to the AMSFonts
+distribution. They used to be included in the AMS-LaTeX distribution for
+pragmatic reasons but their natural home is with the AMSFonts
+distribution.
+
+---Package amstex renamed to amsmath
+
+The amstex package has been renamed amsmath. The old name `amstex' came
+from the fact that version 1.0 was a more or less straight port into
+LaTeX of selected portions from the macro package AmS-TeX written by
+Michael Spivak, but the historical origins of the package are likely of
+less interest to the general usership---especially looking to the
+future---than a straightforward declaration in the name `amsmath' of the
+sort of features that are provided.
+
+Another important reason for the name change was to make possible some
+progress that would be out of the question (because of the impact on
+existing documents) if the name `amstex' were retained. For example,
+unlike amstex, amsmath doesn't automatically load the amsfonts package,
+as that package was moved out to the AMSFonts distribution as described
+above. If this change were not accompanied by a name change, many
+existing documents would have to be updated by hand (adding
+\usepackage{amsfonts}) in order to run without error. A frozen version
+of amstex.sty is provided for processing pre-existing documents; it
+won't have active maintainence henceforth except for bug fixes. For new
+documents, authors should use the amsmath package.
+
+Therefore, "\usepackage{amstex}" is incorrect usage---do not rely on the
+1994 edition of `The LaTeX Companion' in this respect (unless you obtain
+the errata for Chapter 8).
+
+---New documentclass amsproc
+
+A new documentclass amsproc was added for collections of articles, such as
+the proceedings of a conference.
diff --git a/macros/latex-dev/required/amsmath/manifest.txt b/macros/latex-dev/required/amsmath/manifest.txt
new file mode 100644
index 0000000000..ee6b8e3238
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/manifest.txt
@@ -0,0 +1,32 @@
+README.txt
+amsbsy.dtx
+amsbsy.ins
+amsbsy.pdf
+amscd.dtx
+amscd.ins
+amscd.pdf
+amsgen.dtx
+amsgen.ins
+amsgen.pdf
+amsldoc.pdf
+amsldoc.tex
+amsmath.dtx
+amsmath.ins
+amsmath.pdf
+amsopn.dtx
+amsopn.ins
+amsopn.pdf
+amstex.sty
+amstext.dtx
+amstext.ins
+amstext.pdf
+amsxtra.dtx
+amsxtra.ins
+amsxtra.pdf
+diffs-m.txt
+subeqn.pdf
+subeqn.tex
+technote.pdf
+technote.tex
+testmath.pdf
+testmath.tex
diff --git a/macros/latex-dev/required/amsmath/subeqn.pdf b/macros/latex-dev/required/amsmath/subeqn.pdf
new file mode 100644
index 0000000000..2e84ebe942
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/subeqn.pdf
diff --git a/macros/latex-dev/required/amsmath/subeqn.tex b/macros/latex-dev/required/amsmath/subeqn.tex
new file mode 100644
index 0000000000..c34b3f6952
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/subeqn.tex
@@ -0,0 +1,202 @@
+%%% ====================================================================
+%%%  @LaTeX-file{
+%%%     filename  = "subeqn.tex",
+%%%     version   = "1.2c",
+%%%     date      = "1999/11/29",
+%%%     time      = "14:49:29 EST",
+%%%     checksum  = "29866 202 668 6426",
+%%%     author    = "American Mathematical Society",
+%%%     copyright = "Copyright 1999 American Mathematical Society,
+%%%                  all rights reserved.  Copying of this file is
+%%%                  authorized only if either:
+%%%                  (1) you make absolutely no changes to your copy,
+%%%                  including name; OR
+%%%                  (2) if you do make changes, you first rename it
+%%%                  to some other name.",
+%%%     address   = "American Mathematical Society,
+%%%                  Technical Support,
+%%%                  Electronic Products and Services,
+%%%                  P. O. Box 6248,
+%%%                  Providence, RI 02940,
+%%%                  USA",
+%%%     telephone = "401-455-4080 or (in the USA and Canada)
+%%%                  800-321-4AMS (321-4267)",
+%%%     FAX       = "401-331-3842",
+%%%     email     = "tech-support@ams.org (Internet)",
+%%%     supported = "yes",
+%%%     keywords  = "latex, amslatex, ams-latex, amstex",
+%%%     abstract  = "This is part of the AMS-\LaTeX{} distribution.
+%%%                  It is a sample document illustrating the use of
+%%%                  the subequations environment and the effect of
+%%%                  the fleqn option.",
+%%%     docstring = "The checksum field above contains a CRC-16
+%%%                  checksum as the first value, followed by the
+%%%                  equivalent of the standard UNIX wc (word
+%%%                  count) utility output of lines, words, and
+%%%                  characters.  This is produced by Robert
+%%%                  Solovay's checksum utility.",
+%%%  }
+%%% ====================================================================
+\documentclass[fleqn]{article}
+
+\title{Test of subequations environment}
+\author{mjd}
+
+\usepackage{amsmath}
+\numberwithin{equation}{section}
+
+\newcommand{\env}[1]{{\normalfont\texttt{#1}}}
+
+\AtEndDocument{\multipasswarning}
+\newcommand{\multipasswarning}{%
+  \clearpage
+  \typeout{%
+  **********************************************************************}
+  \typeout{%
+  Note: This document needs to run through LaTeX three times, instead of}
+  \typeout{%
+  the usual two, to resolve indirect cross-references.}
+  \typeout{%
+  **********************************************************************}
+}
+
+\makeatletter
+%    Omit the warning message if three passes have been completed (on
+%    first pass \ref{check} is undefined and it is set to 0; on second
+%    pass \ref{check} is 0 and set to 1; on third pass it is 1).
+\def\checkref{\begingroup
+  \@ifundefined{r@check}{\let\r@check\relax\def\@currentlabel{0}}{\def\@currentlabel{1}}%
+  \ifnum1=0\expandafter\@firstoftwo\r@check\relax
+    \global\let\multipasswarning\relax
+  \fi
+  \label{check}%
+  \endgroup}
+\makeatother
+
+\begin{document}
+\section{Prime equation numbers}
+
+First an equation.
+\begin{equation}\label{e:previous}
+A=B
+\end{equation}
+That was equation \eqref{e:previous}.
+
+Then the same, with a prime on the number.\checkref
+\begin{equation}
+\tag{\ref{e:previous}$'$}\label{e:prevprime}
+C=D
+\end{equation}
+And that was equation \eqref{e:prevprime}.
+
+Notice, by the way, that when a \verb"\ref" occurs inside a \verb"\tag",
+and that \verb"\tag" is then \verb"\label"'d, a \verb"\ref" for the the
+second \verb"\label" requires \emph{three} runs of \LaTeX{} in order to
+get the proper value. (If you run through the logic of \LaTeX{}'s
+cross-referencing mechanisms as they apply in this case, you will see
+that this is necessary.)
+
+\section{Subnumbered equations}
+
+Here is a,b,c sub-numbering.
+\begin{subequations}
+\begin{eqnarray}
+A&=&B\\
+D&=&C \label{e:middle}\\
+E&=&F
+\end{eqnarray}
+\end{subequations}
+That was produced with the \env{eqnarray} environment; the middle line
+was labeled as \eqref{e:middle}.
+
+An equation following the end of the \verb"subequations" environment
+should revert to normal numbering:
+\begin{equation}\label{e:check}
+H<K
+\end{equation}
+A check on the labeling: that was equation~\eqref{e:check}.
+
+The sub-numbered equations can be spread out through the text, like
+this:
+\begin{subequations}
+\begin{equation}
+A=B
+\end{equation}
+The \verb"subequations" environment can span arbitrary text between
+subsidiary equations. The only restriction is that if there are any
+numbered equations inside the \verb"subequations" environment that break
+out of the subequation numbering sequence, they would have to be handled
+specially.
+\begin{equation}
+D=C \label{e:newmiddle}
+\end{equation}
+More arbitrary text.
+\begin{equation}
+E=F
+\end{equation}
+\end{subequations}
+Label check: the middle one was \eqref{e:newmiddle}
+
+A final equation for a numbering check.
+\begin{equation}\label{e:final}
+G=H
+\end{equation}
+That equation was labeled as \eqref{e:final}.
+
+\section{Tests of \env{align}, \env{gather}, and other
+AMS-\protect\LaTeX{} environments}
+
+The \env{align} environment:
+\begin{subequations}
+\begin{align}
+\label{align:a}A+B&=B+A\\
+\label{align:b}C&=D+E\\
+\label{align:c}E&=F
+\end{align}
+\end{subequations}
+Label check: that was \eqref{align:a}, \eqref{align:b}, and
+\eqref{align:c}.
+
+The \env{align} environment again:
+\begin{subequations}
+\begin{align}
+\label{xalign:a}A+B&=B&     B&=B+A\\
+\label{xalign:b}C&=D+E&     C\oplus D&=E\\
+\label{xalign:c}E&=F&       E'&=F'
+\end{align}
+\end{subequations}
+Label check: that was \eqref{xalign:a}, \eqref{xalign:b}, and
+\eqref{xalign:c}.
+
+The \env{gather} environment. For the third line we refer to one of the
+numbers in the first \env{align} structure.
+\begin{subequations}
+\begin{gather}
+\label{gather:a}A+B=B\\
+\label{gather:b}C=D+E\\
+\tag{\ref{align:c}$'$}\label{gather:c}E=F
+\end{gather}
+\end{subequations}
+Label check: that was \eqref{gather:a},
+\eqref{gather:b}, and
+\eqref{gather:c}.
+
+The next \env{subequations} environment encompasses two separate
+equations. A \env{split} environment:
+\begin{subequations}
+\begin{equation}
+\label{split:x}
+\begin{split}
+A&=B+C+F\\
+&=G
+\end{split}
+\end{equation}
+and a \env{multline} environment:
+\begin{multline}\label{multline:x}
+A[B]C[D]E[F]G[[H[I]J[K]L[M]N]]=\\
+H[I]J[K]L[M]N[O]P[Q]R[S]T[U]V[W]X[Y]Z
+\end{multline}
+\end{subequations}
+Label check: That was \eqref{split:x} and \eqref{multline:x}.
+
+\end{document}
diff --git a/macros/latex-dev/required/amsmath/technote.pdf b/macros/latex-dev/required/amsmath/technote.pdf
new file mode 100644
index 0000000000..7d7ab397c8
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/technote.pdf
diff --git a/macros/latex-dev/required/amsmath/technote.tex b/macros/latex-dev/required/amsmath/technote.tex
new file mode 100644
index 0000000000..aede450621
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/technote.tex
@@ -0,0 +1,233 @@
+%%% ====================================================================
+%%% @LaTeX-file{
+%%%   filename  = "technote.tex",
+%%%   version   = "2.0",
+%%%   date      = "1999/11/15",
+%%%   time      = "15:07:20 EST",
+%%%   checksum  = "58506 233 1647 12005",
+%%%   author    = "American Mathematical Society",
+%%%   copyright = "Copyright 1995, 1999 American Mathematical Society,
+%%%                all rights reserved.  Copying of this file is
+%%%                authorized only if either:
+%%%                (1) you make absolutely no changes to your copy,
+%%%                including name; OR
+%%%                (2) if you do make changes, you first rename it
+%%%                to some other name.",
+%%%   address   = "American Mathematical Society,
+%%%                Technical Support,
+%%%                Electronic Products and Services,
+%%%                P. O. Box 6248,
+%%%                Providence, RI 02940,
+%%%                USA",
+%%%   telephone = "401-455-4080 or (in the USA and Canada)
+%%%                800-321-4AMS (321-4267)",
+%%%   FAX       = "401-331-3842",
+%%%   email     = "tech-support@ams.org (Internet)",
+%%%   supported = "yes",
+%%%   keywords  = "amsmath, latex",
+%%%   abstract  = "This is part of the AMS-\LaTeX{} distribution. It
+%%%                is a document discussing some technical issues in the
+%%%                contents and interface of AMS-\LaTeX{} packages."
+%%%   docstring = "The checksum field above contains a CRC-16 checksum
+%%%                as the first value, followed by the equivalent of
+%%%                the standard UNIX wc (word count) utility output of
+%%%                lines, words, and characters.  This is produced by
+%%%                Robert Solovay's checksum utility.",
+%%% }
+%%% ====================================================================
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\documentclass{amsdtx}
+
+\title{Technical notes on the \pkg{amsmath} package}
+\author{American Mathematical Society\\Michael Downes}
+\date{1999/10/29}
+
+\markboth
+  {Technical notes on the \pkg{amsmath} package}
+  {Technical notes on the \pkg{amsmath} package}
+\renewcommand{\sectionmark}[1]{}
+
+\providecommand{\etc}[1]{etc.}
+
+\providecommand{\begend}[1]{%
+  {\ntt \symbol{92}begin\symbol{123}#1\symbol{125}}
+    \ldots\ {\ntt\symbol{92}end\symbol{123}#1\symbol{125}}%
+}
+
+\MakeShortVerb{\|}
+
+\begin{document}
+\maketitle
+
+\section{Introduction}
+
+These notes are miscellaneous remarks on some technical questions
+applicable to version 2.0 of \amslatex/.
+
+\section{Deprecated and disallowed commands}
+
+Certain commands that were in the \pkg{amstex} package (the predecessor,
+in \amslatex/ 1.0 and 1.1, of the \pkg{amsmath} package) were moved into
+\pkg{amsxtra} because they seemed to be little-used relics:
+\cn{accentedsymbol}, \qq{sup accents} (\cn{sptilde}, \cn{sphat}, etc.).
+
+Certain other commands\mdash e.g., \cn{over}, \cn{pmatrix}, and
+\cn{cases}\mdash are changed by the \pkg{amsmath} package to produce
+warning messages or error messages, depending on their history; these
+are discussed in more detail in the following sections.
+
+\section{Why do \cn{matrix}, \cn{pmatrix}, and \cn{cases} stop working
+when I add the \pkg{amsmath} package?}
+
+If you used the \fn{plain.tex} versions of \cn{matrix}, \cn{pmatrix}, or
+\cn{cases} in a document and then later converted the document to use
+the \pkg{amsmath} package (or one of the AMS documentclasses, which
+automatically call the \pkg{amsmath} package internally), the instances
+of those commands will produce error messages. The problem is that when
+\latex/ was originally created, it adopted most of its mathematics
+features straight from \fn{plain.tex}. But in the case of \cn{matrix},
+\cn{pmatrix}, \cn{cases} this was a mistake\mdash the \fn{plain.tex}
+syntax for them is decidedly non-\latex/ in style, for example the fact
+that they use \cs{cr} instead of \cn{\\} to mark line breaks, and they
+don't use \cn{begin} and \cn{end}. In basic \latex/ this mistake will be
+perpetuated at least until \latex/3 appears, in order to avoid breaking
+existing documents. But no existing documents that were written with the
+\pkg{amsmath} package have that syntactic problem, as \pkg{amsmath}
+provides proper \latex/-syntax versions of \cn{matrix} and the others.
+The possibility of optionally allowing the \fn{plain.tex} variants to
+make document conversion easier seems ill-advised since those variants
+are so blatantly wrong in a \latex/ context. The \env{array} environment
+ought to have been used instead.
+
+\section{Why do \cn{over}, \cn{atop}, \cn{above} [\dots{\ntt withdelims}]
+ give a warning when I add the \pkg{amsmath} package?}
+
+Using the six generalized fraction commands \cn{over},
+\cn{overwithdelims}, \cn{atop}, \cn{atopwithdelims}, \cn{above},
+\cn{abovewithdelims} is not really a good idea in \latex/, for reasons
+explained below. I construe \latex/'s provision of \cs{frac}, and the
+lack of any mention in the \latex/ book of the primitive fraction
+commands, as an implicit injunction against their use, although I don't
+think Lamport actually spent a lot of time pondering the issue, and the
+basic \latex/ version of \cn{frac} provides access only to \cn{over},
+not to \cn{atop}, \cn{above}, or the \verb'withdelims' variants. The
+\pkg{amsmath} package, however, provides a \cn{genfrac} command that
+gives user-level access to all six of the generalized fraction
+primitives in a way that conforms to the syntactic conventions followed
+by all other \latex/ commands.
+
+Not only is the unusual syntax of the \tex/ primitives rather out of
+place in \latex/, but furthermore that syntax seems to be responsible
+for one of the most significant flaws in \tex/'s mathematical
+typesetting capabilities: the fact that the current mathstyle at any
+given point in a math formula cannot be determined until the end of the
+formula, because of the possibility that a following generalized
+fraction command will change the mathstyle of the \emph{preceding}
+material. To cite two of the worst side effects: \cn{mathchoice} must
+actually typeset all four of its arguments, instead of being able to
+immediately select only one; and, were it possible to always know the
+current math style at a given point, math font selection would be
+greatly simplified and the upper limit of 16 different math font
+\cn{fam}s would never be a problem as \cn{text,script[script]font}
+assignments for any \cn{fam} could take immediate effect and therefore
+could be changed arbitrarily often within a single formula. More
+concretely, math font selection difficulties are responsible for many of
+the more convoluted passages in the source code of \latex/'s NFSS (that
+does font loading on demand) and of the \pkg{amsmath} package, and by
+extension it has historically been responsible for significant delays in
+making new features available to end users and for making those features
+more prone to bugs.
+
+There are additional bad consequences following from the syntax of those
+generalized fraction commands that only become evident when you do some
+writing of nontrivial macros for math use. For example, as things
+currently stand you cannot measure the size of any object in math
+without going through \cn{mathchoice} and \emph{leaving and reentering
+math mode} via \verb'\hbox{$' (which then introduces complications
+regarding \cn{everymath} and \cn{mathsurround}). And it seems that
+uncertainty about the current mathstyle is the only barrier to allowing
+the use of mu units with \cn{vrule}, to make vertical struts in
+constructing compound symbols or notation. And so on and so forth.
+
+\section{The \opt{fleqn} option and \cn{mathindent}}
+
+Strictly speaking, the \pkg{amsmath} package doesn't use \cn{mathindent}
+to control the left indent of displayed equations when the \opt{fleqn}
+option is in effect: it uses an internal parameter \cs{@mathmargin}
+instead. However, for compatibility with existing \latex/ documentation,
+\pkg{amsmath} turns \cn{mathindent} into an alias for \cs{@mathmargin}.
+There is a small risk here: In the plain \latex/ implementation,
+\cn{mathindent} is a dimen register, but with \pkg{amsmath}
+\cs{@mathmargin} is a skip register and, by association, so is
+\cn{mathindent}. If any package or documentclass uses \cn{mathindent} in
+a way that depends on it being a dimen register, when used in
+conjunction with the \pkg{amsmath} package it may be vulnerable to a
+well-known pitfall having to do with the primitive \tex/ lookahead for a
+\texttt{plus} or \texttt{minus} key word. However if the standard
+\latex/ commands \cn{setlength} and \cn{addtolength} are used to modify
+\cn{mathindent} then this problem will not arise.
+
+\section{Why can't I use abbreviations for \protect\begend{align}?}
+
+Authors often like to use abbreviations such as |\beq| |\eeq| for
+|\begin{equation}| |\end{equation}|. For some environments defined by
+the \pkg{amsmath} package, such as \env{align}, \env{gather},
+\env{multline}, and others of the same general type, this does not work:
+An attempt to define |\bal| |\eal| as shorthand for |\begin{align}|
+|\end{align}| will fail with a puzzling error message. This has to do
+with unfortunately nontrivial technical complications: the given
+environments must read their contents as a delimited macro argument
+because they do multipass processing of the contents using algorithms
+inherited from Spivak's \fn{amstex.tex}. The obvious
+solution\mdash substitution of different algorithms that do box shuffling
+instead of token shuffling for the multipass calculations\mdash would
+require rewriting these display environments from the ground up; while
+that is a worthy goal, it was beyond the original scope of the
+\amslatex/ project. Work is under way on an auxiliary package called
+\pkg{breqn} that addresses not only this problem but a number of others;
+at the time of this writing, however [September 1999] it has only
+progressed as far as a beta release.
+
+Some workarounds:
+\begin{itemize}
+\item |\def\bal#1\eal{\begin{align}#1\end{align}}|
+\item Define |\newcommand{\env}[2]{\begin{#1}#2\end{#1}}| and then use
+  |\env{align}{...}|
+\end{itemize}
+
+\section{The \pkg{upref} package}
+
+The reason for splitting out the \pkg{upref} package instead of
+automatically incorporating it in the \cls{amsart} and \cls{amsbook}
+classes is this: It involves low-level surgery on an important \latex/
+command. This means that if ever this command changes in the future (as
+it did between versions 2.09 and 2e of \latex/) we have a maintenance
+problem. And the benefit that \pkg{upref} provides is something that
+most end users don't care much about.
+
+\section{The \pkg{amsintx} package}
+
+After a very preliminary trial release the \pkg{amsintx} package was
+withdrawn to await further development. It is still considered a worthy
+project but has simply not yet made it to the head of the priority queue
+in the AMS \latex/ development program, as it has had to contend with a
+number of other equally worthy projects for development time.
+
+\section{Hyphenation in the documentation}
+
+Hyphenation was allowed for certain long command names in
+\fn{amsldoc.tex}; this presented technical difficulties because \latex/
+normally deactivates hyphenation for tt fonts. The method chosen to
+reinstate hyphenation was to turn off the encoding-specific function
+\cs{OT1+cmtt} that disables the \cs{hyphenchar} for tt fonts; see the
+definition of \cn{allowtthyphens} in \fn{amsdtx.dtx}. Then a list of all
+tt words in the document was gathered (from the \fn{.idx} file, produced
+by the \cn{cn}, \cn{fn}, \cn{pkg}, etc. commands) and \cn{showhyphens}
+was applied to this list. The result was another list in the resulting
+\tex/ log, containing those words in a form suitable for the argument of
+\cn{hyphenation}. That list was then edited by hand to overrule
+undesirable hyphenations; words with acceptable hyphenations were
+dropped from the list, as they don't need to be repeated there.
+
+\end{document}
diff --git a/macros/latex-dev/required/amsmath/testmath.pdf b/macros/latex-dev/required/amsmath/testmath.pdf
new file mode 100644
index 0000000000..d97ff85f73
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/testmath.pdf
diff --git a/macros/latex-dev/required/amsmath/testmath.tex b/macros/latex-dev/required/amsmath/testmath.tex
new file mode 100644
index 0000000000..069944ee9d
--- /dev/null
+++ b/macros/latex-dev/required/amsmath/testmath.tex
@@ -0,0 +1,2342 @@
+%%% ====================================================================
+%%% @LaTeX-file{
+%%%   filename  = "testmath.tex",
+%%%   version   = "2.0",
+%%%   date      = "1999/11/15",
+%%%   time      = "15:09:17 EST",
+%%%   checksum  = "07762 2342 7811 82371",
+%%%   author    = "American Mathematical Society",
+%%%   copyright = "Copyright 1995, 1999 American Mathematical Society,
+%%%                all rights reserved.  Copying of this file is
+%%%                authorized only if either:
+%%%                (1) you make absolutely no changes to your copy,
+%%%                including name; OR
+%%%                (2) if you do make changes, you first rename it
+%%%                to some other name.",
+%%%   address   = "American Mathematical Society,
+%%%                Technical Support,
+%%%                Electronic Products and Services,
+%%%                P. O. Box 6248,
+%%%                Providence, RI 02940,
+%%%                USA",
+%%%   telephone = "401-455-4080 or (in the USA and Canada)
+%%%                800-321-4AMS (321-4267)",
+%%%   FAX       = "401-331-3842",
+%%%   email     = "tech-support@ams.org (Internet)",
+%%%   codetable = "ISO/ASCII",
+%%%   keywords  = "latex, amsmath, examples, documentation",
+%%%   supported = "yes",
+%%%   abstract  = "This is a test file containing extensive examples of
+%%%                mathematical constructs supported by the amsmath
+%%%                package.",
+%%%   docstring = "The checksum field above contains a CRC-16
+%%%                checksum as the first value, followed by the
+%%%                equivalent of the standard UNIX wc (word
+%%%                count) utility output of lines, words, and
+%%%                characters.  This is produced by Robert
+%%%                Solovay's checksum utility.",
+%%% }
+%%% ====================================================================
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\documentclass[draft]{article}
+\pagestyle{headings}
+
+\title{Sample Paper for the \pkg{amsmath} Package\\
+File name: \fn{testmath.tex}}
+\author{American Mathematical Society}
+\date{Version 2.0, 1999/11/15}
+
+\usepackage{amsmath,amsthm}
+
+%    Some definitions useful in producing this sort of documentation:
+\chardef\bslash=`\\ % p. 424, TeXbook
+%    Normalized (nonbold, nonitalic) tt font, to avoid font
+%    substitution warning messages if tt is used inside section
+%    headings and other places where odd font combinations might
+%    result.
+\newcommand{\ntt}{\normalfont\ttfamily}
+%    command name
+\newcommand{\cn}[1]{{\protect\ntt\bslash#1}}
+%    LaTeX package name
+\newcommand{\pkg}[1]{{\protect\ntt#1}}
+%    File name
+\newcommand{\fn}[1]{{\protect\ntt#1}}
+%    environment name
+\newcommand{\env}[1]{{\protect\ntt#1}}
+\hfuzz1pc % Don't bother to report overfull boxes if overage is < 1pc
+
+%       Theorem environments
+
+%% \theoremstyle{plain} %% This is the default
+\newtheorem{thm}{Theorem}[section]
+\newtheorem{cor}[thm]{Corollary}
+\newtheorem{lem}[thm]{Lemma}
+\newtheorem{prop}[thm]{Proposition}
+\newtheorem{ax}{Axiom}
+
+\theoremstyle{definition}
+\newtheorem{defn}{Definition}[section]
+
+\theoremstyle{remark}
+\newtheorem{rem}{Remark}[section]
+\newtheorem*{notation}{Notation}
+
+%\numberwithin{equation}{section}
+
+\newcommand{\thmref}[1]{Theorem~\ref{#1}}
+\newcommand{\secref}[1]{\S\ref{#1}}
+\newcommand{\lemref}[1]{Lemma~\ref{#1}}
+
+\newcommand{\bysame}{\mbox{\rule{3em}{.4pt}}\,}
+
+%       Math definitions
+
+\newcommand{\A}{\mathcal{A}}
+\newcommand{\B}{\mathcal{B}}
+\newcommand{\st}{\sigma}
+\newcommand{\XcY}{{(X,Y)}}
+\newcommand{\SX}{{S_X}}
+\newcommand{\SY}{{S_Y}}
+\newcommand{\SXY}{{S_{X,Y}}}
+\newcommand{\SXgYy}{{S_{X|Y}(y)}}
+\newcommand{\Cw}[1]{{\hat C_#1(X|Y)}}
+\newcommand{\G}{{G(X|Y)}}
+\newcommand{\PY}{{P_{\mathcal{Y}}}}
+\newcommand{\X}{\mathcal{X}}
+\newcommand{\wt}{\widetilde}
+\newcommand{\wh}{\widehat}
+
+\DeclareMathOperator{\per}{per}
+\DeclareMathOperator{\cov}{cov}
+\DeclareMathOperator{\non}{non}
+\DeclareMathOperator{\cf}{cf}
+\DeclareMathOperator{\add}{add}
+\DeclareMathOperator{\Cham}{Cham}
+\DeclareMathOperator{\IM}{Im}
+\DeclareMathOperator{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\DeclareMathOperator{\seg}{seg}
+
+%    \interval is used to provide better spacing after a [ that
+%    is used as a closing delimiter.
+\newcommand{\interval}[1]{\mathinner{#1}}
+
+%    Notation for an expression evaluated at a particular condition. The
+%    optional argument can be used to override automatic sizing of the
+%    right vert bar, e.g. \eval[\biggr]{...}_{...}
+\newcommand{\eval}[2][\right]{\relax
+  \ifx#1\right\relax \left.\fi#2#1\rvert}
+
+%    Enclose the argument in vert-bar delimiters:
+\newcommand{\envert}[1]{\left\lvert#1\right\rvert}
+\let\abs=\envert
+
+%    Enclose the argument in double-vert-bar delimiters:
+\newcommand{\enVert}[1]{\left\lVert#1\right\rVert}
+\let\norm=\enVert
+
+\begin{document}
+\maketitle
+\markboth{Sample paper for the {\protect\ntt\lowercase{amsmath}} package}
+{Sample paper for the {\protect\ntt\lowercase{amsmath}} package}
+\renewcommand{\sectionmark}[1]{}
+
+\section{Introduction}
+
+This paper contains examples of various features from \AmS-\LaTeX{}.
+
+\section{Enumeration of Hamiltonian paths in a graph}
+
+Let $\mathbf{A}=(a_{ij})$ be the adjacency matrix of graph $G$. The
+corresponding Kirchhoff matrix $\mathbf{K}=(k_{ij})$ is obtained from
+$\mathbf{A}$ by replacing in $-\mathbf{A}$ each diagonal entry by the
+degree of its corresponding vertex; i.e., the $i$th diagonal entry is
+identified with the degree of the $i$th vertex. It is well known that
+\begin{equation}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\quad i=1,\dots,n
+\end{equation}
+where $\mathbf{K}(i|i)$ is the $i$th principal submatrix of
+$\mathbf{K}$.
+\begin{verbatim}
+\det\mathbf{K}(i|i)=\text{ the number of spanning trees of $G$},
+\end{verbatim}
+
+Let $C_{i(j)}$ be the set of graphs obtained from $G$ by attaching edge
+$(v_iv_j)$ to each spanning tree of $G$. Denote by $C_i=\bigcup_j
+C_{i(j)}$. It is obvious that the collection of Hamiltonian cycles is a
+subset of $C_i$. Note that the cardinality of $C_i$ is $k_{ii}\det
+\mathbf{K}(i|i)$. Let $\wh X=\{\hat x_1,\dots,\hat x_n\}$.
+\begin{verbatim}
+$\wh X=\{\hat x_1,\dots,\hat x_n\}$
+\end{verbatim}
+Define multiplication for the elements of $\wh X$ by
+\begin{equation}\label{multdef}
+\hat x_i\hat x_j=\hat x_j\hat x_i,\quad \hat x^2_i=0,\quad
+i,j=1,\dots,n.
+\end{equation}
+Let $\hat k_{ij}=k_{ij}\hat x_j$ and $\hat k_{ij}=-\sum_{j\not=i} \hat
+k_{ij}$. Then the number of Hamiltonian cycles $H_c$ is given by the
+relation \cite{liuchow:formalsum}
+\begin{equation}\label{H-cycles}
+\biggl(\prod^n_{\,j=1}\hat x_j\biggr)H_c=\frac{1}{2}\hat k_{ij}\det
+\wh{\mathbf{K}}(i|i),\qquad i=1,\dots,n.
+\end{equation}
+The task here is to express \eqref{H-cycles}
+in a form free of any $\hat x_i$,
+$i=1,\dots,n$. The result also leads to the resolution of enumeration of
+Hamiltonian paths in a graph.
+
+It is well known that the enumeration of Hamiltonian cycles and paths in
+a complete graph $K_n$ and in a complete bipartite graph $K_{n_1n_2}$
+can only be found from \textit{first combinatorial principles}
+\cite{hapa:graphenum}. One wonders if there exists a formula which can
+be used very efficiently to produce $K_n$ and $K_{n_1n_2}$. Recently,
+using Lagrangian methods, Goulden and Jackson have shown that $H_c$ can
+be expressed in terms of the determinant and permanent of the adjacency
+matrix \cite{gouja:lagrmeth}. However, the formula of Goulden and
+Jackson determines neither $K_n$ nor $K_{n_1n_2}$ effectively. In this
+paper, using an algebraic method, we parametrize the adjacency matrix.
+The resulting formula also involves the determinant and permanent, but
+it can easily be applied to $K_n$ and $K_{n_1n_2}$. In addition, we
+eliminate the permanent from $H_c$ and show that $H_c$ can be
+represented by a determinantal function of multivariables, each variable
+with domain $\{0,1\}$. Furthermore, we show that $H_c$ can be written by
+number of spanning trees of subgraphs. Finally, we apply the formulas to
+a complete multigraph $K_{n_1\dots n_p}$.
+
+The conditions $a_{ij}=a_{ji}$, $i,j=1,\dots,n$, are not required in
+this paper. All formulas can be extended to a digraph simply by
+multiplying $H_c$ by 2.
+
+\section{Main Theorem}
+\label{s:mt}
+
+\begin{notation} For $p,q\in P$ and $n\in\omega$ we write
+$(q,n)\le(p,n)$ if $q\le p$ and $A_{q,n}=A_{p,n}$.
+\begin{verbatim}
+\begin{notation} For $p,q\in P$ and $n\in\omega$
+...
+\end{notation}
+\end{verbatim}
+\end{notation}
+
+Let $\mathbf{B}=(b_{ij})$ be an $n\times n$ matrix. Let $\mathbf{n}=\{1,
+\dots,n\}$. Using the properties of \eqref{multdef}, it is readily seen
+that
+
+\begin{lem}\label{lem-per}
+\begin{equation}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B}
+\end{equation}
+where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$.
+\end{lem}
+
+Let $\wh Y=\{\hat y_1,\dots,\hat y_n\}$. Define multiplication
+for the elements of $\wh Y$ by
+\begin{equation}
+\hat y_i\hat y_j+\hat y_j\hat y_i=0,\quad i,j=1,\dots,n.
+\end{equation}
+Then, it follows that
+\begin{lem}\label{lem-det}
+\begin{equation}\label{detprod}
+\prod_{i\in\mathbf{n}}
+\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat y_j\biggr)
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat y_i\biggr)\det\mathbf{B}.
+\end{equation}
+\end{lem}
+
+Note that all basic properties of determinants are direct consequences
+of Lemma ~\ref{lem-det}. Write
+\begin{equation}\label{sum-bij}
+\sum_{j\in\mathbf{n}}b_{ij}\hat y_j=\sum_{j\in\mathbf{n}}b^{(\lambda)}
+_{ij}\hat y_j+(b_{ii}-\lambda_i)\hat y_i\hat y
+\end{equation}
+where
+\begin{equation}
+b^{(\lambda)}_{ii}=\lambda_i,\quad b^{(\lambda)}_{ij}=b_{ij},
+\quad i\not=j.
+\end{equation}
+Let $\mathbf{B}^{(\lambda)}=(b^{(\lambda)}_{ij})$. By \eqref{detprod}
+and \eqref{sum-bij}, it is
+straightforward to show the following
+result:
+\begin{thm}\label{thm-main}
+\begin{equation}\label{detB}
+\det\mathbf{B}=
+\sum^n_{l =0}\sum_{I_l \subseteq n}
+\prod_{i\in I_l}(b_{ii}-\lambda_i)
+\det\mathbf{B}^{(\lambda)}(I_l |I_l ),
+\end{equation}
+where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$
+is the principal submatrix obtained from $\mathbf{B}^{(\lambda)}$
+by deleting its $i_1,\dots,i_l $ rows and columns.
+\end{thm}
+
+\begin{rem}
+Let $\mathbf{M}$ be an $n\times n$ matrix. The convention
+$\mathbf{M}(\mathbf{n}|\mathbf{n})=1$ has been used in \eqref{detB} and
+hereafter.
+\end{rem}
+
+Before proceeding with our discussion, we pause to note that
+\thmref{thm-main} yields immediately a fundamental formula which can be
+used to compute the coefficients of a characteristic polynomial
+\cite{mami:matrixth}:
+\begin{cor}\label{BI}
+Write $\det(\mathbf{B}-x\mathbf{I})=\sum^n_{l =0}(-1)
+^l b_l x^l $. Then
+\begin{equation}\label{bl-sum}
+b_l =\sum_{I_l \subseteq\mathbf{n}}\det\mathbf{B}(I_l |I_l ).
+\end{equation}
+\end{cor}
+Let
+\begin{equation}
+\mathbf{K}(t,t_1,\dots,t_n)
+=\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix},
+\end{equation}
+\begin{verbatim}
+\begin{pmatrix} D_1t&-a_{12}t_2&\dots&-a_{1n}t_n\\
+-a_{21}t_1&D_2t&\dots&-a_{2n}t_n\\
+\hdotsfor[2]{4}\\
+-a_{n1}t_1&-a_{n2}t_2&\dots&D_nt\end{pmatrix}
+\end{verbatim}
+where
+\begin{equation}
+D_i=\sum_{j\in\mathbf{n}}a_{ij}t_j,\quad i=1,\dots,n.
+\end{equation}
+
+Set
+\begin{equation*}
+D(t_1,\dots,t_n)=\frac{\delta}{\delta t}\eval{\det\mathbf{K}(t,t_1,\dots,t_n)
+}_{t=1}.
+\end{equation*}
+Then
+\begin{equation}\label{sum-Di}
+D(t_1,\dots,t_n)
+=\sum_{i\in\mathbf{n}}D_i\det\mathbf{K}(t=1,t_1,\dots,t_n; i|i),
+\end{equation}
+where $\mathbf{K}(t=1,t_1,\dots,t_n; i|i)$ is the $i$th principal
+submatrix of $\mathbf{K}(t=1,t_1,\dots,t_n)$.
+
+Theorem ~\ref{thm-main} leads to
+\begin{equation}\label{detK1}
+\det\mathbf{K}(t_1,t_1,\dots,t_n)
+=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}t^{n-\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda t)}(\overline{I}|\overline I).
+\end{equation}
+Note that
+\begin{equation}\label{detK2}
+\det\mathbf{K}(t=1,t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\envert{I}}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}
+^{(\lambda)}(\overline{I}|\overline{I})=0.
+\end{equation}
+
+Let $t_i=\hat x_i,i=1,\dots,n$. Lemma ~\ref{lem-per} yields
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\begin{verbatim}
+\begin{multline}
+\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
+\det\mathbf{K}(t=1,x_1,\dots,x_n;l |l )\\
+=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
+\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\envert{I}}\per\mathbf{A}^{(\lambda)}(I|I)
+\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\label{sum-ali}
+\end{multline}
+\end{verbatim}
+
+By \eqref{H-cycles}, \eqref{detprod}, and \eqref{sum-bij}, we have
+\begin{prop}\label{prop:eg}
+\begin{equation}
+H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l}
+D_{l},
+\end{equation}
+where
+\begin{equation}\label{delta-l}
+D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}}
+D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix}
+0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
+1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
+\end{equation}
+\end{prop}
+
+\section{Application}
+\label{lincomp}
+
+We consider here the applications of Theorems~\ref{th-info-ow-ow} and
+~\ref{th-weak-ske-owf} to a complete
+multipartite graph $K_{n_1\dots n_p}$. It can be shown that the
+number of spanning trees of $K_{n_1\dots n_p}$
+may be written
+\begin{equation}\label{e:st}
+T=n^{p-2}\prod^p_{i=1}
+(n-n_i)^{n_i-1}
+\end{equation}
+where
+\begin{equation}
+n=n_1+\dots+n_p.
+\end{equation}
+
+It follows from Theorems~\ref{th-info-ow-ow} and
+~\ref{th-weak-ske-owf} that
+\begin{equation}\label{e:barwq}
+\begin{split}
+H_c&=\frac1{2n}
+\sum^n_{{l}=0}(-1)^{l}(n-{l})^{p-2}
+\sum_{l _1+\dots+l _p=l}\prod^p_{i=1}
+\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
+\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split}
+\end{equation}
+\begin{verbatim}
+... \binom{n_i}{l _i}\\
+\end{verbatim}
+and
+\begin{equation}\label{joe}
+\begin{split}
+H_c&=\frac12\sum^{n-1}_{l =0}
+(-1)^{l}(n-l )^{p-2}
+\sum_{l _1+\dots+l _p=l}
+\prod^p_{i=1}\binom{n_i}{l _i}\\
+&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}
+\left(1-\frac{l _p}{n_p}\right)
+[(n-l )-(n_p-l _p)].
+\end{split}
+\end{equation}
+
+The enumeration of $H_c$ in a $K_{n_1\dotsm n_p}$ graph can also be
+carried out by Theorem ~\ref{thm-H-param} or ~\ref{thm-asym}
+together with the algebraic method of \eqref{multdef}.
+Some elegant representations may be obtained. For example, $H_c$ in
+a $K_{n_1n_2n_3}$ graph may be written
+\begin{equation}\label{j:mark}
+\begin{split}
+H_c=&
+\frac{n_1!\,n_2!\,n_3!}
+{n_1+n_2+n_3}\sum_i\left[\binom{n_1}{i}
+\binom{n_2}{n_3-n_1+i}\binom{n_3}{n_3-n_2+i}\right.\\
+&+\left.\binom{n_1-1}{i}
+\binom{n_2-1}{n_3-n_1+i}
+\binom{n_3-1}{n_3-n_2+i}\right].\end{split}
+\end{equation}
+
+\section{Secret Key Exchanges}
+\label{SKE}
+
+Modern cryptography is fundamentally concerned with the problem of
+secure private communication.  A Secret Key Exchange is a protocol
+where Alice and Bob, having no secret information in common to start,
+are able to agree on a common secret key, conversing over a public
+channel.  The notion of a Secret Key Exchange protocol was first
+introduced in the seminal paper of Diffie and Hellman
+\cite{dihe:newdir}. \cite{dihe:newdir} presented a concrete
+implementation of a Secret Key Exchange protocol, dependent on a
+specific assumption (a variant on the discrete log), specially
+tailored to yield Secret Key Exchange. Secret Key Exchange is of
+course trivial if trapdoor permutations exist. However, there is no
+known implementation based on a weaker general assumption.
+
+The concept of an informationally one-way function was introduced
+in \cite{imlelu:oneway}. We give only an informal definition here:
+
+\begin{defn} A polynomial time
+computable function $f = \{f_k\}$ is informationally
+one-way if there is no probabilistic polynomial time algorithm which
+(with probability of the form $1 - k^{-e}$ for some $e > 0$)
+returns on input $y \in \{0,1\}^{k}$ a random element of $f^{-1}(y)$.
+\end{defn}
+In the non-uniform setting \cite{imlelu:oneway} show that these are not
+weaker than one-way functions:
+\begin{thm}[\cite{imlelu:oneway} (non-uniform)]
+\label{th-info-ow-ow}
+The existence of informationally one-way functions
+implies the existence of one-way functions.
+\end{thm}
+We will stick to the convention introduced above of saying
+``non-uniform'' before the theorem statement when the theorem
+makes use of non-uniformity. It should be understood that
+if nothing is said then the result holds for both the uniform and
+the non-uniform models.
+
+It now follows from \thmref{th-info-ow-ow} that
+
+\begin{thm}[non-uniform]\label{th-weak-ske-owf} Weak SKE
+implies the existence of a one-way function.
+\end{thm}
+
+More recently, the polynomial-time, interior point algorithms for linear
+programming have been extended to the case of convex quadratic programs
+\cite{moad:quadpro,ye:intalg}, certain linear complementarity problems
+\cite{komiyo:lincomp,miyoki:lincomp}, and the nonlinear complementarity
+problem \cite{komiyo:unipfunc}. The connection between these algorithms
+and the classical Newton method for nonlinear equations is well
+explained in \cite{komiyo:lincomp}.
+
+\section{Review}
+\label{computation}
+
+We begin our discussion with the following definition:
+
+\begin{defn}
+
+A function $H\colon \Re^n \to \Re^n$ is said to be
+\emph{B-differentiable} at the point $z$ if (i)~$H$ is Lipschitz
+continuous in a neighborhood of $z$, and (ii)~ there exists a positive
+homogeneous function $BH(z)\colon \Re^n \to \Re^n$, called the
+\emph{B-derivative} of $H$ at $z$, such that
+\[ \lim_{v \to 0} \frac{H(z+v) - H(z) - BH(z)v}{\enVert{v}} = 0. \]
+The function $H$ is \textit{B-differentiable in set $S$} if it is
+B-differentiable at every point in $S$. The B-derivative $BH(z)$ is said
+to be \textit{strong} if
+\[ \lim_{(v,v') \to (0,0)} \frac{H(z+v) - H(z+v') - BH(z)(v
+ -v')}{\enVert{v - v'}} = 0. \]
+\end{defn}
+
+
+\begin{lem}\label{limbog} There exists a smooth function $\psi_0(z)$
+defined for $\abs{z}>1-2a$ satisfying the following properties\textup{:}
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item $\psi_0(z)$ is bounded above and below by positive constants
+$c_1\leq \psi_0(z)\leq c_2$.
+\item If $\abs{z}>1$, then $\psi_0(z)=1$.
+\item For all $z$ in the domain of $\psi_0$, $\Delta_0\ln \psi_0\geq 0$.
+\item If $1-2a<\abs{z}<1-a$, then $\Delta_0\ln \psi_0\geq
+c_3>0$.
+\end{enumerate}
+\end{lem}
+
+\begin{proof}
+We choose $\psi_0(z)$ to be a radial function depending only on $r=\abs{z}$.
+Let $h(r)\geq 0$ be a suitable smooth function satisfying $h(r)\geq c_3$
+for $1-2a<\abs{z}<1-a$, and $h(r)=0$ for $\abs{z}>1-\tfrac a2$. The radial
+Laplacian
+\[\Delta_0\ln\psi_0(r)=\left(\frac {d^2}{dr^2}+\frac
+1r\frac d{dr}\right)\ln\psi_0(r)\]
+has smooth coefficients for $r>1-2a$. Therefore, we may
+apply the existence and uniqueness theory for ordinary differential
+equations. Simply let $\ln \psi_0(r)$ be the solution of the differential
+equation
+\[\left(\frac{d^2}{dr^2}+\frac 1r\frac d{dr}\right)\ln \psi_0(r)=h(r)\]
+with initial conditions given by $\ln \psi_0(1)=0$ and
+$\ln\psi_0'(1)=0$.
+
+Next, let $D_\nu$ be a finite collection of pairwise disjoint disks,
+all of which are contained in the unit disk centered at the origin in
+$C$. We assume that $D_\nu=\{z\mid \abs{z-z_\nu}<\delta\}$. Suppose that
+$D_\nu(a)$ denotes the smaller concentric disk $D_\nu(a)=\{z\mid
+\abs{z-z_\nu}\leq (1-2a)\delta\}$. We define a smooth weight function
+$\Phi_0(z)$ for $z\in C-\bigcup_\nu D_\nu(a)$ by setting $\Phi_
+0(z)=1$ when $z\notin \bigcup_\nu D_\nu$ and $\Phi_
+0(z)=\psi_0((z-z_\nu)/\delta)$ when $z$ is an element of $D_\nu$. It
+follows from \lemref{limbog} that $\Phi_ 0$ satisfies the properties:
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item \label{boundab}$\Phi_ 0(z)$ is bounded above and below by
+positive constants $c_1\leq \Phi_ 0(z)\leq c_2$.
+\item \label{d:over}$\Delta_0\ln\Phi_ 0\geq 0$ for all
+$z\in C-\bigcup_\nu D_\nu(a)$,
+the domain where the function $\Phi_ 0$ is defined.
+\item \label{d:ad}$\Delta_0\ln\Phi_ 0\geq c_3\delta^{-2}$
+when $(1-2a)\delta<\abs{z-z_\nu}<(1-a)\delta$.
+\end{enumerate}
+Let $A_\nu$ denote the annulus $A_\nu=\{(1-2a)\delta<\abs{z-z_\nu}<(1-a)
+\delta \}$, and set $A=\bigcup_\nu A_\nu$. The
+properties (\ref{d:over}) and (\ref{d:ad}) of $\Phi_ 0$
+may be summarized as $\Delta_0\ln \Phi_ 0\geq c_3\delta^{-2}\chi_A$,
+where $\chi _A$ is the characteristic function of $A$.
+\end{proof}
+
+Suppose that $\alpha$ is a nonnegative real constant. We apply
+Proposition~\ref{prop:eg} with $\Phi(z)=\Phi_ 0(z) e^{\alpha\abs{z}^2}$. If
+$u\in C^\infty_0(R^2-\bigcup_\nu D_\nu(a))$, assume that $\mathcal{D}$
+is a bounded domain containing the support of $u$ and $A\subset
+\mathcal{D}\subset R^2-\bigcup_\nu D_\nu(a)$. A calculation gives
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2\Phi_ 0(z) e^{\alpha\abs{z}^2}
+\geq c_4\alpha\int_{\mathcal{D}}\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}
++c_5\delta^{-2}\int_ A\abs{u}^2\Phi_ 0e^{\alpha\abs{z}^2}.\]
+
+The boundedness, property (\ref{boundab}) of $\Phi_ 0$, then yields
+\[\int_{\mathcal{D}}\abs{\overline\partial u}^2e^{\alpha\abs{z}^2}\geq c_6\alpha
+\int_{\mathcal{D}}\abs{u}^2e^{\alpha\abs{z}^2}
++c_7\delta^{-2}\int_ A\abs{u}^2e^{\alpha\abs{z}^2}.\]
+
+Let $B(X)$ be the set of blocks of $\Lambda_{X}$
+and let $b(X) = \abs{B(X)}$. If $\phi \in Q_{X}$ then
+$\phi$ is constant on the blocks of $\Lambda_{X}$.
+\begin{equation}\label{far-d}
+ P_{X} = \{ \phi \in M \mid \Lambda_{\phi} = \Lambda_{X} \},
+\qquad
+Q_{X} = \{\phi \in M \mid \Lambda_{\phi} \geq \Lambda_{X} \}.
+\end{equation}
+If $\Lambda_{\phi} \geq \Lambda_{X}$ then
+$\Lambda_{\phi} = \Lambda_{Y}$ for some $Y \geq X$ so that
+\[ Q_{X} = \bigcup_{Y \geq X} P_{Y}. \]
+Thus by M\"obius inversion
+\[ \abs{P_{Y}}= \sum_{X\geq Y} \mu (Y,X)\abs{Q_{X}}.\]
+Thus there is a bijection from $Q_{X}$ to $W^{B(X)}$.
+In particular $\abs{Q_{X}} = w^{b(X)}$.
+
+Next note that $b(X)=\dim X$. We see this by choosing a
+basis for $X$ consisting of vectors $v^{k}$ defined by
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\begin{verbatim}
+\[v^{k}_{i}=
+\begin{cases} 1 & \text{if $i \in \Lambda_{k}$},\\
+0 &\text{otherwise.} \end{cases}
+\]
+\end{verbatim}
+
+\begin{lem}\label{p0201}
+Let $\A$ be an arrangement. Then
+\[ \chi (\A,t) = \sum_{\B \subseteq \A}
+(-1)^{\abs{\B}} t^{\dim T(\B)}. \]
+\end{lem}
+
+In order to compute $R''$ recall the definition
+of $S(X,Y)$ from \lemref{lem-per}. Since $H \in \B$,
+$\A_{H} \subseteq \B$. Thus if $T(\B) = Y$ then
+$\B \in S(H,Y)$. Let $L'' = L(\A'')$. Then
+\begin{equation}\label{E_SXgYy}
+\begin{split}
+R''&= \sum_{H\in \B \subseteq \A} (-1)^{\abs{\B}}
+t^{\dim T(\B)}\\
+&= \sum_{Y \in L''} \sum_{\B \in S(H,Y)}
+(-1)^{\abs{\B}}t^{\dim Y} \\
+&= -\sum_{Y \in L''} \sum_{\B \in S(H,Y)} (-1)^
+{\abs{\B - \A_{H}}} t^{\dim Y} \\
+&= -\sum_{Y \in L''} \mu (H,Y)t^{\dim Y} \\
+&= -\chi (\A '',t).
+\end{split}
+\end{equation}
+
+\begin{cor}\label{tripleA}
+Let $(\A,\A',\A'')$ be a triple of arrangements. Then
+\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \]
+\end{cor}
+
+\begin{defn}
+Let $(\A,\A',\A'')$ be a triple with respect to
+the hyperplane $H \in \A$. Call $H$ a \textit{separator}
+if $T(\A) \not\in L(\A')$.
+\end{defn}
+
+\begin{cor}\label{nsep}
+Let $(\A,\A',\A'')$ be a triple with respect to $H \in \A$.
+\begin{enumerate}
+\renewcommand{\labelenumi}{(\roman{enumi})}
+\item
+If $H$ is a separator then
+\[ \mu (\A) = - \mu (\A'') \]
+and hence
+\[ \abs{\mu (\A)} = \abs{ \mu (\A'')}. \]
+
+\item If $H$ is not a separator then
+\[\mu (\A) = \mu (\A') - \mu (\A'') \]
+and
+\[ \abs{\mu (\A)} = \abs{\mu (\A')} + \abs{\mu (\A'')}. \]
+\end{enumerate}
+\end{cor}
+
+\begin{proof}
+It follows from \thmref{th-info-ow-ow} that $\pi(\A,t)$
+has leading term
+\[(-1)^{r(\A)}\mu (\A)t^{r(\A)}.\]
+The conclusion
+follows by comparing coefficients of the leading
+terms on both sides of the equation in
+Corollary~\ref{tripleA}. If $H$ is a separator then
+$r(\A') < r(\A)$ and there is no contribution
+from $\pi (\A',t)$.
+\end{proof}
+
+The Poincar\'e polynomial of an arrangement
+will appear repeatedly
+in these notes. It will be shown to equal the
+Poincar\'e polynomial
+of the graded algebras which we are going to
+associate with $\A$. It is also the Poincar\'e
+polynomial of the complement $M(\A)$ for a
+complex arrangement. Here we prove
+that the Poincar\'e polynomial is the chamber
+counting function for a real arrangement. The
+complement $M(\A)$ is a disjoint union of chambers
+\[M(\A) = \bigcup_{C \in \Cham(\A)} C.\]
+The number
+of chambers is determined by the Poincar\'e
+polynomial as follows.
+
+\begin{thm}\label{th-realarr}
+Let $\A_{\mathbf{R}}$ be a real arrangement. Then
+\[ \abs{\Cham(\A_{\mathbf{R}})} = \pi (\A_{\mathbf{R}},1). \]
+\end{thm}
+
+\begin{proof}
+We check the properties required in Corollary~\ref{nsep}:
+(i) follows from $\pi (\Phi_{ l},t) = 1$, and (ii) is a
+consequence of Corollary~\ref{BI}.
+\end{proof}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{1}) = xyz(x-z)(x+z)(y-z)(y+z)$}
+\end{figure}
+
+\begin{figure}
+\vspace{5cm}
+\caption[]{$Q(\A_{2})= xyz(x+y+z)(x+y-z)(x-y+z)(x-y-z)$}
+\end{figure}
+
+
+\begin{thm}
+\label{T_first_the_int}
+Let $\phi$ be a protocol for a random pair $\XcY$.
+If one of $\st_\phi(x',y)$ and $\st_\phi(x,y')$ is a prefix of the other
+and $(x,y)\in\SXY$, then
+\[
+\langle \st_j(x',y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y)\rangle_{j=1}^\infty
+=\langle \st_j(x,y')\rangle_{j=1}^\infty .
+\]
+\end{thm}
+\begin{proof}
+We show by induction on $i$ that
+\[
+\langle \st_j(x',y)\rangle_{j=1}^i
+=\langle \st_j(x,y)\rangle_{j=1}^i
+=\langle \st_j(x,y')\rangle_{j=1}^i.
+\]
+The induction hypothesis holds vacuously for $i=0$. Assume it holds for
+$i-1$, in particular
+$[\st_j(x',y)]_{j=1}^{i-1}=[\st_j(x,y')]_{j=1}^{i-1}$. Then one of
+$[\st_j(x',y)]_{j=i}^{\infty}$ and $[\st_j(x,y')]_{j=i}^{\infty}$ is a
+prefix of the other which implies that one of $\st_i(x',y)$ and
+$\st_i(x,y')$ is a prefix of the other. If the $i$th message is
+transmitted by $P_\X$ then, by the separate-transmissions property and
+the induction hypothesis, $\st_i(x,y)=\st_i(x,y')$, hence one of
+$\st_i(x,y)$ and $\st_i(x',y)$ is a prefix of the other. By the
+implicit-termination property, neither $\st_i(x,y)$ nor $\st_i(x',y)$
+can be a proper prefix of the other, hence they must be the same and
+$\st_i(x',y)=\st_i(x,y)=\st_i(x,y')$. If the $i$th message is
+transmitted by $\PY$ then, symmetrically, $\st_i(x,y)=\st_i(x',y)$ by
+the induction hypothesis and the separate-transmissions property, and,
+then, $\st_i(x,y)=\st_i(x,y')$ by the implicit-termination property,
+proving the induction step.
+\end{proof}
+
+If $\phi$ is a protocol for $(X,Y)$, and $(x,y)$, $(x',y)$ are distinct
+inputs in $\SXY$, then, by the correct-decision property,
+$\langle\st_j(x,y)\rangle_{j=1}^\infty\ne\langle
+\st_j(x',y)\rangle_{j=1}^\infty$.
+
+Equation~(\ref{E_SXgYy}) defined $\PY$'s ambiguity set $\SXgYy$
+to be the set of possible $X$ values when $Y=y$.
+The last corollary implies that for all $y\in\SY$,
+the multiset%
+\footnote{A multiset allows multiplicity of elements.
+Hence, $\{0,01,01\}$ is prefix free as a set, but not as a multiset.}
+of codewords $\{\st_\phi(x,y):x\in\SXgYy\}$ is prefix free.
+
+\section{One-Way Complexity}
+\label{S_Cp1}
+
+$\Cw1$, the one-way complexity of a random pair $\XcY$,
+is the number of bits $P_\X$ must transmit in the worst case
+when $\PY$ is not permitted to transmit any feedback messages.
+Starting with $\SXY$, the support set of $\XcY$, we define $\G$,
+the \textit{characteristic hypergraph} of $\XcY$, and show that
+\[
+\Cw1=\lceil\,\log\chi(\G)\rceil\ .
+\]
+
+Let $\XcY$ be a random pair. For each $y$ in $\SY$, the support set of
+$Y$, Equation~(\ref{E_SXgYy}) defined $\SXgYy$ to be the set of possible
+$x$ values when $Y=y$. The \textit{characteristic hypergraph} $\G$ of
+$\XcY$ has $\SX$ as its vertex set and the hyperedge $\SXgYy$ for each
+$y\in\SY$.
+
+
+We can now prove a continuity theorem.
+\begin{thm}\label{t:conl}
+Let $\Omega \subset\mathbf{R}^n$ be an open set, let
+$u\in BV(\Omega ;\mathbf{R}^m)$, and let
+\begin{equation}\label{quts}
+T^u_x=\left\{y\in\mathbf{R}^m:
+ y=\tilde u(x)+\left\langle \frac{Du}{\abs{Du}}(x),z
+\right\rangle \text{ for some }z\in\mathbf{R}^n\right\}
+\end{equation}
+for every $x\in\Omega \backslash S_u$. Let $f\colon \mathbf{R}^m\to
+\mathbf{R}^k$ be a Lipschitz continuous function such that $f(0)=0$, and
+let $v=f(u)\colon \Omega \to \mathbf{R}^k$. Then $v\in BV(\Omega
+;\mathbf{R}^k)$ and
+\begin{equation}
+Jv=\eval{(f(u^+)-f(u^-))\otimes \nu_u\cdot\,
+\mathcal{H}_{n-1}}_{S_u}.
+\end{equation}
+In addition, for $\abs{\wt{D}u}$-almost every $x\in\Omega $ the
+restriction of the function $f$ to $T^u_x$ is differentiable at $\tilde
+u(x)$ and
+\begin{equation}
+\wt{D}v=\nabla (\eval{f}_{T^u_x})(\tilde u)
+\frac{\wt{D}u}{\abs{\wt{D}u}}\cdot\abs{\wt{D}u}.\end{equation}
+\end{thm}
+
+Before proving the theorem, we state without proof three elementary
+remarks which will be useful in the sequel.
+\begin{rem}\label{r:omb}
+Let $\omega\colon \left]0,+\infty\right[\to \left]0,+\infty\right[$
+be a continuous function such that $\omega (t)\to 0$ as $t\to
+0$. Then
+\[\lim_{h\to 0^+}g(\omega(h))=L\Leftrightarrow\lim_{h\to
+0^+}g(h)=L\]
+for any function $g\colon \left]0,+\infty\right[\to \mathbf{R}$.
+\end{rem}
+\begin{rem}\label{r:dif}
+Let $g \colon  \mathbf{R}^n\to \mathbf{R}$ be a Lipschitz
+continuous function and assume that
+\[L(z)=\lim_{h\to 0^+}\frac{g(hz)-g(0)}h\]
+exists for every $z\in\mathbf{Q}^n$ and that $L$ is a linear function of
+$z$. Then $g$ is differentiable at 0.
+\end{rem}
+\begin{rem}\label{r:dif0}
+Let $A \colon \mathbf{R}^n\to \mathbf{R}^m$ be a linear function, and
+let $f \colon \mathbf{R}^m\to \mathbf{R}$ be a function. Then the
+restriction of $f$ to the range of $A$ is differentiable at 0 if and
+only if $f(A)\colon \mathbf{R}^n\to \mathbf{R}$ is differentiable at 0
+and
+\[\nabla(\eval{f}_{\IM(A)})(0)A=\nabla (f(A))(0).\]
+\end{rem}
+
+\begin{proof}
+ We begin by showing that $v\in BV(\Omega;\mathbf{R}^k)$ and
+\begin{equation}\label{e:bomb}
+\abs{Dv}(B)\le K\abs{Du}(B)\qquad\forall B\in\mathbf{B}(\Omega ),
+\end{equation}
+where $K>0$ is the Lipschitz constant of $f$. By \eqref{sum-Di} and by
+the approximation result quoted in \secref{s:mt}, it is possible to find
+a sequence $(u_h)\subset C^1(\Omega ;\mathbf{R}^m)$ converging to $u$ in
+$L^1(\Omega ;\mathbf{R}^m)$ and such that
+\[\lim_{h\to +\infty}\int_\Omega \abs{\nabla u_h}\,dx=\abs{Du}(\Omega ).\]
+The functions $v_h=f(u_h)$ are locally Lipschitz continuous in $\Omega
+$, and the definition of differential implies that $\abs{\nabla v_h}\le
+K\abs{\nabla u_h}$ almost everywhere in $\Omega $. The lower semicontinuity
+of the total variation and \eqref{sum-Di} yield
+\begin{equation}
+\begin{split}
+\abs{Dv}(\Omega )\le\liminf_{h\to +\infty}\abs{Dv_h}(\Omega) &
+=\liminf_{h\to +\infty}\int_\Omega \abs{\nabla v_h}\,dx\\
+&\le K\liminf_{h\to +\infty}\int_\Omega
+\abs{\nabla u_h}\,dx=K\abs{Du}(\Omega).
+\end{split}\end{equation}
+Since $f(0)=0$, we have also
+\[\int_\Omega \abs{v}\,dx\le K\int_\Omega \abs{u}\,dx;\]
+therefore $u\in BV(\Omega ;\mathbf{R}^k)$. Repeating the same argument
+for every open set $A\subset\Omega $, we get \eqref{e:bomb} for every
+$B\in\mathbf{B}(\Omega)$, because $\abs{Dv}$, $\abs{Du}$ are Radon measures. To
+prove \lemref{limbog}, first we observe that
+\begin{equation}\label{e:SS}
+S_v\subset S_u,\qquad\tilde v(x)=f(\tilde u(x))\qquad \forall x\in\Omega
+\backslash S_u.\end{equation}
+In fact, for every $\varepsilon >0$ we have
+\[\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>\varepsilon \}\subset \{y\in
+B_\rho(x): \abs{u(y)-\tilde u(x)}>\varepsilon /K\},\]
+hence
+\[\lim_{\rho\to 0^+}\frac{\abs{\{y\in B_\rho(x): \abs{v(y)-f(\tilde u(x))}>
+\varepsilon \}}}{\rho^n}=0\]
+whenever $x\in\Omega \backslash S_u$. By a similar argument, if $x\in
+S_u$ is a point such that there exists a triplet $(u^+,u^-,\nu_u)$
+satisfying \eqref{detK1}, \eqref{detK2}, then
+\[
+(v^+(x)-v^-(x))\otimes \nu_v=(f(u^+(x))-f(u^-(x)))\otimes\nu_u\quad
+\text{if }x\in S_v
+\]
+and $f(u^-(x))=f(u^+(x))$ if $x\in S_u\backslash S_v$. Hence, by (1.8)
+we get
+\begin{equation*}\begin{split}
+Jv(B)=\int_{B\cap S_v}(v^+-v^-)\otimes \nu_v\,d\mathcal{H}_{n-1}&=
+\int_{B\cap S_v}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}\\
+&=\int_{B\cap S_u}(f(u^+)-f(u^-))\otimes \nu_u\,d\mathcal{H}_{n-1}
+\end{split}\end{equation*}
+and \lemref{limbog} is proved.
+\end{proof}
+
+To prove \eqref{e:SS}, it is not restrictive to assume that $k=1$.
+Moreover, to simplify our notation, from now on we shall assume that
+$\Omega = \mathbf{R}^n$. The proof of \eqref{e:SS} is divided into two
+steps. In the first step we prove the statement in the one-dimensional
+case $(n=1)$, using \thmref{th-weak-ske-owf}. In the second step we
+achieve the general result using \thmref{t:conl}.
+
+\subsection*{Step 1}
+Assume that $n=1$. Since $S_u$ is at most countable, \eqref{sum-bij}
+yields that $\abs{\wt{D}v}(S_u\backslash S_v)=0$, so that
+\eqref{e:st} and \eqref{e:barwq} imply that $Dv=\wt{D}v+Jv$ is
+the Radon-Nikod\'ym decomposition of $Dv$ in absolutely continuous and
+singular part with respect to $\abs{\wt{D} u}$. By
+\thmref{th-weak-ske-owf}, we have
+\begin{equation*}
+\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Dv(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})},\qquad
+\frac{\wt{D}u}{\abs{\wt{D}u}}(t)=\lim_{s\to t^+}
+\frac{Du(\interval{\left[t,s\right[})}
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{equation*}
+$\abs{\wt{D}u}$-almost everywhere in $\mathbf{R}$. It is well known
+(see, for instance, \cite[2.5.16]{ste:sint}) that every one-dimensional
+function of bounded variation $w$ has a unique left continuous
+representative, i.e., a function $\hat w$ such that $\hat w=w$ almost
+everywhere and $\lim_{s\to t^-}\hat w(s)=\hat w(t)$ for every $t\in
+\mathbf{R}$. These conditions imply
+\begin{equation}
+\hat u(t)=Du(\interval{\left]-\infty,t\right[}),
+\qquad \hat v(t)=Dv(\interval{\left]-\infty,t\right[})\qquad
+\forall t\in\mathbf{R}
+\end{equation}
+and
+\begin{equation}\label{alimo}
+\hat v(t)=f(\hat u(t))\qquad\forall t\in\mathbf{R}.\end{equation}
+Let $t\in\mathbf{R}$ be such that
+$\abs{\wt{D}u}(\interval{\left[t,s\right[})>0$ for every $s>t$ and
+assume that the limits in \eqref{joe} exist. By \eqref{j:mark} and
+\eqref{far-d} we get
+\begin{equation*}\begin{split}
+\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}&=\frac {f(\hat
+u(s))-f(\hat u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&=\frac{f(\hat u(s))-f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}u
+}(\interval{\left[t,s\right[}))}%
+{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\\
+&+\frac
+{f(\hat u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)\abs{\wt{D}
+u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+\end{split}\end{equation*}
+for every $s>t$. Using the Lipschitz condition on $f$ we find
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}
+\left\lvert\frac{\hat v(s)-\hat
+v(t)}{\abs{\wt{D}u}(\interval{\left[t,s\right[})} -\frac{f(\hat
+u(t)+\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t)
+\abs{\wt{D}u}(\interval{\left[t,s\right[}))-f(\hat
+u(t))}{\abs{\wt{D}u}(\interval{\left[t,s\right[})}\right\rvert\\
+\le K\left\lvert
+\frac{\hat u(s)-\hat u(t)}
+  {\abs{\wt{D}u}(\interval{\left[t,s\right[})}
+-\frac{\wt{D}u}{\abs{
+\wt{D}u}}(t)\right\rvert.\end{multline*}
+}% end of group with \multlinegap=0pt
+By \eqref{e:bomb}, the function $s\to
+\abs{\wt{D}u}(\interval{\left[t,s\right[})$ is continuous and
+converges to 0 as $s\downarrow t$. Therefore Remark~\ref{r:omb} and the
+previous inequality imply
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0^+}
+\frac{f(\hat u(t)+h\dfrac{\wt{D}u}{\abs{\wt{D}u}}
+(t))-f(\hat u(t))}h\quad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}.\]
+By \eqref{joe}, $\hat u(x)=\tilde u(x)$ for every
+$x\in\mathbf{R}\backslash S_u$; moreover, applying the same argument to
+the functions $u'(t)=u(-t)$, $v'(t)=f(u'(t))=v(-t)$, we get
+\[\frac{\wt{D}v}{\abs{\wt{D}u}}(t)=\lim_{h\to 0}
+\frac{f(\tilde u(t)
++h\dfrac{\wt{D}u}{\abs{\wt{D}u}}(t))-f(\tilde u(t))}{h}
+\qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}\]
+and our statement is proved.
+
+\subsection*{Step 2}
+
+Let us consider now the general case $n>1$. Let $\nu\in \mathbf{R}^n$ be
+such that $\abs{\nu}=1$, and let $\pi_\nu=\{y\in\mathbf{R}^n: \langle
+y,\nu\rangle =0\}$. In the following, we shall identify $\mathbf{R}^n$
+with $\pi_\nu\times\mathbf{R}$, and we shall denote by $y$ the variable
+ranging in $\pi_\nu$ and by $t$ the variable ranging in $\mathbf{R}$. By
+the just proven one-dimensional result, and by \thmref{thm-main}, we get
+\[\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\wt{D}u_y}{\abs{
+\wt{D}u_y}}(t))-f(\tilde u(y+t\nu))}h=\frac{\wt{D}v_y}{\abs{
+\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}\]
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. We claim that
+\begin{equation}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}u_y}
+{\abs{\wt{D}u_y}}(t)\qquad\abs{\wt{D}u_y}\text{-a.e. in }\mathbf{R}
+\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$. In fact, by
+\eqref{sum-ali} and \eqref{delta-l} we get
+\begin{multline*}
+\int_{\pi_\nu}\frac{\wt{D}u_y}{\abs{\wt{D}u_y}}\cdot\abs{\wt{D}u_y
+}\,d\mathcal{H}_{n-1}(y)=\int_{\pi_\nu}\wt{D}u_y\,d\mathcal{H}_{n-1}(y)\\
+=\langle \wt{D}u,\nu\rangle =\frac
+{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}\cdot
+\abs{\langle \wt{D}u,\nu\rangle }=\int_{\pi_\nu}\frac{
+\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}
+(y+\cdot \nu)\cdot\abs{\wt{D}u_y}\,d\mathcal{H}_{n-1}(y)
+\end{multline*}
+and \eqref{far-d} follows from \eqref{sum-Di}. By the same argument it
+is possible to prove that
+\begin{equation}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle
+}}(y+t\nu)=\frac{\wt{D}v_y}{\abs{\wt{D}u_y}}(t)\qquad\abs{
+\wt{D}u_y}\text{-a.e. in }\mathbf{R}\end{equation}
+for $\mathcal{H}_{n-1}$-almost every $y\in \pi_\nu$. By \eqref{far-d}
+and \eqref{E_SXgYy} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(y+t\nu)+h\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(y+t\nu))-f(\tilde
+u(y+t\nu))}{h}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(y+t\nu)\]
+for $\mathcal{H}_{n-1}$-almost every $y\in\pi_\nu$, and using again
+\eqref{detK1}, \eqref{detK2} we get
+\[
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\langle
+\wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde
+u(x))}{h}=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu
+\rangle }}(x)
+\]
+$\abs{\langle \wt{D}u,\nu\rangle}$-a.e. in $\mathbf{R}^n$.
+
+Since the function $\abs{\langle \wt{D}u,\nu\rangle }/\abs{\wt{D}u}$
+is strictly positive $\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere,
+we obtain also
+\begin{multline*}
+\lim_{h\to 0}\frac{f(\tilde u(x)+h\dfrac{\abs{\langle
+\wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\dfrac{\langle \wt{D}
+u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle }}(x))-f(\tilde u(x))}{h}\\
+=\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}(x)\frac
+{\langle \wt{D}v,\nu\rangle }{\abs{\langle
+\wt{D}u,\nu\rangle }}(x)
+\end{multline*}
+$\abs{\langle \wt{D}u,\nu\rangle }$-almost everywhere in $\mathbf{R}^n$.
+
+Finally, since
+\begin{align*}
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}u,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}u,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}u}{\abs{\wt{D}u}},\nu\right\rangle
+        \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n\\
+&\frac{\abs{\langle \wt{D}u,\nu\rangle }}{\abs{\wt{D}u}}
+\frac{\langle \wt{D}v,\nu\rangle }{\abs{\langle \wt{D}u,\nu\rangle}}
+=\frac{\langle \wt{D}v,\nu\rangle }{\abs{\wt{D}u}}
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}},\nu\right\rangle
+        \qquad\abs{\wt{D}u}\text{-a.e. in }\mathbf{R}^n
+\end{align*}
+and since both sides of \eqref{alimo}
+are zero $\abs{\wt{D}u}$-almost everywhere
+on $\abs{\langle \wt{D}u,\nu\rangle }$-negligible sets, we conclude that
+\[
+\lim_{h\to 0}\frac{f\left(
+\tilde u(x)+h\left\langle \dfrac{\wt{D}
+u}{\abs{\wt{D}u}}(x),\nu\right\rangle \right)-f(\tilde u(x))}h
+=\left\langle \frac{\wt{D}v}{\abs{\wt{D}u}}(x),\nu\right\rangle,
+\]
+$\abs{\wt{D}u}$-a.e. in $\mathbf{R}^n$.
+Since $\nu$ is arbitrary, by Remarks \ref{r:dif} and~\ref{r:dif0}
+the restriction of $f$ to
+the affine space $T^u_x$ is differentiable at $\tilde u(x)$ for $\abs{\wt{D}
+u}$-almost every $x\in \mathbf{R}^n$ and \eqref{quts} holds.\qed
+
+It follows from \eqref{sum-Di}, \eqref{detK1}, and \eqref{detK2} that
+\begin{equation}\label{Dt}
+D(t_1,\dots,t_n)=\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}
+\prod_{i\in I}t_i\prod_{j\in I}(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I|\overline I).
+\end{equation}
+Let $t_i=\hat x_i$, $i=1,\dots,n$. Lemma 1 leads to
+\begin{equation}\label{Dx}
+D(\hat x_1,\dots,\hat x_n)=\prod_{i\in\mathbf{n}}\hat x_i
+\sum_{I\in\mathbf{n}}(-1)^{\abs{I}-1}\abs{I}\per \mathbf{A}
+^{(\lambda)}(I|I)\det\mathbf{A}^{(\lambda)}(\overline I|\overline I).
+\end{equation}
+By \eqref{H-cycles}, \eqref{sum-Di}, and \eqref{Dx},
+we have the following result:
+\begin{thm}\label{thm-H-param}
+\begin{equation}\label{H-param}
+H_c=\frac{1}{2n}\sum^n_{l =1}l (-1)^{l -1}A_{l}
+^{(\lambda)},
+\end{equation}
+where
+\begin{equation}\label{A-l-lambda}
+A^{(\lambda)}_l =\sum_{I_l \subseteq\mathbf{n}}\per \mathbf{A}
+^{(\lambda)}(I_l |I_l )\det\mathbf{A}^{(\lambda)}
+(\overline I_{l}|\overline I_l ),\abs{I_{l}}=l .
+\end{equation}
+\end{thm}
+
+It is worth noting that $A_l ^{(\lambda)}$ of \eqref{A-l-lambda} is
+similar to the coefficients $b_l $ of the characteristic polynomial of
+\eqref{bl-sum}. It is well known in graph theory that the coefficients
+$b_l $ can be expressed as a sum over certain subgraphs. It is
+interesting to see whether $A_l $, $\lambda=0$, structural properties
+of a graph.
+
+We may call \eqref{H-param} a parametric representation of $H_c$. In
+computation, the parameter $\lambda_i$ plays very important roles. The
+choice of the parameter usually depends on the properties of the given
+graph. For a complete graph $K_n$, let $\lambda_i=1$, $i=1,\dots,n$.
+It follows from \eqref{A-l-lambda} that
+\begin{equation}\label{compl-gr}
+A^{(1)}_l =\begin{cases} n!,&\text{if }l =1\\
+0,&\text{otherwise}.\end{cases}
+\end{equation}
+By \eqref{H-param}
+\begin{equation}
+H_c=\frac 12(n-1)!.
+\end{equation}
+For a complete bipartite graph $K_{n_1n_2}$, let $\lambda_i=0$, $i=1,\dots,n$.
+By \eqref{A-l-lambda},
+\begin{equation}
+A_l =
+\begin{cases} -n_1!n_2!\delta_{n_1n_2},&\text{if }l =2\\
+0,&\text{otherwise }.\end{cases}
+\label{compl-bip-gr}
+\end{equation}
+Theorem ~\ref{thm-H-param}
+leads to
+\begin{equation}
+H_c=\frac1{n_1+n_2}n_1!n_2!\delta_{n_1n_2}.
+\end{equation}
+
+Now, we consider an asymmetrical approach. Theorem \ref{thm-main} leads to
+\begin{multline}
+\det\mathbf{K}(t=1,t_1,\dots,t_n;l |l )\\
+=\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\prod_{i\in I}t_i\prod_{j\in I}
+(D_j+\lambda_jt_j)\det\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \}).
+\end{multline}
+
+By \eqref{H-cycles} and \eqref{sum-ali} we have the following asymmetrical
+result:
+\begin{thm}\label{thm-asym}
+\begin{equation}
+H_c=\frac12\sum_{I\subseteq\mathbf{n}-\{l \}}
+(-1)^{\abs{I}}\per\mathbf{A}^{(\lambda)}(I|I)\det
+\mathbf{A}^{(\lambda)}
+(\overline I\cup\{l \}|\overline I\cup\{l \})
+\end{equation}
+which reduces to Goulden--Jackson's formula when $\lambda_i=0,i=1,\dots,n$
+\cite{mami:matrixth}.
+\end{thm}
+
+\section{Various font features of the \pkg{amsmath} package}
+\label{s:font}
+\subsection{Bold versions of special symbols}
+
+In the \pkg{amsmath} package \cn{boldsymbol} is used for getting
+individual bold math symbols and bold Greek letters---everything in
+math except for letters of the Latin alphabet,
+where you'd use \cn{mathbf}.  For example,
+\begin{verbatim}
+A_\infty + \pi A_0 \sim
+\mathbf{A}_{\boldsymbol{\infty}} \boldsymbol{+}
+\boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}
+\end{verbatim}
+looks like this:
+\[A_\infty + \pi A_0 \sim \mathbf{A}_{\boldsymbol{\infty}}
+\boldsymbol{+} \boldsymbol{\pi} \mathbf{A}_{\boldsymbol{0}}\]
+
+\subsection{``Poor man's bold''}
+If a bold version of a particular symbol doesn't exist in the
+available fonts,
+then \cn{boldsymbol} can't be used to make that symbol bold.
+At the present time, this means that
+\cn{boldsymbol} can't be used with symbols from
+the \fn{msam} and \fn{msbm} fonts, among others.
+In some cases, poor man's bold (\cn{pmb}) can be used instead
+of \cn{boldsymbol}:
+%  Can't show example from msam or msbm because this document is
+%  supposed to be TeXable even if the user doesn't have
+%  AMSFonts.  MJD 5-JUL-1990
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\begin{verbatim}
+\[\frac{\partial x}{\partial y}
+\pmb{\bigg\vert}
+\frac{\partial y}{\partial z}\]
+\end{verbatim}
+So-called ``large operator'' symbols such as $\sum$ and $\prod$
+require an additional command, \cn{mathop},
+to produce proper spacing and limits when \cn{pmb} is used.
+For further details see \textit{The \TeX book}.
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\begin{verbatim}
+\[\sum_{\substack{i<B\\\text{$i$ odd}}}
+\prod_\kappa \kappa F(r_i)\qquad
+\mathop{\pmb{\sum}}_{\substack{i<B\\\text{$i$ odd}}}
+\mathop{\pmb{\prod}}_\kappa \kappa(r_i)
+\]
+\end{verbatim}
+
+\section{Compound symbols and other features}
+\label{s:comp}
+\subsection{Multiple integral signs}
+
+\cn{iint}, \cn{iiint}, and \cn{iiiint} give multiple integral signs
+with the spacing between them nicely adjusted,  in both text and
+display style.  \cn{idotsint} gives two integral signs with dots
+between them.
+\begin{gather}
+\iint\limits_A f(x,y)\,dx\,dy\qquad\iiint\limits_A
+f(x,y,z)\,dx\,dy\,dz\\
+\iiiint\limits_A
+f(w,x,y,z)\,dw\,dx\,dy\,dz\qquad\idotsint\limits_A f(x_1,\dots,x_k)
+\end{gather}
+
+\subsection{Over and under arrows}
+
+Some extra over and under arrow operations are provided in
+the \pkg{amsmath} package.  (Basic \LaTeX\ provides
+\cn{overrightarrow} and \cn{overleftarrow}).
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\begin{verbatim}
+\begin{align*}
+\overrightarrow{\psi_\delta(t) E_t h}&
+=\underrightarrow{\psi_\delta(t) E_t h}\\
+\overleftarrow{\psi_\delta(t) E_t h}&
+=\underleftarrow{\psi_\delta(t) E_t h}\\
+\overleftrightarrow{\psi_\delta(t) E_t h}&
+=\underleftrightarrow{\psi_\delta(t) E_t h}
+\end{align*}
+\end{verbatim}
+These all scale properly in subscript sizes:
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\begin{verbatim}
+\[\int_{\overrightarrow{AB}} ax\,dx\]
+\end{verbatim}
+
+\subsection{Dots}
+
+Normally you need only type \cn{dots} for ellipsis dots in a
+math formula.  The main exception is when the dots
+fall at the end of the formula; then you need to
+specify one of \cn{dotsc} (series dots, after a comma),
+\cn{dotsb} (binary dots, for binary relations or operators),
+\cn{dotsm} (multiplication dots), or \cn{dotsi} (dots after
+an integral).  For example, the input
+\begin{verbatim}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\].
+\end{verbatim}
+produces
+\begin{quotation}
+Then we have the series $A_1,A_2,\dotsc$,
+the regional sum $A_1+A_2+\dotsb$,
+the orthogonal product $A_1A_2\dotsm$,
+and the infinite integral
+\[\int_{A_1}\int_{A_2}\dotsi\]
+\end{quotation}
+
+\subsection{Accents in math}
+
+Double accents:
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\begin{verbatim}
+\[\Hat{\Hat{H}}\quad\Check{\Check{C}}\quad
+\Tilde{\Tilde{T}}\quad\Acute{\Acute{A}}\quad
+\Grave{\Grave{G}}\quad\Dot{\Dot{D}}\quad
+\Ddot{\Ddot{D}}\quad\Breve{\Breve{B}}\quad
+\Bar{\Bar{B}}\quad\Vec{\Vec{V}}\]
+\end{verbatim}
+This double accent operation is complicated
+and tends to slow down the processing of a \LaTeX\ file.
+
+
+\subsection{Dot accents}
+\cn{dddot} and \cn{ddddot} are available to
+produce triple and quadruple dot accents
+in addition to the \cn{dot} and \cn{ddot} accents already available
+in \LaTeX:
+\[\dddot{Q}\qquad\ddddot{R}\]
+\begin{verbatim}
+\[\dddot{Q}\qquad\ddddot{R}\]
+\end{verbatim}
+
+\subsection{Roots}
+
+In the \pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
+the position of the root index of a radical:
+\begin{verbatim}
+\sqrt[\leftroot{-2}\uproot{2}\beta]{k}
+\end{verbatim}
+gives good positioning of the $\beta$:
+\[\sqrt[\leftroot{-2}\uproot{2}\beta]{k}\]
+
+\subsection{Boxed formulas} The command \cn{boxed} puts a box around its
+argument, like \cn{fbox} except that the contents are in math mode:
+\begin{verbatim}
+\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}
+\end{verbatim}
+\[\boxed{W_t-F\subseteq V(P_i)\subseteq W_t}.\]
+
+\subsection{Extensible arrows}
+\cn{xleftarrow} and \cn{xrightarrow} produce
+arrows that extend automatically to accommodate unusually wide
+subscripts or superscripts.  The text of the subscript or superscript
+are given as an optional resp.\@ mandatory argument:
+Example:
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+  \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\begin{verbatim}
+\[0 \xleftarrow[\zeta]{\alpha} F\times\triangle[n-1]
+  \xrightarrow{\partial_0\alpha(b)} E^{\partial_0b}\]
+\end{verbatim}
+
+\subsection{\cn{overset}, \cn{underset}, and \cn{sideset}}
+Examples:
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\begin{verbatim}
+\[\overset{*}{X}\qquad\underset{*}{X}\qquad
+\overset{a}{\underset{b}{X}}\]
+\end{verbatim}
+
+The command \cn{sideset} is for a rather special
+purpose: putting symbols at the subscript and superscript
+corners of a large operator symbol such as $\sum$ or $\prod$,
+without affecting the placement of limits.
+Examples:
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\begin{verbatim}
+\[\sideset{_*^*}{_*^*}\prod_k\qquad
+\sideset{}{'}\sum_{0\le i\le m} E_i\beta x
+\]
+\end{verbatim}
+
+\subsection{The \cn{text} command}
+The main use of the command \cn{text} is for words or phrases in a
+display:
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\begin{verbatim}
+\[\mathbf{y}=\mathbf{y}'\quad\text{if and only if}\quad
+y'_k=\delta_k y_{\tau(k)}\]
+\end{verbatim}
+
+\subsection{Operator names}
+The more common math functions such as $\log$, $\sin$, and $\lim$
+have predefined control sequences: \verb=\log=, \verb=\sin=,
+\verb=\lim=.
+The \pkg{amsmath} package provides \cn{DeclareMathOperator} and
+\cn{DeclareMathOperator*}
+for producing new function names that will have the
+same typographical treatment.
+Examples:
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\begin{verbatim}
+\[\norm{f}_\infty=
+\esssup_{x\in R^n}\abs{f(x)}\]
+\end{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\begin{verbatim}
+\[\meas_1\{u\in R_+^1\colon f^*(u)>\alpha\}
+=\meas_n\{x\in R^n\colon \abs{f(x)}\geq\alpha\}
+\quad \forall\alpha>0.\]
+\end{verbatim}
+\cn{esssup} and \cn{meas} would be defined in the document preamble as
+\begin{verbatim}
+\DeclareMathOperator*{\esssup}{ess\,sup}
+\DeclareMathOperator{\meas}{meas}
+\end{verbatim}
+
+The following special operator names are predefined in the \pkg{amsmath}
+package: \cn{varlimsup}, \cn{varliminf}, \cn{varinjlim}, and
+\cn{varprojlim}. Here's what they look like in use:
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+       \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+  \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\begin{verbatim}
+\begin{align}
+&\varlimsup_{n\rightarrow\infty}
+       \mathcal{Q}(u_n,u_n-u^{\#})\le0\\
+&\varliminf_{n\rightarrow\infty}
+  \left\lvert a_{n+1}\right\rvert/\left\lvert a_n\right\rvert=0\\
+&\varinjlim (m_i^\lambda\cdot)^*\le0\\
+&\varprojlim_{p\in S(A)}A_p\le0
+\end{align}
+\end{verbatim}
+
+\subsection{\cn{mod} and its relatives}
+The commands \cn{mod} and \cn{pod} are variants of
+\cn{pmod} preferred by some authors; \cn{mod} omits the parentheses,
+whereas \cn{pod} omits the `mod' and retains the parentheses.
+Examples:
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\begin{verbatim}
+\begin{align}
+x&\equiv y+1\pmod{m^2}\\
+x&\equiv y+1\mod{m^2}\\
+x&\equiv y+1\pod{m^2}
+\end{align}
+\end{verbatim}
+
+\subsection{Fractions and related constructions}
+\label{fracs}
+
+The usual notation for binomials is similar to the fraction concept,
+so it has a similar command \cn{binom} with two arguments. Example:
+\begin{equation}
+\begin{split}
+\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+[\sum_{\gamma\in\Gamma_C} I_\gamma&
+=2^k-\binom{k}{1}2^{k-1}+\binom{k}{2}2^{k-2}\\
+&\quad+\dots+(-1)^l\binom{k}{l}2^{k-l}
++\dots+(-1)^k\\
+&=(2-1)^k=1
+\end{split}
+\end{equation}
+\end{verbatim}
+There are also abbreviations
+\begin{verbatim}
+\dfrac        \dbinom
+\tfrac        \tbinom
+\end{verbatim}
+for the commonly needed constructions
+\begin{verbatim}
+{\displaystyle\frac ... }   {\displaystyle\binom ... }
+{\textstyle\frac ... }      {\textstyle\binom ... }
+\end{verbatim}
+
+The generalized fraction command \cn{genfrac} provides full access to
+the six \TeX{} fraction primitives:
+\begin{align}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+  \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+  \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+  \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{align}
+\begin{verbatim}
+\text{\cn{over}: }&\genfrac{}{}{}{}{n+1}{2}&
+\text{\cn{overwithdelims}: }&
+  \genfrac{\langle}{\rangle}{}{}{n+1}{2}\\
+\text{\cn{atop}: }&\genfrac{}{}{0pt}{}{n+1}{2}&
+\text{\cn{atopwithdelims}: }&
+  \genfrac{(}{)}{0pt}{}{n+1}{2}\\
+\text{\cn{above}: }&\genfrac{}{}{1pt}{}{n+1}{2}&
+\text{\cn{abovewithdelims}: }&
+  \genfrac{[}{]}{1pt}{}{n+1}{2}
+\end{verbatim}
+
+\subsection{Continued fractions}
+The continued fraction
+\begin{equation}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+  \cfrac{1}{\sqrt{2}+
+   \cfrac{1}{\sqrt{2}+
+    \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{equation}
+can be obtained by typing
+\begin{verbatim}
+\cfrac{1}{\sqrt{2}+
+ \cfrac{1}{\sqrt{2}+
+  \cfrac{1}{\sqrt{2}+
+   \cfrac{1}{\sqrt{2}+
+    \cfrac{1}{\sqrt{2}+\dotsb
+}}}}}
+\end{verbatim}
+Left or right placement of any of the numerators is accomplished by using
+\cn{cfrac[l]} or \cn{cfrac[r]} instead of \cn{cfrac}.
+
+\subsection{Smash}
+
+In \pkg{amsmath} there are optional arguments \verb"t" and \verb"b" for
+the plain \TeX\ command \cn{smash}, because sometimes it is advantageous
+to be able to `smash' only the top or only the bottom of something while
+retaining the natural depth or height. In the formula
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$ \cn{smash}\verb=[b]= has been
+used to limit the size of the radical symbol.
+\begin{verbatim}
+$X_j=(1/\sqrt{\smash[b]{\lambda_j}})X_j'$
+\end{verbatim}
+Without the use of \cn{smash}\verb=[b]= the formula would have appeared
+thus: $X_j=(1/\sqrt{\lambda_j})X_j'$, with the radical extending to
+encompass the depth of the subscript $j$.
+
+\subsection{The `cases' environment}
+`Cases' constructions like the following can be produced using
+the \env{cases} environment.
+\begin{equation}
+P_{r-j}=
+  \begin{cases}
+    0&  \text{if $r-j$ is odd},\\
+    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
+  \end{cases}
+\end{equation}
+\begin{verbatim}
+\begin{equation} P_{r-j}=
+  \begin{cases}
+    0&  \text{if $r-j$ is odd},\\
+    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
+  \end{cases}
+\end{equation}
+\end{verbatim}
+Notice the use of \cn{text} and the embedded math.
+
+\subsection{Matrix}
+
+Here are samples of the matrix environments,
+\cn{matrix}, \cn{pmatrix}, \cn{bmatrix}, \cn{Bmatrix}, \cn{vmatrix}
+and \cn{Vmatrix}:
+\begin{equation}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{equation}
+%
+\begin{verbatim}
+\begin{matrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{matrix}\quad
+\begin{pmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{pmatrix}\quad
+\begin{bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{bmatrix}\quad
+\begin{Bmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Bmatrix}\quad
+\begin{vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{vmatrix}\quad
+\begin{Vmatrix}
+\vartheta& \varrho\\\varphi& \varpi
+\end{Vmatrix}
+\end{verbatim}
+
+To produce a small matrix suitable for use in text, use the
+\env{smallmatrix} environment.
+\begin{verbatim}
+\begin{math}
+  \bigl( \begin{smallmatrix}
+      a&b\\ c&d
+    \end{smallmatrix} \bigr)
+\end{math}
+\end{verbatim}
+To show
+the effect of the matrix on the surrounding lines of
+a paragraph, we put it here: \begin{math}
+  \bigl( \begin{smallmatrix}
+      a&b\\ c&d
+    \end{smallmatrix} \bigr)
+\end{math}
+and follow it with enough text to ensure that there will
+be at least one full line below the matrix.
+
+\cn{hdotsfor}\verb"{"\textit{number}\verb"}" produces a row of dots in a matrix
+spanning the given number of columns:
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\begin{verbatim}
+\[W(\Phi)= \begin{Vmatrix}
+\dfrac\varphi{(\varphi_1,\varepsilon_1)}&0&\dots&0\\
+\dfrac{\varphi k_{n2}}{(\varphi_2,\varepsilon_1)}&
+\dfrac\varphi{(\varphi_2,\varepsilon_2)}&\dots&0\\
+\hdotsfor{5}\\
+\dfrac{\varphi k_{n1}}{(\varphi_n,\varepsilon_1)}&
+\dfrac{\varphi k_{n2}}{(\varphi_n,\varepsilon_2)}&\dots&
+\dfrac{\varphi k_{n\,n-1}}{(\varphi_n,\varepsilon_{n-1})}&
+\dfrac{\varphi}{(\varphi_n,\varepsilon_n)}
+\end{Vmatrix}\]
+\end{verbatim}
+The spacing of the dots can be varied through use of a square-bracket
+option, for example, \verb"\hdotsfor[1.5]{3}".  The number in square brackets
+will be used as a multiplier; the normal value is 1.
+
+\subsection{The \cn{substack} command}
+
+The \cn{substack} command can be used to produce a multiline
+subscript or superscript:
+for example
+\begin{verbatim}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{verbatim}
+produces a two-line subscript underneath the sum:
+\begin{equation}
+\sum_{\substack{0\le i\le m\\ 0<j<n}} P(i,j)
+\end{equation}
+A slightly more generalized form is the \env{subarray} environment which
+allows you to specify that each line should be left-aligned instead of
+centered, as here:
+\begin{equation}
+\sum_{\begin{subarray}{l}
+        0\le i\le m\\ 0<j<n
+      \end{subarray}}
+ P(i,j)
+\end{equation}
+\begin{verbatim}
+\sum_{\begin{subarray}{l}
+        0\le i\le m\\ 0<j<n
+      \end{subarray}}
+ P(i,j)
+\end{verbatim}
+
+
+\subsection{Big-g-g delimiters}
+Here are some big delimiters, first in \cn{normalsize}:
+\[\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  \biggr)
+\]
+\begin{verbatim}
+\[\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  \biggr)
+\]
+\end{verbatim}
+and now in \cn{Large} size:
+{\Large
+\[\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  \biggr)
+\]}
+\begin{verbatim}
+{\Large
+\[\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  \biggr)
+\]}
+\end{verbatim}
+
+\newpage
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\makeatletter
+
+%% This turns on vertical rules at the right and left margins, to
+%% better illustrate the spacing for certain multiple-line equation
+%% structures.
+\def\@makecol{\ifvoid\footins \setbox\@outputbox\box\@cclv
+   \else\setbox\@outputbox
+     \vbox{\boxmaxdepth \maxdepth
+     \unvbox\@cclv\vskip\skip\footins\footnoterule\unvbox\footins}\fi
+  \xdef\@freelist{\@freelist\@midlist}\gdef\@midlist{}\@combinefloats
+  \setbox\@outputbox\hbox{\vrule width\marginrulewidth
+        \vbox to\@colht{\boxmaxdepth\maxdepth
+         \@texttop\dimen128=\dp\@outputbox\unvbox\@outputbox
+         \vskip-\dimen128\@textbottom}%
+        \vrule width\marginrulewidth}%
+     \global\maxdepth\@maxdepth}
+\newdimen\marginrulewidth
+\setlength{\marginrulewidth}{.1pt}
+\makeatother
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\appendix
+\section{Examples of multiple-line equation structures}
+\label{s:eq}
+
+\textbf{\large Note: Starting on this page, vertical rules are
+added at the margins so that the positioning of various display elements
+with respect to the margins can be seen more clearly.}
+
+\subsection{Split}
+The \env{split} environment is not an independent environment
+but should be used inside something else such as \env{equation}
+or \env{align}.
+
+If there is not enough room for it, the equation number for  a
+\env{split} will be shifted to the previous line, when equation numbers are
+on the left; the number shifts down to the next line when numbers are on
+the right.
+\begin{equation}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+  \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+    \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+   L_{x,y_\varepsilon(\varepsilon s)}
+   \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{equation}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+  \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+    \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+   L_{x,y_\varepsilon(\varepsilon s)}
+   \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+Unnumbered version:
+\begin{equation*}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+  \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+    \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+   L_{x,y_\varepsilon(\varepsilon s)}
+   \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{equation*}
+\begin{split}
+f_{h,\varepsilon}(x,y)
+&=\varepsilon\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+L_{x,y_\varepsilon(\varepsilon u)}\varphi(x)\,du\\
+&= h\int L_{x,z}\varphi(x)\rho_x(dz)\\
+&\quad+h\biggl[\frac{1}{t_\varepsilon}\biggl(\mathbf{E}_{y}
+  \int_0^{t_\varepsilon}L_{x,y^x(s)}\varphi(x)\,ds
+  -t_\varepsilon\int L_{x,z}\varphi(x)\rho_x(dz)\biggr)\\
+&\phantom{{=}+h\biggl[}+\frac{1}{t_\varepsilon}
+  \biggl(\mathbf{E}_{y}\int_0^{t_\varepsilon}L_{x,y^x(s)}
+    \varphi(x)\,ds -\mathbf{E}_{x,y}\int_0^{t_\varepsilon}
+   L_{x,y_\varepsilon(\varepsilon s)}
+   \varphi(x)\,ds\biggr)\biggr]\\
+&=h\wh{L}_x\varphi(x)+h\theta_\varepsilon(x,y),
+\end{split}
+\end{equation*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+If the option \env{centertags} is included in the options
+list of the \pkg{amsmath} package,
+the equation numbers for \env{split} environments will be
+centered vertically on the height
+of  the \env{split}:
+{\makeatletter\ctagsplit@true
+\begin{equation}
+\begin{split}
+ \abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)-\int_{\gamma(t)}^a
+  \frac{d\theta}{k(\theta,t)}
+  \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega\left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{equation}}%
+Some text after to test the below-display spacing.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+Use of \env{split} within \env{align}:
+{\delimiterfactor750
+\begin{align}
+\begin{split}\abs{I_1}
+  &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+&\le C_3\left[\int_\Omega\left(\int_{a}^x
+  g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+  \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+  c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\label{eq:A}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+  -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+  \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+ \left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{align}}%
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+\begin{split}\abs{I_1}
+  &=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+&\le C_3\left[\int_\Omega\left(\int_{a}^x
+  g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\quad\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+  \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+  c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\label{eq:A}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+  -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+  \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+  \left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}
+\end{align}
+\end{verbatim}
+
+%%%%%%%%%%%%%%%%%%
+
+\newpage
+Unnumbered \env{align}, with a number on the second \env{split}:
+\begin{align*}
+\begin{split}\abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+  &\le C_3\left[\int_\Omega\left(\int_{a}^x
+  g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+  \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+  c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+  -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+  \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+  \left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\tag{\theequation$'$}
+\end{align*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align*}
+\begin{split}\abs{I_1}&=\left\lvert \int_\Omega gRu\,d\Omega\right\rvert\\
+  &\le C_3\left[\int_\Omega\left(\int_{a}^x
+  g(\xi,t)\,d\xi\right)^2d\Omega\right]^{1/2}\\
+&\phantom{=}\times \left[\int_\Omega\left\{u^2_x+\frac{1}{k}
+  \left(\int_{a}^x cu_t\,d\xi\right)^2\right\}
+  c\Omega\right]^{1/2}\\
+&\le C_4\left\lvert \left\lvert f\left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\\
+\begin{split}\abs{I_2}&=\left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
+  -\int_{\gamma(t)}^a\frac{d\theta}{k(\theta,t)}
+  \int_{a}^\theta c(\xi)u_t(\xi,t)\,d\xi\right\}dt\right\rvert\\
+&\le C_6\left\lvert \left\lvert f\int_\Omega
+  \left\lvert \wt{S}^{-1,0}_{a,-}
+  W_2(\Omega,\Gamma_l)\right\rvert\right\rvert
+  \left\lvert \abs{u}\overset{\circ}\to W_2^{\wt{A}}
+  (\Omega;\Gamma_r,T)\right\rvert\right\rvert.
+\end{split}\tag{\theequation$'$}
+\end{align*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Multline}
+Numbered version:
+\begin{multline}\label{eq:E}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline}
+To test the use of \verb=\label= and
+\verb=\ref=, we refer to the number of this
+equation here: (\ref{eq:E}).
+
+\begin{verbatim}
+\begin{multline}\label{eq:E}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{multline*}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{multline*}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\iffalse % bugfix needed, error message "Multiple \tag"
+         % [mjd,24-Jan-1995]
+\newpage
+And now an ``unnumbered'' version numbered with a literal tag:
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}
+\end{verbatim}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The same display with \verb=\multlinegap= set to zero.
+Notice that the space on the left in
+the first line does not change, because of the equation number, while
+the second line is pushed over to the right margin.
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}}%
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+{\setlength{\multlinegap}{0pt}
+\begin{multline*}\tag*{[a]}
+\int_a^b\biggl\{\int_a^b[f(x)^2g(y)^2+f(y)^2g(x)^2]
+ -2f(x)g(x)f(y)g(y)\,dx\biggr\}\,dy \\
+ =\int_a^b\biggl\{g(y)^2\int_a^bf^2+f(y)^2
+  \int_a^b g^2-2f(y)g(y)\int_a^b fg\biggr\}\,dy
+\end{multline*}}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\fi % matches \iffalse above [mjd,24-Jan-1995]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Gather}
+Numbered version with \verb;\notag; on the second line:
+\begin{gather}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg(a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\notag\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather}
+\begin{verbatim}
+\begin{gather}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg(a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\notag\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+\colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version.
+\begin{gather*}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg (a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+ \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather*}
+Some text after to test the below-display spacing.
+\begin{verbatim}
+\begin{gather*}
+D(a,r)\equiv\{z\in\mathbf{C}\colon \abs{z-a}<r\},\\
+\seg (a,r)\equiv\{z\in\mathbf{C}\colon
+\Im z= \Im a,\ \abs{z-a}<r\},\\
+c(e,\theta,r)\equiv\{(x,y)\in\mathbf{C}
+ \colon \abs{x-e}<y\tan\theta,\ 0<y<r\},\\
+C(E,\theta,r)\equiv\bigcup_{e\in E}c(e,\theta,r).
+\end{gather*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Align}
+Numbered version:
+\begin{align}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+  -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+  -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{align*}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+  -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align*}
+\gamma_x(t)&=(\cos tu+\sin tx,v),\\
+\gamma_y(t)&=(u,\cos tv+\sin ty),\\
+\gamma_z(t)&=\left(\cos tu+\frac\alpha\beta\sin tv,
+  -\frac\beta\alpha\sin tu+\cos tv\right).
+\end{align*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+A variation:
+\begin{align}
+x& =y && \text {by (\ref{eq:C})}\\
+x'& = y' && \text {by (\ref{eq:D})}\\
+x+x' & = y+y' && \text {by Axiom 1.}
+\end{align}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{align}
+x& =y && \text {by (\ref{eq:C})}\\
+x'& = y' && \text {by (\ref{eq:D})}\\
+x+x' & = y+y' && \text {by Axiom 1.}
+\end{align}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Align and split within gather}
+When using the \env{align} environment within the \env{gather}
+environment, one or the other, or both, should be unnumbered (using the
+\verb"*" form); numbering both the outer and inner environment would
+cause a conflict.
+
+Automatically numbered \env{gather} with \env{split} and \env{align*}:
+\begin{gather}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align*}
+\zeta^0 &=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align*}
+\end{gather}
+Here the \env{split} environment gets a number from the outer
+\env{gather} environment; numbers for individual lines of the
+\env{align*} are suppressed because of the star.
+
+\begin{verbatim}
+\begin{gather}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align*}
+\zeta^0 &=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align*}
+\end{gather}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+The \verb"*"-ed form of \env{gather} with the non-\verb"*"-ed form of
+\env{align}.
+\begin{gather*}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align} \zeta^0&=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align}
+\end{gather*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{gather*}
+\begin{split} \varphi(x,z)
+&=z-\gamma_{10}x-\gamma_{mn}x^mz^n\\
+&=z-Mr^{-1}x-Mr^{-(m+n)}x^mz^n
+\end{split}\\[6pt]
+\begin{align} \zeta^0&=(\xi^0)^2,\\
+\zeta^1 &=\xi^0\xi^1,\\
+\zeta^2 &=(\xi^1)^2,
+\end{align}
+\end{gather*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\subsection{Alignat}
+Numbered version:
+\begin{alignat}{3}
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;}\label{eq:B}\\
+V_j & = v_j, & \qquad X_j & = x_j,
+  & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat}{3}
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;}\label{eq:B}\\
+V_j & = v_j, & \qquad X_j & = x_j,
+  & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+Unnumbered version:
+\begin{alignat*}3
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;} \\
+V_j & = v_j, & \qquad X_j & = x_j,
+  & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat*}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat*}3
+V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
+ & \qquad U_i & = u_i,
+ \qquad \text{for $i\ne j$;} \\
+V_j & = v_j, & \qquad X_j & = x_j,
+  & \qquad U_j & u_j + \sum_{i\ne j} q_i u_i.
+\end{alignat*}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+The most common use for \env{alignat} is for things like
+\begin{alignat}{2}
+x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\
+x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\
+x+x' & = y+y' && \qquad \text {by Axiom 1.}
+\end{alignat}
+Some text after to test the below-display spacing.
+
+\begin{verbatim}
+\begin{alignat}{2}
+x& =y && \qquad \text {by (\ref{eq:A})}\label{eq:C}\\
+x'& = y' && \qquad \text {by (\ref{eq:B})}\label{eq:D}\\
+x+x' & = y+y' && \qquad \text {by Axiom 1.}
+\end{alignat}
+\end{verbatim}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\newpage
+\setlength{\marginrulewidth}{0pt}
+
+\begin{thebibliography}{10}
+
+\bibitem{dihe:newdir}
+W.~Diffie and E.~Hellman, \emph{New directions in cryptography}, IEEE
+Transactions on Information Theory \textbf{22} (1976), no.~5, 644--654.
+
+\bibitem{fre:cichon}
+D.~H. Fremlin, \emph{Cichon's diagram}, 1983/1984, presented at the
+S{\'e}minaire Initiation {\`a} l'Analyse, G. Choquet, M. Rogalski, J.
+Saint Raymond, at the Universit{\'e} Pierre et Marie Curie, Paris, 23e
+ann{\'e}e.
+
+\bibitem{gouja:lagrmeth}
+I.~P. Goulden and D.~M. Jackson, \emph{The enumeration of directed
+closed {E}uler trails and directed {H}amiltonian circuits by
+{L}angrangian methods}, European J. Combin. \textbf{2} (1981), 131--212.
+
+\bibitem{hapa:graphenum}
+F.~Harary and E.~M. Palmer, \emph{Graphical enumeration}, Academic
+Press, 1973.
+
+\bibitem{imlelu:oneway}
+R.~Impagliazzo, L.~Levin, and M.~Luby, \emph{Pseudo-random generation
+from one-way functions}, Proc. 21st STOC (1989), ACM, New York,
+pp.~12--24.
+
+\bibitem{komiyo:unipfunc}
+M.~Kojima, S.~Mizuno, and A.~Yoshise, \emph{A new continuation method
+for complementarity problems with uniform p-functions}, Tech. Report
+B-194, Tokyo Inst. of Technology, Tokyo, 1987, Dept. of Information
+Sciences.
+
+\bibitem{komiyo:lincomp}
+\bysame, \emph{A polynomial-time algorithm for a class of linear
+complementarity problems}, Tech. Report B-193, Tokyo Inst. of
+Technology, Tokyo, 1987, Dept. of Information Sciences.
+
+\bibitem{liuchow:formalsum}
+C.~J. Liu and Yutze Chow, \emph{On operator and formal sum methods for
+graph enumeration problems}, SIAM J. Algorithms Discrete Methods
+\textbf{5} (1984), 384--438.
+
+\bibitem{mami:matrixth}
+M.~Marcus and H.~Minc, \emph{A survey of matrix theory and matrix
+inequalities}, Complementary Series in Math. \textbf{14} (1964), 21--48.
+
+\bibitem{miyoki:lincomp}
+S.~Mizuno, A.~Yoshise, and T.~Kikuchi, \emph{Practical polynomial time
+algorithms for linear complementarity problems}, Tech. Report~13, Tokyo
+Inst. of Technology, Tokyo, April 1988, Dept. of Industrial Engineering
+and Management.
+
+\bibitem{moad:quadpro}
+R.~D. Monteiro and I.~Adler, \emph{Interior path following primal-dual
+algorithms, part {II}: Quadratic programming}, August 1987, Working
+paper, Dept. of Industrial Engineering and Operations Research.
+
+\bibitem{ste:sint}
+E.~M. Stein, \emph{Singular integrals and differentiability properties
+of functions}, Princeton Univ. Press, Princeton, N.J., 1970.
+
+\bibitem{ye:intalg}
+Y.~Ye, \emph{Interior algorithms for linear, quadratic and linearly
+constrained convex programming}, Ph.D. thesis, Stanford Univ., Palo
+Alto, Calif., July 1987, Dept. of Engineering--Economic Systems,
+unpublished.
+
+\end{thebibliography}
+
+\end{document}
+\endinput
diff --git a/macros/latex-dev/required/graphics/README.md b/macros/latex-dev/required/graphics/README.md
index 81f39d1d7b..009e20da95 100644
--- a/macros/latex-dev/required/graphics/README.md
+++ b/macros/latex-dev/required/graphics/README.md
@@ -1,7 +1,7 @@
 The LaTeX `graphics` bundle
 ===========================
 
-Release 2019-10-01 pre-release 2
+Release 2019-10-01 pre-release 3
 
 Overview
 --------
diff --git a/macros/latex-dev/required/graphics/color.dtx b/macros/latex-dev/required/graphics/color.dtx
index d85b78349d..8de7d013a3 100644
--- a/macros/latex-dev/required/graphics/color.dtx
+++ b/macros/latex-dev/required/graphics/color.dtx
@@ -2,7 +2,7 @@
 % \iffalse
 %
 %% color.dtx Copyright (C) 1994--1999 David Carlisle
-%%           Copyright (C) 2005--2016 David Carlisle, LaTeX3 Project
+%%           Copyright (C) 2005-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/color.pdf b/macros/latex-dev/required/graphics/color.pdf
index efdebda318..77198b2e49 100644
--- a/macros/latex-dev/required/graphics/color.pdf
+++ b/macros/latex-dev/required/graphics/color.pdf
diff --git a/macros/latex-dev/required/graphics/drivers.dtx b/macros/latex-dev/required/graphics/drivers.dtx
index 07c201cf87..d693ebd27b 100644
--- a/macros/latex-dev/required/graphics/drivers.dtx
+++ b/macros/latex-dev/required/graphics/drivers.dtx
@@ -3,7 +3,7 @@
 %
 %% drivers.dtx Copyright (C) 1994      David Carlisle Sebastian Rahtz
 %%             Copyright (C) 1995 1996 1997 1998 1999 David Carlisle
-%%             Copyright (C) 2000--2016 David Carlisle, LaTeX3 Project
+%%             Copyright (C) 2000-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/drivers.pdf b/macros/latex-dev/required/graphics/drivers.pdf
index ef6a372bf5..4a25175e87 100644
--- a/macros/latex-dev/required/graphics/drivers.pdf
+++ b/macros/latex-dev/required/graphics/drivers.pdf
diff --git a/macros/latex-dev/required/graphics/epsfig.dtx b/macros/latex-dev/required/graphics/epsfig.dtx
index ba37d771cc..f9197c7b1c 100644
--- a/macros/latex-dev/required/graphics/epsfig.dtx
+++ b/macros/latex-dev/required/graphics/epsfig.dtx
@@ -2,7 +2,7 @@
 % \iffalse
 %
 %% epsfig.dtx Copyright (C) 1994-1996 1999 Sebastian Rahtz
-%%            Copyright (C) 2000--2015,2017 David Carlisle, LaTeX3 Project
+%%            Copyright (C) 2000-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/epsfig.pdf b/macros/latex-dev/required/graphics/epsfig.pdf
index 3aa7fcff62..4347ed4a77 100644
--- a/macros/latex-dev/required/graphics/epsfig.pdf
+++ b/macros/latex-dev/required/graphics/epsfig.pdf
diff --git a/macros/latex-dev/required/graphics/graphics.pdf b/macros/latex-dev/required/graphics/graphics.pdf
index 63a2ed999c..17afa48d1f 100644
--- a/macros/latex-dev/required/graphics/graphics.pdf
+++ b/macros/latex-dev/required/graphics/graphics.pdf
diff --git a/macros/latex-dev/required/graphics/graphicx.dtx b/macros/latex-dev/required/graphics/graphicx.dtx
index aad8460ac5..4134c4eed1 100644
--- a/macros/latex-dev/required/graphics/graphicx.dtx
+++ b/macros/latex-dev/required/graphics/graphicx.dtx
@@ -2,7 +2,7 @@
 % \iffalse
 %
 %% graphicx.dtx Copyright (C) 1994      David Carlisle Sebastian Rahtz
-%%              Copyright (C) 1995--2015,2017 David Carlisle, LaTeX3 Project
+%%              Copyright (C) 1995-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/graphicx.pdf b/macros/latex-dev/required/graphics/graphicx.pdf
index 6137b786f8..73b8ad6c50 100644
--- a/macros/latex-dev/required/graphics/graphicx.pdf
+++ b/macros/latex-dev/required/graphics/graphicx.pdf
diff --git a/macros/latex-dev/required/graphics/grfguide.pdf b/macros/latex-dev/required/graphics/grfguide.pdf
index cd6d72046e..42955a440c 100644
--- a/macros/latex-dev/required/graphics/grfguide.pdf
+++ b/macros/latex-dev/required/graphics/grfguide.pdf
diff --git a/macros/latex-dev/required/graphics/grfguide.tex b/macros/latex-dev/required/graphics/grfguide.tex
index b00a86d307..19888db741 100644
--- a/macros/latex-dev/required/graphics/grfguide.tex
+++ b/macros/latex-dev/required/graphics/grfguide.tex
@@ -1,5 +1,5 @@
 %% grfguide.tex Copyright (C) 1994 1995 1996 1998 1999 David Carlisle
-%%              Copyright (C) 2005 2014 2016 2017 David Carlisle, LaTeX3 Project
+%%              Copyright (C) 2005-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/keyval.dtx b/macros/latex-dev/required/graphics/keyval.dtx
index f656961d0b..1e1581eee3 100644
--- a/macros/latex-dev/required/graphics/keyval.dtx
+++ b/macros/latex-dev/required/graphics/keyval.dtx
@@ -1,7 +1,7 @@
 %
 % \iffalse
 %% keyval.dtx Copyright (C) 1993 1994 1995 1997 1998 1999 David Carlisle
-%%            Copyright (C) 2000--2015 David Carlisle, LaTeX3 Project
+%%            Copyright (C) 2000-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/keyval.pdf b/macros/latex-dev/required/graphics/keyval.pdf
index 8790611726..fd6f74aba0 100644
--- a/macros/latex-dev/required/graphics/keyval.pdf
+++ b/macros/latex-dev/required/graphics/keyval.pdf
diff --git a/macros/latex-dev/required/graphics/lscape.dtx b/macros/latex-dev/required/graphics/lscape.dtx
index 733e183ee6..a5a3dc3220 100644
--- a/macros/latex-dev/required/graphics/lscape.dtx
+++ b/macros/latex-dev/required/graphics/lscape.dtx
@@ -2,7 +2,7 @@
 % \iffalse
 %
 %% lscape.dtx Copyright (C) 1994 1999-2000 David Carlisle
-%%            Copyright (C) 2000--2015 David Carlisle, LaTeX3 Project
+%%            Copyright (C) 2000-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/lscape.pdf b/macros/latex-dev/required/graphics/lscape.pdf
index bf3d93a04c..edb151476c 100644
--- a/macros/latex-dev/required/graphics/lscape.pdf
+++ b/macros/latex-dev/required/graphics/lscape.pdf
diff --git a/macros/latex-dev/required/graphics/rotating.dtx b/macros/latex-dev/required/graphics/rotating.dtx
index 41bd399d4e..149c19d049 100644
--- a/macros/latex-dev/required/graphics/rotating.dtx
+++ b/macros/latex-dev/required/graphics/rotating.dtx
@@ -3,9 +3,9 @@
 %
 %
 % File: rotating.dtx
-%% Copyright 1995--1999 Sebastian Rahtz and Leonor Barroca
-%% Copyright 2001--2003,2007--2009 Robin Fairbairns
-%% Copyright 2016  LaTeX3 Project 
+%% Copyright (C) 1995--1999 Sebastian Rahtz and Leonor Barroca
+%% Copyright (C) 2001--2003,2007--2009 Robin Fairbairns
+%% Copyright (C) 2016-2019 LaTeX3 Project 
 %
 % This work may be distributed and/or modified under the
 % conditions of the LaTeX Project Public License, either version 1.3c
diff --git a/macros/latex-dev/required/graphics/rotating.pdf b/macros/latex-dev/required/graphics/rotating.pdf
index bfaa34d0ab..97b252ecd5 100644
--- a/macros/latex-dev/required/graphics/rotating.pdf
+++ b/macros/latex-dev/required/graphics/rotating.pdf
diff --git a/macros/latex-dev/required/graphics/rotex.pdf b/macros/latex-dev/required/graphics/rotex.pdf
index 1564784475..d064b44420 100644
--- a/macros/latex-dev/required/graphics/rotex.pdf
+++ b/macros/latex-dev/required/graphics/rotex.pdf
diff --git a/macros/latex-dev/required/graphics/trig.dtx b/macros/latex-dev/required/graphics/trig.dtx
index 712db13ba2..2b152578ad 100644
--- a/macros/latex-dev/required/graphics/trig.dtx
+++ b/macros/latex-dev/required/graphics/trig.dtx
@@ -1,6 +1,6 @@
 % \iffalse
 %% File: trig.dtx Copyright (C) 1993 1994 1995 1996 1997 1999 David Carlisle
-%%                Copyright (C) 2000--2015 David Carlisle, LaTeX3 Project
+%%                Copyright (C) 2000-2019 David Carlisle, LaTeX3 Project
 %%
 %% This file is part of the Standard LaTeX `Graphics Bundle'.
 %% It may be distributed under the terms of the LaTeX Project Public
diff --git a/macros/latex-dev/required/graphics/trig.pdf b/macros/latex-dev/required/graphics/trig.pdf
index 2ad8cb7b53..25f75bf255 100644
--- a/macros/latex-dev/required/graphics/trig.pdf
+++ b/macros/latex-dev/required/graphics/trig.pdf
diff --git a/macros/latex-dev/required/tools/README.md b/macros/latex-dev/required/tools/README.md
new file mode 100644
index 0000000000..aa0e7c9f46
--- /dev/null
+++ b/macros/latex-dev/required/tools/README.md
@@ -0,0 +1,54 @@
+The LaTeX `tools` bundle
+========================
+
+Release 2019-10-01 pre-release 3
+
+Overview
+--------
+
+This bundle consists of packages providing a range of basic tools for
+LaTeX users. It is a required part of a LaTeX installation.
+
+Installation
+------------
+
+We no longer distribute installation instructions for the various TeX
+implementations. All modern TeX systems include `tools` as-standard, and end
+users should in general use the release versions supplied in this way.
+
+Release distribution is carried out only through the CTAN archives.
+
+Reporting Bugs
+--------------
+
+If you wish to report a problem or bug in the `tools` bundle
+please use the [Issue Tracker for LaTeX2e on
+GitHub](https://github.com/latex3/latex2e/issues)
+and follow the guidelines that pop up if you press the "New issue" button.
+
+In particular, to check that you are really seeing a bug, please write
+a short, self-contained document that shows the problem. This should
+include the `latexbug` package, which will warn if your test file is
+not suitable for one or the other reason. See the [CONTRIBUTING
+guide](https://github.com/latex3/latex2e/blob/master/CONTRIBUTING.md)
+for further details, or if you need to obtain the `latexbug` package.
+
+If the bug turns out to be with third-party software then please
+contact the developer, and not us!
+
+License
+-------
+
+The contents of this bundle are distributed under the [LaTeX Project
+Public License](https://www.latex-project.org/lppl/lppl-1-3c/),
+version 1.3c or later.
+
+Copyright
+---------
+
+Copyright is maintained on each of these packages by the author(s)
+of the package.
+
+-----
+
+<p>Copyright (C) 1993-2019 The LaTeX Project <br />
diff --git a/macros/latex-dev/required/tools/afterpage.dtx b/macros/latex-dev/required/tools/afterpage.dtx
new file mode 100644
index 0000000000..3fa341aa53
--- /dev/null
+++ b/macros/latex-dev/required/tools/afterpage.dtx
@@ -0,0 +1,385 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: afterpage.dtx Copyright (C) 1994 1994 1995 David Carlisle
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{afterpage}
+%<package>         [2014/10/28 v1.08 After-Page Package (DPC)]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{afterpage}
+\GetFileInfo{afterpage.sty}
+\begin{document}
+\title{The \textsf{afterpage} package\thanks{This file
+        has version number \fileversion, last
+        revised \filedate.}}
+\author{David Carlisle}
+\date{\filedate}
+\MaintainedByLaTeXTeam{tools}
+\maketitle
+\DocInput{afterpage.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \changes{v1.00}{1993/01/25}{Initial version}
+% \changes{v1.05}{1993/07/14}{First public version}
+% \changes{v1.06}{1994/02/01}{Update for LaTeX2e}
+% \changes{v1.07}{1994/05/23}{Documentation Changes}
+% \changes{v1.08}{1995/10/27}
+%      {Use \cs{par} not \cs{endgraf}, for tools/1579}
+% \changes{v1.08}{1995/10/27}
+%      {Try and do something sensible with nested \cs{clearpage},
+%       for tools/1880}
+% \changes{v1.08}{1995/10/27}
+%      {Try and do something sensible with footnotes, for tools/1884}
+%
+%
+% This package implements a command, |\afterpage|, that causes the
+% commands specified in its argument to be expanded after the current
+% page is output.\footnote{This is really a pre-release, to see whether
+% people like the idea of a command like this. This implementation is
+% \emph{not} particularly robust. This implementation does not work in
+% two column mode, and can get `confused' by \LaTeX's floating
+% environments.}
+%
+% \begin{enumerate}
+% \item Sometimes \LaTeX's float positioning mechanism gets overloaded,
+% and all floating |figure|s and |table|s drift to the end of the
+% document. One may flush out all the unprocessed floats by issuing a
+% |\clearpage| command, but this has the effect of making the current
+% page end prematurely. Now you can issue |\afterpage{\clearpage}| and
+% the current page will be filled up with text as usual, but then a
+% |\clearpage| command will flush out all the floats before the next
+% text page begins.
+% \item An earlier mechanism to help with float placement was the
+% optional argument |[H]| (meaning {\bf HERE!}) which was originally
+% added to the standard floating environments by |here.sty|, and is now
+% provided by |float.sty|. However some |[H]| users have commented that
+% they did not really mean `Here!' They actually wanted `Somewhere
+% close'. This can now be achieved by\\
+%  |\afterpage{\clearpage\begin{figure}[H] |\ldots
+%  |\end{figure}}|\\
+% This ensures that the figure is at the top of the next page. (The
+% |\clearpage| stops any other figures drifting past the |[H]| figure.)
+% \item Floating longtables. |longtable.sty| provides the |longtable|
+% environment, a multi-page version of |tabular|. Many |longtable| users
+% have told me that it is difficult to set the text surrounding the long
+% table, and that they wanted a `floating' version. As, presumably,
+% |longtable|s are long, they are probably too large to hold in memory,
+% and float in the way that the |table| environment is floated, however
+% if the table is in a separate file, say |ltfile.tex|, you can now
+% use one of:\\
+% |\afterpage{\clearpage\input{ltfile}}|\\
+% |\afterpage{\clearpage\input{ltfile}\clearpage}|.\\
+% The first form lets text appear on the same page as the end of the
+% longtable, the second ensures that the surrounding text starts again
+% on a new page.
+% \end{enumerate}
+%
+% \StopEventually{}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \begin{macro}{\afterpage}
+% The token register used to save the old output routine.
+%    \begin{macrocode}
+\newtoks\AP@output
+\global\AP@output\expandafter{\the\output}
+%    \end{macrocode}
+%
+% A box register used to save any part of the next page which has
+% already been processed.
+%    \begin{macrocode}
+\newbox\AP@partial
+%    \end{macrocode}
+%
+% A box register used to save any footnote texts that are `tied' to
+% the text that gets saved in |\AP@partial|.
+%    \begin{macrocode}
+\newbox\AP@footins
+%    \end{macrocode}
+%
+% The following macro attempts to get safely into vertical mode, and
+% then invokes a special output routine to grab the current page into
+% |\AP@partial|.
+%    \begin{macrocode}
+\def\AP@savetop{%
+%    \end{macrocode}
+% Now begins a test to see what state we are in. |\AP@noindent|  will
+% be defined so as to return to this state (well, almost!) after
+% afterpage has finished.
+%    \begin{macrocode}
+  \ifvmode
+%    \end{macrocode}
+% Vertical mode. This is the simplest case, do nothing.
+%    \begin{macrocode}
+    \let\AP@noindent\empty
+  \else\ifhmode
+%    \end{macrocode}
+% Horizontal mode.
+% `Back out' into vertical mode, removing the indentation box as we go.
+% If in fact there was no indentation box, the output routine was
+% invoked by |\noindent| (what bad luck!) so we have to remember to
+% re-insert the |\noindent| before the paragraph is seen again.
+% |\everypar| tokens have already been inserted, so don't insert them
+% again.
+%    \begin{macrocode}
+    \setbox\z@\lastbox
+    \edef\AP@noindent
+      {{\everypar{}\ifvoid\z@\noindent\else\indent\fi}}%
+    \par
+  \else
+%    \end{macrocode}
+% The remaining (even worse) possibility that the output routine
+% was triggered by the start of displaymath within a paragraph.
+%
+% Come out of displaymath with |$$|, then adjust the spacing (getting
+% into vmode at the same time). |\AP@noindent| will restart display math
+% later. |\everydisplay| tokens have already been inserted (they apply
+% to the math list that will be started by |\AP@noindent|, even though
+% they were triggered by the display math that was closed by the lines
+% below!). Save the values |\prevgraf| and |\predisplaysize| for use in
+% the re-started math list.
+%    \begin{macrocode}
+    \abovedisplayshortskip\z@\abovedisplayskip\z@
+    \belowdisplayshortskip\z@\belowdisplayskip\z@
+    \xdef\AP@disp{%
+      \predisplaysize\the\predisplaysize
+      \prevgraf\the\prevgraf\relax}%
+    $$\vskip-\baselineskip\vskip-\parskip
+    \edef\AP@noindent{%
+%    \end{macrocode}
+% Do not insert |\everydisplay| tokens again.
+%    \begin{macrocode}
+      \toks@{\the\everydisplay}\everydisplay{}%
+%    \end{macrocode}
+% Start displaymath mode with no spurious paragraph line above it.
+% Restore |\prevgraf| and |\predisplaysize|.  Use |\aftergroup| to
+% restore the correct setting for |\everydisplay| after this display
+% has finished.
+%    \begin{macrocode}
+      {\everypar{}\noindent}$$\AP@disp\aftergroup\noexpand\AP@ed}%
+  \fi\fi
+%    \end{macrocode}
+% Now switch the  output routine and remove everything from the current
+% page into the box |\AP@partial|.
+%    \begin{macrocode}
+  \begingroup
+  \nointerlineskip\null
+    \output{%
+      \global\setbox\AP@partial\vbox{%
+        \unvbox\@cclv
+         \global\setbox\@ne\lastbox}%
+%    \end{macrocode}
+% If the text that is saved in |\AP@partial| had footnotes, we'd
+% better grab them as well otherwise they may come out on a page
+% with the `afterpage' text, before the page that has the
+% footnote mark! (Added at v1.08.)
+%    \begin{macrocode}
+       \global\setbox\AP@footins\box\footins}%
+%    \end{macrocode}
+% Having defined the output routine, trigger it\ldots
+%    \begin{macrocode}
+  \eject
+  \endgroup}
+%    \end{macrocode}
+%
+% |\AP@| stores all the commands that must be executed after the page
+% break.
+%    \begin{macrocode}
+\let\AP@\relax
+%    \end{macrocode}
+%
+% Restore the |\everydisplay| register. |\ignorespaces| prevents a space
+% or newline after |$$| creating rogue a indentation or paragraph.
+%    \begin{macrocode}
+\def\AP@ed{\everydisplay\expandafter{\the\toks@}\ignorespaces}
+%    \end{macrocode}
+%
+% Remove the current vertical list, insert the commands |\AP@|
+% at the top of the page, and then re-insert the saved text.
+%    \begin{macrocode}
+\def\AP@@{%
+  \AP@savetop
+  \global\expandafter\let\expandafter\AP@\expandafter\relax\AP@
+  \par
+%    \end{macrocode}
+% The text originally at the top of this page is now stored in the box
+% |\AP@partial|, including  |\topskip| glue. Now we want to unbox
+% |\AP@partial|, placing the baseline of the first row |\baselineskip|
+% below the baseline of the last line coming from the afterpage text.
+% If we assumed nothing has too much height or depth (and |\topskip| is
+% rigid), it would be fairly trivial to position the contents of
+% |\AP@partial| so that the baseline of the first row was
+% |\baselineskip| below the last row just added.
+%
+% In this version, I thought it might be fun to try to exactly achieve
+% the |\baselineskip|--or--|\lineskip| calculation that \TeX\ normally
+% does internally.  The call to |\addboxcontents| does the right thing
+% (I hope).
+%    \begin{macrocode}
+   \addboxcontents\AP@partial
+%    \end{macrocode}
+% Now re-insert any footnote text. This may not be quite the right
+% place, as the text that has just been unboxed may break over a page
+% in its new position. Also it may not be the right number if the text
+% from |\afterpage| itself contains footnotes. Too bad!
+%    \begin{macrocode}
+  \ifvoid\AP@footins\else
+         \insert\footins{\unvbox\AP@footins}\fi
+%    \end{macrocode}
+% Now repair things if we started off in horizontal mode.
+%    \begin{macrocode}
+  \AP@noindent}
+%    \end{macrocode}
+%
+% If |\AP@| is not |\relax| then the current page already has some
+% `afterpage' commands, so just add the new commands to the end of the
+% list. Otherwise save the commands in |\AP@|. (within a local group),
+% and switch the output routine. (The new output routine just calls the
+% old one if it is invoked by a \LaTeX{} float.
+%    \begin{macrocode}
+\long\def\afterpage#1{%
+  \ifx\AP@\relax
+    \gdef\AP@{{#1\par}}%
+    \global\output{%
+      \the\AP@output
+      \ifnum\outputpenalty>-\@Mi
+        \global\output\expandafter{\the\AP@output}%
+        \aftergroup\AP@@
+      \fi}%
+  \else
+    \expandafter\gdef\expandafter\AP@\expandafter{\AP@{#1\par}}%
+  \fi}
+%    \end{macrocode}
+%
+% If we have got to the end of the document or clearpage
+% just put the stuff out  without any trickery.
+%    \begin{macrocode}
+\let\AP@clearpage\clearpage
+\def\clearpage{%
+  \ifx\AP@\relax
+    \AP@clearpage
+  \else
+    \global\output\expandafter{\the\AP@output}%
+    \AP@clearpage
+%    \end{macrocode}
+% At this point (since v1.08) Need to clear |\AP@| \emph{before}
+% using its expansion, as otherwise hit an infinite loop. Sigh.
+%    \begin{macrocode}
+    \global\expandafter\let\expandafter\AP@\expandafter\relax
+    \expandafter\expandafter\AP@
+  \fi}
+\let\AP@enddocument\enddocument
+\def\enddocument{%
+  \ifx\AP@\relax\else
+    \global\output\expandafter{\the\AP@output}%
+    \AP@clearpage
+    \global\expandafter\let\expandafter\AP@\expandafter\relax
+    \expandafter\expandafter\AP@
+  \fi
+    \AP@enddocument}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\addboxcontents}
+% Given a vbox |#1|, add to the current vertical list such that the end
+% result is equivalent to the list that \TeX\ would have built had the
+% contents of |#1| (apart from any initial glue) been added individually
+% to the current list.
+
+% So essentially, the problem is that of unboxing |#1|, but replacing
+% the glue at the top of |#1| with (something equivalent to) the
+% |\baselineskip| or |\lineskip| glue that \TeX\ would normally have
+% placed before the first box in |#1|. Also |\prevdepth| must be set at
+% the end.
+%    \begin{macrocode}
+\def\addboxcontents#1{{%
+%    \end{macrocode}
+% Perhaps I shouldn't use grouping here, as I probably don't really want
+% to save |#1|. If it is removed, |\splittopskip| and |\splitmaxdepth|
+% would need to be restored by hand.
+%
+% First replace any glue at the top by |\vskip 0pt|.
+%    \begin{macrocode}
+  \splittopskip\z@
+  \splitmaxdepth\maxdimen
+  \setbox#1\vbox{\break\unvbox#1}%
+  \setbox\z@\vsplit#1to\z@
+%    \end{macrocode}
+% Put the breakpoint back.
+%    \begin{macrocode}
+  \setbox#1\vbox{\break\unvbox#1}%
+%    \end{macrocode}
+% Set |\skip@| to be height of |#1| (without top glue)
+%    \begin{macrocode}
+  \skip@\ht#1%
+%    \end{macrocode}
+% Now make the first baseline of the first row be |\vsize| from the top.
+% (This assumes that the first row has height less than |\vsize|.)
+%    \begin{macrocode}
+  \splittopskip\vsize
+  \setbox\z@\vsplit#1to\z@
+%    \end{macrocode}
+% Subtract the new height of |#1| from |\skip@|, and add back on
+% |\splittopskip|, so |\skip@| is now the height of the first row of
+% |#1| This may still be 0pt if (eg) a mark or whatsit is between the
+% top glue and the first box. Save (this height${}-{}$|\splittopskip|)
+% in |\skip\tw@|.
+%    \begin{macrocode}
+  \advance\skip@-\ht#1%
+  \skip\tw@\skip@
+  \advance\skip@\splittopskip
+%    \end{macrocode}
+% Now fake \TeX's |\baselineskip| calculation.
+%    \begin{macrocode}
+  \advance\skip@\prevdepth
+  \advance\skip@-\baselineskip
+  \advance\skip\tw@\ifdim-\skip@<\lineskiplimit\lineskip\else-\skip@\fi
+%    \end{macrocode}
+% Finally add the glue.
+%    \begin{macrocode}
+  \vskip\skip\tw@
+%    \end{macrocode}
+% Now unbox the box, setting |\prevdepth| by hand, as |\unvbox| (unlike
+% |\box|) does not automatically set it.
+%    \begin{macrocode}
+  \global\dimen@i\dp#1%
+  \unvbox#1}%
+  \prevdepth\dimen@i}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
diff --git a/macros/latex-dev/required/tools/afterpage.ins b/macros/latex-dev/required/tools/afterpage.ins
new file mode 100644
index 0000000000..9764bdac6d
--- /dev/null
+++ b/macros/latex-dev/required/tools/afterpage.ins
@@ -0,0 +1,75 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+
+\generate{\file{afterpage.sty}{\from{afterpage.dtx}{package}}}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/afterpage.pdf b/macros/latex-dev/required/tools/afterpage.pdf
new file mode 100644
index 0000000000..3cd429ce02
--- /dev/null
+++ b/macros/latex-dev/required/tools/afterpage.pdf
diff --git a/macros/latex-dev/required/tools/array-2016-10-06.sty b/macros/latex-dev/required/tools/array-2016-10-06.sty
new file mode 100644
index 0000000000..0b619362d4
--- /dev/null
+++ b/macros/latex-dev/required/tools/array-2016-10-06.sty
@@ -0,0 +1,341 @@
+%%
+%% This is an old release of `array.sty',
+%% 
+%% Copyright 1993-2016
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file.
+%% 
+%% This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+%% --------------------------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% 
+%% Package `array' to use with LaTeX 2e
+%% Copyright (C) 1989-1998 Frank Mittelbach, all rights reserved.
+\NeedsTeXFormat{LaTeX2e}[1995/06/01]
+\ProvidesPackage{array}
+         [2016/10/06 v2.4d Tabular extension package (FMi)]
+%%
+
+\def\@addtopreamble#1{\xdef\@preamble{\@preamble #1}}
+\def\@testpach{\@chclass
+ \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
+  \ifnum \@lastchclass=7 5 \else
+   \ifnum \@lastchclass=8 \tw@ \else
+    \ifnum \@lastchclass=9 \thr@@
+   \else \z@
+   \ifnum \@lastchclass = 10 \else
+   \edef\@nextchar{\expandafter\string\@nextchar}%
+   \@chnum
+   \if \@nextchar c\z@ \else
+    \if \@nextchar l\@ne \else
+     \if \@nextchar r\tw@ \else
+   \z@ \@chclass
+   \if\@nextchar |\@ne \else
+    \if \@nextchar !6 \else
+     \if \@nextchar @7 \else
+      \if \@nextchar <8 \else
+       \if \@nextchar >9 \else
+  10
+  \@chnum
+  \if \@nextchar m\thr@@\else
+   \if \@nextchar p4 \else
+    \if \@nextchar b5 \else
+   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
+   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
+\def\@xexpast#1*#2#3#4\@@{%
+   \@tempcnta #2
+   \toks@={#1}\@temptokena={#3}%
+   \let\the@toksz\relax \let\the@toks\relax
+   \def\@tempa{\the@toksz}%
+   \ifnum\@tempcnta >0 \@whilenum\@tempcnta >0\do
+     {\edef\@tempa{\@tempa\the@toks}\advance \@tempcnta \m@ne}%
+       \let \@tempb \@xexpast \else
+       \let \@tempb \@xexnoop \fi
+   \def\the@toksz{\the\toks@}\def\the@toks{\the\@temptokena}%
+   \edef\@tempa{\@tempa}%
+   \expandafter \@tempb \@tempa #4\@@}
+\def\prepnext@tok{\advance \count@ \@ne
+   \toks\count@{}}
+\def\save@decl{\toks\count@ \expandafter{\@nextchar}}
+\def\insert@column{%
+   \the@toks \the \@tempcnta
+   \ignorespaces \@sharp \unskip
+   \the@toks \the \count@ \relax}
+\newdimen\col@sep
+\def\@acol{\@addtopreamble{\hskip\col@sep}}
+\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
+   \let\@sharp\relax \let\@startpbox\relax \let\@endpbox\relax
+   \@xexpast #1*0x\@@
+   \count@\m@ne
+   \let\the@toks\relax
+   \prepnext@tok
+   \expandafter \@tfor \expandafter \@nextchar
+    \expandafter :\expandafter =\@tempa \do
+   {\@testpach
+   \ifcase \@chclass \@classz \or \@classi \or \@classii
+     \or \save@decl \or \or \@classv \or \@classvi
+     \or \@classvii \or \@classviii  \or \@classix
+     \or \@classx \fi
+   \@lastchclass\@chclass}%
+   \ifcase\@lastchclass
+   \@acol \or
+   \or
+   \@acol \or
+   \@preamerr \thr@@ \or
+   \@preamerr \tw@ \@addtopreamble\@sharp \or
+   \or
+   \else  \@preamerr \@ne \fi
+   \def\the@toks{\the\toks}}
+\def\@classx{%
+  \ifcase \@lastchclass
+  \@acolampacol \or
+  \@addamp \@acol \or
+  \@acolampacol \or
+  \or
+  \@acol \@firstampfalse \or
+  \@addamp
+  \fi}
+\def\@classz{\@classx
+   \@tempcnta \count@
+   \prepnext@tok
+   \@addtopreamble{\ifcase \@chnum
+      \hfil
+      \d@llarbegin
+      \insert@column
+      \d@llarend \hfil \or
+      \hskip1sp\d@llarbegin \insert@column \d@llarend \hfil \or
+      \hfil\hskip1sp\d@llarbegin \insert@column \d@llarend \or
+   $\vcenter
+   \@startpbox{\@nextchar}\insert@column \@endpbox $\or
+   \vtop \@startpbox{\@nextchar}\insert@column \@endpbox \or
+   \vbox \@startpbox{\@nextchar}\insert@column \@endpbox
+  \fi}\prepnext@tok}
+\def\@classix{\ifnum \@lastchclass = \thr@@
+       \@preamerr \thr@@ \fi
+       \@classx}
+\def\@classviii{\ifnum \@lastchclass >\z@
+      \@preamerr 4\@chclass 6 \@classvi \fi}
+\def\@arrayrule{\@addtopreamble \vline}
+\def\@classvii{\ifnum \@lastchclass = \thr@@
+   \@preamerr \thr@@ \fi}
+\def\@classvi{\ifcase \@lastchclass
+      \@acol \or
+      \@addtopreamble{\hskip \doublerulesep}\or
+      \@acol \or
+      \@classvii
+      \fi}
+\def\@classii{\advance \count@ \m@ne
+   \save@decl\prepnext@tok}
+\def\@classv{\save@decl
+   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
+   \prepnext@tok}
+\def\@classi{\@classvi
+   \ifcase \@chnum \@arrayrule \or
+      \@classv \fi}
+\def\@startpbox#1{\bgroup
+  \setlength\hsize{#1}\@arrayparboxrestore
+   \everypar{%
+      \vrule \@height \ht\@arstrutbox \@width \z@
+      \everypar{}}%
+   }
+\def\@endpbox{\@finalstrut\@arstrutbox \egroup\hfil}
+\def\@array[#1]#2{%
+  \@tempdima \ht \strutbox
+  \advance \@tempdima by\extrarowheight
+  \setbox \@arstrutbox \hbox{\vrule
+             \@height \arraystretch \@tempdima
+             \@depth \arraystretch \dp \strutbox
+             \@width \z@}%
+  \begingroup
+  \@mkpream{#2}%
+  \xdef\@preamble{\noexpand \ialign \@halignto
+                  \bgroup \@arstrut \@preamble
+                          \tabskip \z@ \cr}%
+  \endgroup
+  \@arrayleft
+  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi \fi
+  \bgroup
+  \let \@sharp ##\let \protect \relax
+  \lineskip \z@
+  \baselineskip \z@
+  \m@th
+  \let\\\@arraycr \let\tabularnewline\\\let\par\@empty \@preamble}
+\def\arraybackslash{\let\\\tabularnewline}
+\newdimen \extrarowheight
+\extrarowheight=0pt
+\def\@arstrut{\unhcopy\@arstrutbox}
+\def\@arraycr{\relax\iffalse{\fi\ifnum 0=`}\fi
+  \@ifstar \@xarraycr \@xarraycr}
+\def\@xarraycr{\@ifnextchar [%
+  \@argarraycr {\ifnum 0=`{}\fi\cr}}
+\def\@argarraycr[#1]{\ifnum0=`{}\fi\ifdim #1>\z@
+  \expandafter\@xargarraycr\else
+  \expandafter\@yargarraycr\fi{#1}}
+\def\@xargarraycr#1{\unskip
+  \@tempdima #1\advance\@tempdima \dp\@arstrutbox
+  \vrule \@depth\@tempdima \@width\z@ \cr}
+\def\@yargarraycr#1{\cr\noalign{\vskip #1}}
+\long\def\multicolumn#1#2#3{%
+   \multispan{#1}\begingroup
+   \def\@addamp{\if@firstamp \@firstampfalse \else
+                \@preamerr 5\fi}%
+   \@mkpream{#2}\@addtopreamble\@empty
+   \endgroup
+   \def\@sharp{#3}%
+   \@arstrut \@preamble
+   \null
+   \ignorespaces}
+\let\d@llarbegin\begingroup
+\let\d@llarend\endgroup
+\def\array{\col@sep\arraycolsep
+  \def\d@llarbegin{$}\let\d@llarend\d@llarbegin\def\@halignto{}%
+  \@tabarray}
+\def\@tabarray{\@ifnextchar[{\@array}{\@array[c]}}
+\def\tabular{\def\@halignto{}\@tabular}
+\expandafter\def\csname tabular*\endcsname#1{%
+       \setlength\dimen@{#1}%
+       \edef\@halignto{to\the\dimen@}\@tabular}
+\def\@tabular{%
+  \leavevmode
+  \hbox \bgroup $\col@sep\tabcolsep \let\d@llarbegin\begingroup
+                                    \let\d@llarend\endgroup
+  \@tabarray}
+\def\endarray{\crcr \egroup \egroup \gdef\@preamble{}}
+\def\endtabular{\endarray $\egroup}
+\expandafter\let\csname endtabular*\endcsname=\endtabular
+\let\@ampacol=\relax        \let\@expast=\relax
+\let\@arrayclassiv=\relax   \let\@arrayclassz=\relax
+\let\@tabclassiv=\relax     \let\@tabclassz=\relax
+\let\@arrayacol=\relax      \let\@tabacol=\relax
+\let\@tabularcr=\relax      \let\@@endpbox=\relax
+\let\@argtabularcr=\relax   \let\@xtabularcr=\relax
+\def\@preamerr#1{\def\@tempd{{..} at wrong position: }%
+   \PackageError{array}{%
+   \ifcase #1 Illegal pream-token (\@nextchar): `c' used\or %0
+    Missing arg: token ignored\or                           %1
+    Empty preamble: `l' used\or                             %2
+    >\@tempd token ignored\or                               %3
+    <\@tempd changed to !{..}\or                            %4
+    Only one column-spec. allowed.\fi}\@ehc}                %5
+\def\newcolumntype#1{%
+  \edef\NC@char{\string#1}%
+  \@ifundefined{NC@find@\NC@char}%
+    {\@tfor\next:=<>clrmbp@!|\do{\if\noexpand\next\NC@char
+        \PackageWarning{array}%
+                       {Redefining primitive column \NC@char}\fi}%
+     \NC@list\expandafter{\the\NC@list\NC@do#1}}%
+    {\PackageWarning{array}{Column \NC@char\space is already defined}}%
+  \@namedef{NC@find@\NC@char}##1#1{\NC@{##1}}%
+  \@ifnextchar[{\newcol@{\NC@char}}{\newcol@{\NC@char}[0]}}
+\def\newcol@#1[#2]#3{\expandafter\@reargdef
+     \csname NC@rewrite@#1\endcsname[#2]{\NC@find#3}}
+\def\NC@#1{%
+  \@temptokena\expandafter{\the\@temptokena#1}\futurelet\next\NC@ifend}
+\def\NC@ifend{%
+  \ifx\next\relax
+    \else\@tempswatrue\expandafter\NC@rewrite\fi}
+\def\NC@do#1{%
+  \expandafter\let\expandafter\NC@rewrite
+    \csname NC@rewrite@\string#1\endcsname
+  \expandafter\let\expandafter\NC@find
+    \csname NC@find@\string#1\endcsname
+  \expandafter\@temptokena\expandafter{\expandafter}%
+        \expandafter\NC@find\the\@temptokena#1\relax}
+\def\showcols{{\def\NC@do##1{\let\NC@do\NC@show}\the\NC@list}}
+\def\NC@show#1{%
+  \typeout{Column #1\expandafter\expandafter\expandafter\NC@strip
+  \expandafter\meaning\csname NC@rewrite@#1\endcsname\@@}}
+\def\NC@strip#1:#2->#3 #4\@@{#2 -> #4}
+\newtoks\NC@list
+\newcolumntype{*}[2]{}
+\long\@namedef{NC@rewrite@*}#1#2{%
+  \count@#1\relax
+  \loop
+  \ifnum\count@>\z@
+  \advance\count@\m@ne
+  \@temptokena\expandafter{\the\@temptokena#2}%
+  \repeat
+  \NC@find}
+\let\@xexpast\relax
+\let\@xexnoop\relax
+\def\save@decl{\toks \count@ = \expandafter\expandafter\expandafter
+                  {\expandafter\@nextchar\the\toks\count@}}
+\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
+   \let\@sharp\relax \let\@startpbox\relax \let\@endpbox\relax
+   \@temptokena{#1}\@tempswatrue
+   \@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
+   \count@\m@ne
+   \let\the@toks\relax
+   \prepnext@tok
+   \expandafter \@tfor \expandafter \@nextchar
+    \expandafter :\expandafter =\the\@temptokena \do
+   {\@testpach
+   \ifcase \@chclass \@classz \or \@classi \or \@classii
+     \or \save@decl \or \or \@classv \or \@classvi
+     \or \@classvii \or \@classviii
+     \or \@classx
+     \or \@classx \fi
+   \@lastchclass\@chclass}%
+   \ifcase\@lastchclass
+   \@acol \or
+   \or
+   \@acol \or
+   \@preamerr \thr@@ \or
+   \@preamerr \tw@ \@addtopreamble\@sharp \or
+   \or
+   \else  \@preamerr \@ne \fi
+   \def\the@toks{\the\toks}}
+\let\@classix\relax
+\def\@classviii{\ifnum \@lastchclass >\z@\ifnum\@lastchclass=\tw@\else
+      \@preamerr 4\@chclass 6 \@classvi \fi\fi}
+\def\@classv{\save@decl
+   \expandafter\NC@ecs\@nextchar\extracolsep{}\extracolsep\@@@
+   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
+   \prepnext@tok}
+\def\NC@ecs#1\extracolsep#2#3\extracolsep#4\@@@{\def\@tempa{#2}%
+  \ifx\@tempa\@empty\else\toks\count@={#1\tabskip#2\relax#3}\fi}
+\def\@tabarray{\@ifnextchar[{\@@array}{\@@array[c]}}
+\let\@@array\@array
+\def\endarray{\crcr \egroup \egroup \@arrayright \gdef\@preamble{}}
+\let\@arrayleft\@empty
+\let\@arrayright\@empty
+\newlength{\extratabsurround}
+\setlength{\extratabsurround}{2pt}
+\newlength{\backup@length}
+\newcommand{\firsthline}{%
+  \multicolumn1c{%
+    \global\backup@length\ht\@arstrutbox
+    \global\advance\backup@length\dp\@arstrutbox
+    \global\advance\backup@length\arrayrulewidth
+     \raise\extratabsurround\copy\@arstrutbox
+    }\\[-\backup@length]\hline
+}
+\newcommand{\lasthline}{\hline\multicolumn1c{%
+    \global\backup@length2\ht\@arstrutbox
+    \global\advance\backup@length2\dp\@arstrutbox
+    \global\advance\backup@length\arrayrulewidth
+    }\\[-\backup@length]%
+    \multicolumn1c{%
+       \lower\extratabsurround\copy\@arstrutbox
+       }%
+}
+\CheckCommand*\@xhline{\ifx\reserved@a\hline
+               \vskip\doublerulesep
+               \vskip-\arrayrulewidth
+             \fi
+      \ifnum0=`{\fi}}
+\renewcommand*\@xhline{\ifx\reserved@a\hline
+               \vskip\doublerulesep
+             \fi
+      \ifnum0=`{\fi}}
+\endinput
+%%
+%% End of file `array.sty'.
diff --git a/macros/latex-dev/required/tools/array.dtx b/macros/latex-dev/required/tools/array.dtx
new file mode 100644
index 0000000000..5590b0a136
--- /dev/null
+++ b/macros/latex-dev/required/tools/array.dtx
@@ -0,0 +1,3092 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%\iffalse   % this is a METACOMMENT !
+%
+%% Package `array' to use with LaTeX 2e
+%% Copyright (C) 1989-1998 Frank Mittelbach, all rights reserved.
+%<+package>\NeedsTeXFormat{LaTeX2e}[1995/06/01]
+%<+package>\providecommand\DeclareRelease[3]{}
+%<+package>\providecommand\DeclareCurrentRelease[2]{}
+%<+package>
+%<+package>\DeclareRelease{}{2016-10-06}{array-2016-10-06.sty}
+%<+package>\DeclareCurrentRelease{}{2019-10-01}
+%<+package>
+%<+package>\ProvidesPackage{array}
+%<+package>         [2019/08/31 v2.4l Tabular extension package (FMi)]
+%
+% \fi
+%
+%%
+%
+%
+% \changes{v2.4g}{2018/04/07}{Renamed internal \cs{mcell@box} to
+%       \cs{ar@mcellbox} and \cs{align@mcell} to \cs{ar@align@mcell}
+%        to avoid conflict with makecell package}
+%
+% \changes{v2.4c}{2008/09/09}{(WR) Typo fix in documentation}
+%
+% \changes{v2.3c}{1995/11/02}{(DPC) minor doc changes}
+%
+% \changes{v2.3a}{1994/10/16}{Added code for \cs{firsthline} and
+%                             friends}
+%
+% \changes{v2.2c}{1994/03/14}{removed check for \cs{@tfor} bug}
+%
+% \changes{v1.0b}{1987/06/04}{`@classi (faster),
+%                        `@classvi (new)   A in preamble means
+%                                         \&\& in `halign.}
+%
+% \changes{v1.1a}{1987/07/05}{New concept:
+%                        preamblechar: c,l,r,C,L,R,A,p,t,{\tt !|},@,!!}
+% \changes{v1.1b}{1987/09/21}{Again p like original \LaTeX{} and z for
+%                        centered `parbox.}
+%
+% \changes{v1.2a}{1987/09/27}{Completely new implementation.}
+% \changes{v1.2b}{1987/10/06}{{\tt !|} does no longer generate space at
+%                        start or end of the preamble. Otherwise `hline
+%                        is too long.}
+% \changes{v1.2b}{1987/10/06}{Enlarged `@arstrutbox by 1pt (Test-Impl)
+%                         with dimen `@strutheight.}
+% \changes{v1.2c}{1987/10/22}{New dimen parameter `extrarowheight
+%                        (default: 0pt).}
+% \changes{v1.2c}{1987/10/22}{Enlarged `@arstrutbox by `extrarowheight.
+%                        Thus you may avoid large characters to
+%                        overprint a `hline.}
+% \changes{v1.2c}{1987/10/22}{Introduced `m@th in `@array to allow
+%                         non-zero values of `mathsurround.}
+% \changes{v1.2d}{1987/11/02}{Completed the documentation.}
+% \changes{v1.2e}{1987/11/03}{Bug fixed: A at start of preamble resulted
+%                        in an error since `@mkpream generated
+%                        `@arstrut \& ... as a preamble.}
+% \changes{v1.2f}{1987/11/09}{`@testpach documented.}
+%
+% \changes{v1.3a}{1987/11/11}{Again a new implementation, with a new
+%                        concept (cf. the documentation).}
+% \changes{v1.3b}{1988/03/17}{`@decl expands now into `@empty, i.e., it
+%                        disappears when the preamble is generated,
+%                        except when the user specifies A\{\} or
+%                        B\{\}.}
+%
+% \changes{v1.4a}{1988/03/18}{Test implementation of use of token
+%                        registers in order to do without `protect.}
+% \changes{v1.4b}{1988/03/19}{Changed erroneous class numbers:
+%                        5 -!> 6
+%                        6 -!> 7
+%                        7 -!> 5
+%                        Corresponding changes in the macros.}
+% \changes{v1.4c}{1988/03/19}{Everything except p,z now works with token
+%                        registers.}
+%
+% \changes{v1.9a}{1988/03/20}{Last (so I hope) major change: 1) Options
+%                        B,A now called !>,<.  These options now point
+%                        to the column they modify.}
+% \changes{v1.9a}{1988/03/20}{2) `protect is no longer necessary. But
+%                           still the macro `@expast needs top be
+%                          modified. `multicolumn still does not work.}
+% \changes{v1.9b}{1988/04/29}{inserted missing `fi in `@testpach.
+%                        Corrected \LaTeX bug in `@tfor.}
+% \changes{v1.9c}{1988/05/07}{Re-introduced `@endpbox.
+%                        `multicolumn now works!! Version number still
+%                        1.9 since the documentation is still not
+%                        finished.}
+% \changes{v1.9c}{1988/05/07}{1) `def `the@toks \{`the ...\} remaining
+%                         only in `@mkpream.  2) Removed `@classiii and
+%                        replaced by `save@decl.}
+% \changes{v1.9c}{1988/05/07}{3) `insert@column contains only `@tempcnta
+%                        and `count@ counters.  4) `@@startpbox and
+%                        `@@endpbox now totally obsolete.}
+% \changes{v1.9d}{1988/05/10}{Replaced `number by `the where the `toks
+%                        registers' contents are used.}
+% \changes{v1.9e}{1988/05/11}{Re-introduced `@xargarraycr and
+%                        `@yargarraycr, since `endtemplate seems to
+%                        be `outer.}
+% \changes{v1.9f}{1988/05/20}{Small changes finally carried out:
+%                        1) `par!=`@empty.
+%                        2) \{..ifnum0!=!`\}...  $\to$ `bgroup and
+%                           analogously `egroup.}
+% \changes{v1.9g}{1988/02/24}{Inserted again \{..ifnum0!=!`\}..,
+%                        c.f. Appendix D of the \protect\TeX{}book.}
+% \changes{v1.9h}{1988/06/28}{No longer necessary to read in the file
+%                        twice.}
+% \changes{v1.9i}{1988/06/28}{Corrected typo in german version.}
+% \changes{v1.9j}{1988/11/23}{In a `r' column an extra `kern`z@ is
+%                        needed.}
+% \changes{v1.9j}{1988/11/23}{Otherwise the `hfil on the left side
+%                        will be removed by the `unskip in
+%                        `insert@column if the entry is empty.}
+% \changes{v1.9k}{1988/06/28}{Corrected typo in german version.}
+% \changes{v1.9k}{1989/01/16}{`begin{Macro} changed to `begin{macro} in
+%                        documentation.}
+%
+% \changes{v2.0a}{1989/05/12}{{\tt\textbackslash @thetoks} changed to
+%                          {\tt\textbackslash the@toks}.}
+% \changes{v2.0a}{1989/05/12}{source changed to reflect new doc.sty
+%                          conventions.}
+% \changes{v2.0a}{1989/05/12}{t option renamed to p to be compatible to
+%                        the original.}
+% \changes{v2.0a}{1989/05/12}{File renamed from arraye.sty to
+%                        array.sty.}
+% \changes{v2.0b}{1989/05/17}{Three forgotten end macro added.}
+% \changes{v2.0b}{1989/05/17}{All lines shortened to 72 or less.}
+% \changes{v2.2a}{1994/02/03}{Upgrade to \LaTeXe}
+%
+% \DoNotIndex{\@depth,\@ehc,\@fortmp,\@height,\@ifnextchar,\@ifstar}
+% \DoNotIndex{\@ifundefined,\@ne,\@nil,\@tempa,\@tempb}
+% \DoNotIndex{\@tempcnta,\@tempd,\@tempdima,\@whilenum,\@width,\\}
+% \DoNotIndex{\@tforloop}
+% \DoNotIndex{\advance}
+% \DoNotIndex{\baselineskip,\begingroup,\bgroup}
+% \DoNotIndex{\cr,\crcr,\csname}
+% \DoNotIndex{\def,\do,\docdate,\dp}
+% \DoNotIndex{\edef,\egroup,\else,\endcsname,\endinput,\expandafter}
+% \DoNotIndex{\fi,\filedate,\fileversion}
+% \DoNotIndex{\gdef}
+% \DoNotIndex{\hbox,\hfil,\hsize,\hskip,\ht}
+% \DoNotIndex{\if,\ifcase,\ifdim,\ifnum,\ifx,\ignorespaces}
+% \DoNotIndex{\kern}
+% \DoNotIndex{\leavevmode,\let,\lineskip}
+% \DoNotIndex{\m@ne,\multispan}
+% \DoNotIndex{\newcount,\newdimen,\noalign}
+% \DoNotIndex{\or}
+% \DoNotIndex{\relax}
+% \DoNotIndex{\setbox,\space,\strutbox}
+% \DoNotIndex{\tabskip,\thr@@,\the,\toks,\toks@,\tw@,\typeout}
+% \DoNotIndex{\unhcopy,\unskip}
+% \DoNotIndex{\vbox,\vcenter,\vline,\vrule,\vtop,\vskip}
+% \DoNotIndex{\xdef}
+% \DoNotIndex{\z@}
+%
+% \GetFileInfo{array.sty}
+%
+% \title{A new implementation of \LaTeX's \textsf{tabular}
+%        and \textsf{array} environment\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{Frank Mittelbach
+%         \and
+%         David Carlisle\thanks{David kindly agreed on the inclusion
+%         of the \texttt{\textbackslash{}newcolumntype} implementation,
+%         formerly in
+%         \texttt{newarray.sty} into this package }}
+%
+% \date{Printed \today}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \MakeShortVerb{\=}
+%
+% \begin{abstract}
+% This article describes an extended implementation of the \LaTeX\
+% \textsf{array}-- and \textsf{tabular}--environments. The special
+% merits of this implementation are further options to format columns
+% and the fact that fragile \LaTeX--commands don't have to be
+% =\protect='ed any more within those environments.
+%
+% The major part of the code for this package dates back to 1988---so
+% does some of its documentation.
+% \end{abstract}
+%
+%
+%
+% \section{Introduction}
+%
+% This new implementation of the \textsf{array}-- and
+% \textsf{tabular}--environments is part of a larger project in which
+% we are trying to improve the \LaTeX\--code in some aspects and to
+% make \LaTeX\ even easier to handle.
+%
+% The reader should be familiar with the general structure of the
+% environments
+% mentioned above. Further information can be found in
+% \cite{bk:lamport} and \cite{bk:GMS94}.
+% The additional options which can be used in the
+% preamble as well as those which now have a slightly different meaning
+% are described in table~\ref{tab:opt}.
+%
+% \DescribeMacro\extrarowheight
+% Additionally we introduce a new
+% parameter called =\extrarowheight=. If it takes a positive
+% length, the value of the parameter is added to the normal height of
+% every row of the table, while
+% the depth will remain the same. This is important for tables
+% with horizontal lines because those lines normally touch the
+% capital letters.
+% For example, we used =\setlength{\extrarowheight}{1pt}=
+% in table~\ref{tab:opt}.
+%
+% \begin{table}[!t]
+% \begin{center}
+%    \setlength{\extrarowheight}{1pt}
+%    \begin{tabular}{|>{\tt}c|m{9cm}|}
+%       \hline
+%     \multicolumn{2}{|c|}{Unchanged options}\\
+%       \hline
+%       l             &  Left adjusted column. \\
+%       c             &  Centered adjusted column. \\
+%       r             &  Right adjusted column. \\
+%       p\{width\}    &  Equivalent to =\parbox[t]{width}=. \\
+%       @\{decl.\}    &  Suppresses inter-column space and inserts
+%                        \texttt{decl.}\ instead. \\
+%       \hline
+%     \multicolumn{2}{|c|}{New options}\\
+%       \hline
+%       m\{width\}    &  Defines a column of width \texttt{width}.
+%                        Every entry will be centered in proportion to
+%                        the rest of the line. It is somewhat like
+%                        =\parbox{width}=. \\
+%       \hline
+%       b\{width\}    &  Coincides with =\parbox[b]{width}=. \\
+%       \hline
+%       >\{decl.\}    &  Can be used before an \texttt{l}, \texttt{r},
+%                        \texttt{c}, \texttt{p}, \texttt{m} or a
+%                        \texttt{b} option. It inserts \texttt{decl.}\
+%                        directly in front of the entry of the column.
+%                        \\
+%       \hline
+%       <\{decl.\}    &  Can be used after an \texttt{l}, \texttt{r},
+%                        \texttt{c}, =p{..}=, =m{..}= or a =b{..}=
+%                        option.  It inserts \texttt{decl.}\ right
+%                        after the entry of the column.  \\
+%       \hline
+%       |             &  Inserts a vertical line. The distance between
+%                        two columns will be enlarged by the width of
+%                        the line
+%                        in contrast to the original definition of
+%                        \LaTeX.  \\
+%       \hline
+%       !\{decl.\}    &  Can be used anywhere and corresponds with the
+%                        \texttt{|} option. The difference is that
+%                        \texttt{decl.} is inserted instead of a
+%                        vertical line, so this option doesn't
+%                        suppress the normally inserted space between
+%                        columns in contrast to =@{...}=.\\
+%       \hline\hline
+%       w\{align\}\{width\} & Sets the cell content in a box of the
+%                        specified \texttt{width} aligned according to
+%                        the \texttt{align} parameter which could be 
+%                        either \texttt{l}, \texttt{c} or
+%                        \texttt{r}. Works essentially like
+%                        =\makebox[=width=][=align=]{=cell=}= so
+%                        silently overprints if the cell content is
+%                        wider than the specified width. If that is
+%                        not desired use \texttt{W} instead.\\
+%       \hline
+%       W\{align\}\{width\} & Like \texttt{w} but spits out an overfull
+%                        box warning (and an overfullrule marker in
+%                        draft mode) when the cell content is too wide
+%                        to fit. This also means that the alignment is
+%                        different if there is too much material,
+%                        because it then always protrudes to the right!\\
+%       \hline
+%    \end{tabular}
+% \end{center}
+% \caption{The  preamble options.} \label{tab:opt}
+% \end{table}
+%
+%
+% We will discuss a few examples using the new preamble options before
+% dealing with the implementation.
+% \begin{itemize}
+%    \item
+%       If you want to use a special font (for example =\bfseries=) in a
+%       flushed left column, this can be done with =>{\bfseries}l=. You
+%       do not have to begin every entry of the column with  =\bfseries=
+%       any more.
+%    \item
+%       In columns which have been generated with \texttt{p}, \texttt{m}
+%       or \texttt{b}, the default value of =\parindent= is
+%       \textsf{0pt}.
+%       This can be changed with \\
+%       =>{\setlength{\parindent}{1cm}}p=.
+%    \item
+%       The \texttt{>}-- and \texttt{<}--options were originally
+%       developed for the following application:
+%       =>{$}c<{$}= generates a column in math
+%       mode in a \textsf{tabular}--environment. If you use this type
+%       of a preamble in an \textsf{array}--environment, you get a
+%       column in LR mode because the additional \$'s cancel the
+%       existing \$'s.
+%    \item
+%       One can also think of more complex applications. A problem
+%       which has
+%       been mentioned several times in \TeX{}hax can be solved with
+%       =>{\centerdots}c=\linebreak[0]=<{\endcenterdots}=.
+%       To center decimals at their
+%       decimal points you (only?) have to define the following macros:
+%       \begin{verbatim}
+%{\catcode`\.\active\gdef.{\egroup\setbox2\hbox\bgroup}}
+%\def\centerdots{\catcode`\.\active\setbox0\hbox\bgroup}
+%\def\endcenterdots{\egroup\ifvoid2 \setbox2\hbox{0}\fi
+%   \ifdim \wd0>\wd2 \setbox2\hbox to\wd0{\unhbox2\hfill}\else
+%     \setbox0\hbox to\wd2{\hfill\unhbox0}\fi
+%   \catcode`\.12 \box0.\box2}
+%\end{verbatim}
+%      Warning: The code is bad, it doesn't work with more than one
+%      dot in a cell and doesn't work when the tabular is used in the
+%      argument of some other command. A much better version is
+%      provided in the \texttt{dcolumn.sty} by David Carlisle.
+%    \item
+%       Using =c!{\hspace{1cm}}c= you get space between two
+%       columns which is enlarged by one centimeter, while
+%       =c@{\hspace{1cm}}c= gives you exactly one centimeter
+%       space between two columns.
+%
+%    \item
+%       A declaration like =w{l}{3cm}= (or even shorter =wl{3cm}=)
+%       works like an =l= column except that the width will always be
+%       =3cm= regardless of the cell content. Same with =w{c}= or
+%       =w{r}=. This means that it is easy to set up tables in which all
+%       columns have predefined widths.
+% \end{itemize}
+%
+% \subsection{Defining new column specifiers}
+%
+% \DeleteShortVerb{\=}
+% \MakeShortVerb{\"}
+% \DescribeMacro{\newcolumntype}
+% Whilst it is handy to be able to type
+% \begin{quote}
+%   ">{"\meta{some declarations}"}{c}<{"\meta{some more
+%   declarations}"}"
+% \end{quote}
+% if you have a one-off column in a table, it is rather inconvenient
+% if you often use columns of this form. The new version allows you
+% to define a new column specifier, say \texttt{x}, which will expand to
+% the primitives column specifiers.\footnote{This command was named
+% \texttt{\textbackslash{}newcolumn} in the \texttt{newarray.sty}.
+% At the moment \texttt{\textbackslash{}newcolumn} is still supported
+% (but gives a warning). In later releases it will vanish.} Thus we
+% may define
+% \begin{quote}
+%   "\newcolumntype{x}{>{"\meta{some declarations}"}{c}<{"\meta{some
+%   more declarations}"}}"\hspace*{-3cm} ^^A no overfull from this line
+% \end{quote}
+% One can then use the \texttt{x} column specifier in the preamble
+% arguments of all \texttt{array} or \texttt{tabular} environments in
+% which you want columns of this form.
+%
+% It is common  to need math-mode and LR-mode columns in the same
+% alignment. If we define:
+% \begin{quote}
+%   "\newcolumntype{C}{>{$}c<{$}}" \\
+%   "\newcolumntype{L}{>{$}l<{$}}" \\
+%   "\newcolumntype{R}{>{$}r<{$}}"
+% \end{quote}
+% Then we can use \texttt{C} to get centred LR-mode in an
+% \texttt{array}, or centred math-mode in a \texttt{tabular}.
+%
+% The example given above for `centred decimal points' could be
+% assigned to a \texttt{d} specifier with the following command.
+% \begin{quote}
+% "\newcolumntype{d}{>{\centerdots}c<{\endcenterdots}}"
+% \end{quote}
+%
+% The above solution always centres the dot in the
+% column. This does not look too good if the column consists of large
+% numbers, but to only a few decimal places. An alternative definition
+% of a \texttt{d} column is
+% \begin{quote}
+%   "\newcolumntype{d}[1]{>{\rightdots{#1}}r<{\endrightdots}}"
+% \end{quote}
+% where the appropriate macros in this case are:\footnote{The package
+% \texttt{dcolumn.sty} contains more robust macros based on these
+% ideas.}
+% \begin{verbatim}
+%   \def\coldot{.}% Or if you prefer, \def\coldot{\cdot}
+%   {\catcode`\.=\active
+%     \gdef.{$\egroup\setbox2=\hbox to \dimen0 \bgroup$\coldot}}
+%   \def\rightdots#1{%
+%     \setbox0=\hbox{$1$}\dimen0=#1\wd0
+%     \setbox0=\hbox{$\coldot$}\advance\dimen0 \wd0
+%     \setbox2=\hbox to \dimen0 {}%
+%     \setbox0=\hbox\bgroup\mathcode`\.="8000 $}
+%   \def\endrightdots{$\hfil\egroup\box0\box2}
+%\end{verbatim}
+% Note that "\newcolumntype" takes the same optional argument as
+% "\newcommand" which declares the number of arguments of the column
+% specifier being defined. Now we can specify "d{2}" in our preamble
+% for a column of figures to at most two decimal places.
+%
+% A rather different use of the "\newcolumntype" system takes
+% advantage of the fact that the replacement text in the
+% "\newcolumntype" command may refer to more than one column. Suppose
+% that a document contains a lot of \texttt{tabular} environments that
+% require the same preamble, but you wish to experiment with different
+% preambles. Lamport's original definition allowed you to do the
+% following (although it was probably a mis-use of the system).
+% \begin{quote}
+%   "\newcommand{\X}{clr}"\\
+%   "\begin{tabular}{\X}" \ldots
+% \end{quote}
+% \texttt{array.sty} takes great care \textbf{not} to expand the
+% preamble, and so the above does not work with the new scheme. With
+% the new version this functionality is returned:
+% \begin{quote}
+% "\newcolumntype{X}{clr}"\\
+% "\begin{tabular}{X}" \ldots
+% \end{quote}
+%
+% The replacement text in a "\newcolumntype" command may refer to any of
+% the primitives of \texttt{array.sty} see table \ref{tab:opt} on page
+% \pageref{tab:opt}, or to any new letters defined in other
+% "\newcolumntype" commands.
+%
+%
+% \DescribeMacro{\showcols}A list of all the currently active
+% "\newcolumntype" definitions is sent to the terminal and log file if
+% the "\showcols" command is given.
+%
+%
+% \subsection{Special variations of \texttt{\textbackslash hline}}
+%
+% The family of \texttt{tabular} environments allows
+% vertical positioning with respect to the baseline of
+% the text in which the environment appears.  By default the
+% environment appears centered, but this can be changed to
+% align with the first or last line in the environment by
+% supplying a \texttt{t} or \texttt{b} value to the
+% optional position argument. However, this does not work
+% when the first or last element in the environment is a
+% "\hline" command---in that case the environment is
+% aligned at the horizontal rule.
+%
+% \pagebreak[3]
+%
+% Here is an example:
+% \begin{center}
+% \begin{minipage}[t]{.4\linewidth}
+% Tables
+% \begin{tabular}[t]{l}
+%   with no\\ hline \\ commands \\ used
+% \end{tabular} versus \\ tables
+% \begin{tabular}[t]{|l|}
+%  \hline
+%   with some \\ hline \\ commands \\
+%  \hline
+% \end{tabular} used.
+% \end{minipage}
+% \begin{minipage}[t]{.5\linewidth}
+% \begin{verbatim}
+% Tables
+% \begin{tabular}[t]{l}
+%  with no\\ hline \\ commands \\ used
+% \end{tabular} versus tables
+% \begin{tabular}[t]{|l|}
+%  \hline
+%   with some \\ hline \\ commands \\
+%  \hline
+% \end{tabular} used.
+% \end{verbatim}
+% \end{minipage}
+% \end{center}
+%
+% \DescribeMacro\firsthline
+% \DescribeMacro\lasthline
+% Using "\firsthline" and "\lasthline" will
+% cure the problem, and the tables will align properly as long
+% as their first or last line does not contain extremely large
+% objects.
+% \begin{center}
+% \begin{minipage}[t]{.4\linewidth}
+% Tables
+% \begin{tabular}[t]{l}
+%   with no\\ line \\ commands \\ used
+% \end{tabular} versus \\ tables
+% \begin{tabular}[t]{|l|}
+%  \firsthline
+%   with some \\ line   \\ commands \\
+%  \lasthline
+% \end{tabular} used.
+% \end{minipage}
+% \begin{minipage}[t]{.5\linewidth}
+% \begin{verbatim}
+% Tables
+% \begin{tabular}[t]{l}
+%   with no\\ line \\ commands \\ used
+% \end{tabular} versus tables
+% \begin{tabular}[t]{|l|}
+%  \firsthline
+%   with some \\ line   \\ commands \\
+%  \lasthline
+% \end{tabular} used.
+% \end{verbatim}
+% \end{minipage}
+% \end{center}
+% \DescribeMacro\extratabsurround
+% The implementation of these two commands contains an extra
+% dimension, which is called "\extratabsurround", to add some
+% additional space at the top and the bottom of such an environment.
+% This is useful if such tables are nested.
+%
+% \section{Final Comments}
+%
+% \subsection{Handling of rules}
+%
+% There are two possible approaches to the handling of horizontal and
+% vertical rules in tables:
+% \begin{enumerate}
+%   \item rules can be placed into the available space without
+%   enlarging the table, or
+%   \item rules can be placed between columns or rows thereby enlarging
+%   the table.
+% \end{enumerate}
+% \texttt{array.sty} implements the second possibility while the
+% default implementation in the \LaTeX{} kernel implements the first
+% concept. Both concepts have their merits but one has to be aware of
+% the individual implications.
+% \begin{itemize}
+% \item
+%   With standard \LaTeX{} adding rules to a table will not affect the
+%   width or height of the table (unless double rules are used), e.g.,
+%   changing a preamble from \verb=lll= to \verb=l|l|l= does not
+%   affect the document other than adding rules to the table. In
+%   contrast, with \texttt{array.sty} a table that just fit the
+%   \verb=\textwidth= might now produce an overfull box.
+% \item
+%   With standard \LaTeX{} modifying the width of rules could result
+%   in ugly looking tables because without adjusting the
+%   \verb=\tabcolsep=, etc.\ the space between rule and column could
+%   get too small (or too large). In fact even overprinting of text is
+%   possible. In contrast, with  \texttt{array.sty} modifying any such
+%   length usually works well as the actual visual white space (from
+%   \verb=\tabcolsep=, etc.) does not depend on the width of the
+%   rules.
+% \item
+%   With standard \LaTeX{} boxed tabulars actually have strange
+%   corners because the horizontal rules end in the middle of the
+%   vertical ones. This looks very unpleasant when a large
+%   \verb=\arrayrulewidth= is chosen. In that case a simple table like
+%\begin{verbatim}
+%\setlength{\arrayrulewidth}{5pt}
+%\begin{tabular}{|l|}
+%  \hline  A \\  \hline
+%\end{tabular}
+%\end{verbatim}
+%   will produce something like
+%   \begin{center}
+%\setlength{\arrayrulewidth}{5pt}
+%\begin{tabular}{@{}l@{}}
+%  \hline  \null\hskip-.5\arrayrulewidth\vline
+%  \hskip\tabcolsep
+%   A\hskip\tabcolsep
+%  \vline\hskip-.5\arrayrulewidth\null \\  \hline
+%\end{tabular}
+%   \quad
+%   instead of
+%   \quad
+%\begin{tabular}{|l|}
+%  \hline  A \\  \hline
+%\end{tabular}
+%   \end{center}
+% \end{itemize}
+%
+% \subsection{Comparisons with older versions of \texttt{array.sty}}
+%
+% There are some differences in the way version 2.1 treats incorrect
+% input, even if the source file does not appear to use any of the
+% extra features of the new version.
+% \begin{itemize}
+% \item A preamble of the form "{wx*{0}{abc}yz}" was treated by
+% versions prior to 2.1 as "{wx}". Version 2.1 treats it as "{wxyz}"
+% \item An incorrect positional argument such as \texttt{[Q]} was
+% treated as \texttt{[c]} by \texttt{array.sty}, but is now treated as
+% \texttt{[t]}.
+% \item A preamble such as "{cc*{2}}" with an error in
+% a $*$-form will generate different errors in the new version. In
+% both cases the error message is not particularly helpful to the
+% casual user.
+% \item Repeated \texttt{<} or \texttt{>} constructions
+% generated an error in earlier versions, but are now allowed in
+% this package.  ">{"\meta{decs1}"}>{"\meta{decs2}"}" is treated the
+% same as ">{"\meta{decs2}\meta{decs1}"}".
+% \item The "\extracolsep"
+% command does not work with the old versions of \texttt{array.sty},
+% see the comments in \texttt{array.bug}. With version 2.1
+% "\extracolsep" may again be used in \texttt{@}-expressions as in
+% standard \LaTeX, and also in \texttt{!}-expressions (but see the
+% note below).
+% \end{itemize}
+%
+% Prior to version 2.4f the space added by the optional argument to "\\"
+% was added inside an m-cell if the last column was of type
+% \texttt{m}. As a result that cell was vertically centered with that
+% space inside, resulting in a strange offset. Since 2.4f, this space
+% is now added after centering the cell.
+% 
+% A similar problem happened when "\extrarowheight" was used. For that
+% reason m-cells now manually position the cell content which
+% allows to ignore this extra space request during the vertical aligment. 
+%
+%
+% \subsection{Bugs and Features}
+%
+% \begin{itemize}
+% \item Error messages generated when parsing the column specification
+%   refer to the preamble argument \textbf{after} it has been re-written
+%   by the "\newcolumntype" system, not to the preamble entered by the
+%   user.  This seems inevitable with any system based on
+%   pre-processing and so is classed as a \textbf{feature}.
+%
+% \item The treatment of multiple \texttt{<} or \texttt{>}
+%   declarations may seem strange at first. Earlier implementations
+%   treated ">{"\meta{decs1}"}>{"\meta{decs2}"}" the same as
+%   ">{"\meta{decs1}\meta{decs2}"}". However this did not give the
+%   user the opportunity of overriding the settings of a
+%   "\newcolumntype" defined using these declarations. For example,
+%   suppose in an \texttt{array} environment we use a \texttt{C}
+%   column defined as above. The \texttt{C} specifies a centred text
+%   column, however ">{\bfseries}C", which re-writes to
+%   ">{\bfseries}>{$}c<{$}" would not specify a bold column as might
+%   be expected, as the preamble would essentially expand to
+%   "\hfil$\bfseries$#$ $\hfil" and so the column entry would not be in the
+%   scope of the "\bfseries"\,! The present version switches the order
+%   of repeated declarations, and so the above example now produces a
+%   preamble of the form "\hfil$" "$\bfseries#$" "$\hfil", and the
+%   dollars cancel each other out without limiting the scope of the
+%   "\bfseries".
+%
+% \item The use of "\extracolsep" has been subject to the following
+%   two restrictions.  There must be at most one "\extracolsep"
+%   command per "@", or "!" expression and the command must be
+%   directly entered into the "@" expression, not as part of a macro
+%   definition. Thus "\newcommand{\ef}{\extracolsep{\fill}}" \ldots
+%   "@{\ef}" does not work with this package. However you can use
+%   something like
+%   "\newcolumntype{e}{@{\extracolsep{\fill}}" instead.
+%
+% \item As noted by the \LaTeX{} book, for the purpose of
+%   "\multicolumn" each column with the exception of the first one
+%   consists of the entry and the \emph{following} inter-column
+%   material. This means that in a tabular with the preamble
+%   "|l|l|l|l|" input such as "\multicolumn{2}{|c|}" in
+%   anything other than the first column is incorrect.
+
+%   In the standard array/tabular implementation this error is not so
+%   noticeable as that version contains negative spacing so that each
+%   "|" takes up no horizontal space. But since in this package the
+%   vertical lines take up their natural width one sees two lines if
+%   two are specified.
+%
+% \end{itemize}
+%
+%
+%
+% \changes{v2.2b}{1994/02/04}{Removed interactive prompt}
+%
+% \StopEventually{
+%
+%
+% \begin{thebibliography}{1}
+%    \bibitem{bk:GMS94} \textsc{M.~Goossens}, \textsc{F.~Mittelbach}
+%       and \textsc{A.~Samarin}.
+%       \newblock The \LaTeX{} Companion.
+%       \newblock
+%       Addison-Wesley, Reading, Massachusetts, 1994.
+%    \bibitem{bk:knuth}  \textsc{D. E. Knuth}.
+%       \newblock  The \TeX{}book (Computers \& Typesetting Volume A).
+%       \newblock
+%       Addison-Wesley, Reading, Massachusetts, 1986.
+%    \bibitem{bk:lamport} \textsc{L. Lamport}.
+%       \newblock
+%       \LaTeX\ --- A Document Preparation System.
+%       \newblock
+%       Addison-Wesley, Reading, Massachusetts, 1986.
+% \end{thebibliography}
+%
+% }   ^^A  end of \StopEventually
+%
+%
+%
+%
+% \section{The documentation driver file}
+%
+% The first bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the
+% \texttt{docstrip} program.
+%    \begin{macrocode}
+%<*driver>
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\documentclass{ltxdoc}
+
+\AtBeginDocument{\DeleteShortVerb{\|}}  % undo the default is not used
+
+ \usepackage{array}
+
+ % Allow large table at bottom
+ \renewcommand{\bottomfraction}{0.7}
+
+\EnableCrossrefs
+ %\DisableCrossrefs   % Say \DisableCrossrefs if index is ready
+
+\RecordChanges                  % Gather update information
+
+\CodelineIndex                  % Index code by line number
+
+ %\OnlyDescription    % comment out for implementation details
+ %\OldMakeindex       % use if your MakeIndex is pre-v2.9
+\begin{document}
+   \DocInput{array.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+%
+% \section{The construction of the preamble}
+%
+% \DeleteShortVerb{\"}
+% \MakeShortVerb{\=}
+%
+% It is obvious that those environments will consist mainly of an
+% =\halign=, because \TeX\ typesets tables using this primitive.
+% That is why we will now take a look at the algorithm which determines
+% a preamble for a =\halign= starting with a given user preamble
+% using the options mentioned above.
+%
+%
+%    The current version is defined at the top of the file looking
+%    something like this
+%    \begin{macrocode}
+%<*package>
+%\NeedsTeXFormat{LaTeX2e}[1994/05/13]
+%\ProvidesPackage{array}[\filedate\space version\fileversion]
+%    \end{macrocode}
+%
+% The most interesting macros of this implementation are without doubt
+% those which are responsible for the construction of the preamble for
+% the =\halign=. The underlying algorithm was developed by
+% \textsc{Lamport} (resp.\ \textsc{Knuth}, see texhax V87\#??), and it
+% has been extended and improved.
+%
+% The user preamble will be read \textsf{token} by \textsf{token}.  A
+% \textsf{token} is a single character like \texttt{c} or a block
+% enclosed in ={...}=. For example the preamble of
+% =\begin{tabular}=\linebreak[0]={lc||c@{\hspace{1cm}}}= consists of
+% the \textsf{token} \texttt{l}, \texttt{c}, \texttt{|}, \texttt{|},
+% \texttt{@} and =\hspace{1cm}=.
+%
+% The currently used \textsf{token} and the one, used before, are needed
+% to decide on how the construction of the preamble has to be
+% continued.
+% In the example mentioned above the \texttt{l} causes the preamble
+% to begin with =\hskip\tabcolsep=. Furthermore
+% =# \hfil= would be appended to define a flush left column.
+% The next \textsf{token} is a \texttt{c}. Because it was preceded by an
+% \texttt{l} it generates a new column. This is done with
+% =\hskip \tabcolsep & \hskip \tabcolsep=. The column which is to
+% be centered will be appended with =\hfil # \hfil=.
+% The \textsf{token} \texttt{|} would then add a space of
+% =\hskip \tabcolsep=
+% and a vertical line because the last
+% \textsf{tokens} was a \texttt{c}.
+% The following \textsf{token} \texttt{|} would only add a space
+% =\hskip \doublerulesep= because it was preceded by the
+% \textsf{token} \texttt{|}. We will not discuss our example further but
+%  rather take a look at the general case of constructing preambles.
+%
+% The example shows that the desired preamble for the
+% =\halign= can be constructed as soon as the action of all
+% combinations
+% of the preamble \textsf{tokens} are specified. There are 18 such
+% \textsf{tokens}
+% so we have $19 \cdot 18 \string= 342$ combinations if we count the
+% beginning of
+% the preamble as a special \textsf{token}. Fortunately, there are many
+% combinations which generate the same spaces, so we can define
+% \textsf{token} classes. We will identify a
+% \textsf{token} within a class with a number, so we can insert the
+% formatting (for example of a column).
+% Table~\ref{tab:Klassen} lists all \textsf{token} classes and
+% their corresponding numbers.
+% \begin{table}[ht]
+% \begin{center}
+%    \begin{tabular}[t]{>{\ttfamily}ccc}
+%       \textsf{token} & =\@chclass= & =\@chnum= \\[2mm]
+%       c   & 0  & 0 \\
+%       l   & 0  & 1 \\
+%       r   & 0  & 2 \\
+%       p-arg    & 0  & 3 \\
+%       t-arg    & 0  & 4 \\
+%       b-arg    & 0  & 5 \\
+%       |   & 1  & 0 \\
+%       !-arg    & 1  & 1 \\
+%       <-arg    & 2  & --- \\
+%       >-arg    & 3  & ---
+%    \end{tabular}
+%    \kern3mm \vrule \kern3mm%
+%    \begin{tabular}[t]{>{\ttfamily}ccc}
+%       \textsf{token} & =\@chclass= & =\@chnum= \\[2mm]
+%       Start    & 4  & --- \\
+%       @-arg    & 5  & --- \\
+%       !   & 6  & --- \\
+%       @   & 7  & --- \\
+%       <   & 8  & --- \\
+%       >   & 9  & --- \\
+%       p   & 10 & 3 \\
+%       t   & 10 & 4 \\
+%       b   & 10 & 5
+%    \end{tabular}
+% \end{center}
+% \caption{Classes of preamble \textsf{tokens}}
+% \label{tab:Klassen}
+% \end{table}
+%
+%
+% \begin{macro}{\@chclass}
+% \begin{macro}{\@chnum}
+% \begin{macro}{\@lastchclass}
+%    The class and the number of the current \textsf{token} are saved in
+%    the
+%    \textsf{count} registers =\@chclass=
+%    and =\@chnum=, while the class of the previous
+%    \textsf{token} is stored in the
+%    \textsf{count} register =\@lastchclass=.
+%    All of the mentioned registers are already allocated in
+%    \texttt{latex.tex},
+%    which is the reason why the following three lines of code are
+%    commented out.
+%    Later throughout the text I will not mention it again explicitly
+%    whenever I use a =%= sign. These parts are already defined in
+%    \texttt{latex.tex}.
+%    \begin{macrocode}
+% \newcount \@chclass
+% \newcount \@chnum
+% \newcount \@lastchclass
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\@addtopreamble}
+%    We will save the already constructed preamble for
+%    the =\halign=
+%    in the global macro =\@preamble=. This will then be
+%     enlarged with
+%    the command =\@addtopreamble=.
+%    \begin{macrocode}
+\def\@addtopreamble#1{\xdef\@preamble{\@preamble #1}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+%
+% \subsection{The character class of a \textsf{token}}
+%
+% \begin{macro}{\@testpach}
+% \changes{v2.0a}{1989/05/12}{p option renamed to m (middle).}
+% \changes{v2.0a}{1989/05/12}{t option renamed to p to be compatible to
+%                         the original.}
+%    With the help of =\@lastchclass= we can now define a macro
+%    which determines the class and the number of a given preamble
+%    \textsf{token}
+%    and assigns them to the registers
+%    =\@chclass= and =\@chnum=.
+% \changes{v2.0f}{1992/02/29}{Argument removed since implicitly known}
+%    \begin{macrocode}
+\def\@testpach{\@chclass
+%    \end{macrocode}
+%    First we deal with the cases in which the \textsf{token}
+%    (=#1=) is the argument of \texttt{!}, \texttt{@}, \texttt{<} or
+%    \texttt{>}. We can see this from the value of =\@lastchclass=:
+%    \begin{macrocode}
+ \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
+  \ifnum \@lastchclass=7 5 \else
+   \ifnum \@lastchclass=8 \tw@ \else
+    \ifnum \@lastchclass=9 \thr@@
+%    \end{macrocode}
+%    Otherwise we will assume that the \textsf{token} belongs to the
+%    class $0$
+%    and assign the corresponding number to =\@chnum= if our
+%    assumption is correct.
+%    \begin{macrocode}
+   \else \z@
+%    \end{macrocode}
+%    If the last \textsf{token} was a \texttt{p}, \texttt{m} or a
+%    \texttt{b}, =\@chnum= already has the right value. This is the
+%    reason for the somewhat curious choice of the \textsf{token}
+%    numbers in class $10$.
+%    \begin{macrocode}
+   \ifnum \@lastchclass = 10 \else
+%    \end{macrocode}
+%    Otherwise we will check if =\@nextchar= is either a \texttt{c},
+%    \texttt{l} or an \texttt{r}.  Some applications change the
+%    catcodes of certain characters like ``\texttt{@}'' in
+%    \texttt{amstex.sty}. As a result the tests below would fail since
+%    they assume non-active character tokens. Therefore we evaluate
+%    =\@nextchar= once thereby turning the first token of its
+%    replacement text into a char. At this point here this should have
+%    been the only char present in =\@nextchar= which put into via a
+%    =\def=.
+% \changes{v2.0f}{1992/02/29}{Ensure to test a char which is not active}
+%    \begin{macrocode}
+   \edef\@nextchar{\expandafter\string\@nextchar}%
+   \@chnum
+   \if \@nextchar c\z@ \else
+    \if \@nextchar l\@ne \else
+     \if \@nextchar r\tw@ \else
+%    \end{macrocode}
+%    If it is a different \textsf{token}, we know that the class was
+%    not $0$. We assign the value $0$ to =\@chnum= because this value
+%    is needed for the \texttt{|}--\textsf{token}. Now we must check
+%    the remaining classes.  Note that the value of =\@chnum= is
+%    insignificant here for most classes.
+%    \begin{macrocode}
+   \z@ \@chclass
+   \if\@nextchar |\@ne \else
+    \if \@nextchar !6 \else
+     \if \@nextchar @7 \else
+      \if \@nextchar <8 \else
+       \if \@nextchar >9 \else
+%    \end{macrocode}
+%    The remaining permitted \textsf{tokens} are \texttt{p},
+%    \texttt{m} and \texttt{b} (class $10$).
+%    \begin{macrocode}
+  10
+  \@chnum
+  \if \@nextchar m\thr@@\else
+   \if \@nextchar p4 \else
+    \if \@nextchar b5 \else
+%    \end{macrocode}
+%    Now the only remaining possibility is a forbidden \textsf{token},
+%    so we choose class $0$ and number $0$ and give an error message.
+%    Then we finish the macro by closing all =\if='s.
+%    \begin{macrocode}
+   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
+   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+%
+% \subsection{Multiple columns ($*$--form)}
+%
+% \begin{macro}{\@xexpast}
+% \begin{macro}{\the@toks}
+% \begin{macro}{\the@toksz}
+%    \label{@xexpast} Now we discuss the macro that deletes all forms
+%    of type =*{=\textit{N\/}=}{=\textit{String\/}=}= from a user
+%    preamble and replaces them with \textit{N} copies of
+%    \textit{String}.  Nested $*$--expressions are dealt with
+%    correctly, that means $*$--expressions are not substituted if
+%    they are in explicit braces, as in =@{*}=.
+%
+%    This macro is called via
+%    =\@xexpast=\meta{preamble}=*0x\@@=.
+%    The $*$--expression =*0x= is being used to terminate the
+%    recursion,
+%    as we shall see later, and =\@@= serves as an argument
+%    delimiter. =\@xexpast= has four arguments. The first
+%    one is the part of the
+%    user preamble before the first $*$--expression while the second
+%    and third ones are the arguments of the first $*$--expression
+%    (that is \textit{N} and \textit{String} in the notation mentioned
+%    above).
+%    The fourth argument is the rest of the preamble.
+%    \begin{macrocode}
+\def\@xexpast#1*#2#3#4\@@{%
+%    \end{macrocode}
+%    The number of copies of \textit{String} (=#2=) that are to be
+%    produced will be saved in a \textsf{count} register.
+%    \begin{macrocode}
+   \@tempcnta #2
+%    \end{macrocode}
+%    We save the part of the preamble which does not
+%    contain a $*$--form (=#1=)
+%    in a \PlainTeX\ \textsf{token} register.
+%    We also save \textit{String} (=#3=) using a \LaTeX\
+%    \textsf{token} register.
+%    \begin{macrocode}
+   \toks@={#1}\@temptokena={#3}%
+%    \end{macrocode}
+%    Now we have to use a little trick to produce \textit{N} copies of
+%    \textit{String}.
+%    We could try =\def\@tempa{#1}= and then
+%    \textit{N} times =\edef\@tempa{\@tempa#3}=. This would have the
+%    undesired effect that all macros within =#1= and =#3=
+%    would be expanded, although, for example, constructions like
+%    =@{..}= are not supposed to be changed.
+%    That is why we =\let= two control sequences to
+%    be equivalent to =\relax=.
+%    \begin{macrocode}
+   \let\the@toksz\relax \let\the@toks\relax
+%    \end{macrocode}
+%    Then we ensure that =\@tempa= contains
+%    ={\the@toksz\the@toks...\the@toks}= (the macro
+%    =\the@toks= exactly \textit{N\/} times) as substitution text.
+%    \begin{macrocode}
+   \def\@tempa{\the@toksz}%
+   \ifnum\@tempcnta >0 \@whilenum\@tempcnta >0\do
+     {\edef\@tempa{\@tempa\the@toks}\advance \@tempcnta \m@ne}%
+%    \end{macrocode}
+%    If \textit{N\/} was greater than zero we prepare for another call
+%    of =\@xexpast=. Otherwise we assume we have reached the end of
+%    the user preamble, because we had appended =*0x\@@= when we first
+%    called =\@xexpast=.  In other words: if the user inserts
+%    =*{0}{..}= in his preamble, \LaTeX\ ignores the rest of it.
+%    \begin{macrocode}
+       \let \@tempb \@xexpast \else
+       \let \@tempb \@xexnoop \fi
+%    \end{macrocode}
+%    Now we will make sure that the part of the user preamble, which
+%    was already dealt with, will be saved again in =\@tempa=.
+%    \begin{macrocode}
+   \def\the@toksz{\the\toks@}\def\the@toks{\the\@temptokena}%
+   \edef\@tempa{\@tempa}%
+%    \end{macrocode}
+%    We have now evaluated the first $*$--expression, and the user
+%    preamble up to this point
+%    is saved in =\@tempa=. We will put the contents of
+%    =\@tempa= and the rest of the user preamble together and work
+%    on the result with =\@tempb=. This macro either corresponds
+%    to =\@xexpast=, so that the next
+%    $*$--expression is handled, or to the macro =\@xexnoop=,
+%    which only ends the recursion by deleting its argument.
+%    \begin{macrocode}
+   \expandafter \@tempb \@tempa #4\@@}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@xexnoop}
+%    So the first big problem is solved. Now it is easy to
+%    specify =\@xexnoop=.
+%    Its argument is delimited by =\@@= and it simply expands to
+%    nothing.
+%    \begin{macrocode}
+%  \def\@xexnoop#1\@@{}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+% \section{The insertion of declarations
+%           (\texttt{>}, \texttt{<}, \texttt{!}, \texttt{@})}
+%
+%
+% The preamble will be enlarged with the help of =\xdef=, but the
+% arguments of \texttt{>}, \texttt{<},~\texttt{!}\ and \texttt{@} are
+% not supposed to be expanded during the construction (we want an
+% implementation that doesn't need a =\protect=). So we have to find a
+% way to inhibit the expansion of those arguments.
+%
+% We will solve this problem with \textsf{token} registers. We need
+% one register for every \texttt{!}\ and \texttt{@}, while we need two
+% for every \texttt{c}, \texttt{l}, \texttt{r}, \texttt{m}, \texttt{p}
+% or \texttt{b}. This limits the number of columns of a table because
+% there are only 256 \textsf{token} registers. But then, who needs
+% tables with more than 100 columns?
+%
+% One could also find a solution which only needs two or three
+% \textsf{token} registers by proceeding similarly as in the macro
+% =\@xexpast= (see page \pageref{@xexpast}). The advantage of our
+% approach is the fact that we avoid some of the problems that arise
+% with the other method\footnote{Maybe there are also historical
+%  reasons.}.
+%
+% So how do we proceed? Let us assume that we had =!{foo}= in the
+% user preamble and say we saved \texttt{foo} in
+% \textsf{token} register $5$. Then we call
+% =\@addtopreamble{\the@toks5}= where
+% =\the@toks= is defined in a way that it does not expand
+% (for example it could be equivalent to =\relax=). Every
+% following call
+% of =\@addtopreamble= leaves =\the@toks5= unchanged in
+% =\@preamble=. If the construction of the preamble is completed
+% we change the definition of =\the@toks= to
+% =\the\toks= and expand =\@preamble= for the last time.
+% During this process all parts of the form
+%    =\the@toks=\meta{Number}
+% will be substituted by the contents of the respective \textsf{token}
+% registers.
+%
+% As we can see from this informal discussion the construction of the
+% preamble has to take place within a group, so that the
+% \textsf{token} registers we use will be freed later on. For that
+% reason we keep all assignments to =\@preamble= global; therefore the
+% replacement text of this macro will remain the same after we leave
+% the group.
+%
+% \begin{macro}{\count@}
+%    We further need a \textsf{count} register to remember which
+%    \textsf{token} register is to be used next. This will be
+%    initialized with $-1$ if we want to begin with the \textsf{token}
+%    register $0$. We use the \PlainTeX\ scratch register =\count@=
+%    because everything takes place locally. All we have to do is
+%    insert =\the@toks= =\the= =\count@= into the preamble.
+%    =\the@toks= will remain unchanged and =\the\count@= expands into
+%    the saved number.
+% \end{macro}
+%
+% \begin{macro}{\prepnext@tok}
+%    The macro =\prepnext@tok= is in charge of preparing the next
+%    \textsf{token} register. For that purpose we increase
+%    =\count@= by $1$:
+%    \begin{macrocode}
+\def\prepnext@tok{\advance \count@ \@ne
+%    \end{macrocode}
+%    Then we locally delete any contents the
+%    \textsf{token} register might have.
+%    \begin{macrocode}
+   \toks\count@{}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\save@decl}
+%    During the construction of the preamble the current
+%    \textsf{token} is always saved in the macro =\@nextchar= (see the
+%    definition of =\@mkpream= on page \pageref{@mkpream}). The macro
+%    =\save@decl= saves it into the next free \textsf{token} register,
+%    i.e.\ in =\toks\count@=.
+% \changes{v2.0c}{1990/08/14}{\cs{relax} removed and added elsewhere.}
+%    \begin{macrocode}
+\def\save@decl{\toks\count@ \expandafter{\@nextchar}}
+%    \end{macrocode}
+%    The reason for the  use of =\relax= is the following
+%    hypothetical situation in the preamble:
+%    \quad =..\the\toks1\the\toks2..= \quad \TeX\ expands
+%    =\the\toks2= first in order to find out if the digit =1=
+%    is followed by other digits. E.g.\ a =5= saved in the
+%    \textsf{token} register $2$ would lead \TeX\ to insert the contents
+%    of \textsf{token} register $15$ instead of $1$ later on.
+%
+% The example above referred to an older version of =\save@decl= which
+% inserted a =\relex= inside the token register. This is now moved to
+% the places where the actual token registers are inserted (look for
+% =\the@toks=) because the old version would still make =@=
+% expressions to moving arguments since after expanding the second
+% register while looking for the end of the number the contents of the
+% token register is added so that later on the whole register will be
+% expanded.  This serious bug was found after nearly two years
+% international use of this package  by Johannes Braams.
+% \end{macro}
+%
+%
+%
+% How does the situation look like, if we want to add another column
+% to the preamble, i.e.\ if we have found a \texttt{c}, \texttt{l},
+% \texttt{r}, \texttt{p}, \texttt{m} or \texttt{b} in the user
+% preamble?  In this case we have the problem of the \textsf{token}
+% register from =>{..}= and =<{..}= having to be inserted at this
+% moment because formatting instructions like =\hfil= have to be set
+% around them. On the other hand it is not known yet, if any =<{..}=
+% instruction will appear in the user preamble at all.
+%
+% We solve this problem by adding two \textsf{token} registers at a
+% time.  This explains, why we have freed the \textsf{token} registers
+% in =\prepnext@tok=.
+%
+% \begin{macro}{\insert@column}
+% \begin{macro}{\@sharp}
+%    We now define the macro =\insert@column= which will do
+%    this work for us.
+%    \begin{macrocode}
+\def\insert@column{%
+%    \end{macrocode}
+%    Here, we assume that the \textsf{count} register
+%    =\@tempcnta= has saved the value $=\count@= - 1$.
+%    \begin{macrocode}
+   \the@toks \the \@tempcnta
+%    \end{macrocode}
+%    Next follows the =#= sign which specifies the place
+%    where the text of the column shall be inserted. To avoid
+%    errors during the expansions in
+%    =\@addtopreamble= we hide this sign in the command
+%    =\@sharp= which is temporarily occupied with
+%    =\relax= during the build-up of the preamble.
+%    To remove unwanted spaces before and after the column text, we set
+%    an =\ignorespaces=  in front and a =\unskip= afterwards.
+% \changes{v2.0e}{1991/02/07}{Added \{\} around \cs{@sharp} for new ftsel}
+% \changes{v2.0h}{1992/06/22}{Removed \{\} again in favour of
+%                             \cs{d@llarbegin}}
+%    \begin{macrocode}
+   \ignorespaces \@sharp \unskip
+%    \end{macrocode}
+%    Then the second \textsf{token} register follows whose number should
+%    be saved in =\count@=.
+%    We make sure that there will be no further expansion after reading
+%    the number, by finishing with =\relax=. The case above is not
+%    critical since it is ended by =\ignorespaces=.
+% \changes{v2.0c}{1990/08/14}{\cs{relax} added to avoid problem
+%                           \cs{the}\cs{toks0}\cs{the}\cs{toks1}.}
+%    \begin{macrocode}
+   \the@toks \the \count@ \relax}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+%
+% \subsection{The separation of columns}
+%
+% \begin{macro}{\@addamp}
+%    In the preamble a =&= has to be inserted between any two columns;
+%    before the first column there should not be a =&=. As the user
+%    preamble may start with a \texttt{|} we have to remember somehow
+%    if we have already inserted a =#= (i.e.\ a column). This is done
+%    with the boolean variable =\if@firstamp= that we test in
+%    =\@addamp=, the macro that inserts the =&=.
+%    \begin{macrocode}
+%    \newif \@iffirstamp
+%    \def\@addamp{\if@firstamp \@firstampfalse
+%                 \else \@addtopreamble &\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@acol}
+% \begin{macro}{\@acolampacol}
+% \begin{macro}{\col@sep}
+%    We will now define some abbreviations for the extensions,
+%    appearing most often in the preamble build-up.
+%    Here =\col@sep= is a \textsf{dimen} register which is set
+%    equivalent to =\arraycolsep= in an \textsf{array}--environment,
+%    otherwise it is set equivalent to =\tabcolsep=.
+%    \begin{macrocode}
+\newdimen\col@sep
+\def\@acol{\@addtopreamble{\hskip\col@sep}}
+%    \def\@acolampacol{\@acol\@addamp\@acol}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{The macro \texttt{\textbackslash @mkpream}}
+%
+% \begin{macro}{\@mkpream}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+% \begin{macro}{\the@toks}
+%    \label{@mkpream}
+%    Now we can define the macro which builds up the preamble for the
+%    =\halign=.
+%    First we initialize =\@preamble=, =\@lastchclass=
+%    and the boolean variable =\if@firstamp=.
+%    \begin{macrocode}
+%\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
+%    \end{macrocode}
+%    During the build-up of the preamble we cannot directly use the
+%    =#= sign; this would lead to an error message in the next
+%    =\@addtopreamble= call.
+%    Instead, we use the command =\@sharp= at places where later
+%    a =#= will be.
+%    This command is at first given the meaning =\relax=;
+%    therefore it will not be expanded when the preamble
+%    is extended.
+%    In the macro =\@array=, shortly before the =\halign=
+%    is carried out, =\@sharp= is given its final meaning.
+%
+%    In a similar way,
+%    we deal with the commands =\@startpbox= and
+%    =\@endpbox=, although the reason is different here: these
+%    macros expand in many \textsf{tokens} which would delay the
+%    build-up of the preamble.
+%    \begin{macrocode}
+%   \let\@sharp\relax\let\@startpbox\relax\let\@endpbox\relax
+%    \end{macrocode}
+%    Two more are needed to deal with the code that handles struts
+%    for extra space after a row from =\\[<space>]=
+%    (=\do@row@strut=) and code that manages m-cells depending on
+%   their heights (=\ar@align@mcell=).
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+%   \let\do@row@strut\relax
+%   \let\ar@align@mcell\relax 
+%    \end{macrocode}
+%    Now we remove possible  $*$-forms in the user preamble with the
+%    command =\@xexpast=.  As we already know, this command saves
+%    its result in the macro =\@tempa=.
+%    \begin{macrocode}
+%   \@xexpast #1*0x\@@
+%    \end{macrocode}
+%    Afterwards we initialize all registers and macros, that we need
+%    for the build-up of the preamble.
+%    Since we want to start with the \textsf{token} register $0$,
+%    =\count@= has to contain the value $-1$.
+%    \begin{macrocode}
+%   \count@\m@ne
+%   \let\the@toks\relax
+%    \end{macrocode}
+%    Then we call up =\prepnext@tok= in order to prepare the
+%    \textsf{token} register $0$ for use.
+%    \begin{macrocode}
+%   \prepnext@tok
+%    \end{macrocode}
+%    To evaluate the user preamble (without stars) saved in
+%    =\@tempa= we use the \LaTeX--macro =\@tfor=.
+%    The strange appearing construction with =\expandafter= is
+%    based on the fact that we have to put the replacement text of
+%    =\@tempa= and not the macro =\@tempa= to this
+%    \LaTeX--macro.
+%    \begin{macrocode}
+%   \expandafter \@tfor \expandafter \@nextchar
+%    \expandafter :\expandafter =\@tempa \do
+%    \end{macrocode}
+%    The body of this loop (the group after the =\do=)
+%    is executed for one \textsf{token} at a time, whereas
+%    the current \textsf{token} is saved in =\@nextchar=.
+%    At first we evaluate the current \textsf{token} with the already
+%    defined macro =\@testpach=, i.e.\ we assign to
+%    =\@chclass= the character class and to =\@chnum=
+%    the character number of this \textsf{token}.
+% \changes{v2.0f}{1992/02/29}{\cs{@testpach} now without arg}
+%    \begin{macrocode}
+%   {\@testpach
+%    \end{macrocode}
+%    Then we branch out depending on the value of =\@chclass= into
+%    different macros that extend the preamble respectively.
+%    \begin{macrocode}
+%   \ifcase \@chclass \@classz \or \@classi \or \@classii
+%     \or \save@decl \or \or \@classv \or \@classvi
+%     \or \@classvii \or \@classviii  \or \@classix
+%     \or \@classx \fi
+%    \end{macrocode}
+%    Two cases deserve our special attention: Since the current
+%    \textsf{token} cannot have the character class $4$ (start) we
+%    have skipped this possibility. If the character class is $3$,
+%    only the content of =\@nextchar= has to be saved into the current
+%    \textsf{token} register; therefore we call up =\save@decl=
+%    directly and save a macro name.  After the preamble has been
+%    extended we assign the value of =\@chclass= to the counter
+%    =\@lastchclass= to assure that this information will be available
+%    during the next run of the loop.
+%    \begin{macrocode}
+%   \@lastchclass\@chclass}%
+%    \end{macrocode}
+%    After the loop has been finished space must still be added to
+%    the created preamble, depending on the last \textsf{token}.
+%    Depending on the value of =\@lastchclass= we perform
+%    the necessary operations.
+%    \begin{macrocode}
+%   \ifcase\@lastchclass
+%    \end{macrocode}
+%    If the last class equals $0$ we add a
+%    =\hskip \col@sep=.
+%    \begin{macrocode}
+%   \@acol \or
+%    \end{macrocode}
+%    If it equals $1$ we do not add any additional space so that the
+%    horizontal lines do not exceed the vertical ones.
+%    \begin{macrocode}
+%   \or
+%    \end{macrocode}
+%    Class $2$ is treated like class $0$ because a =<{...}=  can
+%    only directly follow after class $0$.
+%    \begin{macrocode}
+%   \@acol \or
+%    \end{macrocode}
+%    Most of the other possibilities can only appear if the user
+%    preamble was defective. Class $3$ is not allowed since after a
+%    =>{..}= there must always follow a \texttt{c}, \texttt{l},
+%    \texttt{r}, \texttt{p},\texttt{m} or \texttt{b}. We report an
+%    error and ignore the declaration given by ={..}=.
+%    \begin{macrocode}
+%   \@preamerr \thr@@ \or
+%    \end{macrocode}
+%    If =\@lastchclass= is $4$ the user preamble has been empty.
+%    To continue, we insert a =#= in the preamble.
+%    \begin{macrocode}
+%   \@preamerr \tw@ \@addtopreamble\@sharp \or
+%    \end{macrocode}
+%    Class $5$ is allowed again. In this case
+%    (the user preamble ends with =@{..}=) we need not
+%    do anything.
+%    \begin{macrocode}
+%   \or
+%    \end{macrocode}
+%    Any other case means that the arguments to =@=, \texttt{!},
+%    \texttt{<}, \texttt{>}, \texttt{p}, \texttt{m} or \texttt{b} have
+%    been forgotten. So we report an error and ignore the last
+%    \textsf{token}.
+%    \begin{macrocode}
+%   \else  \@preamerr \@ne \fi
+%    \end{macrocode}
+%    Now that the build-up of the preamble is almost finished we can
+%    insert the \textsf{token} registers and therefore redefine
+%    =\the@toks=. The actual insertion, though, is performed
+%    later.
+%    \begin{macrocode}
+%   \def\the@toks{\the\toks}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+%  \section{The macros \texttt{\textbackslash @classz}
+%           to \texttt{\textbackslash @classx}}
+%
+% The preamble is extended by the macros =\@classz= to
+% =\@classx= which are called by =\@mkpream=
+%  depending on =\@lastchclass=
+% (i.e. the character class of the last \textsf{token}).
+% \begin{macro}{\@classx}
+%    First we define =\@classx= because of its important r\^ole.
+%    When it is called we find that the current
+%    \textsf{token} is \texttt{p}, \texttt{m} or \texttt{b}.
+%    That means that a new column has to start.
+%    \begin{macrocode}
+\def\@classx{%
+%    \end{macrocode}
+%    Depending on the value of =\@lastchclass= different actions
+%    must take place:
+%    \begin{macrocode}
+  \ifcase \@lastchclass
+%    \end{macrocode}
+%    If the last character class was $0$ we separate the columns by
+%    =\hskip\col@sep= followed by =&= and another
+%    =\hskip\col@sep=.
+%    \begin{macrocode}
+  \@acolampacol \or
+%    \end{macrocode}
+%    If the last class was class $1$ --- that means that a vertical
+%    line was
+%    drawn, --- before this line a =\hskip\col@sep= was inserted.
+%    Therefore there has to be only a =&= followed by
+%    =\hskip\col@sep=. But this =&= may be inserted only
+%    if this is not the first column. This process is controlled
+%    by =\if@firstamp= in the macro =\addamp=.
+%    \begin{macrocode}
+  \@addamp \@acol \or
+%    \end{macrocode}
+%    Class $2$ is treated like class $0$ because =<{...}= can only
+%    follow after class $0$.
+%    \begin{macrocode}
+  \@acolampacol \or
+%    \end{macrocode}
+%    Class $3$ requires no actions because all things necessary have
+%    been done by the preamble \textsf{token} \texttt{>}.
+%    \begin{macrocode}
+  \or
+%    \end{macrocode}
+%    Class $4$ means that we are at the beginning of the preamble.
+%    Therefore we start the preamble with =\hskip\col@sep= and
+%    then call =\@firstampfalse=. This makes sure that a later
+%    =\@addamp= inserts the character
+%    =&= into the preamble.
+%    \begin{macrocode}
+  \@acol \@firstampfalse \or
+%    \end{macrocode}
+%    For class $5$ \textsf{tokens} only the character =&= is inserted
+%    as a column separator. Therefore we call =\@addamp=.
+%    \begin{macrocode}
+  \@addamp
+%    \end{macrocode}
+%    Other cases are impossible. For an example
+%    $=\@lastchclass= \string= 6$---as it might appear in a
+%    preamble of the form =...!p...=---\texttt{p} would have
+%    been taken as an  argument of \texttt{!}\ by =\@testpach=.
+%    \begin{macrocode}
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@classz}
+%    If the character class of the last \textsf{token} is $0$ we have
+%    \texttt{c}, \texttt{l}, \texttt{r} or an argument of \texttt{m},
+%    \texttt{b} or\ \texttt{p}. In the first three cases the preamble
+%    must be extended the same way as if we had class $10$. The
+%    remaining two cases do not require any action because the space
+%    needed was generated by the last \textsf{token} (i.e.\
+%    \texttt{m}, \texttt{b} or \texttt{p}). Since =\@lastchclass= has
+%    the value $10$ at this point nothing happens when =\@classx= is
+%    called. So the macro =\@chlassz= may start like this:
+%    \begin{macrocode}
+\def\@classz{\@classx
+%    \end{macrocode}
+%    According to the definition of =\insert@column= we must store
+%    the number of the \textsf{token} register in which a preceding
+%    =>{..}= might have stored its argument into
+%    =\@tempcnta=.
+%    \begin{macrocode}
+   \@tempcnta \count@
+%    \end{macrocode}
+%    To have $=\count@= \string= =\@tmpcnta= + 1$ we prepare
+%    the next \textsf{token} register.
+%    \begin{macrocode}
+   \prepnext@tok
+%    \end{macrocode}
+%    Now the preamble must be extended with the column whose format
+%    can be determined by =\@chnum=.
+%    \begin{macrocode}
+   \@addtopreamble{\ifcase \@chnum
+%    \end{macrocode}
+%    If =\@chnum= has the value $0$ a centered column has to be
+%    generated.
+%    So we begin with stretchable space.
+%    \begin{macrocode}
+      \hfil
+%    \end{macrocode}
+%    We also add a space of 1sp just in case the first thing in the
+%    cell is a command doing an =\unskip=.      
+% \changes{v2.4k}{2018/12/30}{Add extra \cs{hskip} to guard against an
+%   \cs{unskip} at the start of a c-column cell (gh/102)}
+%    \begin{macrocode}
+      \hskip1sp%
+%    \end{macrocode}
+%    The command =\d@llarbegin= follows expanding into =\begingroup=
+%    (in the \textsf{tabular}--environment) or into =$=.  Doing this
+%    (provided an appropriate setting of =\d@llarbegin=) we achieve
+%    that the contents of the columns of an \textsf{array}--environment
+%    are set in math mode while those of a \textsf{tabular}--environment
+%    are set in LR mode.
+%    \begin{macrocode}
+      \d@llarbegin
+%    \end{macrocode}
+%    Now we insert the contents of the two \textsf{token} registers
+%    and the symbol
+%    for the column entry (i.e.\ =#= or
+%    more precise =\@sharp=) using =\insert@column=.
+%    \begin{macrocode}
+      \insert@column
+%    \end{macrocode}
+%    We end this case with =\d@llarend= and =\hfil= where =\d@llarend=
+%    again is either =$= or =\endgroup=.
+%    The strut to enforce a regular row height is placed between the two.
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+%    \begin{macrocode}
+      \d@llarend \do@row@strut \hfil \or
+%    \end{macrocode}
+%    The templates for \texttt{l} and \texttt{r} (i.e.\ =\@chnum= $1$
+%    or $2$) are generated the same way. Since one  =\hfil= is
+%    missing the text is moved to the relevant side.
+%    The =\kern\z@= is needed in case of an empty column
+%    entry. Otherwise
+%    the =\unskip= in =\insert@column= removes the
+%    =\hfil=. Changed to =\hskip1sp= so that it interacts better with
+%    =\@bsphack=.
+% \changes{v2.3f}{1996/04/22}
+%     {(DPC) Extra \cs{kern} keeps tabcolsep in empty l columns
+%             internal/2122}
+% \changes{v2.3i}{1996/06/14}
+%     {Change both \cs{kern}\cs{z@} to \cs{hskip}1sp for latex/2160}
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+%    \begin{macrocode}
+      \hskip1sp\d@llarbegin \insert@column \d@llarend \do@row@strut \hfil \or
+      \hfil\hskip1sp\d@llarbegin \insert@column \d@llarend \do@row@strut \or
+%    \end{macrocode}
+%    The templates for \texttt{p}, \texttt{m} and \texttt{b} mainly
+%    consist of a \textsf{box}. In case of \texttt{m} it is generated
+%    by =\vcenter=.  This command is allowed only in math
+%    mode. Therefore we start with a~=$=.
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+    \setbox\ar@mcellbox\vbox 
+%    \end{macrocode}
+%    The part of the templates which is the same in all three cases
+%    (\texttt{p}, \texttt{m} and \texttt{b})
+%    is built by the macros =\@startpbox= and
+%    =\@endpbox=. =\@startpbox= has an argument:
+%    the width of the column which is stored in the current
+%    \textsf{token} (i.e.\ =\@nextchar=).
+%    Between these two macros we find the well known
+%    =\insert@column=.
+%    The strut is places after the box
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+    \@startpbox{\@nextchar}\insert@column \@endpbox 
+    \ar@align@mcell
+    \do@row@strut \or
+%    \end{macrocode}
+%    The templates for \texttt{p} and \texttt{b} are generated in the
+%    same way though we do not need the =$= characters because we use
+%    =\vtop= or =\vbox=.
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+%    \begin{macrocode}
+   \vtop \@startpbox{\@nextchar}\insert@column \@endpbox\do@row@strut \or
+   \vbox \@startpbox{\@nextchar}\insert@column \@endpbox\do@row@strut
+%    \end{macrocode}
+%    Other values for =\@chnum= are impossible. Therefore we
+%    end the arguments to =\@addtopreamble= and =\ifcase=.
+%    Before we come to the end of =\@classz= we have to
+%    prepare the next \textsf{token} register.
+%    \begin{macrocode}
+  \fi}\prepnext@tok}
+%    \end{macrocode}
+% \end{macro}
+%
+
+%
+% \begin{macro}{\ar@mcellbox}
+%    When dealing with m-cells we need a box to measure the cell
+%    height.
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+\newbox\ar@mcellbox
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\ar@align@mcell}
+%    M-cells are supposed to be vertically centered within the table
+%    row. In the original implementation that was done using
+%    =\vcenter= but the issue with that approach is that it centers
+%    the material based on the math-axis. In most situations that
+%    comes out quit right, but if, for example, an m-cell has only a
+%    single line worth of material inside it will be positioned
+%    differently to a =l=, =c= or =r= cell or to a =p= or =b= cell
+%    with  the same content.
+%
+%    For that reason the new implementation does the centering
+%    manually: First we check the height of the cell and if that is
+%    less or equal to =\ht\@arstrutbox= we assume that this is a
+%    single line cell. In that case  we don't do any vertical maneuvre
+%    and simply output the box, i.e., make it behave like a single
+%    line p-cell.
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+\def\ar@align@mcell{%
+  \ifdim \ht\ar@mcellbox > \ht\@arstrutbox
+%    \end{macrocode}
+%    Otherwise we realign vertically by lowering the box. The question
+%    is how much do we need to move down? If there is any
+%    =\arraystretch= in place then the first line will have some
+%    unusual height and we don't want to consider that when finding
+%    the middle point. So we substract from the cell height the height
+%    of that strut. But of course we want to include the normal height
+%    of the first line (which would be something like =\ht\strutbox=)
+%    so we need to add that. On the other hand, when centering around
+%    the mid-point of the cell, we also need to account for the depth
+%    of the last line (which is nominally something like
+%    =\dp\strutbox=). Both together equals =\baselineskip= so that is
+%    what we add and then lower the cell by half of the resulting value.
+%    \begin{macrocode}
+    \begingroup
+     \dimen@\ht\ar@mcellbox
+     \advance\dimen@-\ht\@arstrutbox
+     \advance\dimen@\baselineskip
+     \lower.5\dimen@\box\ar@mcellbox
+    \endgroup
+  \else % assume one line and align at baseline
+    \box\ar@mcellbox
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+
+%
+% \begin{macro}{\@classix}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+%
+%    In case of class $9$ (\texttt{>}--\textsf{token}) we first check
+%    if the character class of the last
+%    \textsf{token} was $3$. In this case we have a
+%    user preamble of the form =..>{...}>{...}..= which
+%    is not allowed. We only give an error message and continue.
+%    So the declarations defined by the first  =>{...}=
+%    are ignored.
+%    \begin{macrocode}
+%\def\@classix{\ifnum \@lastchclass = \thr@@
+%       \@preamerr \thr@@ \fi
+%    \end{macrocode}
+%    Furthermore, we call up =\@class10= because afterwards always a
+%    new column is started by \texttt{c}, \texttt{l}, \texttt{r},
+%    \texttt{p}, \texttt{m} or \texttt{b}.
+%    \begin{macrocode}
+%       \@classx}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\@classviii}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+%
+%    If the current \textsf{token} is a \texttt{<} the last character
+%    class must be $0$. In this case it is not necessary to extend the
+%    preamble. Otherwise we output an error message, set =\@chclass=
+%    to $6$ and call =\@classvi=.  By doing this we achieve that
+%    \texttt{<} is treated like \texttt{!}.
+%    \begin{macrocode}
+%\def\@classviii{\ifnum \@lastchclass >\z@
+%      \@preamerr 4\@chclass 6 \@classvi \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@arrayrule}
+%    There is only one incompatibility with the original definition:
+%    the definition of =\@arrayrule=. In the original a line without
+%    width\footnote{So the space between \texttt{cc} and \texttt{c|c}
+%    is equal.}  is created by multiple insertions of
+% =\hskip .5\arrayrulewidth=.
+%    We only insert a vertical line into the
+%    preamble.  This is done to prevent problems with \TeX's main
+%    memory when generating tables with many vertical lines in them
+%    (especially in the case of \textsf{floats}).
+%    \begin{macrocode}
+\def\@arrayrule{\@addtopreamble \vline}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classvii}
+%    As a consequence it follows that in case of class $7$
+%    (=@= \textsf{token})  the preamble need not to be extended.
+%    In the original definition $=\@lastchclass= \string= 1$
+%    is treated by inserting =\hskip .5\arrayrulewidth=.
+%    We only check if the last \textsf{token} was of class $3$ which is
+%    forbidden.
+%    \begin{macrocode}
+\def\@classvii{\ifnum \@lastchclass = \thr@@
+%    \end{macrocode}
+%    If this is true we output an error message and
+%    ignore the declarations stored
+%    by the last  =>{...}=, because these are overwritten
+%    by the argument of \texttt{@}.
+%    \begin{macrocode}
+   \@preamerr \thr@@ \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@classvi}
+%    If the current \textsf{token} is a regular \texttt{!}\ and the
+%    last class was $0$ or $2$ we extend the preamble with
+%    =\hskip\col@sep=.  If the last \textsf{token} was of class $1$
+%    (for instance \texttt{|}) we extend with =\hskip \doublerulesep=
+%    because the construction =!{...}= has to be treated like
+%    \texttt{|}.
+%    \begin{macrocode}
+\def\@classvi{\ifcase \@lastchclass
+      \@acol \or
+      \@addtopreamble{\hskip \doublerulesep}\or
+      \@acol \or
+%    \end{macrocode}
+%    Now =\@preamerr...= should follow because a
+%    user preamble of the form =..>{..}!.= is not allowed.
+%    To save memory we call =\@classvii= instead which also
+%    does what we want.
+%    \begin{macrocode}
+      \@classvii
+%    \end{macrocode}
+%    If =\@lastchclass= is $4$ or $5$ nothing has to be done.
+%    Class $6$ to $10$ are not possible.
+%    So we finish the macro.
+%    \begin{macrocode}
+      \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classii}
+% \begin{macro}{\@classiii}
+%    In the case of character classes $2$ and $3$ (i.e.\ the argument
+%    of \texttt{<} or \texttt{>}) we only have to store the current
+%    \textsf{token} (=\@nextchar=) into the corresponding
+%    \textsf{token} register since the preparation and
+%    insertion of these registers
+%    are done by the macro =\@classz=.
+%    This is equivalent to calling =\save@decl= in the case of
+%    class $3$. To save command identifiers we do this call up
+%     in the macro =\@mkpream=.
+%
+%    Class $2$ exhibits a more complicated situation: the
+%    \textsf{token} registers have already been inserted by
+%    =\@classz=. So the value of =\count@= is too high
+%    by one. Therefore we decrease =\count@= by $1$.
+%    \begin{macrocode}
+\def\@classii{\advance \count@ \m@ne
+%    \end{macrocode}
+%    Next we store the current \textsf{token} into the correct
+%    \textsf{token} register by calling =\save@decl= and then
+%    increase the value of =\count@= again. At this point we
+%    can save memory once more (at the cost of time) if we use the
+%     macro =\prepnext@tok=.
+%    \begin{macrocode}
+   \save@decl\prepnext@tok}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\@classv}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+%
+%    If the current \textsf{token} is of class $5$ then it is an
+%    argument of a \texttt{@} \textsf{token}. It must be stored into a
+%    \textsf{token} register.
+%    \begin{macrocode}
+%\def\@classv{\save@decl
+%    \end{macrocode}
+%    We extend the preamble with a command which inserts this
+%    \textsf{token} register into the preamble when its construction
+%    is finished. The user expects that this argument is worked out in
+%    math mode if it was used in an
+%    \textsf{array}--environment. Therefore we surround it with
+%    =\d@llar...='s.
+% \changes{v2.0c}{1990/08/14}{\cs{relax} added to avoid problem
+%                           `the`toks0`the`toks1.}
+%    \begin{macrocode}
+%   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
+%    \end{macrocode}
+%    Finally we must prepare the next \textsf{token} register.
+%    \begin{macrocode}
+%   \prepnext@tok}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classi}
+%    In the case of class $0$ we were able to generate the necessary
+%    space between columns by using the macro =\@classx=.
+%    Analogously the macro =\@classvi= can be used for class $1$.
+%    \begin{macrocode}
+\def\@classi{\@classvi
+%    \end{macrocode}
+%    Depending on =\@chnum= a vertical line
+%    \begin{macrocode}
+   \ifcase \@chnum \@arrayrule \or
+%    \end{macrocode}
+%    or (in case of =!{...}=) the current \textsf{token} --- stored
+%    in =\@nextchar= --- has to be inserted into the preamble.
+%    This corresponds to calling =\@classv=.
+%    \begin{macrocode}
+      \@classv \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\@startpbox}
+%    In =\@classz=  the macro =\@startpbox= is used.
+%    The width of the \textsf{parbox} is passed as an argument.
+%    =\vcenter=, =\vtop= or =\vbox= are already in the
+%    preamble. So we start with the braces for the wanted box.
+% \changes{v2.4i}{2018/09/13}{Add group to prevent color leak (gh/72)}
+%    \begin{macrocode}
+\def\@startpbox#1{\bgroup
+  \color@begingroup
+%    \end{macrocode}
+%    The argument is the width of the box. This information has to be
+%    assigned to =\hsize=.
+%    Then we assign default values to several parameters used in a
+%    \textsf{parbox}.
+% \changes{v2.3k}{1998/05/12}{Use \cs{setlength} to set \cs{hsize},
+%      so that the calc package can be applied here (pr/2793)}
+%    \begin{macrocode}
+  \setlength\hsize{#1}\@arrayparboxrestore
+%    \end{macrocode}
+%    Our main problem is to obtain the same distance between succeeding
+%    lines of the \textsf{parbox}.
+%    We have to remember that the distance between two \textsf{parboxes}
+%    should be defined by =\@arstrut=. That means that it can be
+%    greater than the distance in a \textsf{parbox}.
+%    Therefore it is not enough to set a =\@arstrut= at the
+%    beginning and at the end of the \textsf{parbox}. This would
+%    dimension the distance
+%    between first and second line and the distance between the two
+%    last lines of the \textsf{parbox} wrongly.
+%    To prevent this we set an invisible rule of height
+%    =\@arstrutbox=
+%    at the beginning of the \textsf{parbox}. This has no effect on the
+%    depth of the first line. At the end of the \textsf{parbox} we set
+%    analogously another invisible rule which only affects the depth
+%    of the last line. It is necessary to wait inserting this strut
+%    until the paragraph actually starts to allow for things like
+%    =\parindent= changes via =>{...}=.
+% \changes{v2.1c}{1992/12/14}{Use `everypar to insert strut}
+%    \begin{macrocode}
+   \everypar{%
+      \vrule \@height \ht\@arstrutbox \@width \z@
+      \everypar{}}%
+   }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@endpbox}
+%    If there are any declarations defined by =>{...}=
+%    and =<{...}=
+%    they now follow in the macro =\@classz= --- the contents
+%    of the column in between.
+%    So the macro =\@endpbox= must insert the \textsf{specialstrut}
+%    mentioned earlier and then close the group opened by
+%    =\@startpbox=.
+% \changes{v2.2d}{1994/05/16}{Use \LaTeXe \cs{@finalstrut}}
+% \changes{v2.3g}{1996/05/07}{Add \cs{hfil} for tools/2120}
+% \changes{v2.4i}{2018/09/13}{Add group to prevent color leak (gh/72)}
+%    \begin{macrocode}
+\def\@endpbox{\@finalstrut\@arstrutbox \color@endgroup \egroup\hfil}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \section{Building and calling \texttt{\textbackslash halign}}
+%
+% \begin{macro}{\@array}
+%    After we have discussed the macros needed for the evaluation
+%    of the user preamble we can define the macro =\@array=
+%    which uses these macros to create a =\halign=.
+%    It has two arguments. The first one is a position argument
+%    which can be \texttt{t}, \texttt{b} or \texttt{c}; the
+%    second one describes the wanted preamble,
+%    e.g.\ it has the form =|c|c|c|=.
+%    \begin{macrocode}
+\def\@array[#1]#2{%
+%    \end{macrocode}
+%    First we define a \textsf{strut} whose size basically corresponds
+%     to a normal \textsf{strut} multiplied by the factor
+%    =\arraystretch=.
+%    This \textsf{strut} is then  inserted into every row and enforces
+%     a minimal distance between two rows.
+%    Nevertheless, when using horizontal lines, large letters
+%    (like accented capital letters) still collide with such lines.
+%    Therefore at first we add to the height of a normal \textsf{strut}
+%    the value of the parameter =\extrarowheight=.
+%    \begin{macrocode}
+  \@tempdima \ht \strutbox
+  \advance \@tempdima by\extrarowheight
+  \setbox \@arstrutbox \hbox{\vrule
+             \@height \arraystretch \@tempdima
+             \@depth \arraystretch \dp \strutbox
+             \@width \z@}%
+%    \end{macrocode}
+%    Then we open a group, in which the user preamble is evaluated by
+%    the macro =\@mkpream=. As we know this must happen locally.
+%    This macro creates a preamble for a =\halign= and saves
+%    its result globally in the control sequence =\@preamble=.
+%    \begin{macrocode}
+  \begingroup
+  \@mkpream{#2}%
+%    \end{macrocode}
+%    We again redefine =\@preamble= so that a call up of =\@preamble=
+%    now starts the =\halign=. Thus also the arguments of \texttt{>},
+%    \texttt{<}, \texttt{@} and \texttt{!}, saved in the
+%    \textsf{token} registers are inserted into the preamble.  The
+%    =\tabskip= at the beginning and end of the preamble is set to
+%    \textsf{0pt} (in the beginning by the use of =\ialign=). Also the
+%    command =\@arstrut= is build in, which inserts the
+%    =\@arstrutbox=, defined above. Of course, the opening brace after
+%    =\ialign= has to be implicit as it will be closed in =\endarray=
+%    or another macro.
+% \changes{v2.3m}{1998/12/31}{Added \cs{noexpand} in front of \cs{ialign}
+%    to guard against interesting :-) changes to \cs{halign} done to support
+%    text glyphs in math}
+%
+%    The =\noexpand= in front of =\ialign= does no harm in standard \LaTeX{}
+%    and was added since some experimental support for using text glyphs in math
+%    redefines =\halign= with the result that is becomes expandable with
+%    disastrous results in cases like this.
+%    In the kernel definition for this macro the problem does
+%    not surface because there =\protect= is set (which is not necessary in this
+%    implementation as there is no arbitrary user input that can get expanded) and
+%    the experimental code made the redefinition robust. Whether this is the right
+%    approach is open to question; consider the =\noexpand= a courtesy to allow an
+%    unsupported redefinition of a \TeX{} primitive for the moment (as people rely
+%    on that experimental code).
+%    \begin{macrocode}
+  \xdef\@preamble{\noexpand \ialign \@halignto
+                  \bgroup \@arstrut \@preamble
+                          \tabskip \z@ \cr}%
+%    \end{macrocode}
+%    What we have not explained yet is the macro =\@halignto=
+%    that was just used. Depending on its replacement text the
+%    =\halign= becomes a =\halign= \texttt{to} \meta{dimen}.
+%    Now we close the group again. Thus
+%    =\@startpbox= and =\@endpbox= as well as all
+%    \textsf{token} registers get their former meaning back.
+%    \begin{macrocode}
+  \endgroup
+%    \end{macrocode}
+%     To support the \texttt{delarray.sty} package  we include a hook
+%     into this part of the code which is a no-op in the main package.
+% \changes{v2.1a}{1992/07/03}{Hook for delarray added}
+%    \begin{macrocode}
+  \@arrayleft
+%    \end{macrocode}
+%    Now we decide depending on the position argument in which
+%    \textsf{box} the =\halign= is to be put. (=\vcenter= may be used
+%    because we are in math mode.)
+% \changes{v2.1a}{1992/07/03}{Wrong spec is now equiv to [t]}
+%    \begin{macrocode}
+  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi \fi
+%    \end{macrocode}
+%    Now another implicit opening brace appears; then definitions
+%    which shall stay local follow. While constructing the
+%    =\@preamble= in =\@mkpream= the =#= sign must be
+%    hidden in the macro =\@sharp= which is =\let= to
+%    =\relax= at that moment (see definition of =\@mkpream=
+%    on page~\pageref{@mkpream}).
+%    All these now get their actual meaning.
+%    \begin{macrocode}
+  \bgroup
+  \let \@sharp ##\let \protect \relax
+%    \end{macrocode}
+%    With the above defined \textsf{struts} we fix down the distance
+%    between rows by setting =\lineskip= and =\baselineskip=
+%    to \textsf{0pt}. Since there have to be set =$='s
+%    around every column in the \textsf{array}--environment
+%     the parameter =\mathsurround= should
+%    also be set to \textsf{0pt}. This prevents additional space between
+%    the rows. The
+%    \PlainTeX--macro =\m@th= does this.
+%    \begin{macrocode}
+  \lineskip \z@
+  \baselineskip \z@
+  \m@th
+%    \end{macrocode}
+%    Beside, we have to assign a special meaning (which we still have
+%    to specify) to the line separator =\\=. We also have to
+%    redefine the command =\par= in such a way that empty lines in
+%    =\halign= cannot do any damage. We succeed in doing  so
+%    by choosing something that will disappear when expanding.
+%    After that we only have to call up =\@preamble= to
+%    start the wanted =\halign=.
+%    \changes{1994/12/08}{v2.3b}{add \cs{tabularnewline}}
+%    \begin{macrocode}
+  \let\\\@arraycr \let\tabularnewline\\\let\par\@empty \@preamble}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\arraybackslash}
+% \changes{v2.4a}{2003/12/17}{(DPC) Macro added (from tabularx)}
+% Restore =\\= for use in array and tabular environment (after
+% =\raggedright= etc.).
+%    \begin{macrocode}
+\def\arraybackslash{\let\\\tabularnewline}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\extrarowheight}
+%    The \textsf{dimen} parameter used above also needs to be
+%    allocated.  As a default value we use \textsf{0pt}, to ensure
+%    compatibility with standard \LaTeX.
+%    \begin{macrocode}
+\newdimen \extrarowheight
+\extrarowheight=0pt
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@arstrut}
+%    Now the insertion of =\@arstrutbox= through =\@arstut=
+%    is easy since we know exactly in which mode \TeX\ is while working
+%    on the =\halign= preamble.
+%    \begin{macrocode}
+\def\@arstrut{\unhcopy\@arstrutbox}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \section{The line separator \texttt{\textbackslash\textbackslash}}
+%
+% \begin{macro}{\@arraycr}
+%    In the macro =\@array= the line separator =\\= is
+%    =\let= to the command =\@arraycr=.
+%    Its definition starts with a special brace which I have directly
+%    copied from the original definition. It is
+%    necessary, because the =\futurlet= in =\@ifnextchar=
+%    might
+%    expand a  following =&= \textsf{token} in a construction like
+%    =\\ &=. This would otherwise end the alignment template at a
+%    wrong time. On the other hand we have to be careful to avoid
+%    producing a real group, i.e.\ ={}=, because the command will also
+%    be used for the array environment, i.e.\ in math mode. In that
+%    case an extra ={}= would produce an ord atom which could mess up
+%    the spacing. For this reason we use a combination that does not
+%    really produce a group at all but modifies the master counter so
+%    that a =&= will not be considered belonging to the current
+%    =\halign= while we are looking for a =*= or =[=.
+%    For further information see
+%    \cite[Appendix D]{bk:knuth}.
+% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
+%    \begin{macrocode}
+\def\@arraycr{\relax\iffalse{\fi\ifnum 0=`}\fi
+%    \end{macrocode}
+%    Then we test whether the user is using the star form and ignore
+%    a possible star (I also disagree with this procedure, because a
+%    star does not make any sense here).
+%    \begin{macrocode}
+  \@ifstar \@xarraycr \@xarraycr}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xarraycr}
+%    In the command =\@xarraycr= we test if an optional argument
+%    exists.
+%    \begin{macrocode}
+\def\@xarraycr{\@ifnextchar [%
+%    \end{macrocode}
+%    If it does, we branch out into the macro =\@argarraycr= if
+%    not we close the special brace (mentioned above) and end the row
+%    of the =\halign= with a =\cr=.
+% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
+%    \begin{macrocode}
+  \@argarraycr {\ifnum 0=`{}\fi\cr}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@argarraycr}
+%    If additional space is requested by the user this case is treated
+%    in the macro =\@argarraycr=. First we close the special brace
+%    and then we test if the additional space is positive.
+% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
+%    \begin{macrocode}
+\def\@argarraycr[#1]{\ifnum0=`{}\fi\ifdim #1>\z@
+%    \end{macrocode}
+%    If this is the case we create an invisible vertical rule with
+%    depth =\dp\@arstutbox=${}+{}$\meta{wanted\ space}.
+%    Thus we achieve that all vertical lines specified
+%    in the user preamble by a \texttt{|} are now
+%    generally drawn.
+%    Then the row ends with a =\cr=.
+%
+%    If the space is negative we end the row at once with a =\cr=
+%    and move back up with a =\vskip=.
+%
+%    While testing these macros I found out that the
+%    =\endtemplate=
+%    created by =\cr= and =&= is something like an
+%    =\outer= primitive and therefore it should not appear in
+%    incomplete =\if= statements. Thus the following solution was
+%    chosen which hides the =\cr= in other macros when \TeX\
+%    is skipping conditional text.
+% \changes{v2.3c}{1995/04/23}{Use \cs{expandafter}'s in conditional}
+%    \begin{macrocode}
+  \expandafter\@xargarraycr\else
+  \expandafter\@yargarraycr\fi{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xargarraycr}
+% \begin{macro}{\@yargarraycr}
+%    The following macros were already explained above.
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+%    \begin{macrocode}
+\def\@xargarraycr#1{\unskip\gdef\do@row@strut
+ {\@tempdima #1\advance\@tempdima \dp\@arstrutbox
+   \vrule \@depth\@tempdima \@width\z@\global\let\do@row@strut\relax}%
+%    \end{macrocode}
+%    If the last column is a =\multicolumn= cell then we need to
+%    insert the row strut now as it isn't inside the template (as that
+%    got =\omit=ted).
+% \changes{v2.4h}{2018/04/30}{Fixing issue 42}
+ %    \begin{macrocode}
+   \ifnum\@multicnt >\z@ \do@row@strut \fi
+   \cr}
+\let\do@row@strut\relax
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\@yargarraycr#1{\cr\noalign{\vskip #1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+%
+% \section{Spanning several columns}
+%
+% \begin{macro}{\multicolumn}
+%    If several columns should be held together with a special format
+%    the command =\multicolumn= must be used. It has three
+%    arguments: the number of columns to be covered; the format for
+%    the result column and the actual column entry.
+% \changes{v2.3j}{1998/01/29}{Command made \cs{long} to match
+%      kernel change for pr/2180}
+%    \begin{macrocode}
+\long\def\multicolumn#1#2#3{%
+%    \end{macrocode}
+%    First we combine the given number of columns into a single one;
+%    then we start a new block so that the following definition is kept
+%    local.
+%    \begin{macrocode}
+   \multispan{#1}\begingroup
+%    \end{macrocode}
+%    Since a =\multicolumn= should only describe the format of a
+%    result column, we redefine =\@addamp= in such a way that one gets
+%    an error message if one uses more than one \texttt{c},
+%    \texttt{l}, \texttt{r}, \texttt{p}, \texttt{m} or \texttt{b} in
+%    the second argument. One should consider that this definition is
+%    local to the build-up of the preamble; an \textsf{array}-- or
+%    \textsf{tabular}--environment in the third argument of the
+%    =\multicolumn= is therefore worked through correctly as well.
+%    \begin{macrocode}
+   \def\@addamp{\if@firstamp \@firstampfalse \else
+                \@preamerr 5\fi}%
+%    \end{macrocode}
+%    Then we evaluate the second argument with the help of
+%    =\@mkpream=.
+%    Now we still have to insert the contents of the \textsf{token}
+%    register into the =\@preamble=, i.e.\ we have to say
+%    =\xdef\@preamble{\@preamble}=. This is achieved shorter by
+%    writing:
+%    \begin{macrocode}
+   \@mkpream{#2}\@addtopreamble\@empty
+%    \end{macrocode}
+%    After the =\@preamble= is created we forget all local
+%    definitions and occupations of the \textsf{token} registers.
+%    \begin{macrocode}
+   \endgroup
+%    \end{macrocode}
+%    In the special situation of  =\multicolumn= =\@preamble=
+%    is not needed as preamble for a =\halign= but it is directly
+%    inserted into our table. Thus instead of =\sharp=
+%    there has to be the column entry (=#3=) wanted by the user.
+%    \begin{macrocode}
+   \def\@sharp{#3}%
+%    \end{macrocode}
+%    Now we can pass the =\@preamble= to \TeX\ . For safety
+%    we start with an =\@arstrut=. This should usually be in the
+%    template for the first column however we do not know if this
+%    template was overwritten by our =\multicolumn=.
+%    We also add a =\null= at the right end to prevent any following
+%    =\unskip= (for example from =\\[..]=) to remove the =\tabcolsep=.
+% \changes{v2.2e}{1994/06/01}{Added \cs{null}}
+%    \begin{macrocode}
+   \@arstrut \@preamble
+   \null
+   \ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%   \section{The Environment Definitions}
+%
+% After these preparations we are able to define the environments. They
+% only differ in the initialisations of =\d@llar...=, =\col@sep=
+%  and =\@halignto=.
+%
+% \begin{macro}{\@halignto}
+% \begin{macro}{\d@llarbegin}
+% \begin{macro}{\d@llarend}
+%    =\d@llar= has to be
+%    locally asigned since otherwise nested \textsf{tabular} and \textsf{array}
+%    environments (via =\multicolumn=) are impossible.
+%    For 25 years or so =\@halignto= was set globally (to save space on the
+%    save stack, but that was a mistake: if there is a tabular in the
+%    output routine (e.g., in the running header) then that tabular is 
+%    able overwrite the =\@halignto=
+%    setting of a tabular in the main text resulting in a very weird error.
+% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
+% \changes{v2.0g}{1992/06/18}{`d@llarbegin defined on toplevel.}
+%    When the new font selection scheme is in force we have to
+%    we surround all =\halign= entries
+%    with braces. See remarks in TUGboat 10\#2. Actually we are going
+%    to use =\begingroup= and =\endgroup=. However, this is only
+%    necessary when we are in text mode. In math the surrounding
+%    dollar signs will already serve as the necessary extra grouping
+%    level. Therefore we switch the settings of =\d@llarbegin= and
+%    =\d@llarend= between groups and dollar signs.
+%    \begin{macrocode}
+\let\d@llarbegin\begingroup
+\let\d@llarend\endgroup
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\array}
+%    Our new definition of =\array= then reads:
+% \changes{v2.0d}{1990/08/20}{`d@llar local to preamble.}
+% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
+%    \begin{macrocode}
+\def\array{\col@sep\arraycolsep
+  \def\d@llarbegin{$}\let\d@llarend\d@llarbegin\def\@halignto{}%
+%    \end{macrocode}
+%    Since there might be an optional argument we call another
+%    macro which is also used by the other environments.
+%    \begin{macrocode}
+  \@tabarray}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@tabarray}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+%
+%    This macro tests for a optional bracket and then calls up
+%    =\@array= or =\@array[c]= (as default).
+%    \begin{macrocode}
+%\def\@tabarray{\@ifnextchar[{\@array}{\@array[c]}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\tabular}
+% \begin{macro}{\tabular*}
+%    The environments \textsf{tabular} and \textsf{tabular$*$} differ
+%    only in the initialisation of the command =\@halignto=. Therefore
+%    we define
+% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
+%    \begin{macrocode}
+\def\tabular{\def\@halignto{}\@tabular}
+%    \end{macrocode}
+%     and analogously for the star form. We evaluate the argument first
+%     using =\setlength= so that users of the \texttt{calc} package can
+%     write code like\\ =\begin{tabular*}{(\columnwidth-1cm)/2}...=
+% \changes{v2.3l}{1998/05/13}{Use \cs{setlength} evaluate arg
+%      so that the calc package can be applied here (pr/2793)}
+% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
+%     \begin{macrocode}
+\expandafter\def\csname tabular*\endcsname#1{%
+       \setlength\dimen@{#1}%
+       \edef\@halignto{to\the\dimen@}\@tabular}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@tabular}
+%    The rest of the job is carried out by the =\@tabular= macro:
+%    \begin{macrocode}
+\def\@tabular{%
+%    \end{macrocode}
+%    First of all we have to make sure that we start out in
+%    \textsf{hmode}.  Otherwise we might find our table dangling by
+%    itself on a line.
+%    \begin{macrocode}
+  \leavevmode
+%    \end{macrocode}
+%    It should be taken into consideration that the macro =\@array=
+%    must be called in math mode. Therefore we open a \textsf{box},
+%    insert a =$= and then assign the correct values to =\col@sep= and
+%    =\d@llar...=.
+% \changes{v2.0d}{1990/08/20}{`d@llar local to preamble.}
+%    \begin{macrocode}
+  \hbox \bgroup $\col@sep\tabcolsep \let\d@llarbegin\begingroup
+                                    \let\d@llarend\endgroup
+%    \end{macrocode}
+%    Now everything \textsf{tabular} specific is done and we are able to
+%    call the =\@tabarray= macro.
+%    \begin{macrocode}
+  \@tabarray}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endarray}
+%    \emph{The code below has been replaced long time ago by an
+%    extended version further down but the code and its documentation
+%    was left here for reference. It is now commented out to avoid
+%    confusion.}
+%
+%    When the processing of \textsf{array} is finished we have to
+%    close the =\halign=
+%    and afterwards the surrounding \textsf{box} selected by
+%    =\@array=. To save \textsf{token} space we then redefine
+%    =\@preamble=
+%    because its replacement text isn't longer needed.
+%    \begin{macrocode}
+%\def\endarray{\crcr \egroup \egroup \gdef\@preamble{}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endtabular}
+% \begin{macro}{\endtabular*}
+%    To end a \textsf{tabular} or \textsf{tabular$*$} environment we
+%    call up =\endarray=, close the math mode and then the surrounding
+%    =\hbox=.
+%    \begin{macrocode}
+\def\endtabular{\endarray $\egroup}
+\expandafter\let\csname endtabular*\endcsname=\endtabular
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+%   \section{Last minute definitions}
+%
+%
+% If this file is used as a package file we should =\let= all macros
+% to =\relax= that were used in the original but are no longer
+%  necessary.
+%    \begin{macrocode}
+\let\@ampacol=\relax        \let\@expast=\relax
+\let\@arrayclassiv=\relax   \let\@arrayclassz=\relax
+\let\@tabclassiv=\relax     \let\@tabclassz=\relax
+\let\@arrayacol=\relax      \let\@tabacol=\relax
+\let\@tabularcr=\relax      \let\@@endpbox=\relax
+\let\@argtabularcr=\relax   \let\@xtabularcr=\relax
+%    \end{macrocode}
+%
+% \begin{macro}{\@preamerr}
+%    We also have to redefine the error routine =\@preamerr= since
+%    new kind of errors are possible.
+%    The code for this macro is not perfect yet;
+%    it still needs too much memory.
+%    \begin{macrocode}
+\def\@preamerr#1{\def\@tempd{{..} at wrong position: }%
+   \PackageError{array}{%
+   \ifcase #1 Illegal pream-token (\@nextchar): `c' used\or %0
+    Missing arg: token ignored\or                           %1
+    Empty preamble: `l' used\or                             %2
+    >\@tempd token ignored\or                               %3
+    <\@tempd changed to !{..}\or                            %4
+    Only one column-spec. allowed.\fi}\@ehc}                %5
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \section
+%   [Defining your own column specifiers]
+%   {Defining your own column specifiers\footnotemark}
+%
+% \footnotetext{The code and the documentation in this section was
+%   written by David. So far only the code from newarray was plugged
+%   into array so that some parts of the documentation still claim
+%   that this is newarray and even worse, some parts of the code are
+%   unnecessarily doubled. This will go away in a future release. For
+%   the moment we thought it would be more important to bring both
+%   packages together.}
+% \changes{v2.1a}{1992/07/03}{Newcolumn stuff added}
+%
+% \DeleteShortVerb{\=}
+% \MakeShortVerb{\"}
+%
+%  \begin{macro}{\newcolumn}
+%    In \texttt{newarray.sty} the macro for specifying new columns was
+%    named "\newcolumn". When the functionality was added to
+%    \texttt{array.sty} the command was renamed "\newcolumntype".
+%    Initially both names were supported, but now (In versions of this
+%    package distributed for \LaTeXe) the old name is not defined.
+% \changes{v2.2a}{1994/02/03}{Now made `newcolumn an error}
+% \changes{v2.2a}{1994/02/04}{Removed `newcolumn}
+%    \begin{macrocode}
+%<*ncols>
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\newcolumntype}
+% \changes{v2.1b}{1992/06/07}{Macro renamed from `newcolumn} As
+% described above, the "\newcolumntype" macro gives users the chance
+% to define letters, to be used in the same way as the primitive
+% column specifiers, `c' `p' etc.
+%    \begin{macrocode}
+\def\newcolumntype#1{%
+%    \end{macrocode}
+% "\NC@char" was added in V2.01 so that active characters, like "@" in
+% AMS\LaTeX\ may be used. This trick was stolen from \texttt{array.sty}
+% 2.0h. Note that we need to use the possibly active token,
+% "#1", in several places, as that is the token that actually
+% appears in the preamble argument.
+%    \begin{macrocode}
+  \edef\NC@char{\string#1}%
+%    \end{macrocode}
+% First we check whether there is already a definition for this column.
+% Unlike "\newcommand" we give a warning rather than an error if it is
+% defined. If it is a new column, add "\NC@do" \meta{column} to
+% the list "\NC@list".
+%    \begin{macrocode}
+  \@ifundefined{NC@find@\NC@char}%
+    {\@tfor\next:=<>clrmbp@!|\do
+      {%
+%    \end{macrocode}
+%    We use \cs{noexpand} on the tokens from the list in case one or
+%    the other (typically \texttt{@}, \texttt{!} or \texttt{|}) has
+%    been made active.
+% \changes{v2.4l}{2019/08/31}{Add a necessary \cs{expandafter} (github/148)}
+%    \begin{macrocode}
+        \if\expandafter\noexpand\next\NC@char
+        \PackageWarning{array}%
+                       {Redefining primitive column \NC@char}\fi}%
+     \NC@list\expandafter{\the\NC@list\NC@do#1}}%
+    {\PackageWarning{array}{Column \NC@char\space is already defined}}%
+%    \end{macrocode}
+% Now we define a macro with an argument delimited by the new column
+% specifier, this is used to find occurrences of this specifier in the
+% user preamble.
+%    \begin{macrocode}
+  \@namedef{NC@find@\NC@char}##1#1{\NC@{##1}}%
+%    \end{macrocode}
+% If an optional argument was not given, give a default argument of 0.
+%    \begin{macrocode}
+  \@ifnextchar[{\newcol@{\NC@char}}{\newcol@{\NC@char}[0]}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\newcol@}
+% We can now define the macro which does the rewriting,
+% "\@reargdef" takes the same arguments as "\newcommand", but
+% does not check that the command is new. For a column, say `D' with
+% one argument, define a command "\NC@rewrite@D" with one
+% argument, which recursively calls "\NC@find" on the user preamble
+% after replacing the first token or group with the replacement text
+% specified in the "\newcolumntype" command. "\NC@find" will find the
+% next occurrence of `D' as it will be "\let" equal to
+% "\NC@find@D" by "\NC@do".
+%    \begin{macrocode}
+\def\newcol@#1[#2]#3{\expandafter\@reargdef
+     \csname NC@rewrite@#1\endcsname[#2]{\NC@find#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@}
+% Having found an occurrence of the new column, save the preamble
+% before the column in "\@temptokena", then check to see if we
+% are at the end of the preamble. (A dummy occurrence of the column
+% specifier will be placed at the end of the preamble by "\NC@do".
+%    \begin{macrocode}
+\def\NC@#1{%
+  \@temptokena\expandafter{\the\@temptokena#1}\futurelet\next\NC@ifend}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@ifend}
+% We can tell that we are at the end as "\NC@do" will place a "\relax"
+% after the dummy column.
+%    \begin{macrocode}
+\def\NC@ifend{%
+%    \end{macrocode}
+% If we are at the end, do nothing. (The whole preamble will now be in
+% "\@temptokena".)
+%    \begin{macrocode}
+  \ifx\next\relax
+%    \end{macrocode}
+% Otherwise set the flag "\if@tempswa", and rewrite the column.
+% "\expandafter" introduced 1n V2.01
+%    \begin{macrocode}
+    \else\@tempswatrue\expandafter\NC@rewrite\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@do}
+% If the user has specified `C' and `L' as new columns, the list of
+% rewrites (in the token register "\NC@list") will look like
+% "\NC@do *" "\NC@do C" "\NC@do L".
+% So we need to define "\NC@do" as a one argument macro which
+% initialises the rewriting of the specified column. Let us assume that
+% `C' is the argument.
+%    \begin{macrocode}
+\def\NC@do#1{%
+%    \end{macrocode}
+% First we let "\NC@rewrite" and "\NC@find" be
+% "\NC@rewrite@C" and "\NC@find@C" respectively.
+%    \begin{macrocode}
+  \expandafter\let\expandafter\NC@rewrite
+    \csname NC@rewrite@\string#1\endcsname
+  \expandafter\let\expandafter\NC@find
+    \csname NC@find@\string#1\endcsname
+%    \end{macrocode}
+% Clear the token register "\@temptokena" after putting the present
+% contents of the register in front of the token "\NC@find". At the
+% end we place the tokens `"C\relax"' which "\NC@ifend" will use
+% to detect the end of the user preamble.
+%    \begin{macrocode}
+  \expandafter\@temptokena\expandafter{\expandafter}%
+        \expandafter\NC@find\the\@temptokena#1\relax}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\showcols}
+% This macro is useful for debugging "\newcolumntype" specifications,
+% it is the equivalent of the primitive "\show" command for macro
+% definitions.  All we need to do is locally redefine "\NC@do" to take
+% its argument (say `C') and then "\show" the (slightly modified)
+% definition of "\NC@rewrite@C". Actually as the the list always
+% starts off with "\NC@do *" and we do not want to print the
+% definition of the $*$-form, define "\NC@do" to throw away the first
+% item in the list, and then redefine itself to print the rest of the
+% definitions.
+%    \begin{macrocode}
+\def\showcols{{\def\NC@do##1{\let\NC@do\NC@show}\the\NC@list}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@show}
+% If the column `C' is defined as above, then
+% "\show\NC@rewrite@C" would output\\
+% "\long macro: ->\NC@find >{$}c<{$}".
+% We want to strip the "long macro: ->" and the "\NC@find". So first we
+% use "\meaning" and then apply the macro "\NC@strip" to the tokens so
+% produced and then "\typeout" the required string.
+%    \begin{macrocode}
+\def\NC@show#1{%
+  \typeout{Column #1\expandafter\expandafter\expandafter\NC@strip
+  \expandafter\meaning\csname NC@rewrite@#1\endcsname\@@}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@strip}
+% Delimit the arguments to "\NC@strip" with `\texttt{:}', `\texttt{->}',
+% a space, and "\@@" to pull out the required parts of the output from
+% "\meaning".
+%    \begin{macrocode}
+\def\NC@strip#1:#2->#3 #4\@@{#2 -> #4}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\NC@list}
+% Allocate the token register used for the rewrite list.
+%    \begin{macrocode}
+\newtoks\NC@list
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The $*$--form}
+% We view the $*$-form as a slight generalisation of the system
+% described in the previous subsection. The idea is to define a $*$
+% column by a command of the form:
+% \begin{verbatim}
+% \newcolumntype{*}[2]{%
+%    \count@=#1\ifnum\count@>0
+%       \advance\count@ by -1 #2*{\count@}{#2}\fi}
+% \end{verbatim}
+% \begin{macro}{\NC@rewrite@*}\label{NC@rewrite@*}
+% \changes{v2.4b}{2005/08/23}{Fix occasional spurious space (PR/3755)}
+% This does not work however as "\newcolumntype" takes great care not
+% to expand anything in the preamble, and so the "\if" is never
+% expanded. "\newcolumntype" sets up various other parts of the
+% rewrite correctly though so we can define:
+%    \begin{macrocode}
+\newcolumntype{*}[2]{}
+%    \end{macrocode}
+% Now we must correct the definition of "\NC@rewrite@*". The
+% following is probably more efficient than a direct translation of
+% the idea sketched above, we do not need to put a $*$ in the preamble
+% and call the rewrite recursively, we can just put "#1" copies of
+% "#2" into "\@temptokena". (Nested $*$ forms will be expanded
+% when the whole rewrite list is expanded again, see "\@mkpream")
+%    \begin{macrocode}
+\long\@namedef{NC@rewrite@*}#1#2{%
+%    \end{macrocode}
+% Store the number.
+%    \begin{macrocode}
+  \count@#1\relax
+%    \end{macrocode}
+% Put "#1" copies of "#2" in the token register.
+%    \begin{macrocode}
+  \loop
+  \ifnum\count@>\z@
+  \advance\count@\m@ne
+  \@temptokena\expandafter{\the\@temptokena#2}%
+  \repeat
+%    \end{macrocode}
+% "\NC@do" will ensure that "\NC@find" is "\let" equal
+% to "\NC@find@*".
+%    \begin{macrocode}
+  \NC@find}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Modifications to internal macros of \texttt{array.sty}}
+%
+% \begin{macro}{\@xexpast}
+% \begin{macro}{\@xexnoop}
+%    These macros are used to expand $*$-forms in
+%    \texttt{array.sty}. "\let" them to "\relax" to save space.
+%    \begin{macrocode}
+\let\@xexpast\relax
+\let\@xexnoop\relax
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\save@decl}
+% We do not assume that the token register is free, we add the new
+% declarations to the front of the register. This is to allow user
+% preambles of the form, ">{foo}>{bar}..". Users are not encouraged to
+% enter such expressions directly, but they may result from the
+% rewriting of "\newcolumntype"'s.
+%    \begin{macrocode}
+\def\save@decl{\toks \count@ = \expandafter\expandafter\expandafter
+                  {\expandafter\@nextchar\the\toks\count@}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@mkpream}
+%    The main modification to "\@mkpream" is to replace the call to
+%    "\@xexpast" (which expanded $*$-forms) by a loop which expands
+%    all "\newcolumntype" specifiers.
+% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
+% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
+%    \begin{macrocode}
+\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
+   \let\@sharp\relax 
+%    \end{macrocode}
+%    
+% \changes{v2.4j}{2018/11/13}{Do not expand argument of
+%    \cs{@startpbox} while building the tabular preamble (sx/459285)}
+%    The "\@startpbox" (which is called for "p", "m" or "b" columns)
+%    receives a user supplied argument: the width of the
+%    paragraph-column. Normally that is something harmless like a length or a
+%    simple length expression, but with the calc package involved it
+%    could break under an "\edef" operation, which is how the preamble
+%    is constructed. We now make use of "\unexpanded" here to prevent that. The
+%    "\expandafter" gymnastics is necessary to expand the "#1" at least
+%    once (since it will get "\@nextchar" as its value and need its
+%    content!
+%    \begin{macrocode}
+   \def\@startpbox##1{\unexpanded\expandafter{\expandafter
+                      \@startpbox\expandafter{##1}}}\let\@endpbox\relax
+   \let\do@row@strut\relax
+   \let\ar@align@mcell\relax 
+%    \end{macrocode}
+%    Now we remove possible  $*$-forms and user-defined column
+%    specifiers in the user preamble by repeatedly executing the list
+%    "\NC@list" until the re-writes have no more effect. The
+%    expanded preamble will then be in the token register
+%    "\@temptokena". Actually we need to know at this point that
+%    this is not "\toks0".
+%    \begin{macrocode}
+   \@temptokena{#1}\@tempswatrue
+   \@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
+%    \end{macrocode}
+%    Afterwards we initialize all registers and macros, that we need
+%    for the build-up of the preamble.
+%    \begin{macrocode}
+   \count@\m@ne
+   \let\the@toks\relax
+   \prepnext@tok
+%    \end{macrocode}
+% Having expanded all tokens defined using "\newcolumntype" (including
+% "*"), we evaluate the remaining tokens, which are saved in
+% "\@temptokena".  We use the \LaTeX--macro "\@tfor" to inspect each
+% token in turn.
+%    \begin{macrocode}
+   \expandafter \@tfor \expandafter \@nextchar
+    \expandafter :\expandafter =\the\@temptokena \do
+%    \end{macrocode}
+% "\@testpatch" does not take an argument since \texttt{array.sty} 2.0h.
+%    \begin{macrocode}
+   {\@testpach
+   \ifcase \@chclass \@classz \or \@classi \or \@classii
+     \or \save@decl \or \or \@classv \or \@classvi
+     \or \@classvii \or \@classviii
+%    \end{macrocode}
+%    In \texttt{newarray.sty} class 9 is equivalent to class 10.
+%    \begin{macrocode}
+     \or \@classx
+     \or \@classx \fi
+   \@lastchclass\@chclass}%
+   \ifcase\@lastchclass
+   \@acol \or
+   \or
+   \@acol \or
+   \@preamerr \thr@@ \or
+   \@preamerr \tw@ \@addtopreamble\@sharp \or
+   \or
+   \else  \@preamerr \@ne \fi
+   \def\the@toks{\the\toks}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classix}
+%    \texttt{array.sty} does not allow repeated \texttt{>}
+%    declarations for the same column. This is allowed in
+%    \texttt{newarray.sty} as documented in the introduction. Removing
+%    the test for this case makes class 9 equivalent to class 10, and
+%    so this macro is redundant. It is "\let" to "\relax" to save
+%    space.
+%    \begin{macrocode}
+\let\@classix\relax
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classviii}
+%    In \texttt{newarray.sty} explicitly allow class 2, as repeated
+%    \texttt{<} expressions are accepted by this package.
+%    \begin{macrocode}
+\def\@classviii{\ifnum \@lastchclass >\z@\ifnum\@lastchclass=\tw@\else
+      \@preamerr 4\@chclass 6 \@classvi \fi\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@classv}
+% Class 5 is \texttt{@}-expressions (and is also called by class 1)
+% This macro was incorrect in Version~1. Now we do not expand the
+% "@"-expression, but instead explicitly replace an
+% "\extracolsep" command by an assignment to "\tabskip" by a
+% method similar to the "\newcolumntype" system described above.
+% "\d@llarbegin" "\d@llarend" were introduced in V2.01 to match
+% \texttt{array.sty} 2.0h.
+%    \begin{macrocode}
+\def\@classv{\save@decl
+   \expandafter\NC@ecs\@nextchar\extracolsep{}\extracolsep\@@@
+   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
+   \prepnext@tok}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\NC@ecs}
+% Rewrite the first occurrence of "\extracolsep{1in}" to
+% "\tabskip1in\relax". As a side effect discard any tokens after a
+% second "\extracolsep", there is no point in the user entering two of
+% these commands anyway, so this is not really a restriction.
+%    \begin{macrocode}
+\def\NC@ecs#1\extracolsep#2#3\extracolsep#4\@@@{\def\@tempa{#2}%
+  \ifx\@tempa\@empty\else\toks\count@={#1\tabskip#2\relax#3}\fi}
+%</ncols>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Support for the \texttt{delarray.sty}}
+%
+% The \texttt{delarray.sty} package  extends the array syntax by
+% supporting the notation of delimiters. To this end we extend the
+% array parsing mechanism to include a hook which can be used by this
+% (or another) package to do some additional parsing.
+%
+% \begin{macro}{\@tabarray}
+%    This macro tests for an optional bracket and then calls up
+%    "\@@array" or "\@@array[c]" (as default).
+%    \begin{macrocode}
+%<*package>
+\def\@tabarray{\@ifnextchar[{\@@array}{\@@array[c]}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@array}
+%    This macro tests could then test an optional delimiter before the
+%    left brace of the main preamble argument. Here in the main package
+%    it simply is let to be "\@array".
+%    \begin{macrocode}
+\let\@@array\@array
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endarray}
+% \begin{macro}{\@arrayright}
+%    We have to declare the hook we put into "\@array" above.
+%    A similar hook `"\@arrayright"' will be inserted into the
+%    "\endarray" to gain control. Both defaults to empty.
+%    \begin{macrocode}
+\def\endarray{\crcr \egroup \egroup \@arrayright \gdef\@preamble{}}
+\let\@arrayleft\@empty
+\let\@arrayright\@empty
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Support for \texttt{\textbackslash firsthline} and
+%             \texttt{\textbackslash lasthline}}
+%
+% The Companion~\cite[p.137]{bk:GMS94} suggests two additional
+% commands to control the alignments in case of tabulars with
+% horizontal lines. They are now added to this package.
+%
+%  \begin{macro}{\extratabsurround}
+%    The extra space around a table when "\firsthline" or "\lasthline"
+%    are used.
+%    \begin{macrocode}
+\newlength{\extratabsurround}
+\setlength{\extratabsurround}{2pt}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\backup@length}
+%    This register will be used internally by "\firsthline" and
+%    "\lasthline".
+%    \begin{macrocode}
+\newlength{\backup@length}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\firsthline}
+% \changes{v2.3h}{1996/05/25}{Complete reimplementation}
+%    This code can probably be improved but for the moment it should
+%    serve.
+%
+%    We start by producing a single tabular row without any visible
+%    content that will produce the external reference point in case
+%    "[t]" is used.
+%    \begin{macrocode}
+\newcommand{\firsthline}{%
+  \multicolumn1c{%
+%    \end{macrocode}
+%    Within this row we calculate "\backup@length" to be the height
+%    plus depth of a standard line. In addition we have to add the
+%    width of the "\hline", something that was forgotten in the
+%    original definition.
+%    \begin{macrocode}
+    \global\backup@length\ht\@arstrutbox
+    \global\advance\backup@length\dp\@arstrutbox
+    \global\advance\backup@length\arrayrulewidth
+%    \end{macrocode}
+%    Finally we do want to make the height of this first line be a bit
+%    larger than usual, for this we place the standard array strut
+%    into it but raised by "\extratabsurround"
+%    \begin{macrocode}
+     \raise\extratabsurround\copy\@arstrutbox
+%    \end{macrocode}
+%    Having done all this we end the line and back up by the value of
+%    "\backup@length" and then finally place our "\hline". This should
+%    place the line exactly at the right place but keep the reference
+%    point of the whole tabular at the baseline of the first row.
+%    \begin{macrocode}
+    }\\[-\backup@length]\hline
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lasthline}
+% \changes{v2.3h}{1996/05/25}{Complete reimplementation}
+%    For "\lasthline" the situation is even worse and I got it
+%    completely wrong initially.
+%
+%    The problem in this case is that if the optional argument "[b]"
+%    is used we do want the reference point of the tabular be at the
+%    baseline of the last row but at the same time do want the the
+%    depth of this last line increased by "\extratabsurround" without
+%    changing the placement "\hline".
+%
+%    We start by placing the rule followed by an invisible row.
+%    \begin{macrocode}
+\newcommand{\lasthline}{\hline\multicolumn1c{%
+%    \end{macrocode}
+%    We now calculate "\backup@length" to be the height and depth of
+%    two lines plus the width of the rule.
+%    \begin{macrocode}
+    \global\backup@length2\ht\@arstrutbox
+    \global\advance\backup@length2\dp\@arstrutbox
+    \global\advance\backup@length\arrayrulewidth
+%    \end{macrocode}
+%    This will bring us back to the baseline of the second last row:
+%    \begin{macrocode}
+    }\\[-\backup@length]%
+%    \end{macrocode}
+%    Thus if we now add another invisible row the reference point of
+%    that row will be at the baseline of the last row (and will be the
+%    reference for the whole tabular). Since this row is invisible we
+%    can enlarge its depth by the desired amount.
+%    \begin{macrocode}
+    \multicolumn1c{%
+       \lower\extratabsurround\copy\@arstrutbox
+       }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Getting the spacing around rules right}
+%
+%    Beside a larger functionality \texttt{array.sty} has one
+%    important difference to the standard \texttt{tabular} and
+%    \texttt{array} environments: horizontal and vertical rules make a
+%    table larger or wider, e.g., \verb=\doublerulesep= really denotes
+%    the space between two rules and isn't measured from the middle of
+%    the rules.
+%
+%  \begin{macro}{\@xhline}
+%    For vertical rules this is implemented by the definitions above,
+%    for horizontal rules we have to take out the backspace.
+% \changes{v2.3d}{1995/11/19}{fix space between double rules pr/1945}
+%    \begin{macrocode}
+\CheckCommand*\@xhline{\ifx\reserved@a\hline
+               \vskip\doublerulesep
+               \vskip-\arrayrulewidth
+             \fi
+      \ifnum0=`{\fi}}
+\renewcommand*\@xhline{\ifx\reserved@a\hline
+               \vskip\doublerulesep
+             \fi
+      \ifnum0=`{\fi}}
+%</package>
+%    \end{macrocode}
+%  \end{macro}
+
+% \subsection{Implementing column types \texttt{w} and \texttt{W}}
+%
+% In TugBoat 38/2 an extension was presented that implemented two
+% aditional column types \texttt{w} and \texttt{W}. These have now
+% been added to the package itself.
+%
+%
+%  \begin{macro}{\ar@cellbox}
+%    For \texttt{w} and \texttt{W} column types we need a box to
+%    temporarily hold the cell content.
+% \changes{v2.4f}{2017/11/07}{Macro added}
+%    \begin{macrocode}
+\newsavebox\ar@cellbox
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\newcolumntype w}
+%    The \texttt{w} column type has two arguments: the first holds the
+%    alignment which is either "l", "c", or "r" and the second is the
+%    nominal width of the column.
+% \changes{v2.4f}{2017/11/07}{Column type added}
+%    \begin{macrocode}
+\newcolumntype{w}[2]{%
+%    \end{macrocode}
+%    Before the cell content we start an "lrbox"-environment to
+%    collect the cell material into the previously allocated box
+%    "\ar@cellbox".
+%    \begin{macrocode}
+  >{\begin{lrbox}\ar@cellbox}%
+%    \end{macrocode}
+%    Then comes a specifier for the cell content.  We use "c", but
+%    that doesn't matter as in the end we will always put a box of a
+%    specific width ("#2") into the cells of that column, so "l" or
+%    "r" would give the same result. There is only a difference if
+%    there are also very wide "\multicolumn" rows overwriting the
+%    setting  in which case "c" seems to be slightly better.
+%    \begin{macrocode}
+  c%
+%    \end{macrocode}
+%    At the end of the cell we end the "lrbox" environment so that all
+%    of the cell content is now in box "\ar@cellbox".  As a final step we
+%    put that box into a "\makebox" using the optional arguments of
+%    that command to achieve the correct width and the desired
+%    alignment within that width.
+%    \begin{macrocode}
+  <{\end{lrbox}%
+    \makebox[#2][#1]{\usebox\ar@cellbox}}}
+%    \end{macrocode}
+%  \end{macro}
+
+%
+%
+%  \begin{macro}{\newcolumntype W}
+%    The \texttt{W} is similar but in this case we want a warning if
+%    the cell content is too wide.
+% \changes{v2.4f}{2017/11/07}{Column type added}
+%    \begin{macrocode}
+\newcolumntype{W}[2]
+  {>{\begin{lrbox}\ar@cellbox}%
+   c%
+   <{\end{lrbox}%
+   \let\hss\hfil
+   \makebox[#2][#1]{\unhbox\ar@cellbox}}}
+%    \end{macrocode} 
+%    This is a bit sneaky, as it temporarily disables "\hss", but
+%    given that we know what goes into that box it should be
+%    sufficient.
+%  \end{macro}
+%
+%
+% \PrintIndex
+% \PrintChanges
+%
+% \Finale
+%
+\endinput
+
diff --git a/macros/latex-dev/required/tools/array.pdf b/macros/latex-dev/required/tools/array.pdf
new file mode 100644
index 0000000000..dfb2f3cc61
--- /dev/null
+++ b/macros/latex-dev/required/tools/array.pdf
diff --git a/macros/latex-dev/required/tools/bm.dtx b/macros/latex-dev/required/tools/bm.dtx
new file mode 100644
index 0000000000..2216dcea07
--- /dev/null
+++ b/macros/latex-dev/required/tools/bm.dtx
@@ -0,0 +1,1705 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%
+% \iffalse
+%% Copyright 1996 1997 1998 1999 2002 2003 2004 2016 2017 2019
+%% David Carlisle Frank Mittelbach
+%%
+%% Development of this package was commissioned by Y&Y Inc.
+%
+%
+%<*dtx>
+          \ProvidesFile{bm.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{bm}
+%<driver>\ProvidesFile{bm.drv}
+% \fi
+%         \ProvidesFile{bm.dtx}
+          [2019/07/24 v1.2d Bold Symbol Support (DPC/FMi)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{bm}
+\begin{document}
+\DocInput{bm.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+%
+% \GetFileInfo{bm.dtx}
+%
+% \title{The \textsf{bm} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}\ \thanks{Development of this package
+%         was commissioned by Y\&Y.}}
+%
+% \date{\filedate}
+% \author{David Carlisle with support by Frank Mittelbach}
+%  \MaintainedByLaTeXTeam{tools}
+%  \maketitle
+%
+% \section{Introduction}
+%
+% This package defines commands to access bold math
+% symbols. The basic command is |\bm| which may be used to make the
+% math expression in its argument be typeset using bold fonts.
+%
+% The syntax of |\bm| is:\\
+% |\bm|\marg{math expression}\\
+% So |$\alpha \not= \bm{\alpha}$| produces $\alpha \not= \bm{\alpha}$.
+%
+% |\bm| goes to some trouble to preserve the spacing, so that for
+% instance |\bm<| is a bold $\bm<$ but with the correct |\mathrel|
+% spacing that \TeX\ gives to $<$. The calculations that \TeX\ needs to
+% do for |\bm| can be quite involved and so a definition form is
+% provided.
+%
+% |\DeclareBoldMathCommand|%^^A
+%       \oarg{math version}\marg{cmd}\marg{math expression}
+%
+% Defines |\cmd| to be the bold form of the math expression.
+% The \meta{math version} defaults to `bold' (i.e., |\boldmath|).
+%
+% For relatively simple expressions, the resulting definitions are very
+% efficient, for instance after:\\
+% |\DeclareBoldMathCommand\balpha{\alpha}|\\
+% |\balpha| is a single `mathchardef' token producing a bold alpha,
+% and so is just as fast to execute as |\alpha|.
+%
+% The above command is mainly intended for use in packages.
+% For occasional use in \LaTeX\ documents, and for compatibility
+% with the plain \TeX\ support for the mathtime fonts, a `user-level'
+% version, |\bmdefine| is provided that is equivalent to:\\
+% |\DeclareBoldMathCommand[bold]|.
+%
+% If there is a `heavy' math version defined (usually accessed by a
+% user-command |\heavymath|) then a similar command |\hm|
+% is defined which access these `ultra bold' fonts. Currently this is
+% probably only useful with the `mathtime plus' font collection.
+% Definitions of commands that use these fonts may be made by
+% specifying the optional argument `heavy' to |\DeclareBoldMathCommand|.
+% Again an abbreviation, |\hmdefine|, is provided, equivalent to:\\
+% |\DeclareBoldMathCommand[heavy]|.
+%
+% The command names (but not the implementation) are taken from Michael
+% Spivak's macros to support the mathtime fonts for plain \TeX. In those
+% original macros, the syntax for |\bmdefine| was
+% |\bmdefine\balpha{\bm\alpha}| (with a nested |\bm|). This syntax also
+% works with this package.
+%
+% \section{Font allocation}
+% In order to access bold fonts in the simplest and quickest possible
+% manner, the package normally allocates symbol fonts for bold
+% (and possibly heavy) fonts into the `normal' math version.
+% By default it allocates at most four fonts for |\bm| and at most
+% three fonts for |\hm|. This means that if the mathtime plus font set
+% is being used, seven additional symbol fonts will be used, in addition
+% to the basic four that \LaTeX\ already declares. The mathtime
+% package also declares an extra symbol font, bringing the total to
+% twelve. The maximum number of symbol \emph{and} math alphabet fonts
+% that can be used in a math version is sixteen. So the above allocation
+% scheme does not leave room for many extra math symbols (such as the
+% AMS symbols) or math alphabets (such as |\mathit|).
+%
+% Before loading the \textsf{bm} package you may define |\bmmax|
+% and |\hmmax| to be suitable values, for instance you may want
+% to set |\newcommand\hmmax{0}| if you will not be using |\hm|
+% much, but you do have a heavy math version defined.
+%
+% Even if |\bmmax| is set to zero, |\bm| will still access the correct
+% bold fonts (by accessing the fonts via |\boldmath|) but this method
+% is slower, and does not work with delimiters. Delimiters can only be
+% made bold if the bold font has been allocated.
+%
+% Conversely if you have a non standard font set that makes available
+% extra math delimiters and accents in bold and medium weights you may
+% want to \emph{increase} |\bmmax| so that fonts are allocated for
+% your font set.
+%
+% \section{Features}
+% In most cases this package should work in a fairly self explanatory
+% way, but there are some things that might not be obvious.
+%
+% \subsection{Interaction with Math Alphabet Commands}
+%
+% As mentioned above, |\bm| goes to some trouble to try to make a
+% command that is just like its argument, but using a bold font.
+% This does not always produce the effect that you might expect.
+%\begin{verbatim}
+% $1 g \bm{g}$
+% $2 \mathrm{g \bm{g}}$
+% $3 {g} \bm{{g}}$
+% $4 \mathrm{{g} \bm{{g}}}$
+% $5 \mathrm{g} \bm{\mathrm{g}}$
+%\end{verbatim}
+% produces the following:
+% \begin{flushleft}
+% $1 g \bm{g}$
+% $2 \mathrm{g \bm{g}}$
+% $3 {g} \bm{{g}}$
+% $4 \mathrm{{g} \bm{{g}}}$
+% $5 \mathrm{g} \bm{\mathrm{g}}$
+% \end{flushleft}
+% In math mode `g' is effectively a command that produces the letter `g'
+% from the `letters' alphabet, unless a Math Alphabet command is in
+% effect, in which case the `g' comes from the specified alphabet.
+% |\bm{g}| makes an equivalent command, but which defaults to a bold
+% letter alphabet. So in the first example |\bm{g}| is bold math italic,
+% but in the second example the |\mathrm| applies to both |g| and
+% |\bm{g}| in the same way, and so they are both roman.
+%
+% |\bm| only inspects the `top level' definition of a command, for more
+% complicated expressions, and anything inside a |{ }| group, |\bm|
+% forces bold fonts by essentially the same (slow) technique used by the
+% AMS |\boldsymbol| command (but |\bm| still takes more care of the
+% spacing). So the third example produces identical output to the first
+% (but \TeX\ takes more time producing it).
+%
+% In the fourth example the |\mathrm{\bm{g}}| is essentially
+% equivalent to |\mathrm{\mbox{\boldmath$g$}}|. Currently math alphabet
+% settings are not passed down to `nested' math lists, and so in this
+% example, the |\mathrm| has no effect, and a bold math italic $\bm g$
+% is obtained.
+%
+% Similarly the last example is equivalent to
+% |$\mbox{\boldmath$\mathrm{g}$}}| and so in this case, one obtains a
+% bold roman \textbf{g}.
+%
+% \subsection{Delimiters}
+% \TeX\ can treat character tokens in two\footnote
+%  {Well more than two really.}
+% ways. If there is a preceding
+% |\left| or |\right| it can treat them as a delimiter, otherwise it can
+% treat them as a standard character. For example |\left<\right>|
+% produces $\left<\right>$, which is totally different from |<>|, which
+% produces $<>$.
+%
+% \TeX\ can only do this for character tokens. Commands such as
+% |\langle| do not act in this way. This means that |\bm| has to decide
+% whether to treat a character as a delimiter or not. The rule it uses
+% is, it makes a delimiter command for a character if the previous
+% token in the argument was |\left| or |\right|. So |\left\bm{<}| does
+% not work, but |\bm{\left<}| does.
+%
+% \subsection{Command Arguments}
+%
+% Normally if a command takes arguments the full command, including
+% any arguments, should be included in |\bm|.
+%
+% So |\bm{\overbrace{abc}}| (producing \smash{$\bm{\overbrace{abc}}$})
+% not
+% |\bm{\overbrace}{abc}|. If you do not include all the arguments you
+% will typically get the error message:\\
+% |Runaway argument?|\\
+% |! Forbidden control sequence found while scanning use of|
+%                                                      \texttt{\ldots}
+%
+% However commands defined in terms of the \TeX\ accent and
+% radical primitives \emph{may} be used without their arguments.
+% So |\bm{\hat}{a}| produces $\bm{\hat}{a}$, a bold accent over a
+% non-bold $a$ (compare $\hat{a}$)
+%  whereas |\bm{\hat{a}}| makes both the $a$ and the accent bold,
+% $\bm{\hat{a}}$.
+% Similarly, although the \LaTeX\ command |\sqrt| must be used with its
+% arguments, |\sqrtsign| may be used as in |\bm\sqrtsign{abc}| to
+% produce $\bm\sqrtsign{abc}$ rather than  $\sqrtsign{abc}$ or
+%  $\bm{\sqrtsign{abc}}$
+%
+% If you really need to make a command with arguments use bold fonts
+% without making all of the arguments bold, you can explicitly
+% reset the math version in the argument, eg:\\
+% $\begin{array}{ccc}
+% |\sqrt{xyz}|&|\bm{\sqrt{xyz}}|&|\bm{\sqrt{\mbox{\unboldmath$xyz$}}}|\\
+% \sqrt{xyz}& \bm{\sqrt{xyz}}&  \bm{\sqrt{\mbox{\unboldmath$xyz$}}}
+% \end{array}$
+%
+% \subsection{Bold fonts}
+% This package interrogates the font allocations of the bold and heavy
+% math versions, to determine which bold fonts are available.
+% This means that it is best to load the package \emph{after}
+% any packages that define new symbol fonts, or (like the
+% \textsf{mathtime} package) completely change the symbol font
+% allocations.
+%
+% If no bold font appears to be available for a particular symbol,
+% |\bm| will use `poor man's bold' that is, overprinting the same
+% character in slightly offset
+% positions to give an appearance of boldness.
+%
+% In the standard Computer Modern font set, there is no bold
+% `large symbols' font. In the `mathptm' and (standard) mathtime
+% font sets there are no bold math fonts. In the `mathtime plus'
+% font set there are suitable fonts for bold and heavy math setting,
+% and so |\bm| and |\hm| work well. Similarly in the basic Lucida
+% New Math font set there are no bold math fonts, so |\bm| will
+% use `poor man's bold. However if the Lucida Expert set is used,
+% Then |\bm| will detect, and use the bold math fonts that are
+% available.
+%
+% As discussed above, one may set |\bmmax| higher or lower than its
+% default value of four to control the font allocation system. Finer
+% control may be gained by explicitly declaring bold symbol fonts.
+% Suppose you have a symbol font `xyz' that is available in medium and
+% bold weights, then you would declare this to \LaTeX\ via:\\
+% |\DeclareSymbolFont{extras}  {OMS}{xyz}{m}{n}|\\
+% |\SetSymbolFont{extras}{bold}{OMS}{xyz}{bx}{n}|\\
+% At this point the symbols will be available in the normal math
+% version, and their bold variants in |\boldmath|. If you also
+% declare:\\
+% |\DeclareSymbolFont{boldextras}{OMS}{xyz}{bx}{n}|\\
+% That is, declare a symbol font whose name is formed by prefixing
+% `bold' (or `heavy') to an existing symbol font, then |\bm| (or
+% |\hm|) will use this font directly, rather then accessing the
+% `extras' symbol font via |\boldmath|.
+%
+% \subsection{Strange failures}
+% In order to get the correct spacing, |\bm| has to `investigate' the
+% definition of the commands in its argument. It is possible that
+% some strange constructions could `confuse' this investigation.
+% If this happens then \LaTeX\ will almost certainly stop with a strange
+% error. This should not happen with any of the math symbols
+% defined in the base \LaTeX\ or AMS distributions, or any commands
+% defined in terms of those symbols using normal \LaTeX\ math
+% constructs. However if some command does fail to work inside |\bm|
+% you should always be able to surround it with an extra set of braces
+% |\bm{{\cmd}}| rather than |\bm{\cmd}|. |\bm| will not then attempt
+% to set the correct spacing, so you may need to set it explicitly,
+% for instance, for a relation, |\bm{\mathrel{\cmd}}|.
+%
+% \subsection{AMS package \textsf{amsbsy}}
+% The |\bm| command shares some functionality with the |\boldsymbol|
+% command from the AMS \LaTeX\ collection. To aid in moving documents
+% between these two packages, this package defines |\boldsymbol| and
+% |\heavysymbol| as alternative names for |\bm| and |\hm|.
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \changes{v0.01}{1996/12/01}
+%      {Initial DPC attempt,
+%       remove all assumptions about mathtime encoding}
+% \changes{v0.02}{1996/12/02}
+%      {Add \cs{mathchoice} stuff}
+% \changes{v0.03}{1996/12/12}
+%      {Completely reimplement (again). Add \cs{bmdefine}.}
+% \changes{v0.04}{1996/12/12}
+%      {Add \cs{hm} and support for special active mathcode.}
+% \changes{v0.05}{1996/12/12}
+%      {Assorted fixes}
+% \changes{v0.99}{1997/01/16}
+%      {First public version}
+% \changes{v1.0a}{1997/02/14}
+%      {First ctan version (same as 0.99b)}
+% \changes{v1.0b}{1997/04/14}
+%      {Add to tools bundle.}
+% \changes{v1.0g}{1999/07/05}
+%      {minor doc changes latex/3058}
+%
+%
+%
+% The commands |\bm| and |\hm| work by defining a number of additional
+% symbol fonts corresponding to the standard ones
+%  `operators', `letters', `symbols', and `largesymbols'.
+% The names for these symbols fonts are produced by prefixing the usual
+% name with `bold' or `heavy'.
+%
+% For maximum flexibility we get the font definitions by looking in the
+% corresponding math versions, i.e., into |\mv@bold| and if defined into
+% |\mv@heavy|.
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+% \changes{v0.09}{1996/12/19}
+%      {Always define \cs{bm} even if no bold math}
+%
+% \begin{macro}{\bm@table}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% \changes{v0.12}{1997/01/10}
+%      {Ensure do not allocate too many math group slots.}
+% \changes{v0.99a}{1997/01/17}
+%      {Let \cs{hm} use font allocated for \cs{bm}}
+% \changes{v0.99b}{1997/01/19}
+%      {Restore NFSS internals}
+% \begin{macro}{\bm@boldtable}
+% \begin{macro}{\bm@heavytable}
+% The table, |\bm@table|, (which is locally |\let| to either the bold
+% or heavy version) defines, for each \meta{math group} (\meta{fam}),
+% the `offset' to the bold version of the specified symbol font.
+% If there is no bold symbol font defined, the offset will be
+% set to zero if there is a bold font assigned to this slot in the
+% bold math version, or $-1$ if the font in the bold math version
+% is the same as the one in the normal math version. In this case
+% a `poor man's bold' system of overprinting is used to achieve
+% boldness where this is possible.
+%
+% The settings are made at the time this package is read, and so
+% it is best to load this package late, after any font loading packages
+% have been loaded. Symbol fonts loaded after this package will get the
+% offset of zero, so they will still be made bold by |\bm| as long as an
+% appropriate font is declared for the bold math version.
+%
+% |\bm@boldtable| and |\bm@heavytable| are set up using very similar
+% code, which is temporarily defined to |\bm|, to save wasting a csname.
+% Similarly |\bm@pmb|\ldots\ (which will be defined later) are used
+% as scratch macros.
+%
+% The general plan. Run through the fonts allocated to the normal math
+% version. Ignore \meta{math alphabet} allocations\footnote{For now?}
+% but for each math symbol font, look in the math version specified by
+% |#1| (bold or heavy). If the font there is different, then allocate
+% a new symbol font in the normal math version to access that bold font
+% and place the numerical difference between the allocations of the bold
+% and normal font into the table being built (|\bm@boldtable|, if |#1|
+% is bold). If the symbol allocation is already greater than |\bmmax|
+% do not allocate a new symbol font, but rather set the offset in the
+% table to zero. |\bm| will detect this, and use |\boldmath| on its
+% argument in this case, so the bold font will be accessed but more
+% slowly than using a direct access to a bold font allocated into the
+% normal math version. If the font allocated in the bold math version is
+% the same as the font in the normal math version, set the offset to
+% $-1$, which is a flag value that causes |\bm| to use `poor man's bold'
+% overprinting three copies of the symbol, offset slightly to give an
+% appearance of boldness.
+%
+% Fonts containing delimiters and math accents \emph{must} be allocated
+% into the normal math version if they are to be used with |\bm|. (In
+% these cases |\bm| will produce the normal weight symbol, rather than
+% using |\boldmath| or poor man's bold.)
+%
+%    \begin{macrocode}
+\def\bm#1#2{%
+%    \end{macrocode}
+% This code can not work inside a group, as that would affect any symbol
+% font allocations, so instead use some scratch macros to save and
+% restore the definitions of commands we need to change locally.
+%    \begin{macrocode}
+  \let\bm@pmb\install@mathalphabet
+  \let\bm@pmb@\getanddefine@fonts
+  \let\bm@pmb@@\or
+  \edef\bm@general{\f@encoding/\f@family/\f@series/\f@shape/\f@size}%
+%    \end{macrocode}
+%
+% |#2| specifies the maximum number of fonts to allocate
+% (either |\bmmax| or |\hmmax|). First check against |\count18|
+% that there are that many slots left, and if not reduce accordingly.
+% Put the resulting value in |\@tempcnta|.
+%    \begin{macrocode}
+  \@tempcnta#2%
+  \count@-\count18%
+  \advance\count@-\@tempcnta
+  \advance\count@15\relax
+  \ifnum\count@<\z@
+    \advance\@tempcnta\count@
+  \fi
+%    \end{macrocode}
+% Make |\or| non-expandable, so we can build an |\ifcase| bit-by-bit
+% in a sequence of |\edef|s.
+%    \begin{macrocode}
+  \let\or\relax
+%    \end{macrocode}
+%
+% Initialise the table (to |\@gobble| to remove the first |\or|).
+%    \begin{macrocode}
+  \expandafter\let\csname bm@#1table\endcsname\@gobble
+%    \end{macrocode}
+%
+% Helper macro that adds the next entry to the table being built.
+%    \begin{macrocode}
+  \def\bm@define##1{%
+    \expandafter\xdef\csname bm@#1table\endcsname{%
+      \csname bm@#1table\endcsname\or##1}}%
+%    \end{macrocode}
+%
+% Each symbol font is recorded in the math version list by a sequence
+% such as:\\
+% | \getanddefine@fonts \symsymbols \OMS/cmsy/m/n|\\
+% Where the first argument is a chardef token carrying the number
+% allocated (to symbols, in this example), and the second argument is a
+% csname whose \emph{name} denotes the font used.
+% So locally redefine |\getanddefine@fonts| to compare |#2| with
+% the name in the appropriate slot in the bold math version.
+%    \begin{macrocode}
+  \def\getanddefine@fonts##1##2{%
+    \def\@tempa{##2}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \def\@tempb####1##1####2####3\@nil{\def\@tempb{####2}}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \expandafter\expandafter\expandafter
+      \@tempb\csname mv@#1\endcsname\@nil
+%    \end{macrocode}
+%
+% Now |\@tempa| and  |\@tempb| contain the names of the fonts allocated
+% to this slot in the two math versions.
+%    \begin{macrocode}
+    \ifx\@tempa\@tempb
+%    \end{macrocode}
+% If they are the same, set this offset to $-1$, as a flag to use
+% poor man's bold.
+%    \begin{macrocode}
+      \bm@define\m@ne
+    \else
+%    \end{macrocode}
+% Else make a new name by adjoining |#1| to the name of the symbol font
+% eg, |\symboldsymbols| to match |\symsymbols|. If that font has already
+% been allocated, or if |\@tempcnta| is positive so we can allocate a
+% new slot for this font, then the table will be
+% set with the offset between the two fonts. otherwise set the offset to
+% zero (so |\boldmath| will be used to access the font).
+%    \begin{macrocode}
+      \edef\@tempa{sym#1\expandafter\@gobblefour\string##1}%
+      \ifnum\@tempcnta<%
+           \expandafter\ifx\csname\@tempa\endcsname\relax
+             \@ne
+           \else
+             \m@ne
+           \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+        \bm@define\z@
+      \else
+%    \end{macrocode}
+%
+% If the font is not yet allocated, allocate it now, using
+% an internal hack into |\DeclareMathSymbolFont|.
+%
+% However before allocating it look in the bold math version
+% to see if it is the same, and if so use that. For example
+% with Mathtime the `operators' font in the `heavy' math version
+% is different from that in `normal', but it is the same as
+% the font in `bold' (Times bold). So rather than allocate
+% |\symheavyoperators| just set it equal to |\symboldoperators|.
+%    \begin{macrocode}
+        \expandafter\ifx\csname\@tempa\endcsname\relax
+          \begingroup
+          \escapechar\m@ne
+          \edef\@tempb{\endgroup
+            \noexpand\split@name
+            \expandafter\string\@tempb}%
+          \@tempb/\@nil
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+         \expandafter\ifx
+           \csname symbold\expandafter\@gobblefour\string##1\endcsname
+           \relax
+%    \end{macrocode}
+%  If no font has been allocated for |\bm| yet, then allocate it now.
+%    \begin{macrocode}
+            \expandafter\new@mathgroup\csname\@tempa\endcsname
+            \expandafter\new@symbolfont\csname\@tempa\endcsname
+                       \f@encoding\f@family\f@series\f@shape
+%    \end{macrocode}
+% Reduce by one the number of fonts we can still allocate.
+%    \begin{macrocode}
+            \advance\@tempcnta\m@ne
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+         \else
+%    \end{macrocode}
+% Else do a similar look into the bold mathgroup.
+% Use |\bm@expand| as a scratch macro to save on string space.
+%    \begin{macrocode}
+           \def\bm@expand####1##1####2####3\@nil{\def\bm@expand{####2}}%
+    \expandafter\expandafter\expandafter
+           \bm@expand\csname mv@bold\endcsname\@nil
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+           \ifx\bm@expand\@tempb
+%    \end{macrocode}
+% If the font just found (in heavy) is the same as the font in bold
+% use the slot (in normal) previously allocated for the bold font.
+% (That clear?)
+%    \begin{macrocode}
+             \expandafter\let\csname\@tempa\expandafter\endcsname
+                \csname symbold\expandafter
+                        \@gobblefour\string##1\endcsname
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+           \else
+%    \end{macrocode}
+% Otherwise allocate a new slot for it.
+%    \begin{macrocode}
+             \expandafter\new@mathgroup\csname\@tempa\endcsname
+             \expandafter\new@symbolfont\csname\@tempa\endcsname
+                       \f@encoding\f@family\f@series\f@shape
+             \advance\@tempcnta\m@ne
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+           \fi
+         \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+        \else
+%    \end{macrocode}
+% If the font has been allocated already, use the existing allocation.
+%    \begin{macrocode}
+          \PackageInfo{bm}%
+            {Symbol font \@tempa\space already defined.\MessageBreak
+             Not overwriting it}%
+        \fi
+%    \end{macrocode}
+% Whether the font has just been allocated, or whether it was previously
+% allocated, compute the offset and add it to the table.
+%    \begin{macrocode}
+        \count@\csname\@tempa\endcsname
+        \advance\count@-##1%
+        \bm@define{\the\count@\relax}%
+      \fi
+    \fi}%
+%    \end{macrocode}
+%
+% The math version list also contains information about math alphabet
+% commands, but we want to ignore those  here, so \ldots
+%    \begin{macrocode}
+  \let\install@mathalphabet\@gobbletwo
+%    \end{macrocode}
+%
+% Having set up the local definitions, execute the list for the normal
+% math version.
+%    \begin{macrocode}
+  \mv@normal
+%    \end{macrocode}
+%
+% So now the offsets are all entered into the table, separated by
+% |\or|.
+% Finish off the definition by making this an |\ifcase|. Add a default
+% value of zero, so that any symbol fonts declared later will also
+% work, as long as a bold version is assigned to the bold math version.
+%    \begin{macrocode}
+  \expandafter\xdef\csname bm@#1table\endcsname{%
+    \noexpand\ifcase\@tempcnta
+      \csname bm@#1table\endcsname
+    \noexpand\else
+      \z@
+    \noexpand\fi}%
+%    \end{macrocode}
+%
+% Put things back as they were.
+%    \begin{macrocode}
+  \expandafter\split@name\bm@general\@nil
+  \let\install@mathalphabet\bm@pmb
+  \let\getanddefine@fonts\bm@pmb@
+  \let\or\bm@pmb@@}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bmmax}
+% To save declaring too many symbol fonts, do not auto-declare
+% any more than |\bmmax| bold symbol fonts into the normal math
+% version. Any bold fonts not so allocated will be accessed via
+% |\boldmath| which is slower and doesn't work for delimiters
+% and accents. It may be set in the preamble with |\newcommand|
+% but use |\chardef| here for a slight efficiency gain.
+%
+% If this is set to a higher value before this
+% package is loaded, keep that value.
+%    \begin{macrocode}
+\ifx\bmmax\@undefined
+  \chardef\bmmax=4
+\fi
+%    \end{macrocode}
+%
+% If there is no bold math version, It is very easy to set up
+% the table, no need to use all the tricky code above.
+% Also, at the end of the package redefine the internal macro
+% that |\bm| uses to call |\boldmath|, to use poor man's bold
+% instead.
+%    \begin{macrocode}
+\ifx\mv@bold\@undefined
+  \def\bm@boldtable{\m@ne}
+  \AtEndOfPackage{%
+    \def\bm@gr@up#1#2{%
+      \bm@pmb{#2}}}
+\else
+%    \end{macrocode}
+% Otherwise use the definition of |\bm| above to set up |\bm@boldtable|
+% by comparing the fonts available in the normal and bold math versions.
+%    \begin{macrocode}
+  \bm{bold}\bmmax
+%    \end{macrocode}
+%
+% \begin{macro}{\mathbf}
+% As the bold font has been defined as a symbol font, make |\mathbf|
+% access that rather than have it allocate a new math group for the
+% same font. (Just in case there were no free slots wrap this
+% in an extra test.)
+%    \begin{macrocode}
+  \@ifundefined{symboldoperators}
+    {}
+    {\DeclareSymbolFontAlphabet\mathbf{boldoperators}}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\hmmax}
+%
+% Same for heavy (but default to three this time (enough for mathtime
+% plus, as no heavy operators font).
+%    \begin{macrocode}
+\ifx\hmmax\@undefined
+  \chardef\hmmax=3
+\fi
+%    \end{macrocode}
+%
+% Similarly if there is a heavy math version, set up |\bm@heavytable|.
+% (If there is no heavy math version, do nothing here, as |\hm| will be
+% set to |\bm| later, once that is defined.)
+%    \begin{macrocode}
+\ifx\mv@heavy\@undefined
+\else
+  \bm{heavy}\hmmax
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\bm@general}
+% \changes{v1.0d}{1997/11/15}
+%      {extra code to support prime lookahead and breqn}
+% \changes{v1.0h}{2002/11/22}{Pass math version as third (new) argument}
+% \changes{v1.2d}{2019/07/24}
+%      {guard against active underscore}
+%
+% |\bm| is pretty much |\bmdefine\bm@command| followed by executing
+% |\bm@command|. It would in principle be possible to execute the
+% emboldened tokens directly, rather than building up a macro first,
+% but (as I learned the hard way) it's difficult to do this in the midst
+% of all these nested |\if| constructs.
+% First extract the central bit of code for |\hm| |\bm| |\hmdefine| and
+% |\bmdefine|. Note that in the case of the inline versions they take
+% an argument and brace it, rather than relying on |\bm@general| to pick
+% up the argument. This makes the code robust with respect to premature
+% expansion.
+%    \begin{macrocode}
+\begingroup
+\catcode`\'=\active
+\catcode`\_=\active
+\@firstofone{\endgroup
+\def\bm@general#1#2#3#4#5{%
+  \begingroup
+%    \end{macrocode}
+% \changes{v1.0d}{1997/11/15}
+%      {make nested \cs{bm} vanish completely, not leave a brace group}
+% First locally disable |\bm| and |\hm|, as they would mess things
+% up terribly, and the original Spivak versions used the syntax
+% |\bmdefine\balpha{\bm\alpha}|.
+%    \begin{macrocode}
+    \let\bm\@firstofone
+    \let\hm\@firstofone
+%    \end{macrocode}
+% Now initialise the commands used to save the tokens constructed.
+%    \begin{macrocode}
+    \global\let\bm@command\@empty
+    \let\@let@token\@empty
+%    \end{macrocode}
+% As we want to expand the macros to look at their definition
+% turn off protection. Otherwise the |\protect| will be carried over
+% and apply to the wrong token, eg |{|.
+%    \begin{macrocode}
+    \let\protect\@empty
+    \let\@typeset@protect\@empty
+%    \end{macrocode}
+% Set up either bold or heavy
+%    \begin{macrocode}
+    \def\bm@mathchoice{\bm@m@thchoice#1}%
+    \def\bm@group{\bm@gr@up#1}%
+    \let\bm@table#2%
+%    \end{macrocode}
+% Make sure |\left| and |\right| are really non expandable,
+% and not |\ifx| equal to anything else.
+% \changes{v1.0d}{1997/11/15}
+%      {make sure \cs{left} is primitive}
+%    \begin{macrocode}
+    \let\left\holdinginserts
+%    \end{macrocode}
+% These three save on the number of |\ifx| tests below.
+% \changes{v1.1a}{2003/09/01}{Forgotten to check for \cs{hskip} (pr/3572)}
+%    \begin{macrocode}
+    \let\right\left
+    \let\mskip\mkern
+    \let\hskip\kern
+%    \end{macrocode}
+% Definition of |'| locally modified so as not to use |\futurelet|
+% in the look ahead, but to make the |\prime| available at the top level
+% to be made bold, or heavy or whatever.
+% |'| is locally active for this definition.
+% \changes{v1.0d}{1997/11/15}
+%      {prime code added}
+% \changes{v1.0d}{1997/11/15}
+%      {prime code added}
+% \changes{v1.2d}{2019/07/24}
+%      {guard against active underscore}
+%    \begin{macrocode}
+    \let\bm@prime\copy
+    \let_\relax
+    \def'{\bm@prime\prime\relax}%
+%    \end{macrocode}
+% For optional argument commands. This expandable version of
+% |\@ifnextchar| is not 100\% safe, but works for |\sqrt| unless
+% you put something really strange in the arguments.
+% \changes{v0.11}{1997/01/06}
+%      {\cs{@ifnextchar} made safe.}
+%    \begin{macrocode}
+    \def\@ifnextchar##1##2##3##4{%
+      \if##1##4%
+        \expandafter\@firstoftwo
+      \else
+        \expandafter\@secondoftwo
+      \fi
+      {##2##4}{##3{##4}}}%
+%    \end{macrocode}
+% For Vladimir Volovich\ldots
+% \changes{v1.0f}{1998/12/10}
+%      {Errors and warnings made safe. tools/2917}
+%    \begin{macrocode}
+    \def\GenericWarning##1##2{%
+      \unvcopy{\GenericWarning{##1}{##2}}}%
+    \def\GenericError##1##2##3##4{%
+      \unvcopy{\GenericError{##1}{##2}{##3}{##4}}}%
+%    \end{macrocode}
+% For AMS definitions.
+%    \begin{macrocode}
+    \let\DN@\copy
+    \let\FN@\copy
+    \let\next@\copy
+    \global\let\bm@first\@empty
+%    \end{macrocode}
+%   For AMS version of |\sqrt|: don't expand just wrap in brace group
+%   so that it can be made bold in a safe but slow way. Do the same for
+%   internal accent command
+% \changes{v1.1b}{2003/10/05}{AMS \cs{sqrt} not working}
+%
+% \changes{v1.1c}{2004/02/26}{\cs{accentV} made safe (pr/3625)}
+% Code for AMS accent allows bm to be used (just) with accent
+% but stops the nested accents stacking correctly, this can be
+% corrected by using an extra brace group as usual.
+% |\bm{{\hat{\hat{F}}}}|
+%    \begin{macrocode}
+    \ifx\uproot@\undefined\else
+       \def\root##1\of##2{{\root##1\of{##2}}}%
+    \fi
+    \def\mathaccentV##1{\mathaccent"\accentclass@}%
+%    \end{macrocode}
+% For breqn definitions.
+%    \begin{macrocode}
+    \let\@ifnext\@ifnextchar
+    \let\measure@lhs\copy
+    \let \rel@break\copy
+    \let \bin@break\copy
+    \let \after@open\copy
+    \let \after@close\copy
+%    \end{macrocode}
+% Make sure things like |\pounds| take the `math branch' even
+% in |\bmdefine| (which is not executed in math mode).
+%    \begin{macrocode}
+    \let\ifmmode\iftrue
+%    \end{macrocode}
+%    We have to ensure that the math alphabets have definitions that
+%    correspond the the ``bold'' math version we are going to switch
+%    to. As these definitions are globally assigned when a math
+%    version is changed it is likely that right now we have those of
+%    the normal math version active. Argument |#3| holds either
+%    |\mv@bold| or |\mv@heavy| and we execute that after redefining
+%    |\install@mathalphabet| and |\getanddefine@fonts| suitably.
+%    The definitions are reverted back to their original the moment
+%    the scanning is done
+% \changes{v1.0h}{2002/11/22}{Get math alphabets right (pr/3476)}
+%    \begin{macrocode}
+     \let\install@mathalphabet\def
+     \let\getanddefine@fonts\@gobbletwo
+     #3%
+%    \end{macrocode}
+% The last redefinition just makes |\mathit| type commands re-insert
+% themselves (more or less) as if they are allowed to expand
+% they die horribly if the expansions are put into |\mathchoice|
+% and so executed more than once.
+%    \begin{macrocode}
+    \def\select@group##1##2##3##4{{%
+      \protect##1{##4}}}%
+    \def\use@mathgroup##1##2##3{{%
+      \protect\use@mathgroup##1{##2}{##3}}}%
+%    \end{macrocode}
+%
+% So now start looking at the argument.
+% \changes{v0.10}{1997/01/04}
+%      {Use \cs{bm@end}}
+%    \begin{macrocode}
+    \bm@expand#5\bm@end
+  \endgroup
+%    \end{macrocode}
+%
+% Finally outside the group either execute |\bm@command| (for |\bm|)
+% or save its definition (for |\bmdefine|).
+%    \begin{macrocode}
+  #4}
+%    \end{macrocode}
+% End of the |\@firstofone| above, and the scope of the active |'|.
+%    \begin{macrocode}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm}
+% \changes{v1.0d}{1997/11/15}
+%      {Make \cs{bm} grab its argument even when protected}
+% Set up the bold (rather than heavy) version, and run |\bm@command|
+% right at the end, to execute the emboldened argument.
+% The argument is grabbed by the top level function, and explicitly
+% braced, so that |\bm| works even if the braces are omitted round
+% its argument in a `moving argument'.
+% \changes{v1.0h}{2002/11/22}{Pass math version as third (new) argument}
+%    \begin{macrocode}
+\DeclareRobustCommand\bm{%
+  \bm@general\boldmath\bm@boldtable\mv@bold\bm@command}
+\protected@edef\bm#1{\bm{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DeclareBoldMathCommand}
+% \changes{v0.07}{1996/12/14}
+%      {Macro added}
+% \begin{macro}{\bm@declare}
+% \changes{v0.07}{1996/12/14}
+%      {Macro added}
+% |DeclareBoldMathCommand|%^^A
+%      \oarg{mathversion}\marg{command}\marg{math expression}\\
+% looks like |\bm| except at the end the specified command is
+% globally defined to be |\bm@command|.
+% The \meta{mathversion} defaults to `bold'.
+%    \begin{macrocode}
+\def\DeclareBoldMathCommand{\@testopt\bm@declare{bold}}
+%    \end{macrocode}
+%
+% \changes{v1.0h}{2002/11/22}{Pass math version as third (new) argument}
+%    \begin{macrocode}
+\def\bm@declare[#1]#2{%
+  \expandafter\bm@general
+        \csname #1math\expandafter\endcsname
+        \csname bm@#1table\expandafter\endcsname
+        \csname mv@#1\endcsname
+        {\bm@define#2}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bmdefine}
+% |\bmdefine| Shorthand for |\DeclareBoldMathCommand[bold]|.
+%
+% |\bm| is empty within the definition, so that either\\
+% |\bmdefine\balpha{\bm\alpha}| or  |\bmdefine\balpha{\alpha}| \\
+% may be used. (The former just for compatibility with the original
+% version for plain \TeX).
+%    \begin{macrocode}
+\def\bmdefine{\DeclareBoldMathCommand[bold]}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\hm}
+% \changes{v1.0d}{1997/11/15}
+%      {Make \cs{hm} grab its argument even when protected}
+% \begin{macro}{\hmdefine}
+% Same again for |\hm|.
+%    \begin{macrocode}
+\ifx\mv@heavy\@undefined
+%    \end{macrocode}
+%
+% If there is no heavy math version defined, let |\hm| be defined
+% as |\bm|. Currently there is no warning given, perhaps there should
+% be, or even an error?
+%    \begin{macrocode}
+  \let\hm\bm
+  \let\heavymath\boldmath
+  \let\bm@heavytable\bm@boldtable
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\else
+%    \end{macrocode}
+%
+% Otherwise define |\hm| and |\hmdefine| in direct analogy with the
+% above.
+% \changes{v1.0h}{2002/11/22}{Pass math version as third (new) argument}
+%    \begin{macrocode}
+  \DeclareRobustCommand\hm{%
+    \bm@general\heavymath\bm@heavytable\mv@heavy\bm@command}
+  \protected@edef\hm#1{\hm{#1}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \def\hmdefine{\DeclareBoldMathCommand[heavy]}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bm@end}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% Normally speaking |\outer| declarations should be avoided at all
+% costs. (\LaTeX\ redefines all of plain \TeX's allocation macros
+% to be non-outer.) However this is one place where it seems like a
+% good idea. If a command taking an argument is put in |\bm| without
+% its argument, then the |\@@end| terminating token would be taken as
+%  the argument, and so the rest of the paragraph would be gobbled up
+% and the \LaTeX\ would die horribly. So make the internal terminating
+% token |\outer|. (The actual test for termination is made against
+% |\@@end| not |\bm@end| as this macro will be expanded by the look-ahead
+% system.)
+%    \begin{macrocode}
+\outer\def\bm@end{\@@end}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@expand}
+% \changes{v0.11}{1997/01/06}
+%      {Double up.}
+% \begin{macro}{\bm@exp@nd}
+% \changes{v0.11}{1997/01/06}
+%      {Macro added}
+% |\afterassignment| trick to fully expand the following tokens until
+% the first non-expandable token is revealed. This may discard a space
+% token (which is what \TeX\ is looking for) but that doesn't matter in
+% math mode. The expansion lookahead is done twice in case any stray
+% space tokens have crept in.\footnote{The need for this was noticed
+% while testing \cs{sqrt}. The definition of \cs{root} inherited from
+% plain \TeX\ has an anomalous space token, that is normally harmless
+% (just wastes memory), but which killed earlier versions of this
+%  package.}
+%    \begin{macrocode}
+\def\bm@expand{\afterassignment\bm@exp@nd\count@`\a}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\bm@exp@nd{\afterassignment\bm@test\count@`\a}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bm@test}
+% Normally we will grab the non-expandable token as a macro argument
+% but better check it is not |{| first. Save the previous token
+% so we can check later if it was |\left|, in which case use the delcode
+% rather than the mathcode if the current token is a character.
+%    \begin{macrocode}
+\def\bm@test{%
+  \let\bm@previous\@let@token
+  \futurelet\@let@token\bm@test@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@test@}
+% If looking at a single token, switch to |\bm@test@token|, else if
+% looking at a |{ }| group, grab the whole group with |\bm@group|.
+% A |\bgroup| token will take the wrong branch here (currently not
+% trapped).
+%    \begin{macrocode}
+\def\bm@test@{%
+  \ifx\@let@token\bgroup
+    \expandafter\bm@group
+  \else
+    \expandafter\bm@test@token
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@gr@up}
+% \changes{v1.0c}{1997/10/09}
+%      {Extra brace around argument for \cs{over}}
+% If faced with a group,
+% If we are in math mode, stick it in a |\boldsymbol| like construct
+% and then recurse on |\bm@expand|.
+% Otherwise just use |\bfseries\boldmath|.
+% The actual test is deferred till `run time'.
+% Here and elsewhere could deal with the inner list with an inner call
+% to |\bm|, but that doesn't seem to gain very much, and complicates the
+% code quite a bit.
+%
+% |#1| is either |\boldmath| or |\heavymath|.
+% Need to add an extra set of explicit braces around |#2| as otherwise
+% the math style commands applied in |\mathchoice| might only apply
+% to the first half of an |\over| construction.
+%    \begin{macrocode}
+\def\bm@gr@up#1#2{%
+  \bm@add{{\bm@gr@@p#1{{#2}}}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@gr@@p}
+% |#1| is either |\boldmath| or |\heavymath|.
+%    \begin{macrocode}
+\def\bm@gr@@p#1#2{%
+  \ifmmode
+    \bm@mchoice#1{#2}{#2}{#2}{#2}%
+  \else
+    \bfseries#1#2%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@test@token}
+% If not facing a |{  }| group then test to see what we have.
+% Basic idea: Trap |\mathchardef| tokens, character tokens, and calls to
+% |\mathchar|, |\mathaccent|, etc, and change the \emph{math-group}
+% (fam) to point at the bold version.
+% Other things just copy straight over to the command being built.
+% (Anything inside a |\mathop| or similar will end up being made bold
+% as the |\mathop| will be copied over, but its argument will be made
+% bold by the group code above.
+%    \begin{macrocode}
+\def\bm@test@token#1{%
+  \let\bm@next\@empty
+%    \end{macrocode}
+%
+% Stop here. Note that it is vital that the terminating token
+% is non-expandable and defined, rather than the usual \LaTeX\
+% terminators |\@nil| or |\@@|. (Worse still would be a `quark'
+% like |docstrip|'s |\qStop|.)
+%    \begin{macrocode}
+  \ifx#1\@@end
+%    \end{macrocode}
+%
+% |\bm@mathchoice| uses macro arguments, so need to make the tail
+% recursion explicit here. All the other cases recurse by way of
+% |\afterassignment| which means all the trailing |\fi| are eaten
+% while making the assignment.
+%    \begin{macrocode}
+  \else\ifx#1\mathchoice
+    \let\bm@next\bm@mathchoice
+%    \end{macrocode}
+%
+% The main point: Find these expressions, and change the mathgroup.
+%    \begin{macrocode}
+  \else\ifx#1\mathchar
+    \afterassignment\bm@mathchar\count@
+  \else\ifx#1\mathaccent
+    \afterassignment\bm@mathaccent\count@
+  \else\ifx#1\delimiter
+    \afterassignment\bm@delimiter\count@
+  \else\ifx#1\radical
+    \afterassignment\bm@radical\count@
+%    \end{macrocode}
+%
+% Need to trap spaces otherwise digits will get turned to bold
+% mathchars.
+% \changes{v1.1a}{2003/09/01}{Forgotten to check for \cs{hskip} (pr/3572)}
+%    \begin{macrocode}
+  \else\ifx#1\mkern
+    \bm@register#1{\muskip\z@}%
+  \else\ifx#1\kern
+    \bm@register#1\skip@
+  \else\ifx#1\penalty
+    \bm@register#1\count@
+%    \end{macrocode}
+%
+% \changes{v1.0f}{1998/12/10}
+%      {Add possibility to copy brace group unmodified. tools/2917}
+% |\vcopy| is a flag to copy the next group unchanged to the
+% result command.
+%    \begin{macrocode}
+  \else\ifx#1\unvcopy
+    \let\bm@next\bm@add
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \else\ifcat\noexpand#1\relax
+%    \end{macrocode}
+% Other command, look if it's a mathchardef token (otherwise just add
+% it).
+% \changes{v1.2a}{2016/02/27}
+%      {Additional quotes for testing \cs{Umathchar}}
+%    \begin{macrocode}
+    \xdef\meaning@{\meaning#1}%
+    \expandafter\bm@mchar@test\meaning@""""\@nil#1%
+%    \end{macrocode}
+% \changes{v1.0d}{1997/11/15}
+%      {New active \cs{mathcode} code.}
+% Character token.
+% If it is of catcode 11 or 12, get its mathcode.
+% If that is |"8000| replace the token by its active version, and then
+% let bm expansion look again at the character. Being really active
+% this time, it will expand away (probably).
+%
+% If the previous token was |\left| or |\right|, get the delcode
+% instead of the mathcode.
+%    \begin{macrocode}
+  \else\ifcat.\ifcat a#1.\else#1\fi
+    \count@\mathcode`#1\relax
+    \ifnum\count@=\mathcode`\'%
+      \begingroup\uccode`\~`#1\uppercase{\endgroup
+        \def\bm@next{\bm@expand~}}%
+    \else
+      \ifx\bm@previous\left
+        \count@\delcode`#1\relax
+        \bm@delimiter
+      \else
+%    \end{macrocode}
+% \changes{v1.2b}{2016/07/07}
+%      {Check for mathchar values being reported as if via \cs{Umathchar}}
+% Here we need to check for LuaTeX merging mathchar values with Umathchar.
+%    \begin{macrocode}
+        \ifnum\count@>"8000
+          \Umathcharnumdef\@tempa\count@
+          \xdef\meaning@{\meaning\@tempa}%
+          \expandafter\bm@mchar@test\meaning@""""\@nil\@tempa
+        \else
+          \bm@mathchar
+        \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+      \fi
+    \fi
+  \else
+%    \end{macrocode}
+% And final possibility:
+% a character token of catcode other than 11 or 12.
+%    \begin{macrocode}
+    \bm@add{#1}%
+  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+  \bm@next}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\bm@define}
+% \changes{v0.08}{1996/12/18}
+%      {Defined commands now always robust}
+% End code for |\bmdefine|. Define the given command name to the
+% robust form of the accumulated code.
+%
+% If |\bm@command| is equal to |\@gtempa| then it is a macro whose
+% expansion is a single call to |\mathchar|, so that can be optimised
+% with a |\mathchardef|.
+%    \begin{macrocode}
+\def\bm@define#1{%
+  \begingroup
+    \ifx\bm@command\@gtempa
+      \def\mathchar{\global\mathchardef#1}%
+      \bm@command
+    \else
+%    \end{macrocode}
+% Rather than simply |\let#1\bm@command|, make the defined command
+% robust. |\bm@first| is normally empty, but might be something like
+% |\DOTSI| which needs to be lifted to the top level, in front
+% of any |\protect| because of the lookahead mechanism used
+% in the \textsf{amsmath} package.
+%    \begin{macrocode}
+      \toks@\expandafter{\bm@command}%
+      \xdef#1{\bm@first\noexpand\bm@protect\noexpand#1{\the\toks@}}%
+    \fi
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\bm@protect}
+% \changes{v0.08}{1996/12/18}
+%      {macro added}
+% Commands defined by |\bmdefine| re-insert themselves
+% if protection is enabled.
+%    \begin{macrocode}
+\def\bm@protect#1{%
+  \ifx\protect\@typeset@protect
+    \expandafter\@firstofone
+  \else
+    \protect#1\expandafter\@gobble
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@mchoice}
+% |\boldsymbol|, more or less.
+% |#1| is either |\boldmath| or |\heavymath|.
+%    \begin{macrocode}
+\def\bm@mchoice#1#2#3#4#5{%
+  \mathchoice{\hbox{#1$\displaystyle\m@th#2$}}%
+             {\hbox{#1$\textstyle\m@th#3$}}%
+             {\hbox{#1$\scriptstyle\m@th#4$}}%
+             {\hbox{#1$\scriptscriptstyle\m@th#5$}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@m@thchoice}
+% Action if you find a |\mathchoice|. Add the bold version to
+% |\bm@command| then recurse.
+%
+% |#1| is either |\boldmath| or |\heavymath|.
+%    \begin{macrocode}
+\def\bm@m@thchoice#1#2#3#4#5{%
+  \bm@add{\bm@mchoice#1{#2}{#3}{#4}{#5}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@register}
+% \changes{v0.07}{1996/12/14}
+%      {Macro added}
+% Combined code for setting up |\bm@r@gister| with the correct
+% register type.
+%    \begin{macrocode}
+\def\bm@register#1#2{%
+  \def\@tempa{#1\the#2}%
+  \afterassignment\bm@r@gister#2}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@r@gister}
+% \changes{v0.06}{1996/12/12}
+%      {Support \cs{mskip}}
+% \changes{v0.07}{1996/12/14}
+%      {Combine all register macros}
+% |\mkern| itself would transfer to |\bm@command| without any special
+% test, but any explicit dimension following would be converted to
+% |\mathchar|. So trap this and grab the muskip as a muskip.
+% This is used in |\iiint|. |\penalty| was needed for the
+% AMS  version of |\colon|, and so do most of the others as well.
+%    \begin{macrocode}
+\def\bm@r@gister{%
+  \bm@xadd{\@tempa\space}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\bm@mathchar}
+% \changes{v0.10}{1997/01/04}
+%      {Modify to use \cs{boldmath} or \cs{pmb} if needed.}
+% Change the family (math group) of a mathcode and then
+% use the modified code with |\mathchar|. If there is no
+% suitable bold font in the current math version, use the original
+% unmodified mathcode, but switch to |\boldmath| (if there is a bold
+% font there) or use `poor man's bold'. Note that these other
+% possibilities are only possible here, not for the otherwise similar
+% code for |\delimiter| or |\mathaccent|, as those commands
+% must work with fonts from the same math version.
+%
+% Finally recurse down the list.
+%    \begin{macrocode}
+\def\bm@mathchar{%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \@tempcntb\count@
+  \let\@tempa\bm@group
+%    \end{macrocode}
+%
+% |\bm@changefam| will isolate the math group from the mathcode
+% and look up the offset in the current table.
+%    \begin{macrocode}
+  \bm@changefam{}%
+%    \end{macrocode}
+%
+% If the mathcode has changed, then just add the new |\mathchar|
+% (saving |\@gtempa| allows |\bmdefine| to optimise this to a
+%  mathchardef if it turns out to be the only symbol in the argument).
+%    \begin{macrocode}
+  \ifnum\count@>\@tempcntb
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \ifx\bm@command\@empty
+      \xdef\@gtempa{\mathchar\the\count@\space}%
+    \fi
+    \bm@xadd{\mathchar\the\count@\space}%
+  \else
+%    \end{macrocode}
+%
+% Otherwise grab the math class from the math code
+% and add that (locally zapping |\bm@expand| as we don't want
+% to recurse at this point).
+%    \begin{macrocode}
+    \begingroup
+      \divide\count@"1000
+      \let\bm@expand\relax
+      \bm@xadd\bm@class
+    \endgroup
+%    \end{macrocode}
+% |\@tempa| will be |\bm@group| (which applies |\boldmath| and
+% |\mathchoice|) unless it was changed by |\bm@changefam| to |\bm@pmb|
+% (which applies a `poor man's bold' construction in a |\mathchoice|).
+%    \begin{macrocode}
+    \edef\@tempb{%
+      \noexpand\@tempa{\mathchar\the\count@\space}}%
+    \@tempb
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@umathchar}
+% \changes{v1.2a}{2016/02/27}
+%      {Macro added}
+% \changes{v1.2a}{2017/01/16}
+%      {Test for zero table entry (\cs{boldmath}) added}
+% Version of \verb|\bm@mathchar| for \verb|\Umathchar|, this is easier
+% as no need to take apart the number, the match class and fam are provided
+% as distinct arguments.
+%    \begin{macrocode}
+\def\bm@umathchar#1#2#3{%
+\@tempcnta#2\relax
+\count@\bm@table
+\ifnum\count@=\z@
+  \bm@gr@up\boldmath{\Umathchar#1 #2 #3 }%
+\else
+  \ifnum\count@=\m@ne
+  \else
+    \advance\@tempcnta\count@
+  \fi
+  \bm@xadd{\Umathchar#1\space
+                     \the\@tempcnta\space\space
+                     #3\space}%
+\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@pmb}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% Add a poor man's bold construction to the list being built.
+%    \begin{macrocode}
+\def\bm@pmb#1{%
+  \bm@add{\bm@pmb@{#1}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@pmb@}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% |\pmb| variant. (See \TeX{}Book, or AMS \textsf{amsbsy} package).
+% This one takes a bit more care to use smaller offsets in subscripts.
+%    \begin{macrocode}
+\def\bm@pmb@#1{{%
+  \setbox\tw@\hbox{$\m@th\mkern.4mu$}%
+  \mathchoice
+    \bm@pmb@@\displaystyle\@empty{#1}%
+    \bm@pmb@@\textstyle\@empty{#1}%
+    \bm@pmb@@\scriptstyle\defaultscriptratio{#1}%
+    \bm@pmb@@\scriptscriptstyle\defaultscriptscriptratio{#1}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@pmb@@}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% Helper macro. Box |#3| and set it three times in the style |#1|,
+% offset by an amount reduced by the ratio specified in |#2|.
+%    \begin{macrocode}
+\def\bm@pmb@@#1#2#3{{%
+  \setbox\z@\hbox{$\m@th#1#3$}%
+  \dimen@#2\wd\tw@
+  \rlap{\copy\z@}%
+  \kern\dimen@
+  \raise1.5\dimen@\rlap{\copy\z@}%
+  \kern\dimen@
+  \box\z@}}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@class}
+% \changes{v0.10}{1997/01/04}
+%      {Macro added}
+% Convert a numeric math class back to a math class command.
+% |\mathord| is omitted in class $0$ and $7$ to save space and so
+% things work out right in constructions such as |x^a| where
+% |x^\mathord{a}| would not work.
+%    \begin{macrocode}
+\def\bm@class{%
+  \ifcase\count@
+    \or
+    \mathop\or
+    \mathbin\or
+    \mathrel\or
+    \mathopen\or
+    \mathclose\or
+    \mathpunct\or
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@add}
+% \changes{v0.07}{1996/12/14}
+%      {macro added}
+% A version of |\g@addto@macro| that internally uses a |\begingroup|
+% rather than a brace group\footnote{This bug is fixed in the \LaTeX\
+% kernel of 1996/12/01}, to save creating a mathord.
+%
+% As need to redefine it anyway, save some tokens by making
+% it specific to |\bm@command|, and to execute |\bm@expand|
+% to continue the loop.
+%    \begin{macrocode}
+\def\bm@add#1{%
+  \begingroup
+    \toks@\expandafter{\bm@command#1}%
+    \xdef\bm@command{\the\toks@}%
+  \endgroup
+  \bm@expand}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@xadd}
+% An |\xdef| version of |\bm@add|.
+%    \begin{macrocode}
+\def\bm@xadd#1{%
+  \begingroup
+    \toks@\expandafter{\bm@command}%
+    \xdef\bm@command{\the\toks@#1}%
+  \endgroup
+  \bm@expand}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@mathaccent}
+% \changes{v1.0e}{1997/11/21}
+%      {Use bm on argument group, as spotted on c.t.t.}
+% |\mathaccent| version of |\bm@mathchar|.
+%    \begin{macrocode}
+\def\bm@mathaccent{%
+ \bm@changefam{}%
+%    \end{macrocode}
+% The next four lines were added a v1.0e. Without them |\bm{\hat{A}}|
+% makes the accent bold using |\bm| but the group |{A}| is made bold
+% via a |\mathchoice| construction as for any other group, as |\bm|
+% does not attempt to parse inside brace groups. While that produces
+% something acceptable for lower case letters, it produces
+% $\bm{\hat{{A}}}$ which is not too good. The braces may simply be
+% omitted:
+% |\bm{\hat A}| would work, producing $\bm{\hat A}$, however I did not
+% want to document such a restriction, so now modify bm so that such
+% brace groups are handled gracefully.
+%
+% It would be possible to locally make mathaccents take an argument
+% during the bm look-ahead, so the brace groups would then vanish
+% during expansion, however I would then need to explicitly skip past
+% \meta{filler} and also make sure that the end of parse token
+% was not gobbled in marginal cases like |$\bm\hat$|.
+%
+% So instead do the following which gets rid of \meta{filler}
+% with a redefinition of |\relax|, and just locally changes
+% |\bm@group| so that instead of doing a |\mathchoice| it simply adds
+% |\bgroup| and |\egroup| around the tokens, and lets bm modify the
+% tokens of the `argument'. This means that |\bm{\hat{A}}| now produces
+%\begin{verbatim}
+% \mathaccent 29790 \bgroup \mathchar 30017 \egroup
+%\end{verbatim}
+% The inner math list is a single mathchar, and so \TeX\ will not box
+% it, and the math accent will correctly position, taking into account
+% the skewchar information.
+%
+% As the normal bm lookahead is used, it is automatic that the parse
+% will end without trying to go past |\bm@end|.
+%
+% One disadvantage is that the group will mean that |\bm@previous|
+% will not be correctly updated. However that is only used for
+% delimiter checking, so can not matter here.
+%    \begin{macrocode}
+ \begingroup
+ \def\bm@group##1{\endgroup\bm@xadd{\bgroup}##1\egroup}%
+ \def\bm@test@token{\endgroup\bm@test@token}%
+ \let\relax\@empty
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+ \bm@xadd{\mathaccent\the\count@\space}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@delimiter}
+% \changes{v1.0d}{1997/11/15}
+%      {Support \cs{left}. null delimiter.}
+% Change both families (math groups) of a delcode and then
+% use the modified code with  |\delimiter|. Don't change code `0'
+% as that denotes a null delimiter.
+%    \begin{macrocode}
+\def\bm@delimiter{%
+  \ifnum\count@>\z@
+    \bm@changefam{}%
+    \bm@changefam{000}%
+  \fi
+  \bm@xadd{\delimiter\the\count@\space}}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@radical}
+% Same for |\radical|.
+%    \begin{macrocode}
+\def\bm@radical{%
+ \bm@changefam{}%
+ \bm@changefam{000}%
+ \bm@xadd{\radical\the\count@\space}}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@mchar@}
+% Catcode 12 |\mathchar|, for |\ifx| tests.
+%    \begin{macrocode}
+\edef\bm@mchar@{\meaning\mathchar}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@umchar@}
+% \changes{v1.2a}{2016/02/27}
+%      {Macro added}
+% Catcode 12 |\Umathchar|, for |\ifx| tests.
+%    \begin{macrocode}
+\edef\bm@umchar@{\string\U\expandafter\@gobble\meaning\mathchar}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@mchar@test}
+% Test if the |\meaning| starts with |\mathchar|. If it does, grab the
+% value into |\count@| and call |\bm@mathchar|, else just copy the
+% command into the accumulated tokens.
+% |#1|, |#2|, |#3| are all |\meaning| produced tokens, or `dummy tokens'
+% added at the time this is called. |#4| is the original token, in case
+%  decide not to use the |\meaning|.
+% \changes{v1.2a}{2016/02/27}
+%      {Additional arguments added}
+%    \begin{macrocode}
+\def\bm@mchar@test#1"#2"#3"#4"#5\@nil#6{%
+  \xdef\meaning@{#1}%
+  \ifx\meaning@\bm@mchar@
+    \count@"#2\relax
+    \bm@mathchar
+  \else
+%    \end{macrocode}
+% Test for \verb|\Umathchar|.
+%    \begin{macrocode}
+    \ifx\meaning@\bm@umchar@
+       \bm@umathchar{"#2}{"#3}{"#4}%
+    \else
+%    \end{macrocode}
+% Some other command: copy it straight over. If it is the first thing
+% added, and it is a |\relax| token, save it in |\bm@first| for use
+% in |\bm@define|.
+%    \begin{macrocode}
+      \ifx\bm@previous\@empty
+        \ifx\relax#6%
+          \gdef\bm@first{#6}%
+        \fi
+      \fi
+      \bm@add{#6}%
+    \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@changefam}
+% \changes{v0.10}{1997/01/04}
+%      {Rewrite for new \cs{bm@table} system}
+% Pull out one specified hex digit and passes
+% it to |\bm@modify| to change. argument is empty normally but |000| to
+% access the second math group in a delimiter code.
+%    \begin{macrocode}
+\def\bm@changefam#1{%
+  \@tempcnta\count@
+  \divide\@tempcnta"1000#1 %
+  \multiply\@tempcnta"1000#1 %
+  \advance\@tempcnta-\count@
+  \divide\@tempcnta-"100#1 %
+%    \end{macrocode}
+% Having isolated the required math group (fam), look up
+% the offset in the current table.
+%    \begin{macrocode}
+  \@tempcnta\bm@table
+%    \end{macrocode}
+% If the offset is $-1$, keep |\count@| unchanged, but set |\@tempa|
+% to use poor man's bold. Otherwise increment |\count@| to change the
+% math group specified.
+%    \begin{macrocode}
+  \ifnum\@tempcnta=\m@ne
+    \let\@tempa\bm@pmb
+  \else
+    \multiply\@tempcnta"100#1 %
+    \advance\count@\@tempcnta
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\bm@prime}
+% \changes{v1.0d}{1997/11/15}
+%      {Macro added}
+% Support |'|. Earlier versions did not make the prime bold in a'.
+%
+% |\bm{a''}| will now produce (with the normal encodings)
+%\begin{verbatim}
+%      \mathchar 30049
+%      \bm@prime \mathchar 1584 \relax
+%      \bm@prime \mathchar 1584 \relax
+%\end{verbatim}
+% So |\bm@prime| does essentially the same as the active definition of
+% |'|, which is to start a superscript group then keep adding |\prime|
+% for each |'| (or |\bm@prime|) following. Here modified to grab a
+% |\relax| delimited argument and use that instead of |\prime|.
+% |\bm@prime| is locally |\let| to |'| so the |\ifx| tests in |\pr@m@s|
+% don't need changing.
+%    \begin{macrocode}
+\def\bm@prime{^\bgroup
+  \let\bm@prime'%
+  \def\prim@s##1\relax{##1\futurelet\@let@token\pr@m@s}%
+  \prim@s}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\boldsymbol}
+% \changes{v1.0b}{1997/04/14}
+%      {Macro added}
+% \begin{macro}{\heavysymbol}
+% Finally, to ease conversion of documents between this package and
+% the \textsf{amsbsy} package:
+%    \begin{macrocode}
+\let\boldsymbol\bm
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\heavysymbol\hm
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
diff --git a/macros/latex-dev/required/tools/bm.ins b/macros/latex-dev/required/tools/bm.ins
new file mode 100644
index 0000000000..a148cb93ef
--- /dev/null
+++ b/macros/latex-dev/required/tools/bm.ins
@@ -0,0 +1,75 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+
+\generate{\file{bm.sty}{\from{bm.dtx}{package}}}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/bm.pdf b/macros/latex-dev/required/tools/bm.pdf
new file mode 100644
index 0000000000..a0d1d017d1
--- /dev/null
+++ b/macros/latex-dev/required/tools/bm.pdf
diff --git a/macros/latex-dev/required/tools/calc.dtx b/macros/latex-dev/required/tools/calc.dtx
new file mode 100644
index 0000000000..0bc90f736b
--- /dev/null
+++ b/macros/latex-dev/required/tools/calc.dtx
@@ -0,0 +1,1357 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File `calc.dtx'.
+%% Copyright (C) 1992--1995
+%%          Kresten Krab Thorup and Frank Jensen.
+%% Copyright (C) 1997--2007
+%%          Kresten Krab Thorup, Frank Jensen and the LaTeX3 Project.
+%%
+%% The original authors (fj@hugin.dk and  krab@daimi.aau.dk) have
+%% contributed this package to the LaTeX distribution.
+%% Problems with this package should now be sent using latexbug.tex to
+%% the normal LaTeX bug report address.
+%
+%<*dtx>
+          \ProvidesFile{calc.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{calc}
+%<driver> \ProvidesFile{calc.drv}
+% \fi
+%         \ProvidesFile{calc.dtx}
+          [2017/05/25 v4.3 Infix arithmetic (KKT,FJ)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\EnableCrossrefs
+\RecordChanges
+\usepackage{calc}
+\begin{document}
+\DocInput{calc.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{calc.dtx}
+%
+% \title{The \texttt{calc} package\\Infix notation
+%        arithmetic in \LaTeX\thanks{We thank Frank Mittelbach for his
+%        valuable comments and suggestions which have greatly improved
+%        this package.}}
+% \author{Kresten Krab Thorup, Frank Jensen (and Chris Rowley)}
+% \date{\filedate}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \changes{v4.0d}{1997/11/08}
+%    {Contributed to tools distribution}
+% \changes{v4.1a}{1998/06/07}
+%    {Added text sizes: CAR}
+% \changes{v4.1a}{1998/06/07}
+%    {Attempt to make user-syntax robust: CAR}
+%
+% \newenvironment{calc-syntax}
+%    {\par
+%     \parskip\medskipamount
+%     \def\is{\ \hangindent3\parindent$\longrightarrow$~}%
+%     \def\alt{\ $\vert$~}%
+%     \rightskip 0pt plus 1fil
+%     \def\<##1>{\mbox{\NormalSpaces$\langle$##1\/$\rangle$}}%
+%     \IgnoreSpaces\obeyspaces%
+% }{\par\vskip\parskip}
+% {\obeyspaces\gdef\NormalSpaces{\let =\space}\gdef\IgnoreSpaces{\def {}}}
+%
+% \def\<#1>{$\langle$#1\/$\rangle$}%
+% \def\s#1{\ensuremath{[\![#1]\!]}}
+% \def\savecode#1{\hbox{${}_{\hookrightarrow[#1]}$}}
+% \def\gassign{\Leftarrow}
+% \def\lassign{\leftarrow}
+%
+% \begin{abstract}
+% The \texttt{calc} package reimplements the \LaTeX\ commands
+% |\setcounter|, |\addtocounter|, |\setlength|, and |\addtolength|.
+% Instead of a simple value, these commands now accept an infix
+% notation expression.
+% \end{abstract}
+%
+% \section{Introduction}
+%
+% Arithmetic in \TeX\ is done using low-level operations such as
+% |\advance| and |\multiply|.  This may be acceptable when developing
+% a macro package, but it is not an acceptable interface for the
+% end-user.
+%
+% This package introduces proper infix notation arithmetic which is
+% much more familiar to most people.  The infix notation is more
+% readable and easier to modify than the alternative: a sequence of
+% assignment and arithmetic instructions.  One of the arithmetic
+% instructions (|\divide|) does not even have an equivalent in
+% standard \LaTeX.
+%
+% The infix expressions can be used in arguments to macros (the
+% \texttt{calc} package doesn't employ category code changes to
+% achieve its goals).\footnote{However, it therefore assumes that the
+%    category codes of the special characters, such as \texttt{(*/)}
+%    in its syntax do not change.}
+%
+% \section{Informal description}
+%
+% Standard \LaTeX\ provides the following set of commands to
+% manipulate counters and lengths \cite[pages 194 and~216]{latexman}.
+% \begin{itemize}
+% \item[]\hskip-\leftmargin
+%    |\setcounter{|\textit{ctr}|}{|\textit{num}|}| sets the
+%    value of the counter \textit{ctr} equal to (the value of)
+%    \textit{num}.  (Fragile)
+% \item[]\hskip-\leftmargin
+%    |\addtocounter{|\textit{ctr}|}{|\textit{num}|}|
+%    increments the value of the counter \textit{ctr} by (the
+%    value of) \textit{num}.  (Fragile)
+%
+% \item[]\hskip-\leftmargin
+%    |\setlength{|\textit{cmd}|}{|\textit{len}|}| sets the value of
+%    the length command \textit{cmd} equal to (the value of) \textit{len}.
+%    (Robust)
+% \item[]\hskip-\leftmargin
+%    |\addtolength{|\textit{cmd}|}{|\textit{len}|}| sets the value of
+%    the length command \textit{cmd} equal to its current value plus
+%    (the value of) \textit{len}.  (Robust)
+% \end{itemize}
+% (The |\setcounter| and |\addtocounter| commands have global effect,
+% while the |\setlength| and |\addtolength| commands obey the normal
+% scoping rules.)  In standard \LaTeX, the arguments to these commands
+% must be simple values.  The \texttt{calc} package extends these
+% commands to accept infix notation expressions, denoting values of
+% appropriate types.  Using the \texttt{calc} package, \textit{num} is
+% replaced by \<integer expression>, and \textit{len} is replaced by
+% \<glue expression>.  The formal syntax of \<integer expression> and
+% \<glue expression> is given below.
+%
+% In addition to these commands to explicitly set a length, many \LaTeX\
+% commands take a length argument. After loading this package, most of
+% these commands will accept a  \<glue expression>. This includes
+% the optional width argument of |\makebox|, the width argument of
+% |\parbox|, |minipage|, and a |tabular| |p|-column, and many similar
+% constructions. (This package does not redefine any of these commands,
+% but they are defined by default to read their arguments by |\setlength|
+% and so automatically benefit from the enhanced |\setlength| command
+% provided by this package.)
+%
+% In the following, we shall use standard \TeX\ terminology.  The
+% correspondence between \TeX\ and \LaTeX\ terminology is as follows:
+% \LaTeX\ counters correspond to \TeX's count registers; they hold
+% quantities of type \<number>.  \LaTeX\ length commands correspond to
+% \TeX's dimen (for rigid lengths) and skip (for rubber lengths)
+% registers; they hold quantities of types \<dimen> and \<glue>,
+% respectively.
+%
+% \TeX\ gives us primitive operations to perform arithmetic on registers as
+% follows:
+% \begin{itemize}
+%   \item addition and subtraction on all types of quantities without
+%       restrictions;
+%   \item multiplication and division by an \emph{integer} can be
+%       performed on a register of any type;
+%   \item multiplication by a \emph{real} number (i.e., a number with a
+%       fractional part) can be performed on a register of any type,
+%       but the stretch and shrink components of a glue quantity are
+%       discarded.
+% \end{itemize}
+% The \texttt{calc} package uses these \TeX\ primitives but provides a
+% more user-friendly notation for expressing the arithmetic.
+%
+% An expression is formed of numerical quantities (such as explicit
+% constants and \LaTeX\ counters and length commands) and binary
+% operators (the tokens `\texttt{+}', `\texttt{-}', `\texttt{*}', and
+% `\texttt{/}' with their usual meaning) using the familiar infix
+% notation; parentheses may be used to override the usual precedences
+% (that multiplication/division have higher precedence than
+% addition/subtraction).
+%
+% Expressions must be properly typed.  This means, e.g., that a dimen
+% expression must be a sum of dimen terms: i.e., you cannot say
+% `\texttt{2cm+4}' but `\texttt{2cm+4pt}' is valid.
+%
+% In a dimen term, the dimension part must come first; the same holds
+% for glue terms.  Also, multiplication and division by non-integer
+% quantities require a special syntax; see below.
+%
+% Evaluation of subexpressions at the same level of precedence
+% proceeds from left to right.  Consider a dimen term such as
+% ``\texttt{4cm*3*4}''.  First, the value of the factor \texttt{4cm} is
+% assigned to a dimen register, then this register is multiplied
+% by~$3$ (using |\multiply|), and, finally, the register is multiplied
+% by~$4$ (again using |\multiply|).  This also explains why the
+% dimension part (i.e., the part with the unit designation) must come
+% first; \TeX\ simply doesn't allow untyped constants to be assigned
+% to a dimen register.
+%
+% The \texttt{calc} package also allows multiplication and division by
+% real numbers.  However, a special syntax is required: you must use
+% |\real{|\<decimal constant>|}|\footnote{Actually, instead of
+% \<decimal constant>, the more general \<optional signs>\<factor> can
+% be used.  However, that doesn't add any extra expressive power to
+% the language of infix expressions.} or
+% |\ratio{|\<dimen expression>|}{|\<dimen expression>|}| to denote a
+% real value to be used for multiplication/division.  The first form has
+% the obvious meaning, and the second form denotes the number obtained
+% by dividing the value of the first expression by the value of the
+% second expression.
+%
+%    A later addition to the package (in June 1998) allows an additional
+%    method of specifying a factor of type dimen by setting some text
+%    (in LR-mode) and measuring its dimensions: these are denoted as
+%    follows.
+%\begin{quote}
+%    |\widthof{|\<text>|}|\quad
+%    |\heightof{|\<text>|}|\quad
+%    |\depthof{|\<text>|}|
+%\end{quote}
+%    These calculate the natural sizes of the \<text> in exactly the
+%    same way as is done for the commands |\settowidth| etc.~on
+%    Page~216 of the manual~\cite{latexman}.
+%    In August 2005 the package was further extended to provide the command
+%\begin{quote}
+%    |\totalheightof{|\<text>|}|
+%\end{quote}
+%    This command does exactly what you'd expect from its name.
+%    Additionally the package also provides the command
+%\begin{quote}
+%    |\settototalheight{|\<cmd>|}{|\<text>|}|
+%\end{quote}
+%
+%
+%    Note that there is a small difference in the usage of these two
+%    methods of accessing text dimensions.  After
+%    |\settowidth{\txtwd}{Some text}| you can use:
+%\begin{verbatim}
+%    \setlength{\parskip}{0.68\txtwd}
+%\end{verbatim}
+%    whereas using the more direct access to the width of the text
+%    requires the longer form for multiplication, thus:
+%\begin{verbatim}
+%    \setlength{\parskip}{\widthof{Some text} * \real{0.68}}
+%\end{verbatim}
+%
+% \TeX\ discards the stretch and shrink components of glue when glue
+% is multiplied by a real number.  So, for example,
+%\begin{verbatim}
+%    \setlength{\parskip}{3pt plus 3pt * \real{1.5}}
+%\end{verbatim}
+% will set the paragraph separation to 4.5pt with no stretch or
+% shrink.  Incidentally, note how spaces can be used to enhance
+% readability. When \TeX\ is scanning for a \<number> etc.\ it is
+% common to terminate the scanning with a space token or by inserting
+% \cs{relax}. As of version~4.3 \textsf{calc} allows \cs{relax} tokens
+% to appear in places where they would usually be used for terminating
+% \TeX's scanning. In short this is just before any of \texttt{+-*/)}
+% or at the end of the expression being evaluated.
+%
+% When \TeX\ performs arithmetic on integers, any fractional part of
+% the results are discarded.  For example,
+%\begin{verbatim}
+%    \setcounter{x}{7/2}
+%    \setcounter{y}{3*\real{1.6}}
+%    \setcounter{z}{3*\real{1.7}}
+%\end{verbatim}
+% will assign the value~$3$ to the counter~\texttt{x}, the value~$4$
+% to~\texttt{y}, and the value~$5$ to~\texttt{z}.  This truncation
+% also applies to \emph{intermediate} results in the sequential
+% computation of a composite expression; thus, the following command
+%\begin{verbatim}
+%    \setcounter{x}{3 * \real{1.6} * \real{1.7}}
+%\end{verbatim}
+% will assign~$6$ to~\texttt{x}.
+%
+% As an example of the use of |\ratio|, consider the problem of
+% scaling a figure to occupy the full width (i.e., |\textwidth|) of
+% the body of a page.  Assume that the original dimensions of the
+% figure are given by the dimen (length) variables, |\Xsize| and
+% |\Ysize|.  The height of the scaled figure can then be expressed by
+%\begin{verbatim}
+%    \setlength{\newYsize}{\Ysize*\ratio{\textwidth}{\Xsize}}
+%\end{verbatim}
+%
+%
+%
+% Another new feature introduced in August 2005 was $\max$ and $\min$
+% operations with associated macros
+%\begin{quote}
+%    |\maxof{|\<\textit{type} expression>|}{|\<\textit{type} expression>|}|
+%    \\
+%    |\minof{|\<\textit{type} expression>|}{|\<\textit{type} expression>|}|
+%\end{quote}
+% When \textit{type} is either \meta{glue} or \meta{dimen} these macros
+% are allowed only as part of addition or subtraction but when
+% \textit{type} is \meta{integer} they can also be used when
+% multiplying and dividing. In the latter case they follow the
+% same syntax rules as |\ratio| and |\real| which means they must come
+% after the |*| or the |/|. Thus
+%\begin{verbatim}
+%  \setcounter{x}{3*\maxof{4+5}{3*4}+\minof{2*\real{1.6}}{5-1}}
+%\end{verbatim}
+% will assign $3\times\max(9,12)+\min(3,4)=39$ to |x|. Similarly
+%\begin{verbatim}
+%  \setlength{\parindent}{%
+%    \minof{3pt}{\parskip}*\real{1.5}*\maxof{2*\real{1.6}}{2-1}}
+%\end{verbatim}
+% will assign $\min(13.5\textrm{pt},4.5\cs{parskip})$ to \cs{parindent}
+%
+%
+%
+% \section{Formal syntax}
+%
+% The syntax is described by the following set of rules.
+% Note that the definitions of \<number>, \<dimen>, \<glue>,
+% \<decimal constant>, and \<plus or minus> are
+% as in Chapter~24 of The \TeX book~\cite{texbook}; and \<text>
+% is LR-mode material, as in the manual~\cite{latexman}.
+% We use \textit{type} as a meta-variable, standing for
+% `integer', `dimen', and `glue'.\footnote{This version of the
+% \texttt{calc} package doesn't support evaluation of muglue expressions.}
+%
+% \begin{calc-syntax}
+%    \<\textit{type} expression>^^A
+%       \is  \<\textit{type} term>^^A
+%       \alt \<\textit{type} expression> \<plus or minus> \<\textit{type} term>
+%
+%    \<\textit{type} term>^^A
+%       \is  \<\textit{type} term> \<\textit{type} scan stop>
+%       \alt \<\textit{type} factor>^^A
+%       \alt \<\textit{type} term> \<multiply or divide> \<integer>^^A
+%       \alt \<\textit{type} term> \<multiply or divide> \<real number>^^A
+%       \alt \<\textit{type} term> \<multiply or divide>^^A
+%            \<$\max$ or $\min$ integer>^^A
+%
+%    \<\textit{type} scan stop>^^A
+%       \is  \<empty>^^A
+%       \alt \<optional space>^^A
+%       \alt |\relax|
+%
+%    \<\textit{type} factor>^^A
+%       \is  \<\textit{type}>^^A
+%       \alt \<text dimen factor>^^A
+%       \alt \<$\max$ or $\min$ \textit{type}>^^A
+%       \alt |(|$_{12}$ \<\textit{type} expression> |)|$_{12}$
+%
+%    \<integer> \is \<number>
+%
+%    \<$\max$ or $\min$ \textit{type}> \is \<$\max$ or $\min$ command>^^A
+%               |{| \<\textit{type} expression> |}|^^A
+%               |{| \<\textit{type} expression> |}|
+%
+%    \<$\max$ or $\min$ command> \is |\maxof|^^A
+%                                \alt |\minof|
+%
+%    \<text dimen factor>^^A
+%       \is  \<text dimen command>|{| \<text> |}|
+%
+%    \<text dimen command>^^A
+%       \is   |\widthof|^^A
+%       \alt  |\heightof|^^A
+%       \alt  |\depthof|^^A
+%       \alt  |\totalheightof|^^A
+%
+%    \<multiply or divide>^^A
+%       \is  |*|$_{12}$^^A
+%       \alt |/|$_{12}$
+%
+%    \<real number>^^A
+%       \is  |\ratio{| \<dimen expression> |}{| \<dimen expression> |}|^^A
+%       \alt |\real{| \<optional signs> \<decimal constant> |}|
+%
+%    \<plus or minus>^^A
+%       \is  |+|$_{12}$^^A
+%       \alt |-|$_{12}$
+%
+%    \<decimal constant>^^A
+%       \is  |.|$_{12}$^^A
+%       \alt |,|$_{12}$^^A
+%       \alt \<digit> \<decimal constant>^^A
+%       \alt \<decimal constant> \<digit>
+%
+%    \<digit>^^A
+%       \is  |0|$_{12}$^^A
+%       \alt |1|$_{12}$^^A
+%       \alt |2|$_{12}$^^A
+%       \alt |3|$_{12}$^^A
+%       \alt |4|$_{12}$^^A
+%       \alt |5|$_{12}$^^A
+%       \alt |6|$_{12}$^^A
+%       \alt |7|$_{12}$^^A
+%       \alt |8|$_{12}$^^A
+%       \alt |9|$_{12}$
+%
+%    \<optional signs>^^A
+%       \is  \<optional spaces>^^A
+%       \alt \<optional signs> \<plus or minus> \<optional spaces>
+%
+% \end{calc-syntax}
+%
+%
+% Relying heavily on \TeX\ to do the underlying assignments, it is
+% only natural for \texttt{calc} to simulate \TeX's parsing machinery
+% for these quantities. Therefore it a)~imposes the same restrictions
+% on the catcode of syntax characters as \TeX\ and b)~tries to expand
+% its argument fully. a)~means that implicit characters for the tokens
+% |*|$_{12}$, |/|$_{12}$, |(|$_{12}$, and |)|$_{12}$ will not
+% work\footnote{e\TeX\ also assumes these catcodes when parsing a
+% \cs{numexpr}, \cs{dimexpr}, \cs{glueexpr}, or \cs{muglueexpr} and
+% does not allow implicit characters.} but because of~b), the
+% expansion should allow you to use macros that expand to explicit
+% syntax characters.
+%
+%
+% \StopEventually{
+% \begin{thebibliography}{1}
+%    \bibitem{texbook}
+%       \textsc{D. E. Knuth}.
+%       \newblock \textit{The \TeX{}book} (Computers \& Typesetting Volume A).
+%       \newblock Addison-Wesley, Reading, Massachusetts, 1986.
+%    \bibitem{latexman}
+%       \textsc{L. Lamport}.
+%       \newblock \textit{\LaTeX, A Document Preparation System.}
+%       \newblock Addison-Wesley, Reading, Massachusetts, Second
+%       edition 1994/1985.
+% \end{thebibliography}
+% \PrintChanges
+% }
+%
+% \section{The evaluation scheme}
+% \label{evaluation:scheme}
+%
+% In this section, we shall for simplicity consider only expressions
+% containing `$+$' (addition) and `$*$' (multiplication) operators.
+% It is trivial to add subtraction and division.
+%
+% An expression $E$ is a sum of terms: $T_1+\cdots+T_n$; a term is a
+% product of factors: $F_1*\cdots*F_m$; a factor is either a simple
+% numeric quantity~$f$ (like \<number> as described in the \TeX book),
+% or a parenthesized expression~$(E')$.
+%
+% Since the \TeX\ engine can only execute arithmetic operations in a
+% machine-code like manner, we have to find a way to translate the
+% infix notation into this `instruction set'.
+%
+% Our goal is to design a translation scheme that translates~$X$ (an
+% expression, a term, or a factor) into a sequence of \TeX\ instructions
+% that does the following [Invariance Property]: correctly
+% evaluates~$X$, leaves the result in a global register~$A$ (using a
+% global assignment), and does not perform global assignments to the
+% scratch register~$B$; moreover, the code sequence must be balanced
+% with respect to \TeX\ groups.  We shall denote the code sequence
+% corresponding to~$X$ by \s{X}.
+%
+% In the replacement code specified below, we use the following
+% conventions:
+% \begin{itemize}
+%    \item $A$ and $B$ denote registers; all assignments to~$A$ will
+%       be global, and all assignments to~$B$ will be local.
+%    \item ``$\gassign$'' means global assignment to the register on
+%       the lhs.
+%    \item ``$\lassign $'' means local assignment to the register on
+%       the lhs.
+%    \item ``\savecode C'' means ``save the code~$C$ until the current
+%       group (scope) ends, then execute it.''  This corresponds to
+%       the \TeX-primitive |\aftergroup|.
+%    \item ``$\{$'' denotes the start of a new group, and ``$\}$''
+%       denotes the end of a group.
+% \end{itemize}
+%
+% Let us consider an expression $T_1+T_2+\cdots+T_n$.  Assuming that
+% \s{T_k} ($1\le k\le n$) attains the stated goal, the following code
+% clearly attains the stated goal for their sum:
+% \begin{eqnarray*}
+% \s{T_1+T_2+\cdots+T_n}&\Longrightarrow&
+%       \{\,\s{T_1}\,\} \; B\lassign A \quad
+%       \{\,\s{T_2}\,\} \; B\lassign B+A \\
+%       &&\qquad \ldots \quad \{\,\s{T_n}\,\} \; B\lassign B+A
+%                       \quad A\gassign B
+% \end{eqnarray*}
+% Note the extra level of grouping enclosing each of \s{T_1}, \s{T_2},
+% \ldots,~\s{T_n}.  This will ensure that register~$B$, used to
+% compute the sum of the terms, is not clobbered by the intermediate
+% computations of the individual terms.  Actually, the group
+% enclosing~\s{T_1} is unnecessary, but it turns out to be simpler if
+% all terms are treated the same way.
+%
+% The code sequence ``$\{\,\s{T_2}\,\}\;B\lassign B+A$'' can be translated
+% into the following equivalent code sequence:
+% ``$\{\savecode{B\lassign B+A}\,\s{T_2}\,\}$''.  This observation turns
+% out to be the key to the implementation: The ``$\savecode{B\lassign
+% B+A}$'' is generated \emph{before} $T_2$ is translated, at the same
+% time as the `$+$' operator between $T_1$ and~$T_2$ is seen.
+%
+% Now, the specification of the translation scheme is straightforward:
+% \begin{eqnarray*}
+%    \s{f}&\Longrightarrow&A\gassign f\\[\smallskipamount]
+%    \s{(E')}&\Longrightarrow&\s{E'}\\[\smallskipamount]
+%    \s{T_1+T_2+\cdots+T_n}&\Longrightarrow&
+%       \{\savecode{B\lassign A}\,\s{T_1}\,\} \quad
+%       \{\savecode{B\lassign B+A}\,\s{T_2}\,\} \\
+%       &&\qquad \ldots \quad \{\savecode{B\lassign B+A}\,\s{T_n}\,\}
+%                       \quad A\gassign B
+%                       \\[\smallskipamount]
+%    \s{F_1*F_2*\cdots*F_m}&\Longrightarrow&
+%       \{\savecode{B\lassign A}\,\s{F_1}\,\} \quad
+%       \{\savecode{B\lassign B*A}\,\s{F_2}\,\}\\
+%       &&\qquad \ldots \quad \{\savecode{B\lassign B*A}\,\s{F_m}\,\}
+%                       \quad A\gassign B
+% \end{eqnarray*}
+% By structural induction, it is easily seen that the stated property
+% is attained.
+%
+% By inspection of this translation scheme, we see that we have to
+% generate the following code:
+% \begin{itemize}
+%    \item we must generate ``$\{\savecode{B\lassign
+%       A}\{\savecode{B\lassign A}$'' at the left border of an
+%       expression (i.e., for each left parenthesis and the implicit
+%       left parenthesis at the beginning of the whole expression);
+%    \item we must generate ``$\}A\gassign B\}A\gassign B$'' at the
+%       right border of an expression (i.e., each right parenthesis
+%       and the implicit right parenthesis at the end of the full
+%       expression);
+%    \item `\texttt{*}' is replaced by ``$\}\{\savecode{B\lassign
+%       B*A}$'';
+%    \item `\texttt{+}' is replaced by
+%       ``$\}A\gassign B\}\{\savecode{B\lassign
+%       B+A}\{\savecode{B\lassign A}$'';
+%    \item when we see (expect) a numeric quantity, we insert the
+%    assignment code ``$A\gassign$'' in front of the quantity and let
+%    \TeX\ parse it.
+% \end{itemize}
+%
+% \section{Implementation}
+%
+% For brevity define
+% \begin{calc-syntax}
+%    \<numeric> \is \<number> \alt \<dimen> \alt \<glue> \alt \<muglue>
+% \end{calc-syntax}
+% So far we have ignored the question of how to determine the type of
+% register to be used in the code.  However, it is easy to see that
+% (1)~`$*$' always initiates an \<integer factor>, (2)~all
+% \<numeric>s in an expression, except those which are part of an
+% \<integer factor>, are of the same type as the whole expression, and
+% all \<numeric>s in an \<integer factor> are \<number>s.
+%
+% We have to ensure that $A$ and~$B$ always have an appropriate type
+% for the \<numeric>s they manipulate.  We can achieve this by having
+% an instance of $A$ and~$B$ for each type.  Initially, $A$~and~$B$
+% refer to registers of the proper type for the whole expression.
+% When an \<integer factor> is expected, we must change $A$ and~$B$ to
+% refer to integer type registers.  We can accomplish this by
+% including instructions to change the type of $A$ and~$B$ to integer
+% type as part of the replacement code for~`$*$; if we append such
+% instructions to the replacement code described above, we also ensure
+% that the type-change is local (provided that the type-changing
+% instructions only have local effect).  However, note that the
+% instance of~$A$ referred to in $\savecode{B\lassign B*A}$ is the
+% integer instance of~$A$.
+%
+% We shall use |\begingroup| and |\endgroup| for the open-group and
+% close-group characters.  This avoids problems with spacing in math
+% (as pointed out to us by Frank Mittelbach).
+%
+% \subsection{Getting started}
+%
+% Now we have enough insight to do the actual implementation in \TeX.
+% First, we announce the macro package.\footnote{Code moved to top of file}
+%    \begin{macrocode}
+%<*package>
+%\NeedsTeXFormat{LaTeX2e}
+%\ProvidesPackage{calc}[\filedate\space\fileversion]
+%    \end{macrocode}
+%
+% \subsection{Assignment macros}
+%
+% \begin{macro}{\calc@assign@generic}
+% \changes{v4.2}{2005/08/06}{Removed a few redundant \cs{expandafter}s}
+% The |\calc@assign@generic| macro takes four arguments: (1~and~2) the
+% registers to be used
+% for global and local manipulations, respectively; (3)~the lvalue
+% part; (4)~the expression to be evaluated.
+%
+% The third argument (the lvalue) will be used as a prefix to a
+% register that contains the value of the specified expression (the
+% fourth argument).
+%
+% In general, an lvalue is anything that may be followed by a variable
+% of the appropriate type.  As an example, |\linepenalty| and
+% |\global\advance\linepenalty| may both be followed by an \<integer
+% variable>.
+%
+% The macros described below refer to the registers by the names
+% |\calc@A| and |\calc@B|; this is accomplished by
+% |\let|-assignments.
+%
+% As discovered in Section~\ref{evaluation:scheme}, we have to
+% generate code as
+% if the expression is parenthesized.  As described below,
+% |\calc@open| is the macro that replaces a left parenthesis by its
+% corresponding \TeX\ code sequence.  When the scanning process sees
+% the exclamation point, it generates an |\endgroup| and stops.  As we
+% recall from Section~\ref{evaluation:scheme}, the correct expansion
+% of a right
+% parenthesis is ``$\}A\gassign B\}A\gassign B$''.  The remaining
+% tokens of this expansion are inserted explicitly, except that the
+% last assignment has been replaced by the lvalue part (i.e.,
+% argument~|#3| of |\calc@assign@generic|) followed by |\calc@B|.
+%    \begin{macrocode}
+\def\calc@assign@generic#1#2#3#4{\let\calc@A#1\let\calc@B#2%
+    \calc@open(#4!%
+    \global\calc@A\calc@B\endgroup#3\calc@B}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\calc@assign@count}
+% \begin{macro}{\calc@assign@dimen}
+% \begin{macro}{\calc@assign@skip}
+% We need three instances of the |\calc@assign@generic| macro,
+% corresponding to the types \<integer>, \<dimen>, and \<glue>.
+%    \begin{macrocode}
+\def\calc@assign@count{\calc@assign@generic\calc@Acount\calc@Bcount}
+\def\calc@assign@dimen{\calc@assign@generic\calc@Adimen\calc@Bdimen}
+\def\calc@assign@skip{\calc@assign@generic\calc@Askip\calc@Bskip}
+%    \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+% These macros each refer to two registers, one
+% to be used globally and one to be used locally.
+% We must allocate these registers.
+%    \begin{macrocode}
+\newcount\calc@Acount   \newcount\calc@Bcount
+\newdimen\calc@Adimen   \newdimen\calc@Bdimen
+\newskip\calc@Askip     \newskip\calc@Bskip
+%    \end{macrocode}
+%
+% \subsection{The \LaTeX\ interface}
+%
+% \begin{macro}{\setcounter}
+% \begin{macro}{\addtocounter}
+% \changes{v4.2}{2005/08/06}
+%  {Fix to make \cs{addtocounter} work with \texttt{amstext}}
+% \begin{macro}{\steptocounter}
+% \changes{v4.2}{2005/08/06}
+%  {Avoid redundant processing. PR/3795}
+% \begin{macro}{\setlength}
+% \begin{macro}{\addtolength}
+% As promised, we redefine the following standard \LaTeX\ commands:
+% |\setcounter|,
+% |\addtocounter|, |\setlength|, and |\addtolength|.
+%    \begin{macrocode}
+\def\setcounter#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}%
+   {\calc@assign@count{\global\csname c@#1\endcsname}{#2}}}
+%    \end{macrocode}
+%    \begin{macrocode}
+  \def\addtocounter#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}%
+    {\calc@assign@count{\global\advance\csname c@#1\endcsname}{#2}}}%
+%    \end{macrocode}
+% We also fix \cs{stepcounter} to not go through the whole \texttt{calc}
+% process.
+%    \begin{macrocode}
+  \def\stepcounter#1{\@ifundefined {c@#1}%
+    {\@nocounterr {#1}}%
+    {\global\advance\csname c@#1\endcsname \@ne
+    \begingroup
+      \let\@elt\@stpelt \csname cl@#1\endcsname
+    \endgroup}}%
+%    \end{macrocode}
+% If the \texttt{amstext} package is loaded we must add the
+% |\iffirstchoice@| switch as well. We patch the commands this
+% way since it's good practice when we know how many arguments they take.
+%    \begin{macrocode}
+\@ifpackageloaded{amstext}{%
+ \expandafter\def\expandafter\stepcounter
+    \expandafter#\expandafter1\expandafter{%
+    \expandafter\iffirstchoice@\stepcounter{#1}\fi
+ }
+ \expandafter\def\expandafter\addtocounter
+    \expandafter#\expandafter1\expandafter#\expandafter2\expandafter{%
+    \expandafter\iffirstchoice@\addtocounter{#1}{#2}\fi
+ }
+}{}
+%    \end{macrocode}
+%    \begin{macrocode}
+\DeclareRobustCommand\setlength{\calc@assign@skip}
+\DeclareRobustCommand\addtolength[1]{\calc@assign@skip{\advance#1}}
+%    \end{macrocode}
+% (|\setlength| and |\addtolength| are robust according to
+% \cite{latexman}.)
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{The scanner}
+%
+% We evaluate expressions by explicit scanning of characters.  We do
+% not rely on active characters for this.
+%
+% The scanner consists of two parts, |\calc@pre@scan| and
+% |\calc@post@scan|; |\calc@pre@scan| consumes left parentheses, and
+% |\calc@post@scan| consumes binary operator, |\real|, |\ratio|, and
+% right parenthesis tokens.
+%
+% \begin{macro}{\calc@pre@scan}
+% \begin{macro}{\@calc@pre@scan}
+% \changes{v4.2}{2005/08/06}
+%    {Added macro and force expansion}
+%
+%    Note that this is called at least once on every use of calc
+%    processing, even when none of the extended syntax is present; it
+%    therefore needs to be made very efficient.
+%
+%    It reads the initial part of expressions, until some \<text dimen
+%    factor> or \<numeric> is seen; in fact, anything not explicitly
+%    recognized here is taken to be a \<numeric> of some sort as this
+%    allows unary
+%   `\texttt{+}' and unary `\texttt{-}' to be treated easily and
+%    correctly\footnote{In the few contexts where signs are allowed:
+%    this could, I think, be extended (CAR).} but means that anything
+%    illegal will simply generate a \TeX-level error, often a
+%    reasonably comprehensible one!
+%
+%    The |\romannumeral-`\a| part is a little trick which forces expansion
+%    in case |#1| is a normal macro, something that occurs from time to
+%    time. A conditional test inside will possibly leave a trailing
+%    \cs{fi} but this remnant is removed later when \cs{calc@post@scan}
+%    performs the same trick.
+%
+%    The many |\expandafter|s are needed to efficiently end the nested
+%    conditionals so that |\calc@textsize| and |\calc@maxmin@addsub| can
+%    process their argument.
+% \changes{v4.1a}{1998/06/07}
+%    {Added code for text sizes: CAR}
+% \changes{v4.1b}{1998/07/07}
+%    {Correction to  ifx true case}
+% \changes{v4.2}{2005/08/06}
+%    {Added \cs{maxof} and \cs{minof} operations}
+%    \begin{macrocode}
+\def\calc@pre@scan#1{%
+  \expandafter\@calc@pre@scan\romannumeral-`\a#1}
+\def\@calc@pre@scan#1{%
+  \ifx(#1%
+    \expandafter\calc@open
+  \else
+    \ifx\widthof#1%
+      \expandafter\expandafter\expandafter\calc@textsize
+    \else
+      \ifx\maxof#1%
+        \expandafter\expandafter\expandafter\expandafter
+        \expandafter\expandafter\expandafter\calc@maxmin@addsub
+      \else
+        \calc@numeric% no \expandafter needed for this one.
+      \fi
+    \fi
+  \fi
+  #1}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@open}
+% \begin{macro}{\calc@initB}
+% |\calc@open| is used when there is a left parenthesis right ahead.
+% This parenthesis is replaced by \TeX\ code corresponding to the code
+% sequence ``$\{\savecode{B\lassign A}\{\savecode{B\lassign A}$''
+% derived in Section~\ref{evaluation:scheme}.  Finally,
+% |\calc@pre@scan| is
+% called again.
+%    \begin{macrocode}
+\def\calc@open({\begingroup\aftergroup\calc@initB
+   \begingroup\aftergroup\calc@initB
+   \calc@pre@scan}
+\def\calc@initB{\calc@B\calc@A}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\calc@numeric}
+% |\calc@numeric| assigns the following value to |\calc@A| and then
+% transfers control to |\calc@post@scan|.
+%    \begin{macrocode}
+\def\calc@numeric{\afterassignment\calc@post@scan \global\calc@A}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\widthof}
+% \begin{macro}{\heightof}
+% \begin{macro}{\depthof}
+% \changes{v4.1a}{1998/06/07}
+%    {Added macros: CAR}
+% \begin{macro}{\totalheightof}
+% \changes{v4.2}{2005/08/06}
+%    {Added macro}
+% \changes{v4.2}{2005/08/06}
+%    {Added informative message for reserved macros}
+%
+%    These do not need any particular definition when they are scanned
+%    so, for efficiency and robustness, we make them all equivalent to
+%    the same harmless (I hope) unexpandable command.\footnote{If this
+%    level of safety is not needed then the code can be sped up:
+%    CAR.}  Thus the test in |\@calc@pre@scan| finds any of them.
+%
+%    As we have to check for these commands explicitly we must ensure
+%    that our definition wins. Using \cs{newcommand} gives an error when
+%    loading \texttt{calc} and may be mildly surprising. This should be
+%    a little more informative.
+%    \begin{macrocode}
+\@for\reserved@a:=widthof,heightof,depthof,totalheightof,maxof,minof\do
+{\@ifundefined{\reserved@a}{}{%
+  \PackageError{calc}{%
+  The\space calc\space package\space reserves\space the\space
+  command\space name\space `\@backslashchar\reserved@a'\MessageBreak
+  but\space it\space has\space already\space been\space defined\space
+  with\space the\space meaning\MessageBreak
+  `\expandafter\meaning\csname\reserved@a\endcsname'.\MessageBreak
+  This\space original\space definition\space will\space be\space lost}%
+  {If\space you\space need\space a\space command\space with\space
+  this\space definition,\space you\space must\space use\space a\space
+  different\space name.}}%
+}
+\let\widthof\ignorespaces
+\let\heightof\ignorespaces
+\let\depthof\ignorespaces
+\let\totalheightof\ignorespaces
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@textsize}
+% \changes{v4.1a}{1998/06/07}
+%    {Added macro: CAR}
+% \changes{v4.1a}{1998/06/07}
+%    {Added macro: CAR}
+% \changes{v4.2}{2005/08/06}
+%    {Extended macro with \cs{totalheightof}}
+%    The presence of the above four commands invokes this code, where
+%    we must distinguish them from each other.
+%    This implementation is somewhat optimized by using low-level
+%    code from the commands |\settowidth|, etc.\footnote{It is based on
+%    suggestions by Donald Arseneau and David Carlisle.}
+%
+%    Within the text argument we must restore the normal meanings of
+%    the four user-level commands since arbitrary material can appear
+%    in here, including further uses of calc.
+%    \begin{macrocode}
+\def\calc@textsize #1#2{%
+  \begingroup
+    \let\widthof\wd
+    \let\heightof\ht
+    \let\depthof\dp
+    \def\totalheightof{\ht\dp}%
+%    \end{macrocode}
+% We must expand the argument one level if it's \cs{totalheightof}
+% and it doesn't hurt the other three.
+%    \begin{macrocode}
+    \expandafter\@settodim\expandafter{#1}%
+      {\global\calc@A}%
+      {%
+       \let\widthof\ignorespaces
+       \let\heightof\ignorespaces
+       \let\depthof\ignorespaces
+       \let\totalheightof\ignorespaces
+       #2}%
+  \endgroup
+  \calc@post@scan}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\calc@post@scan}
+% \begin{macro}{\@calc@post@scan}
+% \changes{v4.2}{2005/08/06}{Added macro and force expansion}
+% \changes{v4.3}{2007/08/22}{Discard terminating \cs{relax} tokens and
+%   avoid extra error message from \cs{calc@next}}
+% The macro |\calc@post@scan| is called right after a value has been
+% read.  At this point, a binary operator, a sequence of right
+% parentheses, an optional \cs{relax}, and the end-of-expression mark
+% (`|!|') is allowed.\footnote{Is \texttt{!} a good choice, CAR?}
+% Depending on our findings, we call a suitable macro to generate the
+% corresponding \TeX\ code (except when we detect the
+% end-of-expression marker: then scanning ends, and control is
+% returned to |\calc@assign@generic|).
+%
+% This macro may be optimized by selecting a different order of
+% |\ifx|-tests.  The test for `\texttt{!}' (end-of-expression) is
+% placed first as it will always be performed: this is the only test
+% to be performed if the expression consists of a single \<numeric>.
+% This ensures that documents that do not use the extra expressive
+% power provided by the \texttt{calc} package only suffer a minimum
+% slowdown in processing time.
+%    \begin{macrocode}
+\def\calc@post@scan#1{%
+ \expandafter\@calc@post@scan\romannumeral-`\a#1}
+\def\@calc@post@scan#1{%
+  \ifx#1!\let\calc@next\endgroup \else
+    \ifx#1+\let\calc@next\calc@add \else
+      \ifx#1-\let\calc@next\calc@subtract \else
+        \ifx#1*\let\calc@next\calc@multiplyx \else
+          \ifx#1/\let\calc@next\calc@dividex \else
+            \ifx#1)\let\calc@next\calc@close \else
+              \ifx#1\relax\let\calc@next\calc@post@scan \else
+                \def\calc@next{\calc@error#1}%
+              \fi
+            \fi
+          \fi
+        \fi
+      \fi
+    \fi
+  \fi
+  \calc@next}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@add}
+% \begin{macro}{\calc@subtract}
+% \begin{macro}{\calc@generic@add}
+% \begin{macro}{\calc@addAtoB}
+% \begin{macro}{\calc@subtractAfromB}
+% The replacement code for the binary operators `\texttt{+}' and
+% `\texttt{-}' follow a common pattern; the only difference is the
+% token that is stored away by |\aftergroup|.  After this replacement
+% code, control is transferred to |\calc@pre@scan|.
+%    \begin{macrocode}
+\def\calc@add{\calc@generic@add\calc@addAtoB}
+\def\calc@subtract{\calc@generic@add\calc@subtractAfromB}
+\def\calc@generic@add#1{\endgroup\global\calc@A\calc@B\endgroup
+   \begingroup\aftergroup#1\begingroup\aftergroup\calc@initB
+   \calc@pre@scan}
+\def\calc@addAtoB{\advance\calc@B\calc@A}
+\def\calc@subtractAfromB{\advance\calc@B-\calc@A}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macro}{\real}
+%    \begin{macro}{\ratio}
+%    \begin{macro}{\calc@ratio@x}
+%    \begin{macro}{\calc@real@x}
+%    The multiplicative operators, `\texttt{*}' and `\texttt{/}', may be
+%    followed by a |\real|, |\ratio|, |\minof|, or |\maxof|  token. The
+%    last two of these control sequences are defined by \texttt{calc} as
+%    they are needed by the scanner for addition or subtraction while the
+%    first two are not defined (at least not by the \texttt{calc}
+%    package); this,
+%    unfortunately, leaves them highly non-robust.  We therefore
+%    equate them to |\relax| but only if they have not already been
+%    defined\footnote{Suggested code from David Carlisle.}
+%    (by some other package: dangerous but possible!); this
+%    will also make them appear to be undefined to a \LaTeX{} user
+%    (also possibly dangerous).
+% \changes{v4.1a}{1998/06/07}
+%    {Added macro set-ups to make them robust but undefined: CAR}
+%    \begin{macrocode}
+\ifx\real\@undefined\let\real\relax\fi
+\ifx\ratio\@undefined\let\ratio\relax\fi
+%    \end{macrocode}
+%    In order to test for |\real| or |\ratio|, we define these
+%    two.\footnote{May not need the extra names, CAR?}
+%    \begin{macrocode}
+\def\calc@ratio@x{\ratio}
+\def\calc@real@x{\real}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+% \begin{macro}{\calc@multiplyx}
+% \changes{v4.2}{2005/08/06}
+%    {Added $\protect\max$ and $\protect\min$ operations}
+% \begin{macro}{\calc@dividex}
+% \changes{v4.2}{2005/08/06}
+%    {Added $\protect\max$ and $\protect\min$ operations}
+% Test which operator followed |*| or |/|. If none followed it's just
+% a standard multiplication or division.
+%    \begin{macrocode}
+\def\calc@multiplyx#1{\def\calc@tmp{#1}%
+  \ifx\calc@tmp\calc@ratio@x \let\calc@next\calc@ratio@multiply \else
+    \ifx\calc@tmp\calc@real@x \let\calc@next\calc@real@multiply \else
+      \ifx\maxof#1\let\calc@next\calc@maxmin@multiply \else
+        \let\calc@next\calc@multiply
+      \fi
+    \fi
+  \fi
+  \calc@next#1}
+\def\calc@dividex#1{\def\calc@tmp{#1}%
+  \ifx\calc@tmp\calc@ratio@x \let\calc@next\calc@ratio@divide \else
+    \ifx\calc@tmp\calc@real@x \let\calc@next\calc@real@divide \else
+      \ifx\maxof#1\let\calc@next\calc@maxmin@divide \else
+        \let\calc@next\calc@divide
+      \fi
+    \fi
+  \fi
+  \calc@next#1}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@multiply}
+% \begin{macro}{\calc@divide}
+% \begin{macro}{\calc@generic@multiply}
+% \begin{macro}{\calc@multiplyBbyA}
+% \begin{macro}{\calc@divideBbyA}
+% The binary operators `\texttt{*}' and `\texttt{/}' also insert code
+% as determined above.  Moreover, the meaning of |\calc@A| and
+% |\calc@B| is changed as factors following a multiplication and
+% division operator always have integer type; the original meaning of
+% these macros will be restored when the factor has been read and
+% evaluated.
+%    \begin{macrocode}
+\def\calc@multiply{\calc@generic@multiply\calc@multiplyBbyA}
+\def\calc@divide{\calc@generic@multiply\calc@divideBbyA}
+\def\calc@generic@multiply#1{\endgroup\begingroup
+   \let\calc@A\calc@Acount \let\calc@B\calc@Bcount
+   \aftergroup#1\calc@pre@scan}
+\def\calc@multiplyBbyA{\multiply\calc@B\calc@Acount}
+\def\calc@divideBbyA{\divide\calc@B\calc@Acount}
+%    \end{macrocode}
+% Since the value to use in the multiplication/division operation is
+% stored in the |\calc@Acount| register, the |\calc@multiplyBbyA| and
+% |\calc@divideBbyA| macros use this register.
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@close}
+% |\calc@close| generates code for a right parenthesis (which was
+% derived to be ``$\}A\gassign B\}A\gassign B$'' in
+% Section~\ref{evaluation:scheme}).  After this code, the control is
+% returned to
+% |\calc@post@scan| in order to look for another right parenthesis or
+% a binary operator.
+%    \begin{macrocode}
+\def\calc@close
+   {\endgroup\global\calc@A\calc@B
+    \endgroup\global\calc@A\calc@B
+    \calc@post@scan}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Calculating a ratio}
+%
+% \begin{macro}{\calc@ratio@multiply}
+% \begin{macro}{\calc@ratio@divide}
+% When |\calc@post@scan| encounters a |\ratio| control sequence, it hands
+% control to one of the macros |\calc@ratio@multiply| or |\calc@ratio@divide|,
+% depending on the preceding character. Those macros both forward the
+% control to the macro |\calc@ratio@evaluate|, which performs two steps: (1) it
+% calculates the ratio, which is saved in the global macro token
+% |\calc@the@ratio|; (2) it makes sure that the value of |\calc@B| will be
+% multiplied by the ratio as soon as the current group ends.
+%
+% The following macros call |\calc@ratio@evaluate| which multiplies
+% |\calc@B| by the ratio, but |\calc@ratio@divide| flips the arguments
+% so that the `opposite' fraction is actually evaluated.
+%    \begin{macrocode}
+\def\calc@ratio@multiply\ratio{\calc@ratio@evaluate}
+\def\calc@ratio@divide\ratio#1#2{\calc@ratio@evaluate{#2}{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\calc@Ccount}
+% \begin{macro}{\calc@numerator}
+% \begin{macro}{\calc@denominator}
+% We shall need two registers for temporary usage in the
+% calculations.  We can save one register since we can reuse
+% |\calc@Bcount|.
+%    \begin{macrocode}
+\newcount\calc@Ccount
+\let\calc@numerator=\calc@Bcount
+\let\calc@denominator=\calc@Ccount
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\calc@ratio@evaluate}
+% Here is the macro that handles the actual evaluation of ratios.  The
+% procedure is
+% this: First, the two expressions are evaluated and coerced to
+% integers. The whole procedure is enclosed in a group to be able to
+% use the registers |\calc@numerator| and |\calc@denominator| for temporary
+% manipulations.
+%    \begin{macrocode}
+\def\calc@ratio@evaluate#1#2{%
+   \endgroup\begingroup
+      \calc@assign@dimen\calc@numerator{#1}%
+      \calc@assign@dimen\calc@denominator{#2}%
+%    \end{macrocode}
+% Here we calculate the ratio.  First, we check for negative numerator
+% and/or denominator; note that \TeX\ interprets two minus signs the
+% same as a plus sign.  Then, we calculate the integer part.
+% The minus sign(s), the integer part, and a decimal point, form the
+% initial expansion of the |\calc@the@ratio| macro.
+%    \begin{macrocode}
+      \gdef\calc@the@ratio{}%
+      \ifnum\calc@numerator<0 \calc@numerator-\calc@numerator
+         \gdef\calc@the@ratio{-}%
+      \fi
+      \ifnum\calc@denominator<0 \calc@denominator-\calc@denominator
+         \xdef\calc@the@ratio{\calc@the@ratio-}%
+      \fi
+      \calc@Acount\calc@numerator
+      \divide\calc@Acount\calc@denominator
+      \xdef\calc@the@ratio{\calc@the@ratio\number\calc@Acount.}%
+%    \end{macrocode}
+% Now we generate the digits after the decimal point, one at a time.
+% When \TeX\ scans these digits (in the actual multiplication
+% operation), it forms a fixed-point number with 16~bits for
+% the fractional part.  We hope that six digits is sufficient, even
+% though the last digit may not be rounded correctly.
+%    \begin{macrocode}
+      \calc@next@digit \calc@next@digit \calc@next@digit
+      \calc@next@digit \calc@next@digit \calc@next@digit
+   \endgroup
+%    \end{macrocode}
+% Now we have the ratio represented (as the expansion of the global
+% macro |\calc@the@ratio|) in the syntax \<decimal constant>
+% \cite[page~270]{texbook}.  This is fed to |\calc@multiply@by@real|
+% that will
+% perform the actual multiplication.  It is important that the
+% multiplication takes place at the correct grouping level so that the
+% correct instance of the $B$ register will be used.  Also note that
+% we do not need the |\aftergroup| mechanism in this case.
+%    \begin{macrocode}
+   \calc@multiply@by@real\calc@the@ratio
+   \begingroup
+   \calc@post@scan}
+%    \end{macrocode}
+% \end{macro}
+% The |\begingroup| inserted before the |\calc@post@scan| will be
+% matched by the |\endgroup| generated as part of the replacement of a
+% subsequent binary operator or right parenthesis.
+% \begin{macro}{\calc@next@digit}
+%    \begin{macrocode}
+\def\calc@next@digit{%
+      \multiply\calc@Acount\calc@denominator
+      \advance\calc@numerator -\calc@Acount
+      \multiply\calc@numerator 10
+      \calc@Acount\calc@numerator
+      \divide\calc@Acount\calc@denominator
+      \xdef\calc@the@ratio{\calc@the@ratio\number\calc@Acount}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\calc@multiply@by@real}
+% In the following code, it is important that we first assign the
+% result to a dimen register.  Otherwise, \TeX\ won't allow us to
+% multiply with a real number.
+%    \begin{macrocode}
+\def\calc@multiply@by@real#1{\calc@Bdimen #1\calc@B \calc@B\calc@Bdimen}
+%    \end{macrocode}
+% (Note that this code wouldn't work if |\calc@B| were a muglue
+% register.  This is the real reason why the \texttt{calc} package
+% doesn't support muglue expressions.  To support muglue expressions
+% in full, the |\calc@multiply@by@real| macro must use a muglue register
+% instead of |\calc@Bdimen| when |\calc@B| is a muglue register;
+% otherwise, a dimen register should be used.  Since integer
+% expressions can appear as part of a muglue expression, it would be
+% necessary to determine the correct register to use each time a
+% multiplication is made.)
+% \end{macro}
+%
+% \subsection{Multiplication by real numbers}
+%
+% \begin{macro}{\calc@real@multiply}
+% \begin{macro}{\calc@real@divide}
+% This is similar to the |\calc@ratio@evaluate| macro above, except that
+% it is considerably simplified since we don't need to calculate the
+% factor explicitly.
+%    \begin{macrocode}
+\def\calc@real@multiply\real#1{\endgroup
+   \calc@multiply@by@real{#1}\begingroup
+   \calc@post@scan}
+\def\calc@real@divide\real#1{\calc@ratio@evaluate{1pt}{#1pt}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{$\max$ and $\min$ operations}
+%
+% \begin{macro}{\maxof}
+% \begin{macro}{\minof}
+% \changes{v4.2}{2005/08/06}
+%    {Added macros}
+% With version 4.2, the $\max$ and $\min$ operators were
+% added to \texttt{calc}. The user functions for them are \cs{maxof} and
+% \cs{minof} respectively.
+% These macros are internally similar to \cs{widthof} etc.\ in that they
+% are unexpandable and easily recognizable by the scanner.
+%    \begin{macrocode}
+\let\maxof\@@italiccorr
+\let\minof\@@italiccorr
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\calc@Cskip}
+% \begin{macro}{\ifcalc@count@}
+% The $\max$ and $\min$ operations take two arguments so we need an extra
+% \<skip> register. We also add a switch for determining when to perform
+% a \<skip> or a \<count> assignment.
+%    \begin{macrocode}
+\newskip\calc@Cskip
+\newif\ifcalc@count@
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%  \begin{macro}{\calc@maxmin@addsub}
+%  \begin{macro}{\calc@maxmin@generic}
+% \changes{v4.2}{2005/08/06}{Macros added}
+% When doing addition or subtraction with a $\max$ or $\min$ operator, we
+% first check if |\calc@A| is a \<count> register or not and then set the
+% switch. Then call the real function which sets |\calc@A| to the desired
+% value and continue as usual with |\calc@post@scan|.
+%    \begin{macrocode}
+\def\calc@maxmin@addsub#1#2#3{\begingroup
+  \ifx\calc@A\calc@Acount%
+    \calc@count@true
+  \else
+    \calc@count@false
+  \fi
+  \calc@maxmin@generic#1{#2}{#3}%
+  \endgroup
+  \calc@post@scan
+}
+%    \end{macrocode}
+% Check the switch and do either \<count> or \<skip> assignments. Note that
+% |\maxof| and |\minof| are not set to |>| and |<| until after the
+% assignments, which ensures we can nest them without problems. Then set
+% |\calc@A| to the correct one.
+%    \begin{macrocode}
+\def\calc@maxmin@generic#1#2#3{%
+  \begingroup
+    \ifcalc@count@
+      \calc@assign@count\calc@Ccount{#2}%
+      \calc@assign@count\calc@Bcount{#3}%
+      \def\minof{<}\def\maxof{>}%
+      \global\calc@A\ifnum\calc@Ccount#1\calc@Bcount
+        \calc@Ccount\else\calc@Bcount\fi
+    \else
+      \calc@assign@skip\calc@Cskip{#2}%
+      \calc@assign@skip\calc@Bskip{#3}%
+      \def\minof{<}\def\maxof{>}%
+      \global\calc@A\ifdim\calc@Cskip#1\calc@Bskip
+        \calc@Cskip\else\calc@Bskip\fi
+    \fi
+  \endgroup
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\calc@maxmin@divmul}
+% \begin{macro}{\calc@maxmin@multiply}
+% \begin{macro}{\calc@maxmin@divide}
+% \changes{v4.2}{2005/08/06}{Macros added}
+% When doing division or multiplication we must be using \<count> registers
+% so we set the switch. Other than that it is almost business as usual when
+% multiplying or dividing. |#1| is the instruction to either multiply or
+% divide |\calc@B| by |\calc@A|, |#2| is either |\maxof| or |\minof| which
+% is waiting in the input stream and |#3| and |#4| are the calc expressions.
+% We end it all as usual by calling |\calc@post@scan|.
+%    \begin{macrocode}
+\def\calc@maxmin@divmul#1#2#3#4{%
+  \endgroup\begingroup
+  \calc@count@true
+  \aftergroup#1%
+  \calc@maxmin@generic#2{#3}{#4}%
+  \endgroup\begingroup
+  \calc@post@scan
+}
+%    \end{macrocode}
+% The two functions called when seeing a |*| or a |/|.
+%    \begin{macrocode}
+\def\calc@maxmin@multiply{\calc@maxmin@divmul\calc@multiplyBbyA}
+\def\calc@maxmin@divide  {\calc@maxmin@divmul\calc@divideBbyA}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \section{Reporting errors}
+% \begin{macro}{\calc@error}
+% \changes{v4.0d}{1997/11/08}
+%    {Use \cs{PackageError} for error messages (DPC)}
+% \changes{v4.0e}{1997/11/11}
+%    {typo fixed}
+% If |\calc@post@scan| reads a character that is not one of `\texttt{+}',
+% `\texttt{-}', `\texttt{*}', `\texttt{/}', or `\texttt{)}', an error
+% has occurred, and this is reported to the user.  Violations in the
+% syntax of \<numeric>s will be detected and reported by \TeX.
+% \changes{v4.1a}{1998/06/07}
+%    {Improved, I hope, error message: CAR}
+%    \begin{macrocode}
+\def\calc@error#1{%
+   \PackageError{calc}%
+     {`#1' invalid at this point}%
+     {I expected to see one of: + - * / )}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \section{Other additions}
+% \begin{macro}{\@settodim}
+% \changes{v4.2}{2005/08/06}
+%    {Changed kernel macro}
+% \begin{macro}{\settototalheight}
+% \changes{v4.2}{2005/08/06}
+%    {Added macro}
+% The kernel macro \cs{@settodim} is changed so that it runs through a list
+% containing \cs{ht}, \cs{wd}, and \cs{dp} and than advance the length
+% one step at a time. We just have to use a scratch register in case the
+% user decides to put in a \cs{global} prefix on the length register.
+% A search on the internet confirmed that some people do that kind of thing.
+%    \begin{macrocode}
+\def\@settodim#1#2#3{%
+  \setbox\@tempboxa\hbox{{#3}}%
+  \dimen@ii=\z@
+  \@tf@r\reserved@a #1\do{%
+  \advance\dimen@ii\reserved@a\@tempboxa}%
+  #2=\dimen@ii
+  \setbox\@tempboxa\box\voidb@x}
+%    \end{macrocode}
+% Now the user level macro is straightforward.
+%    \begin{macrocode}
+\def\settototalheight{\@settodim{\ht\dp}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% That's the end of the package.
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+\endinput
+
diff --git a/macros/latex-dev/required/tools/calc.pdf b/macros/latex-dev/required/tools/calc.pdf
new file mode 100644
index 0000000000..694dfa5023
--- /dev/null
+++ b/macros/latex-dev/required/tools/calc.pdf
diff --git a/macros/latex-dev/required/tools/changes.txt b/macros/latex-dev/required/tools/changes.txt
new file mode 100644
index 0000000000..e169707750
--- /dev/null
+++ b/macros/latex-dev/required/tools/changes.txt
@@ -0,0 +1,1671 @@
+=======================================================================
+This file lists changes to the LaTeX2e files in reverse chronological order.
+It is provided for convenience only.  It therefore makes no claims to
+completeness or accuracy and it contains some references to files that
+are not part of the distribution.
+=======================================================================
+
+
+2019-09-09  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* varioref.dtx (subsection{Options}:
+	Option arabic added
+
+2019-08-31  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx: Add a necessary \expandafter so that redefinitions
+	of primitive specifiers	give a warning (github/148)
+
+2019-08-25  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* varioref.dtx: \labelformat and \Ref now available in the kernel
+        so removed from this package but only if running on new kernel
+
+	(subsection{Options}):
+	Provide options space and nospace
+
+	(subsection{Defining the main macros}):
+	Don't drop a preceding space completely but reinsert it later
+	after setting a label;
+	Command \vp@gerefstar, \vref@star and \Vref@star added to support
+	hyperref better
+
+	(subsubsection{Supporting ranges}):
+	Added \vpagerefcompare, \vpagrefnearby and \vpagerefcomparenearby
+
+2019-03-01  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx (subsection{The output routines}):
+	Provide minrows counter for balancing.
+
+2019-02-06  David Carlisle  <David.Carlisle@latex-project.org>
+
+	* longtable.dtx: Document the extra color groups
+
+#########################
+# 2019-01-05 Release
+#########################
+
+2019-01-05  David Carlisle  <David.Carlisle@latex-project.org>
+
+	* xr.dtx: Fix to last update to avoid breaking \include handling.
+	(gh/106)
+
+2018-12-30  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx (section{The macros \texttt{\textbackslash @classz}):
+	Add extra \hskip1sp to guard against an \unskip at the start of
+	a c-column cell (gh/102)
+
+2018-12-27  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx (subsection{The output routines}):
+	Removed dead code, the case where this can go wrong is too
+	obscure to worry about it (gh/101)
+
+#########################
+# 2018-12-01 Release
+#########################
+
+2018-11-13    <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx: Do not expand argument of \@startpbox
+	while building the tabular preamble (sx/459285)
+
+2018-11-09  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx:
+	Support star with \docolaction (test first then execute)
+
+2018-10-13  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* trace.dtx (section{Implementation}):
+	Only reset \tracingoutput if not set by \showoutput earlier
+
+2018-10-01  David Carlisle  <David.Carlisle@latex-project.org>
+
+	* xr.dtx: Update to handle \if tests in the aux file.
+	  https://tex.stackexchange.com/a/452321
+
+2018-09-13  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx (section{The macros \@classz):
+	Add group to prevent color leak (github/72)
+
+#########################
+# 2018-04-01 PL 5 Release
+#########################
+
+2018-06-26  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx (subsection{Not balancing the columns}):
+	Re-add end penalty for multicols* environment to guard
+	against leftovers (git/53)
+
+2018-04-30  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx Explicitly place the row strut inside \\ before
+	hitting \cr in case the last cell is a multicolumn cell
+	(issue 42)
+
+2018-04-20  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: restoring column status when leaving a boxed
+	multicols so that any further \docolaction will know the
+	currect column (issue/39)
+
+2018-04-07  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx: Renamed internal \mcell@box to
+	\ar@mcellbox and \align@mcell to \ar@align@mcell
+        to avoid conflict with makecell package
+
+2018-01-28  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx:  use a single output routine that does both
+	balancing and cutting rather than changing them
+
+2017-11-07  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx: fixed bug reported on stack exchange SX68732 about
+	bad vertical placement with last column being an m-column
+
+	* array.dtx: fixed bug with m-cells when \extrarowheight is used
+
+	* array.dtx: added w and W column types to support lcr columns with
+	fixed width
+        (see TUB paper in 38/2: https://www.latex-project.org/publications )
+
+2017-09-28  David Carlisle  <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: set \linewidth as well as \hsize in the column
+	widths documentation.
+
+2017-04-11  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: Make \clearpage behave like \newpage (pr/4511)
+
+2017-01-16  David Carlisle  <latex-bugs@latex-project.org>
+
+	* bm.dtx: further fixes to luatex code branch for
+	https://tex.stackexchange.com/questions/349001
+
+2016-10-06  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* array.dtx: Fixed a 25 year old bug that surfaced for the first time.
+	\@halignto needs to be managed locally (pr/4488)
+
+2016-07-07  David Carlisle  <latex-bugs@latex-project.org>
+
+	* bm.dtx: additional tests to cope with luatex's new treatment of
+	\mathchar.
+
+2016-07-01  David Carlisle  <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: show [tcb] optional argument in tabularx
+	syntax description.
+
+2016-06-07  David Carlisle  <latex-bugs@latex-project.org>
+
+	* shellesc.dtx: typos in messages, and
+	improve use with plain etex or luatex
+
+2016-04-29  David Carlisle  <latex-bugs@latex-project.org>
+
+	* shellesc.dtx: in classic tex code accidentally defined
+	\ShellEscape twice instead of defining \DelayedShellEscape
+	(Ulrike Fischer)
+
+2016-04-07  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: Reset \boxmaxdepth back to \maxdimen when outputting
+	 pages (issue SX302532).
+
+2016-02-27  David Carlisle  <latex-bugs@latex-project.org>
+
+	* bm.dtx: add initial support for \Umathchardef defined tokens.
+
+2016-02-16  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* varioref.dtx: Delay generating a "may loop" warning or error
+	until we know that we aren't using \reftextfaraway
+	-- thanks to Morten Hoegholm for the fix
+
+2016-02-09  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* varioref.dtx: revamped some of the documentation to better
+	explain how varioref could be used in a multi-lingual context
+
+2016-02-08  Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: Ensure we are back in vmode before using
+        \prevdepth (pr/4448)
+        \col@number already initialized in the kernel, so not initializing
+	it in the package in case the document is in two-column (pr/4435)
+
+2016-02-03  David Carlisle  <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: support end code of {foo\endtabulax bar} again
+          (Reported by Ulrike Fischer)
+
+2016-02-02  David Carlisle  <latex-bugs@latex-project.org>
+
+	* shellesc.dtx: Documentation typos (via Johannes_B at tex.sx)
+
+2016-01-08  David Carlisle  <latex-bugs@latex-project.org>
+
+	* shellesc.dtx: Added new package
+
+2015-09-22 Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* varioref.dtx: Fixed blunder from 2005 - galician option
+	clearly never used
+
+2015-08-19 Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: Reset \@textfloatsheight after page finishes (sx261884)
+
+2015-04-02  Joseph Wright <joseph.wright@morningstar2.co.uk>
+        * TDS-style zip improvements
+
+2015-04-02 Joseph Wright <latex-team@latex-project.org>
+       * Update CTAN link in README
+
+2015-03-31 Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: Another rewrite of \remove@discardable@items to
+	capture the case of \vspace (remove) and \vspace* (keep) correctly
+
+2015-03-25 Frank Mittelbach  <Frank.Mittelbach@latex-project.org>
+
+	* multicol.dtx: additional tracing info if forced breaks result in
+	overflow of column heights
+
+2015-03-23  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Detect when columns get too large during balancing
+	because the user requested more forced breaks than available
+	columns.
+
+	Fixed the logic for removing excess white space at column bottoms
+	(this is a source of trouble for sure)
+
+2015-03-07  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: - Use only `0.0001fil' for stretching in \vfilmaxdepth
+	 - Set \boxmaxdepth in multi@column@out to avoid material getting too
+	far down
+	 - Redesign the implementation of \end{multicols*}
+
+2014-11-07 Joseph Wright <latex-bugs@latex-project.org>
+
+       * Rename 00readme.txt to README (named README.txt in the development
+         repository)
+
+2014-10-28 Frank Mittelbach   <latex-bugs@latex-project.org>
+
+	* multicol.dtx: In \end{multicols*} only add vertical space if not
+	doing already doing \raggedcolumns and add \null to hide the final
+	fill if added so that it doesn't get removed again.
+
+2014-10-28  Frank Mittelbach  <latex-bugs@latex-project.org>
+	* afterpage.dtx, array.dtx, bm.dtx, calc.dtx, dcolumn.dtx,
+	delarray.dtx, enumerate.dtx, ftnright.dtx, hhline.dtx, layout.dtx,
+	longtable.dtx, multicol.dtx, showkeys.dtx, tabularx.dtx,
+	theorem.dtx, trace.dtx, varioref.dtx, verbatim.dtx, xspace.dtx
+
+	Fixed typos found by Karl Berry in documentation (no version number change)
+
+2014-09-12  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: change ragged columns to not just fill the
+	column but also back up by \maxdepth if they otherwise become
+	overfull as adding glue at the bottom means the column will
+	never have any depth and before they had. (pr/4395)
+
+	\maxdepth is applied to all column boxes. That was initially not
+	necessary as \splitmaxdepth was doing the trick. However, the
+	moment those boxes get reboxed this information is lost and
+	resulted in some subtle errors. (pr/4395)
+
+	Suppress even really bad overfull warnings while looping
+
+2014-08-24  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: set \prevdepth to 0pt (in the right place)
+	after adding the multicol material. Was not happening in boxed mode.
+	Test for excessive depth of columns using > not = (which nearly
+	ever will be correct)
+
+2014-07-03    <latex-bugs@latex-project.org>
+
+	* varioref.dtx: correct Romanian default text as suggested
+
+2014-06-19  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: color-leak fix introduced a spacing problem in
+	boxed mode as the added color commands were hiding any space
+	at the bottom of the box material (which thus didn't get
+	discarded)
+
+2014-05-14  David Carlisle  <latex-bugs@latex-project.org>
+
+	* readme.txt: rename to 00readme.txt.
+
+2014-05-13  David Carlisle  <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: If \endtabularx not found, act as if it was at the start of
+	the end code.
+
+2014-04-24    David Carlisle  <david.carlisle@latex-project.org>
+
+	* showkeys.dtx: modify \cite redefinition so {} in the optional argument
+          works (tools/4162)
+
+2014-04-23  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Support \docolaction
+
+2014-04-22  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	   Bug fix: color leak (https://tex.stackexchange.com/questions/138783)
+	   Bug fix: space at column bottom (https://tex.stackexchange.com/questions/121692)
+	   Bug fix: Reset \@mparbottom after page finishes
+
+2014-04-22  David Carlisle  <david.carlisle@latex-project.org>
+
+	* tabularx.dtx: allow code before \endtabularx (pr/3722)
+
+2012-02-06  David Carlisle  <david.carlisle@latex-project.org>
+
+	* tabularx.dtx: Avoid exceeding maxdimen
+          https://tex.stackexchange.com/questions/29194/how-to-typeset-tabularx-with-34-columns-error-message
+
+2011-12-20  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: RL language support fixed
+                        Support for \enlargethispage
+                        Balancing concept improved
+                        Bug fix: Only re-add output penalty if it was
+                                 explicit in the source.
+
+2011/11/24  David Carlisle  <david.carlisle@latex-project.org>
+
+	* showkeys.dtx: revert change made at v3.14 because of tools/4173
+
+2011-10-02  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Previous fix need one more expansion
+%                            (pr/4159,pr/4171)
+
+2010-11-12  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Avoid even \protected@edef in \vref@pagenum
+	         to pacify french babel (pr/4093)
+
+2010-10-24  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: right-to-left language support added
+
+2010-08-06  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* multicol.dtx: typo corrections only -- thanks to Laurent Lyaudet
+
+2010-08-04  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Correct spacing -- same mistake as in \vref (pr/4123)
+                        Defaults for esperanto added
+
+2010-04-06  Will Robertson  <will.robertson@latex-project.org>
+
+	* xspace.dtx: Improve edge case for xspace (tools/3895)
+
+2010-02-25  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* ftnright.dtx: Check for split footnotes (pr/4099)
+
+2009-09-13  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Use \protected@edef to avoid problems
+              in complicated setups, e.g., microtype (pr/4080)
+
+2009-06-12  Frank Mittelbach  <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Incorrect text in \reftextafter (pr/4070)
+
+2008-04-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: clarified customization with Babel in use.
+
+2007-09-07 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Added defaults for islandic
+
+2007-05-26 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: fixed missspellings of \extrasbazil and \extrasportuges
+
+2006-09-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Make the color of the rule between columns (if
+	any) a hook called \columnseprulecolor. Defaults to \normalcolor
+
+2006-05-23 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: support for bulgarian added.
+
+2006-05-14 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: support for croatian added.
+
+2006-05-08 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Bug fix for verbatim in output routine.
+
+2006-02-23 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Added \@minipagefalse to \end@dblfloat. Otherwise
+	that switch may end up being true after a figure* has ended,
+	messing up spacing afterwards randomly.
+
+2006-02-12 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Modified so the \@let@token can be \outer. Avoid
+	re-doing eTeX setup step multiple times for the original call of
+	\xspace.
+
+2006-01-09 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: Make \tag* and starred AMS environments work
+	(pr/3693). Fix varioref support so \vref* also works
+	(pr/3373). Added \showkeyslabelformat to avoid hard-wiring the
+	label format.
+
+2005-12-02 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Bahasa Malaysia defaults added.
+
+2005-11-26 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Single hyphen rather than -- in range for spanish
+	and galician.
+
+2005-11-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Added a few more brazil strings
+	Added a few more finnish strings
+	Added further galician defaults (and corrected spelling)
+	Corrections in italian strings
+
+2005-10-04 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Improved expansion method. Added use of higher level
+	functions for conditional processing. Simplified the code so that
+	difference between eTeX and non-eTeX is minimal.
+
+2005-09-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: corrected typo in documentation
+
+2005-09-14 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: corrected one default for polish
+
+2005-08-23 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* array.dtx: Removed spurious space.
+
+2005-08-06 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* calc.dtx: Improved expansion of arguments, added new
+	  commands \maxof, \minof, \totalheightof and
+	  \settototalheight.
+
+2005-07-26 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Improve test by exiting if \@let@token is a
+	  letter. Add \xspaceremoveexception.
+
+2005-07-24 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: small change in italian.
+                        small fix in german and ngerman (pr/3793)
+
+2005-06-09 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: fixed bug in Dutch localization (pr/3791)
+	added localization for romanian (pr/3790)
+
+2005-05-07 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Improve handling of active characters.
+
+2005-04-24 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Ukranian defaults added (by Mykola Lyakhovych)
+
+2005-04-09 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Basque defaults added (by I\~naki Larra\~naga
+	Murgoitio)
+
+2004-12-07 Morten Hoegholm <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Make extensible (tools/3712), fix active
+	  characters (tools/3747) and update documentation.
+
+2004-10-30 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Added missing defaults for italian (by Lapo Mori)
+
+2004-07-03 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: fixing errors that happen only if multicol is
+	compiled with a special combination of docstrip modules.
+
+2004-05-08 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Use \@nil for testing in \is@pos@num
+
+2004-02-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:  fixed a bug in magyar option
+
+2004-02-15 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Avoid self-referencing definition of
+	\@footnotetext (pr/3618)
+
+2003-12-29 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* fileerr.dtx: attempt to set exit code when reading x.tex (pr/3538)
+
+2003-12-19 David Carlisle <latex-bugs@latex-project.org>
+
+	* array.dtx: add \arraybackslash
+
+2003-10-05 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* bm.dtx: AMS version of \sqrt not working
+
+2003-09-01 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* bm.dtx: Forgotten to check for \hskip (pr/3572)
+
+2003-08-22 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Added \@noligs again, as I can be sure that
+	it is defined in the LaTeX kernel, so that other packages
+	can rely on \@noligs always being used.
+
+2003-04-30 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* trace.dtx: added option full to trace everything; set a few more
+	switches back to no-tracing on exit; make \tracingall trace full
+	even when full is not specified
+
+2003-04-17 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Catch problem with \columnbreak
+	in last line (found by Ulrike Fischer)
+
+2003-04-08 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Collect one additional line per column to account
+	for vanishing space at column breaks
+
+2003-03-29 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Options}):
+	Afrikaans option contributed by Danie Els <dnjels@sun.ac.za>.
+
+2003-03-18 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: changed the tracing output a bit
+
+2003-03-15 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Further corrections to the micro-spacing around the boxes produced
+	by multicols, so that grid typesetting (given right values for
+	other parameters) becomes a possibility.
+	Also added option "grid" which currently does nothing except
+	producing a warning if the grid might got lost.
+
+2003-02-17 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Add a kern to cancel potential depth of previous line at the
+	beginning of a multicols and also suppsed \lineskip
+
+	\multicolovershoot set back to 0pt as a default 2pt was simply
+	wrong in some applications (pr/3465)
+
+2003-01-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: changed error message when possible loop was
+	detected.
+
+	* somedefs.dtx: added version number to \ProvidesPackage line
+	(pr/3490)
+
+	* varioref.dtx: typo added a blank line into one macro
+
+2003-01-08 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Use \vref@label instead of \label to avoid
+	problems with amsmath. (pr/3489)
+
+2002-11-22 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* bm.dtx: Get math alphabets right (pr/3476)
+
+2002-11-06 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Changed default for \reftextbefore for options
+	english and american.
+	This is an incompatible change, but the original was bad English!
+	Changed default for \reftext...range for dutch as well.
+
+2002-06-18 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* fileerr.dtx: added space after ! better to match TeX's error
+	style (pr/3414)
+
+	* varioref.dtx: 	Use \vpageref inside \ref not \@vpageref
+	to get spacing correct (pr/3403)
+
+2002-06-14 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added \labelformat to support references that
+	automatically add "text" around the referenced number.
+
+	added \Ref and \Vref to generated references at the beinning of a
+	sentence (might be needed if \reformat is used)
+
+	added \vpagerefnum to support referencing the "number" within
+	commands like \refpageafter, e.g.
+
+	   \renewcommand\reftextfaceafter {on page~\thevpagerefnum}
+
+	texts for "slovak" and "slovene" options added
+
+2001-09-04 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: correct typo in name \vref -> \vr@f
+
+2001-07-24 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* trace.dtx: use ltxdoc not ltugboat class for docu
+
+2001-05-28 Chris Rowley <latex-bugs@latex-project.org>
+
+	* dcolumn.dtx:
+
+        Documentation of centring improved (pr/3315)
+
+2001-04-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: changed my mind and also added \vpagerefrange*
+
+	* trace.dtx: added package to tools distribution
+
+2001-04-12 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Defining the main macros}): Added
+	\vref* and \vpageref* which do not add a space in front of the
+	generated text (ever) so that they can be used in situations like
+	(\vref{foo} ...) without added a space after the open parenthesis.
+
+2001-01-12 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Updated nynorsk defaults
+
+2000-12-30 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Updated Danish defaults
+
+2000-10-23 Chris Rowley <latex-bugs@latex-project.org>
+
+	* longtable.dtx:
+
+	Added a \noexpand (as in array.sty) for mathtext.sty
+
+2000-09-25 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx: Added the option italian as suggested by Claudio
+	Beccari, back in august 1998...
+
+2000-09-21 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx: Added the option german as proposed by Karsten
+	Tinnefeld <karsten@tinnefeld.com> in PR 3259
+
+2000-08-23 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Updated defaults for catalan
+
+2000-08-21 Chris Rowley <latex-bugs@latex-project.org>
+
+	* verbatim.dtx:
+
+2000-07-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: fixed color problem with rules between columns
+	(their color did depend on the color of the text at the break)
+
+2000-07-09 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: Don't output space if optional argument
+        to \vpageref is empty (pr/3230)
+
+2000-06-11 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{The output routines}): when
+	doing boxed mode do not restrict height of columns to \@colroom
+	(pr/3212)
+
+2000-05-05 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{Starting and ): Detect and fix
+	problem if a multicols ends at the top of a page
+
+2000-04-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added defaults for Czech
+
+2000-04-15 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* ftnright.dtx: Don't use math mode for footnote symbol
+                        (pr/3172)
+
+2000-01-11 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added naustrian and ngerman options
+
+2000-01-07 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Disable hyphenation even if the font allows it.
+
+1999-12-14 Rainer Schoepf <latex-bugs@latex-project.org>
+
+1999-12-02 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: even more portugese defaults
+
+1999-11-25 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added portuguese defaults
+
+1999-10-21 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: allow multi-paragraph footnotes again. This functionality
+	was lost when the footnotes got reimplemented some time ago. (Problem
+	reported by Niels Ferguson)
+
+1999-09-03 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* DEFAULT.hea: updated for LPPL 1.2
+
+	* DEFAULT.pre: updated for LPPL 1.2
+
+1999-07-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Added some additional tracing code.
+	When balancing check that last column doesn't contain a forced
+        page break; if it does reject the solution.
+
+1999-07-09 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* updated headers to reflect LPPL 1.1
+
+1999-06-18 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: added documentation for \columnsep
+
+1999-06-12 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: minor documentation updates
+
+1999-05-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* tools.ins: added colbreak guard for multicol.sty
+
+1999-05-26 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{Manual column breaking}):
+	Added a \columnbreak command to allow manual column breaks.
+
+1999-05-01 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: reworded license text slightly
+
+1999-03-22 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: re-add \cs{mark} command which was commented out
+	by mistake at some point in 1998 (pr/2978)
+
+1999-03-05 David Carlisle <latex-bugs@latex-project.org>
+
+	* enumerate.dtx: extension hook tools/2916}
+
+	* verbatim.dtx: Add \begingroup/\endgroup to definition of
+	\verbatim(*)/\endverbatim(*) so that they can safely be
+	used without \begin/\end.  Suggested by Donald Arseneau.
+
+1999-03-04 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* manifest.txt: Corrected typo.
+
+1999-03-03 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* tools.ins: New copyright info and preamble.
+
+1999-02-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: fixed reference to ltx3info.tex in license
+
+1999-02-13 David Carlisle <latex-bugs@latex-project.org>
+
+	* readme.txt: lppl
+
+1999-02-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: changed license text
+
+1998-12-31 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx: Added \noexpand in front of \ialign
+	to guard against interesting :-) changes to \halign done to support
+	text glyphs in math
+
+1998-12-03 Johannes Braams <latex-bugs@latex-project.org>
+
+	* ftnright.dtx: Made \@makecol colorsafe by adding
+	\color@begingroup, \color@endgroup and \normalcolor.
+
+1998-11-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: taken out fix for (pr/1866) as it produce undesired
+	results (see comments in doc of \vref)      (pr/2909)
+
+	* varioref.dtx: Added two new user commands \vrefrange and
+	\vpagerefrange to support referencing a range of labels.
+	Also added customising commands \reftextlabelrange and
+	\reftextpagerange to support the above commands.
+	Added draft and final option (draft will turn errors into warnings).
+	Added austrian defaults (same a german).
+	Added greek defaults.
+	Removed incorrect warning for italian.
+	Added hungarian defaults.
+	Added russian defaults.
+	Added utility command \vrefpagenum and used it to shorten code
+	this will also fix a problem that in certain circumstances varioref
+	was not warning that another run was needed.
+
+1998-09-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: test if document ends in middle of multicols
+	and if so issue an error message instead of dying with an OR loop
+	pr/2873
+
+1998-08-17 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: new logic for dealing with \@footnotetext macro:
+	instead of redefining its definition completely, thereby possibly
+	overwriting a class change, we locally set \columnwidth to \textwidth
+	and then call the original definition. this will also solves a problem
+	with the situation of a footnote inside multicols inside a minipage
+	would vanish.
+
+	* varioref.dtx: added defaults for greek contributed by
+	Apostolos Syropoulos <apostolo@obelix.ee.duth.gr>
+
+1998-06-22 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* layout.dtx: renamed \bs to \LayOutbs to avoid possible conflicts
+	with other packages using this command. Originally the package
+	redefined \bs in case it already had a definition.
+	Also rename \type to \LayOuttype for the same reason.
+
+	Added \@doendpe to definition of
+	\endverbatim(*) (pr/3234)
+
+1998-06-17 Chris Rowley <latex-bugs@latex-project.org>
+
+	* calc.dtx:
+
+        Added \widthof etc
+
+        Made \ratio and \real robust
+
+        Enhanced documentation
+2004-02-27    <david.carlisle@latex-project.org>
+
+	* bm.sty: fix for "new" AMS math accent code. tools/3256
+
+2004-02-01    <david.carlisle@latex-project.org>
+
+	* longtable.dtx: \nobreak after table head, for tools/3484
+
+1998-05-13 David Carlisle <latex-bugs@latex-project.org>
+
+	* tabularx.dtx:  Use \setlength so calc syntax may be used in
+	the width argument. tools/2793.
+
+	* longtable.dtx: Use \setlength so calc syntax may be used in p
+	arguments. tools/2793.
+
+1998-05-13 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx: also allow calc syntax in first arg of tabular*
+        (pr/2793)
+
+1998-05-12 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx: set the \hsize for p columns (and others) via
+	\setlength so that calc syntax can be applied (pr/2793)
+
+1998-05-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: support for amsmath displays (pr2175)
+	Actually this probably should be fixed in amsmath instead.
+
+1998-04-25 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added galician defaults contributed by Matthias
+	Moebius.
+
+1998-03-09 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: replace ~ by \nobreak\space so that \vref obeys
+	setting of \frenchspacing  (pr/1866)
+
+1998-01-29 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Removed group around contents of optional argument
+	to \begin{multicols}{2}[...] so that the use of \section within
+	this argument works better.
+
+	* array.dtx: made \multicolumn long to match kernel change for
+	pr/2180 (forgotten at that time)
+
+1998-01-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{Not balancing the columns}):
+	added support for a version of multicols (star form) that doesn't
+	balance the columns on the last page.
+	Fixed a bit of the documentation (so that a toc is possible).
+
+1997-12-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx: moving a docstrip guard. this doesn't change
+	the style but prevents some code being added at the end of
+	the driver file
+
+1997-12-14 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: redefine \@footnotetext only within environment
+	not globally any longer. pr/2689 + some docu updates
+
+	* fileerr.dtx: fixed file date. pr/2689
+
+1997-12-06 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added default for polish language.
+
+1997-11-22 David Carlisle <latex-bugs@latex-project.org>
+
+	* bm.dtx: Make \bm{\hat{A}} work like \bm{\hat A} (from c.t.t).
+
+1997-11-18 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx: now finally set \columnwidth to width of column
+	  pr2664
+
+1997-11-16 David Carlisle <latex-bugs@latex-project.org>
+
+	* bm.dtx: support mathcode hex 8000 (like prime) properly.
+	Support null delimiter \left. constructions.
+	Support breqn package.
+
+1997-11-11 David Carlisle <latex-bugs@latex-project.org>
+
+	* calc.dtx: Fix error message inserted at the weekend.
+
+1997-11-08 David Carlisle <latex-bugs@latex-project.org>
+
+	* manifest.txt: add calc.
+
+	* Makefile (FILES): add calc
+
+	* tools.ins: add calc.
+
+	* calc.dtx: Contributed to the distribution by
+	Kresten Krab Thorup and Frank Jensen. One minor change, use
+	\PackageError rather than the primitive \errormessge.
+
+1997-10-16 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: avoid using % in aux file. tools/2631
+
+1997-10-13 David Carlisle <latex-bugs@latex-project.org>
+
+	* xspace.dtx: test for space token added for tools/2632
+
+1997-10-09 David Carlisle <latex-bugs@latex-project.org>
+
+	* bm.dtx: Add extra braces around group code so \bm{\frac..} does
+	the right thing. (Spotted on c.t.t)
+
+1997-10-06 David Carlisle <latex-bugs@latex-project.org>
+
+	* dcolumn.dtx: Document use of math mode. tools/2616.
+
+1997-09-18 David Carlisle <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: Fix \write catch for tools/2607.
+ 	(Fix page 401 of TeXBook at same time...)
+
+1997-07-09 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* tabularx.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* showkeys.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* multicol.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* longtable.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* layout.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* delarray.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+	* array.dtx: Documentation fixes by Andreas Schwab
+ 	<schwab@issan.informatik.uni-dortmund.de>.
+
+1997-07-07 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* tools.ins:  added q.tex and r.tex files so that "run" and
+	  "quit" mode is now also supported.
+
+	* fileerr.dtx: added q.tex and r.tex files so that "run" and
+	  "quit" mode is now also supported.
+
+1997-06-28 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: New email address for David K.
+
+1997-06-13 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: support cite package for tools/2490
+
+1997-06-12 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx: added support for catalan
+
+1997-06-05 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* multicol.dtx: Applied improvement of documentation, kindly done
+ 	by Robin Fairbairns.
+
+1997-05-13 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* fontsmpl.dtx: Replaced \@changed@x@err by
+ 	\TextSymbolUnavailable, according to the change in ltoutenc.dtx.
+
+1997-04-30 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx (\verbatiminput): Added code to check for
+	existence of file to be input and print error message if not.
+
+1997-04-14 David Carlisle <latex-bugs@latex-project.org>
+
+	* tools.ins: add bm
+
+	* bm.dtx: Add to tools bundle.
+	Add \boldsymbol as alias for \bm
+
+1997-02-26 David Carlisle <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: Spurious brace removed. Jean-Pierre Drucbert.
+
+1997-02-20 David Carlisle <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: improve behaviour in case table too wide.
+
+1996-12-06 David Carlisle <latex-bugs@latex-project.org>
+
+	* xspace.dtx: alltt support. tools/2322.
+
+1996-11-21 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: new page break control.
+
+1996-11-02 David Carlisle <latex-bugs@latex-project.org>
+
+	* readme.txt: Add old docstrip note.
+
+1996-11-01 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: colour option.  tools/2297.
+
+	* tools.ins: new style.
+
+1996-10-24 David Carlisle <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Fix guards for driver document. tools/2206
+
+1996-09-25 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx (\verbatiminput): Added \@addtofilelist and
+ 	\ProvidesFile so that the name of the file read in appears in the
+ 	\listfiles output.
+
+1996-09-23 David Carlisle <latex-bugs@latex-project.org>
+
+	* dcolumn.dtx: Fix case where no decimal point is used
+        in the `new' case of a the third argument being n.m.
+
+Fri Sep  6 15:24:17 1996  David Carlisle  <carlisle@cs.man.ac.uk>
+
+        * showkeys.dtx: more changes following from /2252.
+
+Fri Aug 30 18:09:48 1996  David Carlisle  <carlisle@cs.man.ac.uk>
+
+        * showkeys.dtx: more fudges for AMS tools/2252, and extra
+        group from Donald A. tools/2147
+
+Wed Jul 10 11:15:30 1996  David Carlisle  <carlisle@cs.man.ac.uk>
+
+        * showkeys.dtx: Missing percent added for tools/2215
+
+1996-06-14 David Carlisle <latex-bugs@latex-project.org>
+
+	* array.dtx: change \kern\z@ to \hskip1sp for latex/2160
+	A few long lines wrapped.
+
+1996-06-04 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: \verbatim@noligs@list now processed after
+	\dospecials (PR 2138).
+
+1996-05-25 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx (subsection{Support for
+          \texttt{\textbackslash firsthline} and ):
+	  Complete reimplementation after Mark Wooding pointed out that
+	  they were everything else than correct --- hope i got it
+	  right this time :-)
+
+1996-05-24 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Add a warning to re run LaTeX \AtEndDocument if
+	any longtable has failed to align on this run.
+
+1996-05-17 David Carlisle <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Add / to list of punctuation characters.
+
+	* showkeys.dtx: use \protected@edef rather than \def
+	so that the expansion of any macros is printed. tools/2147
+
+1996-05-07 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: add \hfil to match array package change.
+
+	* array.dtx: add \hfil to \@endpbox for tools/2120 (and to match
+	kernel version).
+
+1996-04-22 David Carlisle <latex-bugs@latex-project.org>
+
+	* array.dtx: Extra \kern\z@ for empty l colummns. latex/2122
+
+1996-04-16 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Version 4.02 using new algorithm of David Kastrup
+	to align tables without \setlongtables command.
+
+1996-02-28 David Carlisle <latex-bugs@latex-project.org>
+
+	* dcolumn.dtx: New feature (tools/2093) D{.}{.}{3.2} specifies a
+	column of figures that should be centred, assuming 3 places to
+	the left of the decimal point and 2 to the right.
+
+1996-02-01 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: allow \multicolumn and \hline to work inside
+	tabulars inside longtables. tools/2068
+
+1996-01-13 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Explain why with \OnlyDescription there will be an unresolved
+	reference pr/2047.
+
+1996-01-03 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: (Martin Schr"oder) remove ! which causes a
+	makeindex error in \changes entry. tools/2035
+
+1996-01-01 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* ftnright.dtx:
+	Finally got around to take out ltxdoc and use article for
+        documentation. pr/536
+	Also cleaned up use of ProvidesPackage.
+
+1995-12-28 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx:
+	Fixed section headings so that a toc is possible. pr/2033.
+
+	* multicol.dtx:
+	Fixed index entries. pr/2036
+
+1995-12-12 David Carlisle <latex-bugs@latex-project.org>
+
+	* tools.dst: Add trap for old docstrip.
+
+1995-11-23 David Carlisle <latex-bugs@latex-project.org>
+
+	* theorem.dtx: Fix \@newctr usage (Ulrik Vieth)
+
+	* layout.dtx: Documentation fixes (J"org Knappen).
+
+	* indentfirst.dtx: (Ulrik Vieth) Fix \GetFileInfo usage.
+          In the documentation.
+
+1995-11-22 David Carlisle <latex-bugs@latex-project.org>
+
+	* tools.dst: New style concurrent generation.
+
+	* showkeys.dtx: Fix \harvarditem: add SK code after the implicit
+	  \item (as for \cite) not before.
+
+1995-11-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* theorem.dtx:
+	Ensure that there is an error message if one of the counters
+	in newtheorem are undefined pr/1861.
+
+	* array.dtx (subsection{Getting the spacing around rules right}):
+	ensure that the space between \hline\hline is visually \doublerulesep
+	and does not depend of the rulewidth (as it does with standard latex)
+	pr/1945
+	Added some documentation about rule handling concepts.
+
+1995-11-09 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: (Anil K Goel) Really measure the size of the
+	  first row of the table not `assume' the size from the array
+	  strut. (Avoids really bad first page break with two headings)
+
+	* showkeys.dtx: Take more care over redefining \protect commands
+
+1995-11-02 David Carlisle <latex-bugs@latex-project.org>
+
+	* array.dtx: Minor doc changes, no more ooverfull hboxes...
+
+1995-10-30 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : Added command \layout* wbhich recomputes the values
+	it needs before making the picture of the layout. (PR 1465)
+
+1995-10-30 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: Fix for tools/1744 (notref/varioref case)
+          Add final and draft options
+          Fix inner vmode case which could cause extra white space
+          to be added.
+
+1995-10-29 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx (section{The implementation}): Added the options
+	spanish, braziolian and portugues, as provided by
+	Ausberto S. Castro V. <ascv@inf.ufrgs.br> (PR 1837)
+
+1995-10-27 David Carlisle <latex-bugs@latex-project.org>
+
+	* afterpage.dtx: tools/1579/1880/1884
+
+1995-10-19 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Added defaults for Italian pr/1888
+
+	* multicol.dtx:
+	Added \@largefloatcheck so that floats being too large
+        will produce a warning.  pr/1890
+
+1995-09-22 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Corrected vertical spacing if verbatim is nested
+ 	in quote (and other) environment. This error was introduced with
+	version v1.3c (1990/02/26). Clarified documentation on how to
+	define new verbatim-like environments.
+
+1995-08-06 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* tools.dst:
+	Updated copying conditions so that it is allowed to distribute
+	unpacked files together with the sources.
+
+1995-08-04 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Changed class used for documentation from
+	article to ltxdoc. pr/1788
+
+1995-06-25 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : The june 1995 release of LaTeX no longer needs two
+	hash marks when defining a newcommand inside the argument of
+	\DeclareOption.
+
+1995-06-15 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: replace ## by # in \DeclareOption, latex/1557
+
+1995-05-25 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Modify Caption handling again.
+
+1995-05-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Updated \DeclareOption declarations to reflect ##1 -> #1 change. pr/1557
+
+1995-05-07 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* fontsmpl.dtx:
+	Removed \pagestyle{empty} so that all pages produced by fontsmpl.tex
+	are numbered. pr/1559
+
+1995-05-03 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Removed extra backslash in argument to \cs.
+
+1995-05-02 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Explitly reset page height for tools/1584.
+        Modify caption handling.
+
+1995-04-26 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Removed \fileversion and \filedate.
+
+1995-04-25 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Modify brace hacks cf tools/1571
+        Allow 1100 longtables in a single document---A bug reported on a
+	`real document' by Mike Van Geest!
+
+	* showkeys.dtx: Fix inner horz mode case.
+        Add option handling: notref and notcite to stop the
+        redefinitions of those commands.
+
+1995-04-23 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx (section{The line separator \\}):
+	Fixed a serious bug that was present right from the beginning:
+        in some cases the last column of an array line could get an extra
+	math ord messing up the spacing. pr/1571.
+	(subsection{Bugs and Features}):
+	Added comment about the fact that a column (execpt for the first) refers to
+	the column specifier plus intercolumn material to the *right*.
+	Therefore \multicolumn{2}{|c|} is normally incorrect. pr/1443
+
+1995-04-08 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : Added the options 'integers' and 'reals'. The
+	default is the option 'integers'; this results in the 'old'
+	behaviour, where the values of parameters are presented
+	truncated. Using the option 'reals' will switch to presenting the
+	real val;ues of the parameters. This also affects the definition
+	of \Show and \Type.
+
+1995-04-06 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Options}):
+	Added norsk and nynorsk strings.
+	Modified Warning message about undefined Option texts.
+
+1995-04-03 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : Simplified the definition of \Show and \Type, the
+	effect is that now the complete value is shown (PR #1520)
+
+1995-03-20 David Carlisle <latex-bugs@latex-project.org>
+
+	* tabularx.dtx: Allow \tabularx to be used inside
+          \newenvironment definitions
+
+1995-03-17 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: Fix for tools/1434  (showkeys affecting footnote
+	  placement)
+
+1995-03-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Fixed colour support (thanks to David)
+	Clarified copyright notice.
+	Updated driver file.
+
+1995-03-16 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: Fix for tools/1181 (Bad placement in with \item
+	  and \bibitem) and tools/1496  (Working with new ams*)
+
+1995-03-14 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : Added the options french and francais (thanks to
+	Eric Picheral <Eric.Picheral@univ-rennes1.fr> who provided the
+	translations); introduced \notshown
+
+1995-01-10 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Added swedish strings.
+
+1994-12-08 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Add \tabularnewline.
+
+	* array.dtx: Add \tabularnewline.
+
+1994-11-22 David Carlisle <latex-bugs@latex-project.org>
+
+	* tools.dst: Avoid generating error messages on `.tex'.
+
+1994-11-15 David Carlisle <latex-bugs@latex-project.org>
+
+	* xspace.dtx: Make robust, add !
+
+1994-10-29 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx : Some of the dutch words should really be one word
+	instead of two (PR #1078)
+
+1994-10-25 Rainer Schoepf <latex-bugs@latex-project.org>
+
+	* verbatim.dtx: Changed code for handling verbatim as first thing
+	after an \item command. (This change had already been done in the
+	LaTeX2e kernel.)
+
+	* verbatim.dtx: Removed extra \typeout lines.
+
+1994-10-15 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx (subsection{Support for ...):
+	Added \firsthline and \lasthline from Companion.
+
+1994-10-03 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Correct change from 26 of August. Leave old code only add the new
+	one.
+
+1994-09-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Added strings for breton language, this also means adding a new option.
+
+1994-09-25 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Added danish strings.
+
+1994-09-23 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Options}):
+	Added finnish strings.
+
+1994-09-09 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: add \citefullauthor for (forthcoming) natbib.
+
+1994-09-08 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx: Stored texts in control sequences to allow the use
+	of other languages. Added the options english (default) and
+	dutch.
+
+	* tools.dst: Added the layout package
+
+1994-09-07 David Carlisle <latex-bugs@latex-project.org>
+
+	* showkeys.dtx: Version 3, supports varioref ref styles, and
+	  natbib and harvard citation styles.
+	  Also modify `internal vertical mode' case, to cope with modified
+	  \caption behaviour in the LaTeX2e classes.
+	  Modify \GetFileInfo usage, as suggested by Patrick Daly.
+
+1994-08-26 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{The output routines}):
+ 	Check explicitly for void boxes before assigning the current column
+	   width to their width, because void boxes will not change.
+	Extract the kept marks before adding a penalty -10000 to the output box
+	  when balancing, otherwise no marks will be found. (This bug was
+	  introduced recently.
+
+1994-08-08 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* tools.dst:
+	Added a better informational message about the problems
+	that can arise when LaTeX tries to generate the file `.tex'
+
+1994-07-24 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Options}):
+	Added dutch defaults as suggested by Frank Poppe.
+	Explicitly expand label argument before passing it to \label, so that
+	varioref will work with babel.
+	Correct misspelling in spanish option.
+
+1994-07-14 Johannes Braams <latex-bugs@latex-project.org>
+
+	* layout.dtx: Moved the identification code to the front of the
+	file.
+	Needed to interchange to calls to \ttfamily and \footnotsize as
+	\footnotesize calls \normalfont in compatibility mode.
+	Added a check for negative arrowlength to \InsideHArrow
+
+1994-06-30 David Carlisle <latex-bugs@latex-project.org>
+
+	* longtable.dtx: Obey a \nofiles declaration. Remove special
+	  handling of letter class, not needed for the latex2e version of
+	  letter.
+
+	* showkeys.dtx: Correct \ProvidesPackage usage (previously had two
+	  \providesPackage commands),
+
+1994-06-21 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx (subsection{Options}):
+	Added french defaults as suggested by Daniel Flippo.
+
+1994-06-20 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Correction was buggy, brace placed incorrectly.
+
+1994-06-11 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	\vpageref[above][one ]{one} didn't work because first
+	optional argument wasn't passed (found by Patrick Daly).
+
+1994-06-07 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (section{New macros and hacks for version 1.2}):
+	Updated float commands to contain \color@endgroup etc. so
+	that they work together with the color.sty package.
+	(Found by SPQR)
+
+1994-06-01 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx:
+	Added  \null to the end of \multicolumn. This fixes
+	a bug that was long fixed in the original but never made it
+	into array.sty.
+	Use PackageError/Warning interface.
+
+1994-06-01 David Carlisle <latex-bugs@latex-project.org>
+
+	* somedefs.dtx: Use new style error commands.
+
+1994-05-28 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx:
+	Do not alloc \col@number any longer.
+	Use Standard Warning/info messages.
+
+	* fileerr.dtx:
+	Added file to the collection.
+
+1994-05-28 David Carlisle <latex-bugs@latex-project.org>
+
+	* manifest.txt: First draft.
+
+	* readme.txt: First draft.
+1994-05-27 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Warning about looping pages displayed in wrong order
+	(found by Wolfgang Christen).
+	(subsection{Defining the main macros}):
+	Added help message for loop error.
+	Use PackageError rather than \errmessage.
+	Use DeclareRobustCommand.
+	Added \NeedTeXFormat.
+
+1994-05-26 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* multicol.dtx (subsection{Starting and ):
+	fixed bug with "premulticols" not being a register
+	(tried to \the a string in tracing mode)
+
+1994-05-18 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* varioref.dtx:
+	Added defaults for brazil.
+
+1994-05-16 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx (section{The macros \texttt{\protect):
+	Use \@finalstrut in \@endpbox
+
+1994-03-23 Braams J.L. <latex-bugs@latex-project.org>
+
+	* layout.dtx : repaired bug in twosided mode.
+
+	Changed vertical positioning of the arrows identifying
+	\amrginparsep and \marginparwidth
+
+	Repaired bug in the preparation of the table of dimensions.
+
+	Produce two pages in twoside mode
+
+	Removed use of \wlog
+
+1994-03-14 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx:
+	Removed identification \typeout's.
+	Removed the check for the old version of the \@tfor macro.
+
+1994-02-28 Frank Mittelbach <latex-bugs@latex-project.org>
+
+	* array.dtx:
+	Moved the driver code in front so that the documentation can be
+        processed by simply running the file through LaTeX2e.
+
+	* ftnright.dtx:
+	Moved the driver code in front so that the documentation can be
+        processed by simply running the file through LaTeX2e.
+
+	* multicol.dtx:
+	Balance code rewritten; many changes to documentation etc.
+	Changed driver code slightly.
+	Moved the driver code in front so that the documentation can be
+        processed by simply running the file through LaTeX2e.
+
+	* theorem.dtx:
+	Changed driver code slightly.
+	Moved the driver code in front so that the documentation can be
+        processed by simply running the file through LaTeX2e.
+
diff --git a/macros/latex-dev/required/tools/dcolumn.dtx b/macros/latex-dev/required/tools/dcolumn.dtx
new file mode 100644
index 0000000000..38a4ab0da2
--- /dev/null
+++ b/macros/latex-dev/required/tools/dcolumn.dtx
@@ -0,0 +1,361 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: dcolumn.dtx Copyright (C) 1992-1996 1999-2001 David Carlisle
+%
+%<*dtx>
+          \ProvidesFile{dcolumn.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{dcolumn}
+%<driver>\ProvidesFile{dcolumn.drv}
+% \fi
+%         \ProvidesFile{dcolumn.dtx}
+          [2014/10/28 v1.06 decimal alignment package (DPC)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+ \usepackage{dcolumn}
+ \DeleteShortVerb{\|}
+\begin{document}
+ \DocInput{dcolumn.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{dcolumn.dtx}
+%
+% \title{The \textsf{dcolumn} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}}
+% \author{David Carlisle}
+% \date{\filedate}
+% \author{David Carlisle}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+% \changes{v1.00}{1992/02/17}{Initial version}
+% \changes{v1.01}{1992/06/12}{Re-issue for the new doc and docstrip.}
+% \changes{v1.02}{1994/03/14}{Re-issue for LaTeX2e}
+% \changes{v1.03}{1996/02/28}{New feature, after tools/2093}
+% \changes{v1.05}{1999/07/05}
+%      {Minor doc changes latex/3058}
+% \changes{v1.06}{2001/05/28}
+%      {More doc changes (suggested by BNB, done by CAR) latex/3315}
+%
+%
+%
+% \begin{abstract}
+% This package defines a system for defining columns of entries in an
+% \texttt{array} or \texttt{tabular} which are to be aligned on a
+% `decimal point'.
+% \end{abstract}
+%
+% \MakeShortVerb{\"}
+%
+% This package defines {\tt D} to be a column specifier with three
+% arguments.\\
+% "D{"\meta{sep.tex}"}{"\meta{sep.dvi}"}{"\meta{decimal
+% places}"}"
+%
+% \meta{sep.tex} should be a single character, this is used as the
+% separator in the {\tt .tex} file. Thus it will usually be `{\tt.}' or
+% `{\tt,}'.
+%
+% \mbox{\meta{sep.dvi}} is used as the separator in the output, this may
+% be the same as the first argument, but may be any math-mode
+% expression, such as "\cdot". It should be noted that \texttt{dcolumn}
+% always uses math mode for the digits as well as the separator.
+%
+% \meta{decimal places} should be the maximum number of decimal places
+% in the column. If this is negative, any number of decimal places can
+% be used in the column, and all entries will be centred on
+% (the leading edge of) the
+% separator. Note that this can cause a column to be too wide, compare
+% the first two columns in the example below. If this argument is
+% positive, the column uses macros equivalent to "\rightdots"
+% "\endrightdots" of {\tt array.sty}, otherwise the macros are
+% essentially equivalent to "\centerdots" "\endcenterdots".
+%
+% You may not want to use all three entries in the {\tt array} or {\tt
+% tabular} preamble, so you may define your own preamble specifiers
+% using "\newcolumntype".
+%
+% For example we may say:
+%
+% \noindent"\newcolumntype{d}[1]{D{.}{\cdot}{#1}}"
+%
+% {\tt d} takes a single argument specifying the number of decimal
+% places, and the {\tt .tex} file should use {\tt.}, with $\cdot$ being
+% used in the output.
+%
+% \noindent"\newcolumntype{.}{D{.}{.}{-1}}"
+%
+% {\tt .} specifies a column of entries to be centred on the~$.$.
+%
+% \noindent"\newcolumntype{,}{D{,}{,}{2}}"
+%
+% {\tt ,} specifies takes a column of entries with at most two decimal
+% places after a~$,$.
+%
+% \newcolumntype{d}[1]{D{.}{\cdot}{#1}}
+% \newcolumntype{.}{D{.}{.}{-1}}
+% \newcolumntype{,}{D{,}{,}{2}}
+%
+% The following table begins "\begin{tabular}{|d{-1}|d{2}|.|,|}"
+%
+% \begin{center}
+% \begin{tabular}{|d{-1}|d{2}|.|,|}
+% 1.2   & 1.2   &1.2    &1,2    \\
+% 1.23  & 1.23  &12.5   &300,2  \\
+% 1121.2& 1121.2&861.20 &674,29 \\
+% 184   & 184   &10     &69     \\
+% .4    & .4    &       &,4     \\
+%       &       &.4     &
+% \end{tabular}
+% \end{center}
+%
+% Note that the first column, which had a negative \meta{decimal places}
+% argument is wider than the second column, so that the decimal point
+% appears in the middle of the column.
+% Also note that this package deals correctly with entries with no
+% decimal part, no integer part, and blank entries.
+%
+% If you have table headings (inserted with "\multicolumn{1}{c}{..}"
+% to over-ride the "D" column type) then it may be that neither of the
+% above `centred' or `right aligned' forms is quite what you want.
+% \begin{center}\small
+% \begin{tabular}[t]{|D..{-1}|D..{1}|D..{5.1}|}
+%\multicolumn{1}{|c|}{head}&
+%\multicolumn{1}{c|}{head}&
+%\multicolumn{1}{c|}{head}\\[3pt]
+% 1.2  & 1.2  &1.2 \\
+% 11212.2& 11212.2&11212.2  \\
+% .4    & .4    &.4
+% \end{tabular}
+% \hfill
+% \begin{tabular}[t]{|D..{-1}|D..{1}|D..{1.1}|}
+%\multicolumn{1}{|c|}{wide heading}&
+%\multicolumn{1}{c|}{wide heading}&
+%\multicolumn{1}{c|}{wide heading}\\[3pt]
+% 1.2  & 1.2  &1.2 \\
+% .4    & .4    &.4
+% \end{tabular}
+% \end{center}
+%
+% In both of these tables the first column is set with "D{.}{.}{-1}"
+% to produce a column centered on the ".", and the second column is
+% set with "D{.}{.}{1}" to produce a right aligned column.
+%
+% The centered column produces columns that are wider than necessary
+% to fit in the numbers under a heading as it has to ensure that the
+% decimal point is centred. The right aligned column two does not have
+% this drawback, but under a wide heading a column of small right
+% aligned figures looks a bit odd.
+%
+% In version v1.03 a third possibility is introduced. The third
+% \meta{decimal places} argument may specify \emph{both} the number of
+% digits to the left and to the right of the decimal place. The third
+% column in the first table above is set with "D{.}{.}{5.1}" and in the
+% second  table,  "D{.}{.}{1.1}", to specify
+% `five places to the left and one to the right' and `one place to the
+% left and% one to the right' respectively.  (You may use `,' or other
+% tokens, not necessarily `.' in this argument.) The column of figures
+% is then positioned such that a number with the specified numbers of
+% digits is centred in the column.
+%
+% This notation also enables columns that are centred on the mid-point
+% of the separator, rather than its leading edge; for example
+% "D{+}{\,\pm\,}{3,3}" will give nice, symmetric layout of up to three
+% digits on either side of a $\pm$ sign.
+%
+% \StopEventually{}
+%
+%
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% First we load {\tt array.sty} if it not already loaded.
+%    \begin{macrocode}
+\RequirePackage{array}
+%    \end{macrocode}
+%
+% The basic ideas behind these macros are explained in the documentation
+% for {\tt array.sty}. However they use three
+% tricks which may be useful in other contexts.
+% \begin{itemize}
+% \item The separator is surrounded in extra "{ }", so that it is set
+% with "\mathord" spacing, otherwise, for instance a `,' would have
+% extra space after it.
+% \item The separator is not given its special definition by making it
+% active, as this would not work for an entry such as "& .5 &", as the
+% first token of an alignment entry is read {\em before\/} the preamble
+% part, in case it is an "\omit", in which case the preamble is to be
+% omitted. Instead we switch the mathcode to (hex) 8000, which makes the
+% token act as if it were active.
+% \item Although \verb|\mathcode`.="8000|  makes {\tt.} act as if it
+% were active, it is still not allowed in constructions such as
+% "\def.{}", even in math-mode, so we have to construct an active
+% version of the separator, this is done by making it the uppercase of
+% "~", and then using the construct\\
+% "\uppercase{\def~}{"\meta{definition}"}".\\
+% Note that the \meta{definition} is not uppercased, so the definition
+% can refer to the standard, non-active use of the separator.
+% \end{itemize}
+%
+% \begin{macro}{\DC@}
+% \changes{v1.03}{1996/02/28}{New feature, after tools/2093}
+% Set up uppercase tables as required, and then grab the first part of
+% the numerical argument into "\count@".
+%    \begin{macrocode}
+\def\DC@#1#2#3{%
+  \uccode`\~=`#1\relax
+  \m@th
+  \afterassignment\DC@x\count@#3\relax{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DC@x}
+% \changes{v1.03}{1996/02/28}{Macro added}
+% If "\count@" is negative, centre on the decimal point. If it is
+% positive either "#1" will be empty in which case bad out decimal
+% part to the number of digits specified by "\count@" or (new feature
+% in v1.03) it is none empty in which case "\count@" contains the
+% number of digits to the left of the point, and "#1" contains a junk
+% token (probably ".") followed by the number of digits to the right
+% of the point. In either of these latter cases, "\DC@right" is used.
+%    \begin{macrocode}
+\def\DC@x#1\relax#2#3{%
+  \ifnum\z@>\count@
+    \expandafter\DC@centre
+  \else
+    \expandafter\DC@right
+  \fi
+  {#2}{#3}{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DC@centre}
+% If centering on the decimal point, just need to box up the two halves.
+%    \begin{macrocode}
+\def\DC@centre#1#2#3{%
+  \let\DC@end\DC@endcentre
+  \uppercase{\def~}{$\egroup\setbox\tw@=\hbox\bgroup${#2}}%
+  \setbox\tw@=\hbox{${\phantom{{#2}}}$}%
+  \setbox\z@=\hbox\bgroup$\mathcode`#1="8000 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DC@endcentre}
+% and then pad out the smaller of the two boxes so there is the same
+% amount of stuff either side of the point.
+%    \begin{macrocode}
+\def\DC@endcentre{$\egroup
+    \ifdim \wd\z@>\wd\tw@
+      \setbox\tw@=\hbox to\wd\z@{\unhbox\tw@\hfill}%
+    \else
+      \setbox\z@=\hbox to\wd\tw@{\hfill\unhbox\z@}\fi
+    \box\z@\box\tw@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DC@right}
+% \changes{v1.03}{1996/02/28}{Re-implemented, after tools/2093}
+% This deals with both the cases where a specified number of decimal
+% places is given.
+%    \begin{macrocode}
+\def\DC@right#1#2#3{%
+  \ifx\relax#3\relax
+%    \end{macrocode}
+% If "#3" is empty, add "\hfill" to right align the column, and
+% Just set "\DC@rl" to begin a group, so nothing fancy is done with
+% the whole number part.
+%    \begin{macrocode}
+    \hfill
+    \let\DC@rl\bgroup
+  \else
+%    \end{macrocode}
+% Otherwise  set "\DC@rl" so that the whole number part is put in a
+% box "\count@" times as wide as a digit.
+% In order to share code with the other branch, then move "#3" (the
+% number of decimal places) into "\count@" throwing away the `.' from
+% the user syntax.
+% \changes{v1.04}{1996/09/23}{Add \cs{hfill} so integer part
+%               is still flush right if no decimal point used.}
+%    \begin{macrocode}
+    \edef\DC@rl{to\the\count@\dimen@ii\bgroup\hss\hfill}%
+    \count@\@gobble#3\relax
+  \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \let\DC@end\DC@endright
+%    \end{macrocode}
+% Box 2 contains the decimal part, set to "\dimen@" which is
+% calculated below to be "\count@" times the width of a digit, plus
+% the with of the `decimal point'.
+%    \begin{macrocode}
+  \uppercase{\def~}{$\egroup\setbox\tw@\hbox to\dimen@\bgroup${#2}}%
+   \setbox\z@\hbox{$1$}\dimen@ii\wd\z@
+   \dimen@\count@\dimen@ii
+   \setbox\z@\hbox{${#2}$}\advance\dimen@\wd\z@
+   \setbox\tw@\hbox to\dimen@{}%
+%    \end{macrocode}
+% Box 0 contains the whole number part, either just at its natural
+% size for right aligned columns, or set to (the old value of)
+% "\count@" times the width of a digit. "\DC@rl" defined above
+% determines the two cases.
+%    \begin{macrocode}
+   \setbox\z@\hbox\DC@rl$\mathcode`#1="8000 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DC@endright}
+% \changes{v1.03}{1996/02/28}{Re-implemented, after tools/2093}
+% Just finish off the second box, and then put out both boxes.
+%    \begin{macrocode}
+\def\DC@endright{$\hfil\egroup\box\z@\box\tw@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{D}
+% The user interface, define the {\tt D} column to take three arguments.
+% For special purposes, you may need to directly access "\DC@" rather
+% than the "D" column, eg to get a bold version you could use
+%\begin{verbatim}
+% \newcolumntype{E}[3]{>{\boldmath\DC@{#1}{#2}{#3}}c<{\DC@end}}
+%\end{verbatim}
+%    \begin{macrocode}
+\newcolumntype{D}[3]{>{\DC@{#1}{#2}{#3}}c<{\DC@end}}
+%</package>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \Finale
+\endinput
diff --git a/macros/latex-dev/required/tools/dcolumn.pdf b/macros/latex-dev/required/tools/dcolumn.pdf
new file mode 100644
index 0000000000..b169bf93aa
--- /dev/null
+++ b/macros/latex-dev/required/tools/dcolumn.pdf
diff --git a/macros/latex-dev/required/tools/delarray.dtx b/macros/latex-dev/required/tools/delarray.dtx
new file mode 100644
index 0000000000..8814fc2a58
--- /dev/null
+++ b/macros/latex-dev/required/tools/delarray.dtx
@@ -0,0 +1,206 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: delarray.dtx Copyright (C) 1991-1994 David Carlisle
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{delarray}
+%<package>         [2014/10/28 v1.01 array delimiter package (DPC)]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{delarray}
+\GetFileInfo{delarray.sty}
+\begin{document}
+\title{The \textsf{delarray} package\thanks{This file
+        has version number \fileversion, last
+        revised \filedate.}}
+\author{David Carlisle}
+\date{\filedate}
+ \MaintainedByLaTeXTeam{tools}
+ \maketitle
+ \DocInput{delarray.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+%
+% \changes{v1.00}{1992/07/06}
+%    {Initial version after merging of newarray.sty to array.sty}
+%
+% \changes{v1.01}{1994/03/14}
+%    {Update to LaTeX2e}
+%
+%
+% \section{Examples}
+%
+%
+% The addition to {\tt array.sty} added in {\tt delarray.sty} is
+% a system of implicit |\left| |\right| pairs. If you want an array
+% surrounded by parentheses, you can enter:\\
+% |\begin{array}({cc})| \ldots
+% \[  \begin{array}({cc})a&b\\c&d\end{array}   \]
+%
+% Similarly if an environment equivalent to \PlainTeX's |\cases| could
+% be defined by:\\
+% |\begin{array}\{{lL}.| \ldots
+%
+% \newcolumntype{L}{>{$}l<{$}}
+% \[  f(x)=\begin{array}\{{lL}.
+%           0        &if $x=0$\\
+%           \sin(x)/x&otherwise
+%           \end{array}  \]
+% Here |L| is supposed to denote a column of left aligned L-R text. It
+% may be defined via: |\newcolumntype{L}{>{$}l<{$}}|, as discussed in
+% {\tt array.sty}.
+% Note that as the delimiters must always be used in pairs, the  `|.|'
+% must be used to denote a  `null delimiter'.
+%
+% This feature is especially useful if the |[t]| or |[b]|
+% arguments are also used. In these cases the result is not equivalent
+% to surrounding the environment by |\left|\ldots|\right|, as
+% can be seen from the following example:
+% \[
+% \begin{array}[t]({c}) 1\\2\\3 \end{array}
+% \begin{array}[c]({c}) 1\\2\\3 \end{array}
+% \begin{array}[b]({c}) 1\\2\\3 \end{array}
+% \quad\mbox{not}\quad
+% \left(\begin{array}[t]{c} 1\\2\\3 \end{array}\right)
+% \left(\begin{array}[c]{c} 1\\2\\3 \end{array}\right)
+% \left(\begin{array}[b]{c} 1\\2\\3 \end{array}\right)
+% \]
+% \begin{verbatim}
+% \begin{array}[t]({c}) 1\\2\\3 \end{array}
+% \begin{array}[c]({c}) 1\\2\\3 \end{array}
+% \begin{array}[b]({c}) 1\\2\\3 \end{array}
+% \quad\mbox{not}\quad
+% \left(\begin{array}[t]{c} 1\\2\\3 \end{array}\right)
+% \left(\begin{array}[c]{c} 1\\2\\3 \end{array}\right)
+% \left(\begin{array}[b]{c} 1\\2\\3 \end{array}\right)
+% \end{verbatim}
+%
+%
+% \StopEventually{}
+%
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\RequirePackage{array}[1994/02/03]
+%    \end{macrocode}
+%
+% \begin{macro}{\@tabarray}
+%    This macro tests for an optional bracket and then calls up
+%    |\@@array| or |\@@array[c]| (as default).
+%    \begin{macrocode}
+\def\@tabarray{\@ifnextchar[{\@@array}{\@@array[c]}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@array}
+%    This macro tests for an optional delimiter before the left brace
+%    of the main preamble argument. If there is no delimiter,
+%    |\@arrayleft| and |\@arrayright| are made a no-ops, and
+%    |\@array| is called with the positional argument. Otherwise
+%    call |\@del@array|.
+%    \begin{macrocode}
+\def\@@array[#1]{\@ifnextchar\bgroup
+  {\let\@arrayleft\relax\let\@arrayright\relax\@array[#1]}%
+  {\@del@array[#1]}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@del@array}
+%    We now know that we have an {\tt array} (or {\tt tabular}) with
+%    delimiters.
+%    \begin{macrocode}
+\def\@del@array[#1]#2#3#4{%
+%    \end{macrocode}
+% The following line is completely redundant but it does catch errors
+% involving delimiters  before the processing of the alignment begins.
+% A common error is likely to be omitting the `.' in a
+% |\cases|-type construction. This causes the first token of the
+% alignment to be gobbled, possibly causing lots of spurious errors
+% before the cause of the error, the missing delimiter, is discovered as
+% |\@arrayright| puts the alignment and the delimiters together.
+%    \begin{macrocode}
+  \setbox\z@\hbox{$\left#2\right#4$}%
+%    \end{macrocode}
+% In the case of a `c' argument we do not need to rebox the alignment,
+% so we can define |\@arrayleft| and |\@arrayright| just to
+% insert the delimiters.
+%    \begin{macrocode}
+  \if#1c\def\@arrayleft{\left#2}\def\@arrayright{\right#4}%
+%    \end{macrocode}
+% Otherwise we (should) have a {\tt[t]} or {\tt[b]} argument, so first we
+% store the alignment, without delimiters in box0.
+%    \begin{macrocode}
+  \else\def\@arrayleft{\setbox\z@}%
+%    \end{macrocode}
+% Then after the alignment is finished:
+%    \begin{macrocode}
+  \def\@arrayright{%
+%    \end{macrocode}
+% Calculate the amount the box needs to be lowered (this will be
+% negative in the case of |[b]|). A little bit of arithmetic cf.\
+% the \TeX{}Book, Appendix G, rule 8. We calculate the amount this
+% way, rather than just taking the difference between the depth of box0
+% and the depth of the box defined below, as the depth of that box may
+% be affected by the delimiters if |\delimitershortfall| or
+% |\delimiterfactor| have non-standard values.
+%    \begin{macrocode}
+     \dimen@=\dp\z@
+     \advance\dimen@-\ht\z@
+     \divide \dimen@ by \tw@
+     \advance\dimen@ by\fontdimen22 \textfont\tw@
+%    \end{macrocode}
+% Now lower the alignment and the delimiters into place.
+%    \begin{macrocode}
+     \lower\dimen@\hbox{$\left#2\vcenter{\unvbox\z@}\right#4$}}%
+%    \end{macrocode}
+% End the |\if#1c|
+%    \begin{macrocode}
+  \fi
+%    \end{macrocode}
+% Now that we have defined |\@arrayleft| and |\@arrayright|, call
+% |\@array|.
+%    \begin{macrocode}
+  \@array[#1]{#3}}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+%
+% \subsection{newarray.sty}
+% All the features of the old {\tt newarray} style option have been
+% merged into the {\tt array} or {\tt delarray} options.
+% \changes{v1.00}{1992/07/06}
+%    {Stop generating a `shell' newarray.sty}
+%
+%
+% \Finale
+\endinput
diff --git a/macros/latex-dev/required/tools/delarray.pdf b/macros/latex-dev/required/tools/delarray.pdf
new file mode 100644
index 0000000000..6f80eb57c4
--- /dev/null
+++ b/macros/latex-dev/required/tools/delarray.pdf
diff --git a/macros/latex-dev/required/tools/enumerate.dtx b/macros/latex-dev/required/tools/enumerate.dtx
new file mode 100644
index 0000000000..984d36d415
--- /dev/null
+++ b/macros/latex-dev/required/tools/enumerate.dtx
@@ -0,0 +1,335 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: enumerate.dtx Copyright  1993 1994 1999 David Carlisle
+%
+%<*dtx>
+          \ProvidesFile{enumerate.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{enumerate}
+%<driver> \ProvidesFile{enumerate.drv}
+% \fi
+%         \ProvidesFile{enumerate.dtx}
+          [2015/07/23 v3.00 enumerate extensions (DPC)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{enumerate}
+\begin{document}
+\DocInput{enumerate.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{enumerate.dtx}
+% \title{The \textsf{enumerate} package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{David Carlisle}
+% \date{\filedate}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+% \changes{v1.00}{1990/00/00}{First version (since lost)}
+% \changes{v2.00}{1991/07/25}{New Algorithm}
+% \changes{v2.01}{1992/06/26}{Re-issue for the new doc and docstrip.}
+% \changes{v2.02}{1994/01/31}{Update for LaTeX2e}
+% \changes{v3.00}{1999/03/05}{Add extension hook for tools/2916}
+% \changes{v3.00}{2015/07/23}{Documentation fixes tools/2916}
+%
+% \begin{abstract}
+% This package gives the enumerate environment an optional argument
+% which determines the style in which the counter is printed.
+%
+% An occurrence of one of the tokens |A a I i| or |1| produces the value
+% of the counter printed with (respectively) |\Alph \alph \Roman \roman|
+% or |\arabic|.
+%
+% These letters may be surrounded by any strings involving any other
+% \TeX\ expressions, however the tokens |A a I i 1| must be inside a
+% |{ }| group if they are not to be taken as special.
+% \end{abstract}
+%
+% \section{Examples}
+%\showboxdepth=10
+% \showboxbreadth=10
+% \[
+% \parbox{2.2in}{\hbadness2000
+% \begin{enumerate}[EX i.]
+% \item one one one one one one one
+%        one one one one one\label{LA}
+% \item two
+%     \begin{enumerate}[{example} a)]
+%     \item one of two  one of two  one of two\label{LB}
+%     \item two of two
+%     \end{enumerate}
+% \end{enumerate}
+% \begin{enumerate}[{A}-1]
+% \item one\label{LC}
+% \item two
+% \end{enumerate}}
+% \hspace{20pt}
+% \vcenter{\hsize=2.4in
+% \begin{verbatim}
+% \begin{enumerate}[EX i.]
+% \item one one one one one one one
+%        one one one one\label{LA}
+% \item two
+%     \begin{enumerate}[{example} a)]
+%     \item one of two  one of two
+%           one of two\label{LB}
+%     \item two of two
+%     \end{enumerate}
+% \end{enumerate}
+%
+% \begin{enumerate}[{A}-1]
+% \item one\label{LC}
+% \item two
+% \end{enumerate}
+% \end{verbatim}
+% }\]
+%
+% |\label| and |\ref| may be used as with the standard {\tt
+% enumerate} environment. |\ref| only produces the counter value,
+% not the whole label. |\ref| prints the value in the same style
+% as |\item|, as determined by the presence of one of the tokens
+% |A a I i 1| in the optional argument. In the above example
+% |\ref{LA}|, |\ref{LB}| and |\ref{LC}| produce
+% `\ref{LA}',  `\ref{LB}' and `\ref{LC}' respectively.
+%
+% \StopEventually{}
+%
+%\section{Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \begin{macro}{\@enlab}
+% Internal token register used to build up the label command from the
+% optional argument.
+%    \begin{macrocode}
+\newtoks\@enLab
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enQmark}
+% This just expands to a `?'. |\ref| will produce this, if no counter
+% is printed.
+%    \begin{macrocode}
+\def\@enQmark{?}
+%    \end{macrocode}
+% \end{macro}
+%
+% The next four macros build up the command that will print the item
+% label. They each gobble one token or group from the optional argument,
+% and add corresponding tokens to the register |\@enLab|. They each end
+% with a call to |\@enloop|, which starts the processing of the next
+% token.
+% \begin{macro}{\@enLabel}
+% Add the counter to the label. |#2| will be one of the `special'
+% tokens |A a I i 1|, and is thrown away. |#1| will be a command
+% like |\Roman|.
+%    \begin{macrocode}
+\def\@enLabel#1#2{%
+  \edef\@enThe{\noexpand#1{\@enumctr}}%
+  \@enLab\expandafter{\the\@enLab\csname the\@enumctr\endcsname}%
+  \@enloop}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enSpace}
+% \begin{macro}{\@enSp@ce}
+% Add a space to the label. The tricky bit is to gobble the space token,
+% as you can not do this with a macro argument.
+%    \begin{macrocode}
+\def\@enSpace{\afterassignment\@enSp@ce\let\@tempa= }
+\def\@enSp@ce{\@enLab\expandafter{\the\@enLab\space}\@enloop}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@enGroup}
+% Add a |{ }| group to the label.
+%    \begin{macrocode}
+\def\@enGroup#1{\@enLab\expandafter{\the\@enLab{#1}}\@enloop}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enOther}
+% Add anything else to the label
+%    \begin{macrocode}
+\def\@enOther#1{\@enLab\expandafter{\the\@enLab#1}\@enloop}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enloop}
+% \begin{macro}{\@enloop@}
+% The body of the main loop.
+% Eating tokens this way instead of using |\@tfor| lets you see
+% spaces and {\bf all} braces. |\@tfor| would treat {\tt a} and
+% |{a}| as  special, but not |{{a}}|.
+%    \begin{macrocode}
+\def\@enloop{\futurelet\@entemp\@enloop@}
+%    \end{macrocode}
+%    \begin{macrocode}
+\def\@enloop@{%
+  \ifx A\@entemp         \def\@tempa{\@enLabel\Alph  }\else
+  \ifx a\@entemp         \def\@tempa{\@enLabel\alph  }\else
+  \ifx i\@entemp         \def\@tempa{\@enLabel\roman }\else
+  \ifx I\@entemp         \def\@tempa{\@enLabel\Roman }\else
+  \ifx 1\@entemp         \def\@tempa{\@enLabel\arabic}\else
+  \ifx \@sptoken\@entemp \let\@tempa\@enSpace         \else
+  \ifx \bgroup\@entemp   \let\@tempa\@enGroup         \else
+  \ifx \@enum@\@entemp   \let\@tempa\@gobble          \else
+                         \let\@tempa\@enOther
+%    \end{macrocode}
+%    Hook for possible extensions
+%    \begin{macrocode}
+                         \@enhook
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+             \fi\fi\fi\fi\fi\fi\fi\fi
+%    \end{macrocode}
+% \end{macro}
+% Process the current token, then look at the next.
+%    \begin{macrocode}
+  \@tempa}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enhook}
+% Hook for possible extensions.
+% Some packages may want to extend the number of special characters
+% that are associated with counter representations. This feature
+% was requested to enable Russian alphabetic counting, but here
+% I give an example of a footnote symbol counter, triggered by |*|.
+%
+% To enable a new counter type based on a letter, you just need
+% to add a new |\ifx| clause by analogy with the code above.
+% So for example to make |*| trigger footnote symbol counting.
+% a package should do the following.
+%
+% Initialise the hook, in case the package is loaded before
+% \textsf{enumerate}.
+%\begin{verbatim}
+% \providecommand\@enhook{}
+%\end{verbatim}
+%
+% Add to the hook a new |\ifx| clause that associates |*| with the
+% |\fnsymbol| counter command.
+%\begin{verbatim}
+% \g@addto@macro\@enhook{%
+%   \ifx *\@entemp
+%     \def\@tempa{\@enLabel\fnsymbol}%
+%   \fi}
+%\end{verbatim}
+% This code sequence should work whether it is loaded before or after
+% this enumerate package. Any number of new counter types may be added
+% in this way.
+%
+% At this point we just need initialise the hook, taking care not
+% to over write any definitions another package may already have added.
+%    \begin{macrocode}
+\providecommand\@enhook{}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\enumerate}
+% The new {\tt enumerate} environment. This is the first half of the
+% original enumerate environment. If there is an optional argument, call
+% |\@@enum@| to define the label commands, otherwise call
+% |\@enum@| which is the second half of the original definition.
+%    \begin{macrocode}
+\def\enumerate{%
+  \ifnum \@enumdepth >3 \@toodeep\else
+      \advance\@enumdepth \@ne
+      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\fi
+  \@ifnextchar[{\@@enum@}{\@enum@}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@enum@}
+% Handle the optional argument..
+%    \begin{macrocode}
+\def\@@enum@[#1]{%
+%    \end{macrocode}
+% Initialise the loop which will break apart the optional argument.
+% The command to print the label is built up in |\@enlab|.
+% |\@enThe| will be used to define |\theenum|\,$n$.
+%    \begin{macrocode}
+  \@enLab{}\let\@enThe\@enQmark
+%    \end{macrocode}
+% The |\@enum@| below is never expanded, it is used to detect the end
+% of the token list.
+%    \begin{macrocode}
+  \@enloop#1\@enum@
+%    \end{macrocode}
+% Issue a warning if we did not find one of the `special' tokens.
+%    \begin{macrocode}
+  \ifx\@enThe\@enQmark\@warning{The counter will not be printed.%
+   ^^J\space\@spaces\@spaces\@spaces The label is: \the\@enLab}\fi
+%    \end{macrocode}
+% Define |\labelenum|$\,n$ and |\theenum|$\,n$.
+%    \begin{macrocode}
+  \expandafter\edef\csname label\@enumctr\endcsname{\the\@enLab}%
+  \expandafter\let\csname the\@enumctr\endcsname\@enThe
+%    \end{macrocode}
+% Set the counter to 7 so that we get the width of `vii' if roman
+% numbering is in force then set |\leftmargin|$\,n$. to the width of the
+% label plus |\labelsep|.
+%    \begin{macrocode}
+  \csname c@\@enumctr\endcsname7
+  \expandafter\settowidth
+            \csname leftmargin\romannumeral\@enumdepth\endcsname
+            {\the\@enLab\hspace{\labelsep}}%
+%    \end{macrocode}
+% Finally call |\@enum@| which is the second half of the original
+% definition.
+%    \begin{macrocode}
+  \@enum@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@enum@}
+% All the list parameters have now been defined, so call |\list|. This
+% is taken straight from the original definition of |\enumerate|.
+%    \begin{macrocode}
+\def\@enum@{\list{\csname label\@enumctr\endcsname}%
+           {\usecounter{\@enumctr}\def\makelabel##1{\hss\llap{##1}}}}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
+\endinput
diff --git a/macros/latex-dev/required/tools/enumerate.pdf b/macros/latex-dev/required/tools/enumerate.pdf
new file mode 100644
index 0000000000..70a69f6ce1
--- /dev/null
+++ b/macros/latex-dev/required/tools/enumerate.pdf
diff --git a/macros/latex-dev/required/tools/fileerr.dtx b/macros/latex-dev/required/tools/fileerr.dtx
new file mode 100644
index 0000000000..3b5895a5f6
--- /dev/null
+++ b/macros/latex-dev/required/tools/fileerr.dtx
@@ -0,0 +1,123 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \def\fileversion{v1.1a} \def\filedate{2003/12/28}
+% \iffalse    This is a METACOMMENT
+% Doc-Source file to use with LaTeX2e
+% Copyright (C) 1994-2004 Frank Mittelbach, all rights reserved.
+% \fi
+% \title{File not found error\thanks{This file has version
+% \fileversion\ last revised \filedate}}
+% \author{Frank Mittelbach}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \changes{v1.0e}{97/07/07}{Added q and r replies (PR/2525).}
+%
+% \section{Introduction}
+%    When \LaTeXe{} is unable to find a file it will ask for an
+%    alternative file name. However, sometimes the problem is
+%    only noticed by \TeX{}, and in that case \TeX{} insists on
+%    getting a valid file name; any other attempt to leave this
+%    error loop will fail.\footnote{On some systems, \TeX{}
+%    accepts a special character denoting the end of file to
+%    return from this loop, e.g.\ Control-D on UNIX or Control-Z
+%    on DOS.} Many users try to respond in the same way as to
+%    normal error messages, e.g.\ by typing \meta{return}, or |s|
+%    or |x|, but \TeX{} will interpret this as a file name and
+%    will ask again.
+%    \par To provide a graceful exit out of this loop, we define
+%    a number of files which emulate the normal behavior of
+%    \TeX{} in the error loop as far as possible.
+%    \par After installing these files the user can respond with
+%    |h|,  |q|, |r|, |s|, |e|, |x|, and on some systems also with
+%    \meta{return} to \TeX's missing file name question.
+% \StopEventually{}
+%
+% \section{The documentation driver}
+%    This code will generate the documentation. Since it is the
+%    first piece of code in the file, the documentation can be
+%    obtained by simply processing this file with \LaTeXe.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+\begin{document} \DocInput{fileerr.dtx}  \end{document}
+%</driver>
+%    \end{macrocode}
+% \section{The files}
+%
+% \subsection{Asking for help with {\tt h}}
+%    When the user types |h| in the file error loop \TeX{} will
+%    look for the file |h.tex|. In this file we put a message
+%    informing the user about the situation (we use |^^J| to
+%    start new lines in the message) and then finish with a
+%    normal |\errmessage| command thereby bringing up \TeX's
+%    normal error mechanism.
+%    \begin{macrocode}
+%<*help>
+\newlinechar=`\^^J
+\message{! The file name provided could not be found.^^J%
+Use `<enter>' to continue processing,^^J%
+`S' to scroll  future errors^^J%
+`R' to run without stopping,^^J%
+`Q' to run quietly,^^J%
+or `X' to terminate TeX}
+\errmessage{}
+%</help>
+%    \end{macrocode}
+%
+% \subsection{Scrolling this and further errors with {\tt s}}
+%    For the response |s| we put a message into the file |s.tex|
+%    and start |\scrollmode| to scroll further error messages in
+%    this run.  On systems that allow |.tex| as a file name we
+%    can also trap a single \meta{return} from the user.
+%    \begin{macrocode}
+%<+scroll|return|run,batch> \message{File ignored}
+%<+scroll>            \scrollmode
+%<+run>               \nonstopmode
+%<+batch>             \batchmode
+%    \end{macrocode}
+%
+% \subsection{Exiting the run with {\tt x} or {\tt e}}
+%
+%    If the user enters |x| or |e| to stop \TeX{}, we need to put
+%    something into the corresponding file which will force \TeX{} to
+%    give up.  We achieve this by turning off terminal output and then
+%    asking \TeX{} to stop: first by using the internal \LaTeX{} name
+%    |\@@end|, and if that doesn't work because something other than
+%    \LaTeX{} is used, by trying the \TeX{} primitive |\end|.  The
+%    |\errmessage| is there to ensure that \TeX{}'s internal "history"
+%    variable is set to |error_message_issued|. This in turn will
+%    hopefully set the exit code on those operating systems that
+%    implement return codes (though there is no guarantee for this).
+% \changes{v1.1a}{2003/12/28}{Attempt to set exit code (pr/3538).}
+%    \begin{macrocode}
+%<+edit|exit>  \batchmode \errmessage{}\csname @@end\endcsname \end
+%    \end{macrocode}
+%    We end every file with an explicit |\endinput| which prevents
+%    the docstrip program from putting the character table into
+%    the generated files.
+%    \begin{macrocode}
+\endinput
+%    \end{macrocode}
+%%
+% \Finale
diff --git a/macros/latex-dev/required/tools/fileerr.pdf b/macros/latex-dev/required/tools/fileerr.pdf
new file mode 100644
index 0000000000..2bd1aff4b3
--- /dev/null
+++ b/macros/latex-dev/required/tools/fileerr.pdf
diff --git a/macros/latex-dev/required/tools/fontsmpl.dtx b/macros/latex-dev/required/tools/fontsmpl.dtx
new file mode 100644
index 0000000000..961bdda71f
--- /dev/null
+++ b/macros/latex-dev/required/tools/fontsmpl.dtx
@@ -0,0 +1,338 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \title{A font sampler}
+% \author{Alan Jeffrey}
+% \date{v0.11}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+%%
+%
+% \changes{v0.01}{1994/05/01}{Created this test document as part of
+%    accents.dtx.}
+% \changes{v0.02}{1994/05/12}{Added the t1enc and ot1enc packages.}
+% \changes{v0.03}{1994/05/14}{Moved fontsmpl to its own dtx file.}
+% \changes{v0.03}{1994/05/14}{Removed the t1enc and ot1enc packages.}
+% \changes{v0.04}{1994/05/14}{Removed some debugging code, improved
+%    documentation.}
+% \changes{v0.05}{1994/05/14}{Tidied up some more.  Removed the fontenc
+%    package.}
+% \changes{v0.06}{1994/10/27}{Added testing for all the commands in
+%    ltoutenc.}
+% \changes{v0.06}{1994/10/27}{Switched off error for `commands not
+%    defined in this encoding'.}
+% \changes{v0.07}{1994/10/29}{Added testing for \cs{dots},
+%    \cs{copyright} and \cs{textregistered}.}
+% \changes{v0.07}{1994/10/29}{Replaced ??? for missing characters by
+%    \textbf{?}.}
+% \changes{v0.08}{1994/10/30}{Added testing for \cs{k} and \cs{t}.}
+% \changes{v0.08}{1994/10/30}{Removed testing for any glyphs not in
+%    usrguide.}
+% \changes{v0.08}{1994/10/30}{Allowed overfull boxes in the accent test
+%    to extend out into the right margin.}
+% \changes{v0.10}{1995/09/19}{Corrected placement of docstrip guard.}
+% \changes{v0.11}{1997/05/13}{Replaced \cs{@changed@x@err} by
+%    \cs{TextSymbolUnavailable}, according to the change in
+%    \texttt{ltoutenc.dtx}.}
+%
+% \section{Introduction}
+%
+% This document describes the font test document |fontsmpl.tex| and the
+% accompanying package |fontsmpl.sty|.  This produces a test of a font
+% family, printing a sample text, a table of accents, and a sample of
+% commands such as |\pounds|.
+%
+% It can be used in two ways.  The |fontsmpl| package provides the
+% command |\fontsample|, which produces a sample of the current font.
+%
+% The |fontsmpl| document prompts interactively for a font family (for
+% example `|cmr|') and produces a sample of that family.
+%
+% \StopEventually{}
+%
+% \section{Documentation}
+%
+% This docstrip document has three docstrip options:
+% \begin{itemize}
+% \item |document| the code for |fontsmpl.tex|.
+% \item |package| the code for |fontsmpl.sty|.
+% \item |driver| this documentation.
+% \end{itemize}
+% The code for the driver is:
+%    \begin{macrocode}
+%<*driver>
+\NeedsTeXFormat{LaTeX2e}
+\documentclass{ltxdoc}
+\begin{document}
+   \DocInput{fontsmpl.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+% \section{Font sample document}
+%
+% The sample document prompts for a family, and uses the |fontsmpl|
+% package.  If there is a file |fontsmpl.cfg|, this is loaded.
+% \changes{v0.9}{1995/05/07}{Removed \cs{pagestyle} empty}
+% \begin{macrocode}
+%<*document>
+\NeedsTeXFormat{LaTeX2e}
+\documentclass{article}
+\usepackage{fontsmpl}
+\makeatletter
+\InputIfFileExists{fontsmpl.cfg}{}{}
+\makeatother
+\typein[\family]{Please enter a family name (for example `cmr').}
+\title{Test of \LaTeX{} font family `\family'}
+\author{Font sample produced with `fontsmpl'}
+\raggedright
+\begin{document}
+\maketitle
+\fontfamily{\family}\selectfont
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\itshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\slshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\scshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\upshape\bfseries
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\itshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\slshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\scshape
+\fontencoding{T1}\selectfont\fontsample
+\fontencoding{OT1}\selectfont\fontsample
+\end{document}
+%</document>
+%    \end{macrocode}
+%
+% \section{Font sample package}
+%
+% The |fontsmpl| package is a \LaTeXe{} package.
+%    \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{fontsmpl}[1994/10/29 Font sample package]
+%    \end{macrocode}
+%
+% \begin{macro}{\fontsample}
+%    The |\fontsample| command prints out a sample text, a
+%    selection of glyphs, and a table of accents.
+%    \begin{macrocode}
+\newcommand{\fontsample}{%
+   Test of font \f@encoding/\f@family/\f@series/\f@shape.
+   \fontsampletext
+   \fontsampleglyphs
+   \fontsampleaccents
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fontsampletext}
+%    A sample text, taken from Knuth's |testfont.tex|.
+%    \begin{macrocode}
+\newcommand{\fontsampletext}{%
+   Some text:
+   \begin{quote}\begin{flushleft}
+      On November 14, 1885, Senator \& Mrs.~Leland Stanford called
+      together at their San Francisco mansion the 24~prominent men who
+      had been chosen as the first trustees of The Leland Stanford
+      Junior University.  They handed to the board the Founding Grant
+      of the University, which they had executed three days before.
+      This document---with various amendments, legislative acts, and
+      court decrees---remains as the University's charter.  In bold,
+      sweeping language it stipulates that the objectives of the
+      University are ``to qualify students for personal success and
+      direct usefulness in life; and to promote the publick welfare by
+      exercising an influence in behalf of humanity and civilization,
+      teaching the blessings of liberty regulated by law, and
+      inculcating love and reverence for the great principles of
+      government as derived from the inalienable rights of man to life,
+      liberty, and the pursuit of happiness.''
+   \\
+      (!`THE DAZED BROWN FOX QUICKLY GAVE 12345--67890 JUMPS!)
+   \\
+      ?`But aren't Kafka's Schlo\ss\
+      and \AE sop's \OE uvres often na\"\i ve vis-\`a-vis the
+      d\ae monic ph\oe nix's official r\^ole in fluffy s\t ouffl\'es?
+   \\
+
+   \end{flushleft}\end{quote}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fontsampleglyphs}
+% \begin{macro}{\fontsampleglyph}
+%    A list of sample glyph commands.
+%    \begin{macrocode}
+\newcommand{\fontsampleglyphs}{%
+   Some glyphs:
+   \begin{quote}\begin{flushleft}
+      \fontsampleglyph{\#}
+      \fontsampleglyph{\$}
+      \fontsampleglyph{\%}
+      \fontsampleglyph{\&}
+      \fontsampleglyph{\AA}
+      \fontsampleglyph{\AE}
+      \fontsampleglyph{\DH}
+      \fontsampleglyph{\DJ}
+      \fontsampleglyph{\L}
+      \fontsampleglyph{\NG}
+      \fontsampleglyph{\OE}
+      \fontsampleglyph{\O}
+      \fontsampleglyph{\P}
+      \fontsampleglyph{\SS}
+      \fontsampleglyph{\S}
+      \fontsampleglyph{\TH}
+      \fontsampleglyph{\_}
+      \fontsampleglyph{\aa}
+      \fontsampleglyph{\ae}
+      \fontsampleglyph{\copyright}
+      \fontsampleglyph{\dag}
+      \fontsampleglyph{\ddag}
+      \fontsampleglyph{\dh}
+      \fontsampleglyph{\dj}
+      \fontsampleglyph{\dots}
+      \fontsampleglyph{\guillemotleft}
+      \fontsampleglyph{\guillemotright}
+      \fontsampleglyph{\guilsinglleft}
+      \fontsampleglyph{\guilsinglright}
+      \fontsampleglyph{\i}
+      \fontsampleglyph{\j}
+      \fontsampleglyph{\l}
+      \fontsampleglyph{\ng}
+      \fontsampleglyph{\oe}
+      \fontsampleglyph{\o}
+      \fontsampleglyph{\pounds}
+      \fontsampleglyph{\quotedblbase}
+      \fontsampleglyph{\quotesinglbase}
+      \fontsampleglyph{\ss}
+      \fontsampleglyph{\textasciicircum}
+      \fontsampleglyph{\textasciitilde}
+      \fontsampleglyph{\textbackslash}
+      \fontsampleglyph{\textbar}
+      \fontsampleglyph{\textbullet}
+      \fontsampleglyph{\textcompwordmark}
+      \fontsampleglyph{\textemdash}
+      \fontsampleglyph{\textendash}
+      \fontsampleglyph{\textexclamdown}
+      \fontsampleglyph{\textgreater}
+      \fontsampleglyph{\texthyphenchar}
+      \fontsampleglyph{\textless}
+      \fontsampleglyph{\textperiodcentered}
+      \fontsampleglyph{\textquestiondown}
+      \fontsampleglyph{\textquotedblleft}
+      \fontsampleglyph{\textquotedblright}
+      \fontsampleglyph{\textquotedbl}
+      \fontsampleglyph{\textquoteleft}
+      \fontsampleglyph{\textquoteright}
+      \fontsampleglyph{\textvisiblespace}
+      \fontsampleglyph{\th}
+      \fontsampleglyph{\{}
+      \fontsampleglyph{\}}
+   \end{flushleft}\end{quote}
+}
+\newcommand{\fontsampleglyph}[1]{%
+   \ifx#1\@undefined
+      {\typewriterfont\string#1}~is~undefined
+   \else
+      {\typewriterfont\string#1}~is~`#1'
+   \fi
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fontsampleaccents}
+% \begin{macro}{\fontsampleaccent}
+%    A sample of accents.
+%    \begin{macrocode}
+\newcommand{\fontsampleaccents}{%
+   Some accents:
+   \begin{quote}\begin{flushleft}
+         \fontsampleaccent{\"} \\
+         \fontsampleaccent{\'} \\
+         \fontsampleaccent{\.} \\
+         \fontsampleaccent{\=} \\
+         \fontsampleaccent{\H} \\
+         \fontsampleaccent{\^} \\
+         \fontsampleaccent{\`} \\
+         \fontsampleaccent{\b} \\
+         \fontsampleaccent{\c} \\
+         \fontsampleaccent{\d} \\
+         \fontsampleaccent{\k} \\
+         \fontsampleaccent{\u} \\
+         \fontsampleaccent{\v} \\
+         \fontsampleaccent{\~}
+   \end{flushleft}\end{quote}
+}
+\newcommand{\fontsampleaccent}[1]{%
+   \makebox[1em][r]{\typewriterfont\string#1}
+   \makebox[15em][l]{%
+      #1A#1C#1D#1E#1G#1I#1L#1N%
+      #1O#1R#1S#1T#1U#1Y#1Z%
+      #1a#1c#1d#1e#1g#1\i#1i#1l#1n%
+      #1o#1r#1s#1t#1u#1y#1z%
+   }
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\typewriterfont}
+%    Not all sites have the T1 typewriter fonts, so we set the
+%    typewriter font to be a fixed font.
+%    \begin{macrocode}
+\DeclareFixedFont{\typewriterfont}
+   {\encodingdefault}{\ttdefault}{\mddefault}{\updefault}{10}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TextSymbolUnavailable}
+%    Switch off the error message from missing glyphs.
+%    \begin{macrocode}
+\def\TextSymbolUnavailable#1{%
+   \textbf{?}\PackageInfo{fontsmpl}{%
+      Command \protect#1 undefined in encoding \f@encoding%
+   }%
+}
+%</package>
+%    \end{macrocode}
+% \end{macro}
+%\Finale
+\endinput
+
+
diff --git a/macros/latex-dev/required/tools/fontsmpl.pdf b/macros/latex-dev/required/tools/fontsmpl.pdf
new file mode 100644
index 0000000000..20626d2340
--- /dev/null
+++ b/macros/latex-dev/required/tools/fontsmpl.pdf
diff --git a/macros/latex-dev/required/tools/ftnright.dtx b/macros/latex-dev/required/tools/ftnright.dtx
new file mode 100644
index 0000000000..5739172f85
--- /dev/null
+++ b/macros/latex-dev/required/tools/ftnright.dtx
@@ -0,0 +1,1018 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%\iffalse   % this is a METACOMMENT !
+%
+%% Package `ftnright' to use with LaTeX 2e
+%% Copyright (C) 1989-2004 Frank Mittelbach, all rights reserved.
+%<+package>\NeedsTeXFormat{LaTeX2e}[1995/06/01]
+%<+package>\ProvidesPackage{ftnright}
+%<+package>         [2014/10/28 v1.1f footnote layout package (FMi)]
+%
+% \fi
+%%
+%%
+%
+%
+%  \DoNotIndex{\;}
+%^^A  \DoNotIndex{\@cclv}
+%^^A  \DoNotIndex{\@colht}
+%^^A  \DoNotIndex{\@colroom}
+%  \DoNotIndex{\@combinedblfloats}
+%  \DoNotIndex{\@combinefloats}
+%  \DoNotIndex{\@dblfloatplacement}
+%  \DoNotIndex{\@deferlist}
+%  \DoNotIndex{\@empty}
+%^^A  \DoNotIndex{\@fcolmadefalse}
+%^^A  \DoNotIndex{\@firstcolumnfalse}
+%^^A  \DoNotIndex{\@firstcolumntrue}
+%  \DoNotIndex{\@freelist}
+%  \DoNotIndex{\@ixpt}
+%^^A  \DoNotIndex{\@leftcolumn}
+%^^A  \DoNotIndex{\@m}
+%^^A  \DoNotIndex{\@makecol}
+%^^A  \DoNotIndex{\@makefntext}
+%^^A  \DoNotIndex{\@maxdepth}
+%  \DoNotIndex{\@midlist}
+%^^A  \DoNotIndex{\@outputbox}
+%^^A  \DoNotIndex{\@outputdblcol}
+%^^A  \DoNotIndex{\@outputpage}
+%  \DoNotIndex{\@ptsize}
+%^^A  \DoNotIndex{\@setsize}
+%  \DoNotIndex{\@spaces}
+%^^A  \DoNotIndex{\@startcolumn}
+%^^A  \DoNotIndex{\@startdblcolumn}
+%  \DoNotIndex{\@tempdima}
+%  \DoNotIndex{\@textbottom}
+%  \DoNotIndex{\@texttop}
+%^^A  \DoNotIndex{\@thefnmark}
+%  \DoNotIndex{\@viiipt}
+%  \DoNotIndex{\@whilesw}
+%  \DoNotIndex{\@width}
+%^^A  \DoNotIndex{\@xstartcol}
+%  \DoNotIndex{\@xpt}
+%  \DoNotIndex{\advance}
+%  \DoNotIndex{\begingroup}
+%  \DoNotIndex{\box}
+%^^A  \DoNotIndex{\boxmaxdepth}
+%^^A  \DoNotIndex{\columnseprule}
+%^^A  \DoNotIndex{\columnwidth}
+%  \DoNotIndex{\count}
+%  \DoNotIndex{\def}
+%  \DoNotIndex{\dimen}
+%  \DoNotIndex{\dp}
+%  \DoNotIndex{\else}
+%  \DoNotIndex{\endgroup}
+%  \DoNotIndex{\fi}
+%  \DoNotIndex{\filedate}
+%  \DoNotIndex{\filename}
+%  \DoNotIndex{\fileversion}
+%^^A  \DoNotIndex{\footins}
+%^^A  \DoNotIndex{\footnoterule}
+%^^A  \DoNotIndex{\footnotesep}
+%^^A  \DoNotIndex{\footnotesize}
+%^^A  \DoNotIndex{\ftn@amount}
+%  \DoNotIndex{\gdef}
+%  \DoNotIndex{\global}
+%  \DoNotIndex{\hbox}
+%  \DoNotIndex{\hfil}
+%  \DoNotIndex{\hss}
+%  \DoNotIndex{\ht}
+%^^A  \DoNotIndex{\if@fcolmade}
+%^^A  \DoNotIndex{\if@firstcolumn}
+%  \DoNotIndex{\ifcase}
+%^^A  \DoNotIndex{\ifvoid}
+%  \DoNotIndex{\ifx}
+%^^A  \DoNotIndex{\insert}
+%  \DoNotIndex{\ixpt}
+%  \DoNotIndex{\let}
+%  \DoNotIndex{\llap}
+%  \DoNotIndex{\long}
+%^^A  \DoNotIndex{\maxdepth}
+%^^A  \DoNotIndex{\newdimen}
+%^^A  \DoNotIndex{\newskip}
+%  \DoNotIndex{\noindent}
+%  \DoNotIndex{\normalsize}
+%  \DoNotIndex{\or}
+%^^A  \DoNotIndex{\parindent}
+%^^A  \DoNotIndex{\preparefootins}
+%^^A  \DoNotIndex{\rcol@footinsskip}
+%^^A  \DoNotIndex{\saved@footinsskip}
+%  \DoNotIndex{\setbox}
+%  \DoNotIndex{\skip}
+%  \DoNotIndex{\space}
+%^^A  \DoNotIndex{\strutbox}
+%^^A  \DoNotIndex{\textheight}
+%^^A  \DoNotIndex{\textwidth}
+%  \DoNotIndex{\unvbox}
+%  \DoNotIndex{\vbox}
+%  \DoNotIndex{\viiipt}
+%  \DoNotIndex{\vrule}
+%  \DoNotIndex{\vskip}
+%^^A  \DoNotIndex{\wlog}
+%  \DoNotIndex{\xdef}
+%  \DoNotIndex{\xpt}
+%  \DoNotIndex{\z@}
+%
+% \changes{v1.1a}{1994/01/24}{Upgrades for LaTeX2e}
+% \changes{v1.1b}{1994/01/24}{Driver moved in front}
+% \changes{v1.1c}{1996/01/01}{Use article.cls for documentation}
+%
+% \renewcommand{\.}{\penalty500} %^^A for certain breaks
+%
+% \setlength{\hfuzz}{2pt} ^^A allow small overshot in verbatim
+%
+% \GetFileInfo{ftnright.sty}
+%
+% \title{Footnotes in a multi-column layout\thanks
+%   {The \LaTeX{} package {\tt \filename} which is described
+%    in this article has the version number \fileversion{} dated
+%    \filedate.}}
+% \author{Frank Mittelbach}
+%
+%
+% \maketitle
+%
+% \pageshrink 1pt  %^^A compensate for the \thanks marker
+%
+%
+% \section{Preface to version 1.1}
+%
+% The new release is a basically unchanged version of the original. I
+% upgraded the macros so that they work with \LaTeXe{} and used some
+% of the additional flexibility introduced therein. For example, the
+% command |\preparefootins| is now automatically called at
+% |\begin{document}|, thus allowing the user to adjust the
+% |\textheight| in the preamble.
+%
+% It is not surprisingly that I was forced to change some of the
+% macros because they dig deep into \LaTeX{}'s output routines.
+% Fortunately this is something normally not necessary when upgrading
+% other \LaTeX~2.09 styles to \LaTeXe{} packages.
+%
+% I also upgraded the documentation to conform to the \LaTeXe{}
+% terminology, e.g., this is a package since document classes will not
+% know about it. However it is very likely that i have missed some
+% necessary corrections.
+%
+% \section{Introduction}
+%
+%
+% The placement of footnotes in a multicolumn layout always bothered
+% me. The approach taken by \LaTeX{} (i.e., placing the footnotes
+% separately under each column) might be all right if nearly no
+% footnotes are present. But it looks clumsy when both columns contain
+% footnotes, especially when they occupy different amounts of space.
+%
+% In the multicolumn package~\cite{art:FMi89b}, I used page-wide
+% footnotes at the bottom of the page, but again the result doesn't
+% look very pleasant since short footnotes produce undesired gaps of
+% white space. Of course, the main goal of this package was a
+% balancing algorithm for columns which would allow switching between
+% different numbers of columns on the same page. With this feature,
+% the natural place for footnotes seems to be the bottom of the
+% page\footnote{You cannot use column footnotes at the bottom, since
+% the number of columns can differ on one page.} but looking at some
+% of the results it seems best to avoid footnotes in such a layout
+% entirely.
+%
+%
+% Another possibility is to turn footnotes into endnotes, i.e.,
+% printing them at the end of every chapter or the end of the entire
+% document.  But I assume everyone who has ever read a book using such
+% a layout will agree with me, that it is a pain to search back and
+% forth, so that the reader is tempted to ignore the endnotes
+% entirely.
+%
+% When I wrote the article about ``Future extensions of
+% \TeX{}''~\cite{inproc:FMi90} I was again dissatisfied with the
+% outcome of the footnotes, and since this article should show certain
+% aspects of high quality typesetting, I decided to give the footnote
+% problem a try and modified the \LaTeX{} output routine for this
+% purpose.  The layout I used was inspired by the yearbook of the
+% Gutenberg Gesellschaft Mainz \cite{book:GG}.  Later on, I found that
+% it is also recommended by Jan White \cite{book:JWh88}. On the layout
+% of footnotes I also consulted books by Jan Tschichold
+% \cite{book:JTs87} and Manfred Simoneit \cite{book:MSi89}, books I
+% would recommend to everyone being able to read German texts.
+%
+%
+% \subsection{Description of the new layout}
+%
+% The result of this effort is presented in this paper and the reader
+% can judge for himself whether it was successful or
+% not.\footnote{Please note, that this option only changed the
+% placement of footnotes. Since this article also makes use of the
+% {\tt doc} package \cite{bk:GMS94}, that assigns tiny numbers to
+% code lines sprinkled throughout the text, the resulting design is
+% not perfect. This package is now a standard part of \LaTeXe.}
+% The main idea for this layout is to assemble the
+% footnotes of all columns on a page and place them all together at
+% the bottom of the right column. Allowing for enough space between
+% footnotes and text, and in addition, setting the footnotes in
+% smaller type\footnote{The standard layout in \TUB{} uses the same
+% size for footnotes and text, giving the footnotes, in my opinion,
+% much too much prominence.} I decided that one could omit the
+% footnote separator rule which is used in most publications prepared
+% with \TeX{}.\footnote{People who prefer the rule can add it by
+% redefining the command {\tt\bslash footnoterule}
+% \cite[p.~156]{book:LLa86}. Please, note, that this command should
+% occupy no space, so that a negative space should be used to
+% compensate for the width of the rule used.} Furthermore, I decided
+% to place the footnote markers\footnote{\label{thisftn}The tiny
+% numbers or symbols, e.g., the `\ref{thisftn}' in front of this
+% footnote.} at the baseline instead of raising them as
+% superscripts.\footnote{Of course, this is done only for the mark
+% preceding the footnote text and not the one used within the main
+% text where a raised number or symbol set in smaller type will help
+% to keep the flow of thoughts, uninterrupted.}
+%
+% All in all, I think this generates a neat layout, and surprisingly
+% enough, the necessary changes to the \LaTeX{} output routine are
+% nevertheless astonishingly simple.
+%
+% \subsection{The use of the package}
+%
+% This package might be used together with any other  package
+% for \LaTeX{} which does not change the three internals changed by
+% {\tt \filename}.\footnote{These are the macros {\tt\bslash
+% @startcolumn}, {\tt\bslash @makecol}, and {\tt\bslash @outputdblcol},
+% as we will see below.  Of course, the package will take only effect
+% with a document class using a two-column layout (like {\tt ltugboat})
+% or when the user additionally specifies {\tt twocolumn} as a
+% document class option in the {\tt\bslash documentclass} command.} In
+% most cases, it is best to use this  package as the very last
+% package in the preamble to make sure that its
+% settings are not overwritten by other packages.
+%
+% It is unfortunate that the current \LaTeX{} has nearly no provisions
+% to make such changes without overwriting the internal routines. In
+% the \LaTeX3 implementation, we will certainly add some hooks that
+% will make such changes more easy.
+%
+%
+% \subsection{Limitations}
+%
+% If in the first column there is more than a full column worth of footnote
+% material the material will be split resulting in footnotes out of
+% order. This issue is now detected and generates an error but the package is
+% unable to gracefully handle it. This gives you two options: either rearrange
+% your input so that it will use less footnotes in the first column (or add
+% some pagebreaks at suitable places) or allow explicitly for more material to
+% be gathered. The latter can be achieved by adding
+%\begin{verbatim}
+%\makeatletter
+%\def\preparefootins{%
+%  \global\rcol@footinsskip\skip\footins
+%  \global\skip\footins\z@
+%  \global\count\footins\z@
+%  \global\dimen\footins2\textheight}
+%\makeatother
+%\end{verbatim}
+% to the preamble of your document. However, with this you allow two columns
+% worth of footnote material and that means that some of your footnotes are
+% likely to be detached from their reference and show up on a later page!
+%
+% \StopEventually{
+%
+% \begin{small}
+% \begin{thebibliography}{1}
+%
+% \bibitem{bk:GMS94} \textsc{M.~Goossens}, \textsc{F.~Mittelbach}
+%       and \textsc{A.~Samarin}.
+%       \newblock The \LaTeX{} Companion.
+%       \newblock
+%       Addison-Wesley, Reading, Massachusetts, 1994.
+%
+% \bibitem{book:GG}
+% Hans-Joachim Koppitz, editor.
+% \newblock {\em {Gutenberg Jahrbuch}}.
+% \newblock Gutenberg-Gesellschaft, Mainz.
+%
+% \bibitem{book:LLa86}
+% Leslie Lamport.
+% \newblock {\em {\LaTeX:} A Document Preparation System}.
+% \newblock Addison-Wesley, Reading, Massachusetts, 1986.
+%
+% \bibitem{src:ltxiii94}
+% \LaTeX3 project.
+% \newblock \LaTeXe distribution, 1994.
+% \newblock Sources for {\LaTeXe} the successor to \LaTeX~2.09.
+%
+% \bibitem{art:FMi89b}
+% Frank Mittelbach
+% \newblock An environment for multi-column output.
+% \newblock {\em TUGboat}, 10(3):407--415, November 1989.
+%
+% \bibitem{inproc:FMi90}
+% Frank Mittelbach
+% \newblock E-{\TeX}: Guidelines to future {\TeX} extensions.
+% \newblock In Lincoln K. Durst, editor, {\em \TUB}, 11(3):
+%   {\em 1990 TUG Annual Meeting Proceedings}, pages
+%   337--345, September 1990.
+%
+% \bibitem{book:MSi89}
+% Manfred Siemoneit.
+% \newblock {\em Typographisches {G}estalten}.
+% \newblock Polygraph Verlag, Frankfurt am Main, second edition, 1989.
+%
+% \bibitem{book:JTs87}
+% Jan Tschichold.
+% \newblock {\em {Ausgew\"ahlte Aufs\"atze \"uber Fragen der Gestalt des
+%   Buches}}.
+% \newblock Birkh\"auser Verlag, Basel, 1987.
+% \newblock Second printing.
+%
+% \bibitem{book:JWh88}
+% Jan White.
+% \newblock {\em Graphic Design for the Electronic Age}.
+% \newblock Watson Guptill, Xerox Press, New York, 1988.
+%
+% \end{thebibliography}
+% \end{small}
+%
+%      \onecolumn
+%      \PrintIndex
+%      \PrintChanges
+%   }
+%
+%
+%
+% \section{The documentation driver}
+%
+% The first bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the {\tt
+% docstrip} program. If you don't want to make any changes to the
+% presentation you can alternatively process the \texttt{.dtx} file
+% directly with \LaTeXe{} to obtain the documentation.
+% \changes{v1.0d}{1992/04/19}{Added driver file to source}
+% \changes{v1.0e}{1993/05/13}{Added history generation}
+%    \begin{macrocode}
+%<*driver>
+\documentclass[twocolumn]{article}
+
+\usepackage{ftnright}
+\usepackage{doc}
+\AtBeginDocument{\MakeShortVerb{\|}}
+
+\newcommand{\TUB}{{\sl TUGboat\/}}
+\renewcommand\DescribeMacro[1]{\fbox
+          {\PrintDescribeMacro{#1}}}
+\renewcommand\DescribeEnv[1]{\fbox
+          {\PrintDescribeEnv{#1}}}
+\renewcommand\PrintMacroName[1]{}
+
+\setlength{\parindent}{1em}
+\setlength{\parskip}
+          {2pt plus1pt minus1pt}
+\setlength{\headsep}{20pt}
+\setlength{\columnsep}{1.5pc}
+\renewcommand{\bottomfraction}{.4}
+
+\flushbottom
+\CodelineIndex
+\RecordChanges      % produce history
+\EnableCrossrefs
+
+\setcounter{IndexColumns}{2}
+\IndexPrologue{\section{Index}
+ All numbers denote code lines where
+ the corresponding entry is used,
+ underlined entries point to the
+ definition.}
+
+\begin{document}
+  \DocInput{ftnright.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+% \section{The Implementation}
+%
+%
+% As usual, we start by identifying the current version of this package
+% file in the transcript file.\footnote{Nico Poppelier suggested
+% omitting the {\tt\bslash typeout} statements in the production
+% version of the files to avoid showing all that unnecessary
+% information to the user. While I accept his criticism as valid, I
+% decided that this information should at least be placed into the
+% transcript file to make it easier to detect problems arising from
+% the use of older versions. This happens now automatically as the command
+% \texttt{\string\ProvidesPackage} will only write to the transcript file.}
+% This actually happens at the very top of this file so it is commented out
+% here.
+%\begin{verbatim}
+%\ProvidesPackage{ftnright}[\filedate\space
+%               LaTeX2e package \fileversion]
+%\end{verbatim}
+%
+% To implement the layout described, above we have to distinguish
+% between the left and the right column on a page. For this purpose
+% \LaTeX{} maintains the switch |\if@firstcolumn|. When assembling
+% material for the left (i.e., the first) column, footnotes should
+% take up no space, since they are held over for the second column. In
+% the second column these footnotes are combined with the ones found
+% there and placed a suitable distance from the main text at the
+% bottom of this column.
+%
+% This means that we have to change certain parameters for the
+% insertion |\footins| when we construct the second column. The right
+% place to do this is in the \LaTeX{} macro |\@outputdblcol| which we
+% are going to change later on.  What settings for the insertion
+% parameters are appropriate? For setting the first column
+% |\count|\.|\footins| and |\skip|\.|\footins| should both be zero
+% since footnotes are held over while for the second column
+% |\count|\.|\footins| should be $1000$ and the |\skip|\.|\footins|
+% has to be set to the desired separation between main text and
+% footnotes.\footnote{A value of $1000$ means that there is a
+% one-to-one relationship between the real size of the footnote and
+% the size finally occupied by the footnote on the current page.}
+%
+%
+% We will allow one column of footnotes (i.e., the right column) at
+% most, so that |\dimen|\.|\footins| has to equal |\textheight|. In
+% principle, it would be possible to allow for even more footnotes,
+% but this would complicate matters enormously.\footnote{It is not
+% possible to make {\tt\bslash dimen\bslash footins} larger than
+% {\tt\bslash textheight} directly, because this would result in a
+% full left column (with text) and more than one column of footnotes.
+% Instead, one has to make footnotes visible to the page generation
+% algorithm again at the moment when a full column of footnotes is
+% assembled, but we still have some space left in the first column. It
+% is a nice enhancement, and, I suppose, it is of some value for
+% preparing publications in certain disciplines, so here is the
+% challenge~\ldots}
+%
+%
+% \begin{macro}{\preparefootins}
+% \begin{macro}{\saved@footinsskip}
+%    Since a document usually starts with a left column, we have to
+%    set |\count| and |\skip|\.|\footins| on top-level to zero. For
+%    this purpose, we define a macro |\preparefootins| which will
+%    first save the current value of |\skip|\.|\footins| in a safe
+%    place. This saved value will be used later for the second column.
+%    In this way, it is possible for the user or a designer of a
+%    document class to adjust this parameter without fiddling with the
+%    code of this package file.
+%    \begin{macrocode}
+%<*package>
+\def\preparefootins{%
+  \global\rcol@footinsskip\skip\footins
+  \global\skip\footins\z@
+  \global\count\footins\z@
+%    \end{macrocode}
+%    We will also assign |\textheight| to |\dimen|\.|\footins| to
+%    allow the user to change this parameter in the preamble.
+%    \begin{macrocode}
+  \global\dimen\footins\textheight}
+%    \end{macrocode}
+%    It is necessary to make the assignments above |\global| because
+%    we are going to use this macro in the output routine which has an
+%    implicit grouping level to keep the changes made by it local.
+%  \end{macro}
+%    Of course, we have to allocate the {\sf skip} register that we
+%    used above:
+%    \begin{macrocode}
+\newskip\rcol@footinsskip
+%    \end{macrocode}
+%    \end{macro}
+%
+%
+% \begin{macro}{\@outputdblcol}
+%    Now we have all the necessary tools available to tackle
+%    |\@outputdblcol|.  We have to remember that when
+%    |\if@firstcolumn| equals |\iftrue|, we are currently starting to
+%    build the second column, i.e., that the first column is already
+%    assembled. Therefore, the macro will start with the following
+%    code:
+%    \begin{macrocode}
+\def\@outputdblcol{\if@firstcolumn
+  \global\@firstcolumnfalse
+%    \end{macrocode}
+%    After changing the switch, we save the first column (which was
+%    placed by preceding macros in |\@outputbox|) in the box register
+%    |\@leftcolumn|. Since we are inside the output routine, all those
+%    assignments have to be |\global| to take any effect.
+%    \begin{macrocode}
+  \global\setbox\@leftcolumn\box\@outputbox
+%    \end{macrocode}
+%    Then, we make the footnotes visible to the page generation
+%    algorithm by setting |\count\footins| to $1000$ (|\@m| is an
+%    abbreviation for this number) and |\skip\footins| to its saved
+%    value (i.e., |\rcol@footinsskip|).
+%    \begin{macrocode}
+  \global\count\footins\@m
+  \global\skip\footins\rcol@footinsskip
+%    \end{macrocode}
+%    We also have to reinsert all footnotes left over from the first
+%    column to make sure that they are reconsidered by the page
+%    generation algorithm of \TeX{} using the new values for |\count|
+%    and |\skip|\.|\footins|. But this will be done later in the
+%    macro |\@startcolumn|.
+%
+%    If we have just finished the right column, i.e., when
+%    |\if@firstcolumn| equals |\iffalse|, we will reset the |\footins|
+%    parameters as explained above using the utility macro
+%    |\preparefootins|.
+%    \begin{macrocode}
+ \else \preparefootins
+%    \end{macrocode}
+%    Then, we compose both columns in |\@outputbox|, combine them with
+%    all page-wide floats for this page (|\@combinedblfloats|), attach
+%    header and footer, and ship out the result (|\@outputpage|).
+%    Finally we look to see whether it is possible to generate
+%    following pages consisting only of page-wide
+%    floats.\footnote{This part is copied directly from the original
+%    \LaTeX{} macro. Details about the used macros, their interfaces
+%    and meanings can be found in the \LaTeXe{} source
+%    code~\cite{src:ltxiii94}.}
+%    \begin{macrocode}
+  \global\@firstcolumntrue
+  \setbox\@outputbox\vbox{\hbox to\textwidth
+    {\hbox to\columnwidth
+                  {\box\@leftcolumn\hss}%
+     \hfil\vrule\@width\columnseprule\hfil
+     \hbox to\columnwidth
+                  {\box\@outputbox\hss}}}%
+  \@combinedblfloats\@outputpage
+  \begingroup
+   \@dblfloatplacement\@startdblcolumn
+   \@whilesw\if@fcolmade\fi
+    {\@outputpage\@startdblcolumn}%
+  \endgroup
+ \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@startcolumn}
+% \changes{v1.0b}{1990/08/11}{Macro added to correct float problems}
+%    There is a fundamental flaw in \LaTeX's output routine for float
+%    columns and float pages: split footnotes, i.e., footnotes which
+%    are only partly typeset on the preceding page are not resolved.
+%    They are held over until \LaTeX{} starts a page (or column)
+%    containing text besides floats again. For our current layout,
+%    this would mean, that if \LaTeX{} decided to make the right
+%    column of a page a float column, footnotes from the left column
+%    would appear on a later page. A real cure for this problem would
+%    be to rewrite two-thirds of \LaTeX{}'s output routine, so I am
+%    leaving this open for the interested reader.
+%
+% \begin{figure}[b]
+%   \fbox{%^^A
+% \newlength{\puzzlewd}%^^A
+% \setlength{\puzzlewd}{\columnwidth}%^^A
+% \addtolength{\puzzlewd}{-2.1\fboxsep}%^^A
+% \begin{minipage}{\puzzlewd}
+%    \vspace{17pt}
+%    \begin{center}
+%      \bf Puzzle:
+%    \end{center}
+%    \vspace{-3pt}
+%    \small
+%    \begin{quote}
+% \rightskip \leftmargini plus 2.5em
+% Given a simple \TeX{} document containing only straight text, is
+% it possible for the editor,  after
+% deleting one sentence, to end up with a document
+% producing an extra page?
+%
+% We assume that the deleted text contains no \TeX{} macros and
+% that the document was prepared
+% with a standard macro package like the one used for \TUB\/ production.
+%    \end{quote}
+%    \vspace{7pt}
+%    \begin{flushright}
+%       The answer will be given in the next issue.
+%    \end{flushright}
+%    \vspace{7pt}
+% \end{minipage}}
+% \end{figure}
+%
+%    But the problem shows up even if only one float is contributed to
+%    the right column since \LaTeX{} assumes that the whole column is
+%    usable, whereas some of it might actually be already devoted to
+%    footnotes from the left column. So we have to change the output
+%    routine at least in the part that contributes floats to the next
+%    column. The macro involved is called |\@startcolumn|. The first
+%    thing we do is to check and see whether any deferred floats
+%    exists.
+%    \begin{macrocode}
+\def\@startcolumn{%
+ \ifx\@deferlist\@empty
+%    \end{macrocode}
+%    If not, we set the switch |\if@fcolmade| to {\tt false} which
+%    says that we did not succeed in making a float column. Then, we
+%    set |\@colroom| to |\@colht|. The register |\@colht| holds the
+%    amount of space that is available for floats, text, and footnotes
+%    in one column, i.e., it equals |\textheight| minus the space
+%    devoted to page-wide floats. |\@colroom| is a similar register
+%    which holds the value |\@colht| minus space for column floats
+%    that are already contributed to the current column. Of course,
+%    both values should be equal when we start a new column.
+%    \begin{macrocode}
+   \global\@fcolmadefalse
+   \global\@colroom\@colht
+ \else
+%    \end{macrocode}
+%    If there are floats waiting for a change to be processed, the
+%    situation is more difficult. In this case, we have to reduce both
+%    |\@colht| and |\@colroom| by the amount of space that will be
+%    needed for the footnotes from the left column. So we must check
+%    whether such footnotes are present. As we have not reinserted
+%    them in |\@outputdblcol|, we can check the |\footins| box.
+%    \begin{macrocode}
+   \ifvoid\footins\else
+%    \end{macrocode}
+%    If there are some, we measure the space that will be occupied by
+%    them. This measurement is not really exact. If  we have a full
+%    column of footnotes, it will be too high, but this does matter
+%    since we need it only for an upper bound on the free space
+%    available for floats.
+%    \begin{macrocode}
+     \ftn@amount\ht\footins
+     \advance\ftn@amount\dp\footins
+     \advance\ftn@amount\skip\footins
+   \fi
+%    \end{macrocode}
+%    We then reduce the |\@colht| by this amount and again assign
+%    |\@colroom| the value of |\@colht|. If no footnotes are present,
+%    we subtract zero, so there is no harm in doing this operation
+%    all the time.
+%    \begin{macrocode}
+   \global\advance\@colht-\ftn@amount
+   \global\@colroom\@colht
+%    \end{macrocode}
+%    Now, we call another internal \LaTeX{} macro that will try to
+%    contribute floats to the next column. It will use the register
+%    |\@colht| when trying to build up a float column, which is the
+%    reason for reducing this register. If it succeeds, it will set the
+%    switch |\if@fcolmade| to {\tt true}, otherwise, to {\tt false}. If
+%    no float column is possible, it will try to place some or all of
+%    the deferred floats to the top or the bottom of the next column,
+%    thereby, using and reducing the value of the register |\@colroom|.
+%    \begin{macrocode}
+   \@xstartcol
+%    \end{macrocode}
+%    Afterwards, we have to restore the correct values for |\@colht|
+%    and |\@colroom| again, but this time, they may differ, so that we
+%    have to |\advance| both registers separately by |\ftn@amount|.
+%    \begin{macrocode}
+   \global\advance\@colht\ftn@amount
+   \global\advance\@colroom\ftn@amount
+ \fi
+%    \end{macrocode}
+%    Now, after doing the things depending on the status of the
+%    |\@deferlist|, we have to incorporate the left over footnotes in
+%    the new column. First we check whether a float column was
+%    produced by |\@xstartcol| or not.
+%    \begin{macrocode}
+ \if@fcolmade
+%    \end{macrocode}
+%    If so, we do something awful. To make use of the |\@makecol|
+%    macro, which attaches footnotes to |\box| $255$ and places the
+%    result in the box register |\@outputbox|, we have to assign
+%    |\@outputbox| (i.e., the result of |\@xstartcol|) to |\box|
+%    $255$.\footnote{In German, we call this ``from the back through
+%    the chest into the eyes''.}
+%    \begin{macrocode}
+  \setbox\@cclv\box\@outputbox
+  \@makecol
+ \else
+%    \end{macrocode}
+%    If no float column was produced, we reinsert the held over
+%    footnotes so that they can be reconsidered by the page generation
+%    algorithm of \TeX.  But it is necessary to ensure that this
+%    operation is done only when footnotes are actually
+%    present.\footnote{Otherwise, we might get an undesired extra
+%    vertical space coming from {\tt\bslash skip\bslash footins}, even
+%    if there are no footnotes on the page.}
+%    \begin{macrocode}
+   \ifvoid\footins\else
+     \insert\footins{\unvbox\footins}\fi
+ \fi}
+%    \end{macrocode}
+% \begin{macro}{\ftn@amount}
+%    Of course, we also have to allocate the {\sf dimen} register. It
+%    will be automatically initialized to zero.
+%    \begin{macrocode}
+\newdimen\ftn@amount
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+
+%  \begin{macro}{\@xstartcol}
+% \changes{v1.1a}{1994/01/24}{Macro reintroduced}
+%    The macro |\@xtsartcol| was removed in \LaTeXe{} but we introduce
+%    it here again for the moment.
+%    \begin{macrocode}
+\def\@xstartcol{%
+  \@tryfcolumn \@deferlist
+  \if@fcolmade
+  \else
+    \begingroup
+      \let \@tempb \@deferlist
+      \global \let \@deferlist \@empty
+      \let \@elt \@scolelt
+      \@tempb
+    \endgroup
+  \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\@makecol}
+%    The other internal macro that we have to change is |\@makecol|, a
+%    macro that is called whenever one column of material is assembled
+%    and column floats and footnotes have to be added. Again, we have
+%    to distinguish between actions for the first and the second
+%    column.
+%    \begin{macrocode}
+\def\@makecol{\if@firstcolumn
+%    \end{macrocode}
+%    For the first column, we leave the footnotes in their box and
+%    simply save the contents of box $255$ in the |\box| register
+%    |\@outputbox|.
+%    \begin{macrocode}
+  \setbox\@outputbox\box\@cclv
+%    \end{macrocode}
+%
+%    But if the user erroneously forgot to specify a twocolumn layout, we
+%    will always typeset the first column, so that the footnotes are
+%    never printed.  Therefore we better check for this special case
+%    and output the footnotes on a separate page in an
+%    emergency.\footnote{Otherwise, the footnotes are held over for
+%    ever, preventing \TeX{} from finishing the document successfully.
+%    Instead, \TeX{} will produce infinity many empty pages at the end
+%    of the document, trying in vain to output the held over
+%    footnotes.  This problem was found by Rainer Sch\"opf when we
+%    prepared the paper for the Cork conference.}
+% \changes{v1.0c}{1990/08/24}{Introduced crude recovery if
+%                           twocolumn false.}
+% \changes{v1.0d}{1992/06/19}{Better help message}
+%    \begin{macrocode}
+  \if@twocolumn \else
+    \ifvoid\footins \else
+      \@latexerr{ftnright package
+                 used in one-column mode}%
+   {The ftnright package was designed to
+    work with LaTeX's standard^^Jtwocolumn
+    option. It does *not* work with the
+    multicol package.^^JSo please specify
+    `twocolumn' in the
+    \noexpand\documentclass command.}%
+      \shipout\box\footins \fi\fi
+%    \end{macrocode}
+%    What we also need to check is if there is so much footnote material that
+%    it resulted in a footnote being split. If that happens the whole
+%    algorithm falls apart and the footnotes get out of sync.  For the
+%    moment we simply detect it here, perhaps some better scheme can be
+%    implemented. One way to avoid this is to allow more than |\textheight| of
+%    footnotes in |\preparefootins|. However, that isn't such a good idea
+%    either as that means that a footnote from column one, might end up
+%    completely on a later page.
+% \changes{v1.1f}{2010/02/25}{Check for split footnotes (pr/4099)}
+%    \begin{macrocode}
+  \ifnum\insertpenalties>\z@
+      \@latexerr{ftnright package
+                 scrambled footnotes}%
+    {There is too much footnote material in
+     the first column  and ftnright^^Jis
+     unable to cope with this.^^JYou need
+     to reduce the amount to get a properly
+     formatted page.}%
+  \fi
+ \else
+%    \end{macrocode}
+%    When we construct the second column, we must first check whether
+%    footnotes are actually present. If not, we perform the same
+%    actions as before.
+%    \begin{macrocode}
+  \ifvoid\footins
+    \setbox\@outputbox\box\@cclv
+  \else
+%    \end{macrocode}
+%    But, if footnotes are present, it may be possible that the whole
+%    column consists of footnotes, i.e., |\box| $255$ is empty. In
+%    this case, there is no use in placing any glue (|\skip\footins|)
+%    in front,\footnote{In fact, it would be a mistake since this glue
+%    was not taken into account when the footnotes where assembled, so
+%    it would produce an overfull box.} so we have to check for this
+%    possibility.
+%    \begin{macrocode}
+    \setbox\@outputbox\vbox
+      {\ifvoid\@cclv \else
+         \unvbox\@cclv
+         \vskip\skip\footins\fi
+%    \end{macrocode}
+%    But in any case, we place the |\footnoterule| in front of the
+%    footnotes even if this macro is not used by this
+%    package.\footnote{This decision is certainly open to criticism,
+%    since there is nothing to separate. On the other hand, a rule or
+%    some other ornament in front of the footnotes is part of the
+%    design which should be used consistently throughout a document.
+%    As a last argument in favor of the rule, consider the situation
+%    where \LaTeX{} decided to place only floats and footnotes into
+%    the right hand column. In this case a separator again seems
+%    adequate. In this situation one can even argue that it is
+%    necessary to put in the {\tt \bslash skip\.\bslash footins}.}
+%    This ends the if-statement testing whether footnotes are present
+%    or not. It also ends the code which differs depending on the
+%    column number.
+% \changes{v1.1d}{1998/12/02}{Added the color@group macros and
+%    \texttt{\protect\bslash normalcolor} to make this colorsafe}
+%    \begin{macrocode}
+         \color@begingroup
+         \normalcolor
+         \footnoterule\unvbox\footins
+         \color@endgroup}\fi
+  \fi
+%    \end{macrocode}
+%    Now the column floats are added at the top and the bottom, and
+%    the |\@outputbox| is adjusted to the full column height so that
+%    the glue inside will stretch in certain situations.\footnote{It
+%    is an interesting question as to whether the current layout works
+%    well with bottom floats or not. Actually, I would prefer to place
+%    the footnotes below the bottom floats instead of above, as it is
+%    done here. At least when the floats are part of the document and
+%    not puzzles thrown in.  But I was too lazy to implement it
+%    because I seldom use floats. If somebody implements this layout
+%    (some parts of this macro have to be changed) I would be
+%    interested in seeing the code and some sample results.} Again,
+%    this code is copied verbatim from the original source, so I won't
+%    dwell on details.\footnote{I only changed {\tt\bslash dimen128}
+%    into {\tt\bslash @tempdima} which is, besides being faster and
+%    shorter, only a cosmetic change. The use of this hardwired {\sf
+%    dimen} register seems to indicate that this part of \LaTeX{} was
+%    written very early and left unchanged since then: an interesting
+%    fact for software archaeologists.}\footnote{For the \LaTeXe{}
+%    upgrade I had to add the support for the
+%    {\tt\string\enlargethispage} command---let's hope I did it in the
+%    correct way.}
+% \changes{v1.1a}{1994/01/24}{Upgrades for LaTeX2e}
+%    \begin{macrocode}
+  \xdef\@freelist{\@freelist\@midlist}%
+  \global \let \@midlist \@empty
+  \@combinefloats
+  \ifvbox\@kludgeins
+    \@makespecialcolbox
+  \else
+   \setbox\@outputbox\vbox to\@colht
+     {\boxmaxdepth\maxdepth
+      \@texttop
+      \@tempdima\dp\@outputbox
+      \unvbox\@outputbox
+      \vskip-\@tempdima
+      \@textbottom}%
+  \fi
+  \global\maxdepth\@maxdepth}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\footnotesize}
+% \changes{v1.1a}{1994/01/24}{Upgrades for LaTeX2e}
+%    Now we can tackle the remaining small changes to the standard
+%    layout.  I decided to use a smaller size for footnotes but with a
+%    slightly larger leading than usual. This means that we have to
+%    redefine the |\footnotesize| macro which depends on options like
+%    {\tt 11pt} etc. Fortunately, there is a simple way to find out
+%    the main size of the document: the macro |\@ptsize| contains $0$,
+%    $1$, or $2$ standing for $10$, $11$, or $12$ points document text
+%    size.\footnote{In the new release I used the definitions from the
+%    class option files \texttt{size1?.clo} and modified them
+%    slightly. In the previous release there was no correction for the
+%    list parameters etc., thus giving you incorrect spacing if
+%    somebody used display lists in footnotes.}
+%    \begin{macrocode}
+\ifcase \@ptsize
+\renewcommand\footnotesize{%
+ \@setfontsize\footnotesize\@viiipt{9.9}%
+ \abovedisplayskip 6\p@\@plus2\p@\@minus4\p@
+ \abovedisplayshortskip \z@ \@plus\p@
+ \belowdisplayshortskip
+                    3\p@\@plus\p@\@minus2\p@
+ \def\@listi{\leftmargin\leftmargini
+           \topsep 3\p@ \@plus\p@ \@minus\p@
+           \parsep 2\p@ \@plus\p@ \@minus\p@
+           \itemsep \parsep}%
+ \belowdisplayskip \abovedisplayskip
+}
+\or
+\renewcommand\footnotesize{%
+ \@setfontsize\footnotesize\@ixpt{11.1}%
+ \abovedisplayskip 8\p@\@plus2\p@\@minus4\p@
+ \abovedisplayshortskip \z@ \@plus\p@
+ \belowdisplayshortskip
+                 4\p@ \@plus2\p@ \@minus2\p@
+ \def\@listi{\leftmargin\leftmargini
+          \topsep 4\p@ \@plus2\p@\@minus2\p@
+          \parsep 2\p@ \@plus\p@ \@minus\p@
+          \itemsep \parsep}%
+ \belowdisplayskip \abovedisplayskip
+}
+\or
+\renewcommand\footnotesize{%
+ \@setfontsize\footnotesize\@xpt{12.3}%
+ \abovedisplayskip10\p@\@plus2\p@\@minus5\p@
+ \abovedisplayshortskip \z@ \@plus3\p@
+ \belowdisplayshortskip
+                 6\p@ \@plus3\p@ \@minus3\p@
+ \def\@listi{\leftmargin\leftmargini
+         \topsep 6\p@ \@plus2\p@ \@minus2\p@
+         \parsep 3\p@ \@plus2\p@ \@minus\p@
+         \itemsep \parsep}%
+ \belowdisplayskip \abovedisplayskip
+}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\footnoterule}
+%    Setting footnotes in smaller type and separating them with
+%    sufficient space from the main text allow us to omit the
+%    |\footnoterule| normally used.
+%    \begin{macrocode}
+\let\footnoterule\@empty
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\footnotesep}
+% \changes{v1.1a}{1994/01/24}{Upgrades for LaTeX2e}
+%    Individual footnotes are separated from each other by a more or
+%    less baseline skip of the text size. This can be specified with
+%    the following code:
+%    \begin{macrocode}
+\AtBeginDocument
+  {\global\footnotesep\ht\strutbox}
+%    \end{macrocode}
+%    The use of the \LaTeXe{} hook |\AtBeginDocument| is a big help
+%    since it allows us to defer everything that might depend on user
+%    setting inside the preamble to the |\begin{document}| environment
+%    start.
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\@makefntext}
+%    And finally, a small but nice change, to the mark at the
+%    beginning of the footnote text. We will place it at the baseline
+%    instead of raising it as a superscript. Additionally, it will get
+%    a dot as punctuation.
+% \changes{v1.0c}{1990/08/24}{Added dot as recommended by Tschichold.}
+% \changes{v1.1e}{2000/04/14}{Don't use math mode for footnote symbol
+%                             (pr/3172)}
+%    \begin{macrocode}
+\long\def\@makefntext#1{\parindent 1em
+   \noindent\hbox to 2em{}%
+   \llap{\@thefnmark.\,\,}#1}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \section{Initialisation}
+%
+% We defined the macro |\preparefootins| above,  but we also have to use
+% it to prepare typesetting the first column. As a default for the
+% separation of footnotes and text on the second column, we use the
+%    following:
+%    \begin{macrocode}
+\setlength{\skip\footins}
+          {10pt plus 5pt minus 3pt}
+\AtBeginDocument{\preparefootins}
+%</package>
+%    \end{macrocode}
+% Of course, this value can be changed by the user as
+% described in the introduction.
+%
+% \Finale
+%
+%
+%
+
+\endinput
diff --git a/macros/latex-dev/required/tools/ftnright.pdf b/macros/latex-dev/required/tools/ftnright.pdf
new file mode 100644
index 0000000000..0a2e5747b5
--- /dev/null
+++ b/macros/latex-dev/required/tools/ftnright.pdf
diff --git a/macros/latex-dev/required/tools/hhline.dtx b/macros/latex-dev/required/tools/hhline.dtx
new file mode 100644
index 0000000000..1da01d757b
--- /dev/null
+++ b/macros/latex-dev/required/tools/hhline.dtx
@@ -0,0 +1,322 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: hhline.dtx Copyright (C) 1991-1994 David Carlisle
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{hhline}
+%<package>         [2014/10/28 v2.03 Table rule package (DPC)]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{hhline}
+\GetFileInfo{hhline.sty}
+\begin{document}
+\title{The \textsf{hhline} package\thanks{This file
+        has version number \fileversion, last
+        revised \filedate.}}
+\author{David Carlisle}
+\date{\filedate}
+ \MaintainedByLaTeXTeam{tools}
+ \maketitle
+ \DeleteShortVerb{\|}
+ \DocInput{hhline.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+%
+% \changes{v1.00}{1991/06/04}{Initial Version}
+% \changes{v2.00}{1991/11/06}
+%     {Add tilde which allows \cmd\cline-like constructions.}
+% \changes{v2.01}{1992/06/26}
+%    {Re-issue for the new  doc and docstrip.}
+% \changes{v2.02}{1994/03/14}
+%    {Update for LaTeX2e.}
+% \changes{v2.03}{1994/05/23}
+%    {New style warning.}
+%
+%
+%
+% \MakeShortVerb{\"}
+%
+% \begin{abstract}
+% "\hhline" produces a line like "\hline", or a double line like
+% "\hline\hline", except for its interaction with vertical lines.
+% \end{abstract}
+%
+% \arrayrulewidth=1pt
+% \doublerulesep=3pt
+%
+% \section{Introduction}
+% The argument to "\hhline" is similar to the preamble of an {\tt
+% array} or {\tt tabular}. It consists of a list of tokens with the
+% following meanings:
+% \[
+% \begin{tabular}{cl}
+%   "="   & A double hline the width of a column.\\
+%   "-"   & A single hline the width of a column.\\[10pt]
+%   "~"   & A column with no hline.\\[10pt]
+%
+%   "|"   & A vline which `cuts' through a double (or single) hline.\\
+%   ":"   & A vline which is broken by a double hline.\\[10pt]
+%
+%   "#"   & A double hline segment between two vlines.\\
+%   "t"   & The top half of a double hline segment.\\
+%   "b"   & The bottom half of a double hline segment.\\
+%
+%   "*"   & "*{3}{==#}" expands to "==#==#==#",
+%                   as in the {\tt*}-form for the preamble.
+% \end{tabular}
+% \]
+% If a double vline is specified ("||" or "::") then the hlines
+% produced by "\hhline" are broken. To obtain the effect of an hline
+% `cutting through' the double vline, use a "#" or omit the vline
+% specifiers, depending on whether or not you wish the double vline to
+% break.
+%
+% The tokens {\tt t} and {\tt b} must be used between two vertical
+% rules. "|tb|" produces the same lines  as "#", but is much less
+% efficient. The main use for these are to make constructions like
+% "|t:" (top left corner) and ":b|" (bottom right corner).
+%
+% If "\hhline" is used to make a single hline, then the argument
+% should only contain the tokens "-", "~"  and "|" (and
+% {\tt*}-expressions).
+%
+% An example using most of these features is:
+% \[
+% \vcenter{\hsize=2in\begin{verbatim}
+% \begin{tabular}{||cc||c|c||}
+% \hhline{|t:==:t:==:t|}
+% a&b&c&d\\
+% \hhline{|:==:|~|~||}
+% 1&2&3&4\\
+% \hhline{#==#~|=#}
+% i&j&k&l\\
+% \hhline{||--||--||}
+% w&x&y&z\\
+% \hhline{|b:==:b:==:b|}
+% \end{tabular}
+% \end{verbatim}
+% }
+% \qquad
+% \begin{tabular}{||cc||c|c||}
+% \hhline{|t:==:t:==:t|}
+% a&b&c&d\\
+% \hhline{|:==:|~|~||}
+% 1&2&3&4\\
+% \hhline{#==#~|=#}
+% i&j&k&l\\
+% \hhline{||--||--||}
+% w&x&y&z\\
+% \hhline{|b:==:b:==:b|}
+% \end{tabular}
+% \]
+%
+% The lines produced by \LaTeX's "\hline" consist of a single (\TeX\
+% primitive) "\hrule". The lines produced by "\hhline" are made
+% up of lots of small line segments. \TeX\ will place these very
+% accurately in the {\tt .dvi} file, but the program that you use to
+% print the {\tt .dvi} file may not line up these segments exactly. (A
+% similar problem can occur with diagonal lines in the {\tt picture}
+% environment.)
+%
+% If this effect causes a problem, you could try a different driver
+% program, or if this is not possible, increasing "\arrayrulewidth"
+% may help to reduce the effect.
+%
+% \StopEventually{}
+%
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \begin{macro}{\HH@box}
+% Makes a box containing a double hline segment. The most common case,
+% both rules of length "\doublerulesep" will be stored in "\box1", this
+% is not initialised until "\hhline" is called as the user may change
+% the parameters "\doublerulesep" and "\arrayrulewidth". The two
+% arguments to "\HH@box" are the widths (ie lengths) of the top and
+% bottom rules.
+%    \begin{macrocode}
+\def\HH@box#1#2{\vbox{%
+  \hrule \@height \arrayrulewidth \@width #1
+  \vskip \doublerulesep
+  \hrule \@height \arrayrulewidth \@width #2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\HH@add}
+% Build up the preamble in the register "\toks@".
+%    \begin{macrocode}
+\def\HH@add#1{\toks@\expandafter{\the\toks@#1}}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\HH@xexpast}
+% \begin{macro}{\HH@xexnoop}
+% We `borrow' the version of "\@xexpast" from Mittelbach's array.sty,
+% as this allows "#" to appear in the argument list.
+%    \begin{macrocode}
+\def\HH@xexpast#1*#2#3#4\@@{%
+   \@tempcnta #2
+   \toks@={#1}\@temptokena={#3}%
+   \let\the@toksz\relax \let\the@toks\relax
+   \def\@tempa{\the@toksz}%
+   \ifnum\@tempcnta >0 \@whilenum\@tempcnta >0\do
+     {\edef\@tempa{\@tempa\the@toks}\advance \@tempcnta \m@ne}%
+       \let \@tempb \HH@xexpast \else
+       \let \@tempb \HH@xexnoop \fi
+   \def\the@toksz{\the\toks@}\def\the@toks{\the\@temptokena}%
+   \edef\@tempa{\@tempa}%
+   \expandafter \@tempb \@tempa #4\@@}
+
+\def\HH@xexnoop#1\@@{}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\hhline}
+% Use a simplified version of "\@mkpream" to break apart the argument
+% to "\hhline". Actually it is oversimplified, It assumes that the
+% vertical rules are at the end of the column. If you were to specify
+% "c|@{xx}|" in the array argument, then "\hhline" would not be
+% able to access the first vertical rule. (It ought to have an "@"
+% option, and add "\leaders" up to the width of a box containing the
+% "@"-expression. We use a loop made with "\futurelet" rather
+% than "\@tfor" so that we can use "#" to denote the crossing of
+% a double hline with a double vline.\\
+% "\if@firstamp" is true in the first column and false otherwise.\\
+% "\if@tempswa"  is true if the previous entry was a vline
+%                     (":", "|" or "#").
+%    \begin{macrocode}
+\def\hhline#1{\omit\@firstamptrue\@tempswafalse
+%    \end{macrocode}
+% Put two rules of width "\doublerulesep" in "\box1"
+%    \begin{macrocode}
+\global\setbox\@ne\HH@box\doublerulesep\doublerulesep
+%    \end{macrocode}
+% If Mittelbach's {\tt array.sty} is loaded, we do not need the negative
+% "\hskip"'s around vertical rules.
+%    \begin{macrocode}
+  \xdef\@tempc{\ifx\extrarowheight\HH@undef\hskip-.5\arrayrulewidth\fi}%
+%    \end{macrocode}
+% Now expand the {\tt*}-forms and add dummy tokens ( "\relax" and
+% "`" ) to either end of the token list. Call "\HH@let" to start
+% processing the token list.
+%    \begin{macrocode}
+    \HH@xexpast\relax#1*0x\@@\toks@{}\expandafter\HH@let\@tempa`}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\HH@let}
+% Discard the last token, look at the next one.
+%    \begin{macrocode}
+\def\HH@let#1{\futurelet\@tempb\HH@loop}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\HH@loop}
+% The main loop. Note we use "\ifx" rather than "\if" in
+% version~2 as the new token "~" is active.
+%    \begin{macrocode}
+\def\HH@loop{%
+%    \end{macrocode}
+% If next token is "`", stop the loop and put the lines into this row
+% of the alignment.
+%    \begin{macrocode}
+  \ifx\@tempb`\def\next##1{\the\toks@\cr}\else\let\next\HH@let
+%    \end{macrocode}
+% "|", add a vertical rule (across either a double or
+% single hline).
+%    \begin{macrocode}
+  \ifx\@tempb|\if@tempswa\HH@add{\hskip\doublerulesep}\fi\@tempswatrue
+          \HH@add{\@tempc\vline\@tempc}\else
+%    \end{macrocode}
+% ":", add a broken vertical rule (across a double hline).
+%    \begin{macrocode}
+  \ifx\@tempb:\if@tempswa\HH@add{\hskip\doublerulesep}\fi\@tempswatrue
+      \HH@add{\@tempc\HH@box\arrayrulewidth\arrayrulewidth\@tempc}\else
+%    \end{macrocode}
+% "#", add a double hline segment between two vlines.
+%    \begin{macrocode}
+  \ifx\@tempb##\if@tempswa\HH@add{\hskip\doublerulesep}\fi\@tempswatrue
+         \HH@add{\@tempc\vline\@tempc\copy\@ne\@tempc\vline\@tempc}\else
+%    \end{macrocode}
+% "~", A column with no hline (this gives an effect similar to
+% \verb+\cline+).
+%    \begin{macrocode}
+  \ifx\@tempb~\@tempswafalse
+           \if@firstamp\@firstampfalse\else\HH@add{&\omit}\fi
+              \HH@add{\hfil}\else
+%    \end{macrocode}
+% "-", add a single hline across the column.
+%    \begin{macrocode}
+  \ifx\@tempb-\@tempswafalse
+           \if@firstamp\@firstampfalse\else\HH@add{&\omit}\fi
+              \HH@add{\leaders\hrule\@height\arrayrulewidth\hfil}\else
+%    \end{macrocode}
+% "=", add a double hline across the column.
+%    \begin{macrocode}
+  \ifx\@tempb=\@tempswafalse
+       \if@firstamp\@firstampfalse\else\HH@add{&\omit}\fi
+%    \end{macrocode}
+%     Put in as many copies of "\box1" as possible with
+%     "\leaders", this may leave gaps at the ends, so put an extra box
+%     at each end, overlapping the "\leaders".
+%    \begin{macrocode}
+       \HH@add
+          {\rlap{\copy\@ne}\leaders\copy\@ne\hfil\llap{\copy\@ne}}\else
+%    \end{macrocode}
+% "t", add the top half of a double hline segment, in a "\rlap"
+% so that it may be used with {\tt b}.
+%    \begin{macrocode}
+  \ifx\@tempb t\HH@add{\rlap{\HH@box\doublerulesep\z@}}\else
+%    \end{macrocode}
+% "b", add the bottom half of a double hline segment in a "\rlap"
+% so that it may be used with {\tt t}.
+%    \begin{macrocode}
+  \ifx\@tempb b\HH@add{\rlap{\HH@box\z@\doublerulesep}}\else
+%    \end{macrocode}
+% Otherwise ignore the token, with a warning.
+%    \begin{macrocode}
+  \PackageWarning{hhline}%
+      {\meaning\@tempb\space ignored in \noexpand\hhline argument%
+       \MessageBreak}%
+  \fi\fi\fi\fi\fi\fi\fi\fi\fi
+%    \end{macrocode}
+% Go around the loop again.
+%    \begin{macrocode}
+  \next}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+\endinput
diff --git a/macros/latex-dev/required/tools/hhline.pdf b/macros/latex-dev/required/tools/hhline.pdf
new file mode 100644
index 0000000000..d4ccc822d4
--- /dev/null
+++ b/macros/latex-dev/required/tools/hhline.pdf
diff --git a/macros/latex-dev/required/tools/indentfirst.dtx b/macros/latex-dev/required/tools/indentfirst.dtx
new file mode 100644
index 0000000000..16b99653cd
--- /dev/null
+++ b/macros/latex-dev/required/tools/indentfirst.dtx
@@ -0,0 +1,77 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: indent.dtx Copyright (C) 1991-1994 David Carlisle
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{indentfirst}
+%<package>         [1995/11/23 v1.03 Indent first paragraph (DPC)]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{indentfirst}
+\GetFileInfo{indentfirst.sty}
+\begin{document}
+\title{The \textsf{indentfirst} package\thanks{This file
+        has version number \fileversion, last
+        revised \filedate.}}
+\author{David Carlisle}
+\date{\filedate}
+\MaintainedByLaTeXTeam{tools}
+\maketitle
+\DocInput{indentfirst.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% \changes{v1.00}{1991/01/02}{Initial version}
+% \changes{v1.01}{1992/06/26}{Re-issue for the new doc and docstrip}
+% \changes{v1.02}{1994/01/31}{Re-issue for LaTeX2e}
+% \changes{v1.03}{1995/11/23}{Typo fixes in documentation}
+%
+% \begin{abstract}
+% Make the first line of all sections etc., be indented by the usual
+% paragraph indentation. This should work with all the standard document
+% classes.
+% \end{abstract}
+%
+% \CheckSum{4}^^A  Still I think a record:-)
+%
+% \StopEventually{}
+%
+% \begin{macro}{\if@afterindent}
+% \LaTeX\ uses the switch |\if@afterindent| to decide whether to indent
+% after a section heading. We just need to make sure that this is always
+% true.
+%    \begin{macrocode}
+%<*package>
+\let\@afterindentfalse\@afterindenttrue
+\@afterindenttrue
+%</package>
+%    \end{macrocode}
+% \end{macro}
+%
+% \Finale
+%
diff --git a/macros/latex-dev/required/tools/indentfirst.pdf b/macros/latex-dev/required/tools/indentfirst.pdf
new file mode 100644
index 0000000000..8ac0d1f3e8
--- /dev/null
+++ b/macros/latex-dev/required/tools/indentfirst.pdf
diff --git a/macros/latex-dev/required/tools/layout.dtx b/macros/latex-dev/required/tools/layout.dtx
new file mode 100644
index 0000000000..848eb54fb2
--- /dev/null
+++ b/macros/latex-dev/required/tools/layout.dtx
@@ -0,0 +1,1025 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%\iffalse
+%    This file is built for \LaTeXe, so we make sure an error is
+%    generated when it is used with another format
+%<*dtx>
+\ProvidesFile{layout.dtx}
+%</dtx>
+%<+package>\NeedsTeXFormat{LaTeX2e}
+%<+package>\ProvidesPackage{layout}
+%<+driver>\ProvidesFile{layout.drv}
+%\ProvidesFile{layout.dtx}
+                [2014/10/28 v1.2c Show layout parameters]
+%
+%    A short driver is provided that can be extracted if necessary by
+%    the \textsf{DocStrip} program provided with \LaTeXe.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+
+\usepackage{layout}
+
+\newcommand\Lopt[1]{\textsf{#1}}
+\pagestyle{myheadings}
+\DisableCrossrefs
+\begin{document}
+\DocInput{layout.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%\fi
+% \changes{v1.1c}{1994/07/13}{Moved Identification code to the front
+%    and removed the permanent use of \cs{filedate} and friends}
+% \changes{v1.1d}{1994/09/08}{Stored texts in control sequences to
+%    allow other languages}
+%
+% \GetFileInfo{layout.dtx}
+% \title{Displaying page layout variables}
+% \author{Kent McPherson a.o.\thanks{Converted for \LaTeXe\ by
+%        Johannes Braams and modified by Hideo Umeki}}
+% \date{\filedate}
+%
+% \markboth{layout package version \fileversion\space as of \filedate}
+%          {layout package version \fileversion\space as of \filedate}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \section{Introduction}
+%
+%    This \LaTeXe\ package is a reimplementation of
+%    \texttt{layout.sty} by Kent McPherson. It defines the command
+%    |\layout| which produces an overview of the layout of the current
+%    document. The command |\layout*| recomputes the values it uses to
+%    produce the overview.
+%
+%    The figure on the next page shows the output of the |\layout|
+%    command for this document.
+%
+% \begin{figure}[p]
+% \layout
+% \end{figure}
+%
+% \StopEventually{}
+%
+% \section{The implementation}
+%
+% \changes{v1.1b}{1994/03/23}{removed the \cs{wlog} as
+%    \cs{ProvidesPackage} does that now}
+% \changes{v1.1d}{1994/09/08}{Added language options dutch and
+%    english}
+%
+%    This package prints a figure to illustrate the layout that is
+%    implemented by the document class. In the figure several words
+%    appear. They are stored in control sequences to be able to select
+%    a different language.
+% \changes{v1.1e}{1994/10/29}{The dutch texts should be one word.}
+% \changes{v1.1f}{1995/03/14}{Added \cs{notshown}}
+% \changes{v1.1f}{1995/03/14}{Added option french}
+% \changes{v1.1j}{1995/10/29}{Added the options spanish, brazilian and
+%    portuguese}
+% \changes{v1.1k}{1995/11/23}{Documentation fixes}
+% \changes{v1.2}{1998/04/13}{Redesign of the output by Hideo Umeki}
+% \changes{v1.2c}{2000/09/21}{Added option german}
+% \changes{v1.2c}{2000/09/25}{Added option for italian by Claudio Beccari}
+%    \begin{macrocode}
+%<*package>
+\DeclareOption{dutch}{%
+  \def\Headertext{Kopregel}
+  \def\Bodytext{Broodtekst}
+  \def\Footertext{Voetregel}
+  \def\MarginNotestext{Marge\\Notities}
+  \def\oneinchtext{een inch}
+  \def\notshown{niet getoond}
+  }
+\DeclareOption{german}{%
+  \def\Headertext{Kopfzeile}
+  \def\Bodytext{Haupttext}
+  \def\Footertext{Fu{\ss}zeile}
+  \def\MarginNotestext{Rand-\\ notizen}
+  \def\oneinchtext{ein Zoll}
+  \def\notshown{ohne Abbildung}
+  }
+\DeclareOption{ngerman}{\ExecuteOptions{german}}
+\DeclareOption{english}{%
+  \def\Headertext{Header}
+  \def\Bodytext{Body}
+  \def\Footertext{Footer}
+  \def\MarginNotestext{Margin\\Notes}
+  \def\oneinchtext{one inch}
+  \def\notshown{not shown}
+  }
+\DeclareOption{french}{%
+  \def\Headertext{Ent\^{e}te}
+  \def\Bodytext{Corps}
+  \def\Footertext{Pied de page}
+  \def\MarginNotestext{Marge\\Notes}
+  \def\oneinchtext{un pouce}
+  \def\notshown{non affich\'{e}}
+  }
+\DeclareOption{francais}{\ExecuteOptions{french}}
+\DeclareOption{spanish}{%
+  \def\Headertext{Encabezamiento}
+  \def\Bodytext{Cuerpo}
+  \def\Footertext{Pie de p\'agina}
+  \def\MarginNotestext{Notas\\ Marginales}
+  \def\oneinchtext{una pulgada}
+  \def\notshown{no mostradas}
+  }
+\DeclareOption{portuguese}{%
+  \def\Headertext{Cabe\c{c}alho}
+  \def\Bodytext{Corpo}
+  \def\Footertext{Rodap\'e}
+  \def\MarginNotestext{Notas\\ Marginais}
+  \def\oneinchtext{uma polegada}
+  \def\notshown{n\~ao mostradas}
+  }
+\DeclareOption{brazilian}{%
+  \def\Headertext{Cabe\c{c}alho}
+  \def\Bodytext{Corpo}
+  \def\Footertext{Rodap\'e}
+  \def\MarginNotestext{Notas\\ Marginais}
+  \def\oneinchtext{uma polegada}
+  \def\notshown{n\~ao mostradas}
+  }
+\DeclareOption{italian}{%
+  \def\Headertext{Testatina}
+  \def\Bodytext{Corpo}
+  \def\Footertext{Piedino}
+  \def\MarginNotestext{Note\\ Marginali}
+  \def\oneinchtext{un pollice}
+  \def\notshown{non mostrato}
+  }
+%    \end{macrocode}
+%
+%    This package has an option \Lopt{verbose}. Using it will make the
+%    command |\layout| type some of the parameters on the terminal.
+%    \begin{macrocode}
+\DeclareOption{verbose}{\let\LayOuttype\typeout}
+\DeclareOption{silent}{\let\LayOuttype\@gobble}
+%    \end{macrocode}
+%
+% \changes{v1.1h}{1995/04/07}{Added the options \Lopt{integers}
+%    (default) and \Lopt{reals}}
+%
+%    The normal behaviour of this package when showing the values of
+%    the parameters is to truncate them. However, if you want to see
+%    the real parameter values you can use the option \Lopt{reals} to
+%    get that effect.
+% \changes{v1.1i}{1995/06/25}{\LaTeX\ release 1995/06/01 no longer
+%    needs double hashmarks in the argument of \cs{DeclareOption}}
+%    \begin{macrocode}
+\def\lay@value{}
+\DeclareOption{integers}{%
+  \renewcommand*{\lay@value}[2]{%
+    \expandafter\number\csname #1@#2\endcsname pt}}
+\DeclareOption{reals}{%
+  \renewcommand*{\lay@value}[2]{\the\csname #2\endcsname}}
+%    \end{macrocode}
+%
+%    The default language is English, the default mode is
+%    \Lopt{silent} and the default way of showing parameter values is
+%    to use integers.
+%    \begin{macrocode}
+\ExecuteOptions{english,silent,integers}
+\ProcessOptions
+%    \end{macrocode}
+%
+% \begin{macro}{\LayOutbs}
+%    Define |\LayOutbs| to produce a backslash. We use a definition
+%    which also works with OT1 fonts.
+% \changes{v1.2b}{1998/06/21}{Renamed \cs{bs} to avoid possible conflicts
+%   with other packages}
+%    \begin{macrocode}
+\newcommand\LayOutbs{}
+\chardef\LayOutbs`\\
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ConvertToCount}
+%    This macro stores the value of a \emph{length} register in a
+%    \emph{count} register.
+%    \begin{macrocode}
+\def\ConvertToCount#1#2{%
+%    \end{macrocode}
+%    First copy the value
+%    \begin{macrocode}
+  #1=#2
+%    \end{macrocode}
+%    Then divide it by 65536.
+%    \begin{macrocode}
+  \divide #1 by 65536}
+%    \end{macrocode}
+%    The result of this is that the \emph{count} register holds the
+%    value of the \emph{length} register in points.
+% \end{macro}
+%
+% \begin{macro}{\SetToHalf}
+% \begin{macro}{\SetToQuart}
+%    Small macros used in computing positions.
+%    \begin{macrocode}
+\def\SetToHalf#1#2{#1=#2\relax\divide#1by\tw@}
+\def\SetToQuart#1#2{#1=#2\relax\divide#1by4}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Identify}
+%    A small macro used in identifying dimensions.
+%    \begin{macrocode}
+\def\Identify#1{%
+  \put(\PositionX,\PositionY){\circle{20}}
+  \put(\PositionX,\PositionY){\makebox(0,0){\tiny #1}}
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\InsideHArrow}
+%    This macro is used to produce two horizontal arrows inside a box.
+%    The argument gives the width of the box.
+% \changes{v1.1c}{1994/07/14}{Added check for a negative arrow length}
+%    \begin{macrocode}
+\def\InsideHArrow#1{{%
+  \ArrowLength = #1
+  \divide\ArrowLength by \tw@
+  \advance\ArrowLength by -10
+  \advance\PositionX by -10
+  \ifnum\ArrowLength<\z@
+    \put(\PositionX,\PositionY){\vector(1,0){-\ArrowLength}}
+    \advance\PositionX by 20
+    \put(\PositionX,\PositionY){\vector(-1,0){-\ArrowLength}}
+  \else
+    \put(\PositionX,\PositionY){\vector(-1,0){\ArrowLength}}
+    \advance\PositionX by 20
+    \put(\PositionX,\PositionY){\vector(+1,0){\ArrowLength}}
+  \fi
+}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\InsideVArrow}
+%    This macro is used to produce two vertical arrows inside a box.
+%    The argument gives the height of the box.
+%    \begin{macrocode}
+\def\InsideVArrow#1{{%
+  \ArrowLength = #1
+  \divide\ArrowLength by \tw@
+  \advance\ArrowLength by -10
+  \advance\PositionY by -10
+  \put(\PositionX,\PositionY){\vector(0,-1){\ArrowLength}}
+  \advance\PositionY by 20
+  \put(\PositionX,\PositionY){\vector(0,+1){\ArrowLength}}
+}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\OutsideHArrow}
+%    This macro is used to produce two horizontal arrows to delimit a
+%    length. The first argument is the position for the right arrow,
+%    the second argument gives the length and the third specifies the
+%    length of the arrows.
+%    \begin{macrocode}
+\def\OutsideHArrow#1#2#3{{%
+  \PositionX = #1
+  \advance\PositionX by #3
+  \put(\PositionX,\PositionY){\vector(-1,0){#3}}
+  \PositionX = #1 \advance\PositionX-#2
+  \advance\PositionX by -#3
+  \put(\PositionX,\PositionY){\vector(+1,0){#3}}
+}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\OutsideVArrow}
+%    This macro is used to produce two vertical arrows to delimit a
+%    length. The first argument is the position for the lower arrow,
+%    the second argument gives the length and the third and fourth
+%    specify the lenghts of the lower and upper arrow.
+%    \begin{macrocode}
+\def\OutsideVArrow#1#2#3#4{{%
+  \PositionY = #1
+  \advance\PositionY by -#3
+  \put(\PositionX,\PositionY){\vector(0,+1){#3}}
+  \PositionY = #1
+  \advance\PositionY#2
+  \advance\PositionY#4
+  \put(\PositionX,\PositionY){\vector(0,-1){#4}}
+}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Show}
+% \changes{v1.1g}{1995/04/03}{Simplified the definition, now show
+%    complete value}
+% \changes{v1.1h}{1995/04/07}{Use \cs{lay@value} to show the value
+%    because of the option which decides which of two ways of doing it
+%    should be used}
+%
+%    Macro used in the table that shows the setting of the parameters.
+%    \begin{macrocode}
+\def\Show#1#2{\LayOutbs #2 = \lay@value{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Type}
+% \changes{v1.1g}{1995/04/03}{Simplified the definition, now show
+%    complete value}
+% \changes{v1.1h}{1995/04/07}{Use \cs{lay@value} to show the value
+%    because of the option which decides which of two ways of doing it
+%    should be used}
+% \changes{v1.2b}{1998/06/21}{Renamed \cs{type} to \cs{LayOuttype}
+%   to avoid possible conflicts with other packages}
+%
+%    Macro used to show a setting of a parameter on the terminal.
+%    \begin{macrocode}
+\def\Type#1#2{%
+  \LayOuttype{#2 = \lay@value{#1}{#2}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\oneinch}
+%    A constant, giving the length of an inch in points (approximately)
+%    \begin{macrocode}
+\newcount\oneinch
+\oneinch=72
+%    \end{macrocode}
+% \end{macro}
+%
+%    Because the overview of the layout is produced in a figure
+%    environment we need to allocate a number of counters that are
+%    used to store the values of various dimensions.
+%
+% \begin{macro}{\cnt@paperwidth}
+% \begin{macro}{\cnt@paperheight}
+%    The dimensions of the paper
+%    \begin{macrocode}
+\newcount\cnt@paperwidth
+\newcount\cnt@paperheight
+\ConvertToCount\cnt@paperwidth\paperwidth
+\ConvertToCount\cnt@paperheight\paperheight
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@hoffset}
+% \begin{macro}{\cnt@voffset}
+%    the offsets,
+%    \begin{macrocode}
+\newcount\cnt@hoffset
+\newcount\cnt@voffset
+\ConvertToCount\cnt@hoffset\hoffset
+\ConvertToCount\cnt@voffset\voffset
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@textheight}
+% \begin{macro}{\cnt@textwidth}
+%    dimensions of the text area,
+%    \begin{macrocode}
+\newcount\cnt@textheight
+\newcount\cnt@textwidth
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@topmargin}
+% \begin{macro}{\cnt@oddsidemargin}
+% \begin{macro}{\cnt@evensidemargin}
+%    margins,
+%    \begin{macrocode}
+\newcount\cnt@topmargin
+\newcount\cnt@oddsidemargin
+\newcount\cnt@evensidemargin
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@headheight}
+% \begin{macro}{\cnt@headsep}
+%    dimensions of the running heads,
+%    \begin{macrocode}
+\newcount\cnt@headheight
+\newcount\cnt@headsep
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@marginparsep}
+% \begin{macro}{\cnt@marginparwidth}
+% \begin{macro}{\cnt@marginparpush}
+%    marginal paragraphs,
+%    \begin{macrocode}
+\newcount\cnt@marginparsep
+\newcount\cnt@marginparwidth
+\newcount\cnt@marginparpush
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cnt@footskip}
+%    the distance between the running footers and the text,
+%    \begin{macrocode}
+\newcount\cnt@footskip
+%    \end{macrocode}
+% \end{macro}
+%    and the height of the footers, which is needed here to display a
+%    box, but which isn't used by \LaTeX.
+% \begin{macro}{\fheight}
+%    \begin{macrocode}
+\newcount\fheight
+\fheight=12
+%    \end{macrocode}
+% \end{macro}
+%
+%    Apart from integer representations of the page layout parameters
+%    we also need registers to store reference values in.
+%
+% \begin{macro}{\ref@top}
+%    The position of the top of the `printable area' is
+%    one inch below the top of the paper by default. The value of
+%    |\ref@top| is relative to the lower left corner of the picture
+%    environment that will be used.
+%
+%    \begin{macrocode}
+\newcount\ref@top
+\ref@top=\cnt@paperheight \advance\ref@top by -\oneinch
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ref@hoffset}
+% \begin{macro}{\ref@voffset}
+%    For the offsets,
+%    \begin{macrocode}
+\newcount\ref@hoffset
+\newcount\ref@voffset
+%    \end{macrocode}
+%    The |\hoffset| and |\voffset| values are added to the default
+%    offset of one inch.
+%    \begin{macrocode}
+\ref@hoffset=\cnt@hoffset  \advance\cnt@hoffset by \oneinch
+\ref@voffset=\cnt@voffset
+%    \end{macrocode}
+%
+%    |\cnt@voffset| is converted to be relative to the origin of the
+%    picture.
+%    \begin{macrocode}
+\cnt@voffset=\ref@top
+\advance\cnt@voffset by -\ref@voffset
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\ref@head}
+%    and the text areas, running heads,
+%    \begin{macrocode}
+\newcount\ref@head
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ref@body}
+%    body of the text
+%    \begin{macrocode}
+\newcount\ref@body
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ref@foot}
+%    and running footers.
+%    \begin{macrocode}
+\newcount\ref@foot
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ref@margin}
+% \begin{macro}{\ref@marginwidth}
+% \begin{macro}{\ref@marginpar}
+%    These are different for even and odd pages, so they are computed
+%    by |\layout|.
+%    \begin{macrocode}
+\newcount\ref@margin
+\newcount\ref@marginwidth
+\newcount\ref@marginpar
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%    The following are a number of scratch registers, used in the
+%    positioning of the various pices of the picture.
+%    \begin{macrocode}
+\newcount\Interval
+\newcount\ExtraYPos
+\newcount\PositionX
+\newcount\PositionY
+\newcount\ArrowLength
+%    \end{macrocode}
+%
+%  \begin{macro}{\lay@getvalues}
+% \changes{v1.1j}{1995/10/30}{Added macro to compute values at later
+%    time}
+%    All values that might change during the document are computed by
+%    calling the macro |\lay@getvalues|. By default this macro is
+%    executed at |\begin{document}|.
+%    \begin{macrocode}
+\def\lay@getvalues{%
+  \ConvertToCount\cnt@textheight\textheight
+  \ConvertToCount\cnt@textwidth\textwidth
+  \ConvertToCount\cnt@topmargin\topmargin
+  \ConvertToCount\cnt@oddsidemargin\oddsidemargin
+  \ConvertToCount\cnt@evensidemargin\evensidemargin
+  \ConvertToCount\cnt@headheight\headheight
+  \ConvertToCount\cnt@headsep\headsep
+  \ConvertToCount\cnt@marginparsep\marginparsep
+  \ConvertToCount\cnt@marginparwidth\marginparwidth
+  \ConvertToCount\cnt@marginparpush\marginparpush
+  \ConvertToCount\cnt@footskip\footskip
+  \ref@head=\ref@top
+    \advance\ref@head by -\ref@voffset
+    \advance\ref@head by -\cnt@topmargin
+    \advance\ref@head by -\cnt@headheight
+  \ref@body=\ref@head
+    \advance\ref@body by -\cnt@headsep
+    \advance\ref@body by -\cnt@textheight
+  \ref@foot=\ref@body
+    \advance\ref@foot by -\cnt@footskip
+  }
+\AtBeginDocument{\lay@getvalues}
+%    \end{macrocode}
+%  \end{macro}
+%  \begin{macro}{\computevalues}
+%
+% \begin{macro}{\layout}
+% \begin{macro}{\layout*}
+%    The command |\layout| makes the picture and table that display
+%    the current settings of the layout parameters.
+%
+% \changes{v1.1b}{1994/03/23}{Produce two pages in twoside mode}
+% \changes{v1.1j}{1995/10/30}{Added \cs{layout*}}
+%    \begin{macrocode}
+\newcommand\layout{%
+  \@ifstar{\lay@getvalues\lay@xlayout}{\lay@xlayout}}
+\def\lay@xlayout{%
+  \lay@layout
+  \if@twoside
+    \lay@layout
+  \fi}
+%    \end{macrocode}
+%
+% \begin{macro}{\lay@layout}
+%    The internal macro |\lay@layout| does all the dirty work.
+%    \begin{macrocode}
+\newcommand\lay@layout{%
+  \thispagestyle{empty}
+%    \end{macrocode}
+%
+%    The actions of |\layout| depend on the pagestyle.
+%    \begin{macrocode}
+  \if@twoside
+    \ifodd\count\z@
+%    \end{macrocode}
+%
+%    Here we deal with an odd page in the twosided case.
+%
+%    \begin{macrocode}
+      \typeout{Two-sided document style, odd page.}
+%    \end{macrocode}
+%
+%    So we compute |\ref@marginwidth|, |\ref@marginpar| and
+%    |\ref@margin|.
+% \changes{v1.1}{1994/02/23}{Added check for reversemargin}
+%    \begin{macrocode}
+      \ref@marginwidth=\cnt@oddsidemargin
+      \ref@marginpar=\oneinch
+      \advance\ref@marginpar by \ref@hoffset
+      \advance\ref@marginpar by \cnt@oddsidemargin
+      \ref@margin\ref@marginpar
+      \if@reversemargin
+        \advance\ref@marginpar by -\cnt@marginparsep
+        \advance\ref@marginpar by -\cnt@marginparwidth
+      \else
+        \advance\ref@marginpar by \cnt@textwidth
+        \advance\ref@marginpar by \cnt@marginparsep
+      \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \else
+%    \end{macrocode}
+%
+%    Here we deal with an even page in the twosided case.
+%
+%    \begin{macrocode}
+  \typeout{Two-sided document style, even page.}
+%    \end{macrocode}
+%
+%    So we compute |\ref@marginwidth|, |\ref@marginpar| and
+%    |\ref@margin|.
+% \changes{v1.1}{1994/02/23}{Added check for reversemargin}
+%    \begin{macrocode}
+      \ref@marginwidth=\cnt@evensidemargin
+      \ref@marginpar=\oneinch
+      \advance\ref@marginpar by \ref@hoffset
+      \advance\ref@marginpar by \cnt@evensidemargin
+      \ref@margin\ref@marginpar
+      \if@reversemargin
+        \advance\ref@marginpar by \cnt@textwidth
+        \advance\ref@marginpar by \cnt@marginparsep
+      \else
+        \advance\ref@marginpar by -\cnt@marginparsep
+        \advance\ref@marginpar by -\cnt@marginparwidth
+      \fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \fi
+  \else
+%    \end{macrocode}
+%
+%    Finally we the case for single sided printing.
+%
+% \changes{v1.1}{1994/02/23}{Added check for reversemargin}
+%    \begin{macrocode}
+    \typeout{One-sided document style.}
+    \ref@marginwidth=\cnt@oddsidemargin
+    \ref@marginpar=\oneinch
+    \advance\ref@marginpar by \ref@hoffset
+    \advance\ref@marginpar by \cnt@oddsidemargin
+    \ref@margin\ref@marginpar
+    \if@reversemargin
+      \advance\ref@marginpar by -\cnt@marginparsep
+      \advance\ref@marginpar by -\cnt@marginparwidth
+    \else
+      \advance\ref@marginpar by \cnt@textwidth
+      \advance\ref@marginpar by \cnt@marginparsep
+    \fi
+  \fi
+%    \end{macrocode}
+%
+%
+%  Now we begin the picture environment; dividing all the lengths by
+%  two is done by setting |\unitlength| to \texttt{0.5pt}
+%    \begin{macrocode}
+  \setlength{\unitlength}{.5pt}
+  \begin{picture}(\cnt@paperwidth,\cnt@paperheight)
+    \centering
+    \thicklines
+%    \end{macrocode}
+%
+%    First we have the pagebox and reference lines,
+%
+%    \begin{macrocode}
+    \put(0,0){\framebox(\cnt@paperwidth,\cnt@paperheight){\mbox{}}}
+    \put(0,\cnt@voffset){\dashbox{10}(\cnt@paperwidth,0){\mbox{}}}
+    \put(\cnt@hoffset,0){\dashbox{10}(0,\cnt@paperheight){\mbox{}}}
+%    \end{macrocode}
+%
+%    then the header,
+%
+%    \begin{macrocode}
+    \put(\ref@margin,\ref@head){%
+      \framebox(\cnt@textwidth,\cnt@headheight)%
+        {\footnotesize\Headertext}}
+%    \end{macrocode}
+%
+%    the body of the text area,
+%
+%    \begin{macrocode}
+    \put(\ref@margin,\ref@body){%
+      \framebox(\cnt@textwidth,\cnt@textheight){\Bodytext}}
+%    \end{macrocode}
+%
+%     the footer
+%
+%    \begin{macrocode}
+    \put(\ref@margin,\ref@foot){%
+      \framebox(\cnt@textwidth,\fheight){\footnotesize\Footertext}}
+%    \end{macrocode}
+%
+%    and the space for marginal notes.
+%
+%    \begin{macrocode}
+    \put(\ref@marginpar,\ref@body){%
+      \framebox(\cnt@marginparwidth,\cnt@textheight)%
+               {\footnotesize\shortstack{\MarginNotestext}}}
+%    \end{macrocode}
+%
+%    Then we start putting in `arrows' to mark the various parameters.
+%    From here we use |\thinlines|.
+%    \begin{macrocode}
+    \thinlines
+%    \end{macrocode}
+%
+%    |\PositionX| and |\PositionY| will be the coordinates of the center of
+%    the arrow displaying |\textwidth|.
+%    \begin{macrocode}
+    \SetToHalf\PositionX\cnt@textwidth
+    \advance\PositionX by \ref@margin
+%    \end{macrocode}
+%    The arrow should be a bit above the bottom of the `body box'.
+%    \begin{macrocode}
+    \PositionY = \ref@body
+    \advance\PositionY by 50
+%    \end{macrocode}
+%    An identifying number is put here, in a circle.
+%    \begin{macrocode}
+    \Identify{8}
+%    \end{macrocode}
+%    Then the arrow is drawn.
+%    \begin{macrocode}
+    \InsideHArrow\cnt@textwidth
+%    \end{macrocode}
+%
+%    Now the |\textheight|
+%    \begin{macrocode}
+    \SetToHalf\PositionY\cnt@textheight
+    \advance\PositionY by \ref@body
+%    \end{macrocode}
+%
+%    The x-position of the arrow is at $4/5$ of the width of the `body
+%    box'.
+%    \begin{macrocode}
+    \PositionX = \cnt@textwidth
+    \divide\PositionX by 5
+    \multiply \PositionX by 4
+    \advance\PositionX by \ref@margin
+%    \end{macrocode}
+%
+%    An identifying number is put here, in a circle.
+%    \begin{macrocode}
+    \Identify{7}
+    \InsideVArrow\cnt@textheight
+%    \end{macrocode}
+%
+%
+%    The |\hoffset|,
+% \changes{v1.2}{1998/04/13}{\cs{PositionY} for label 1 is
+%    fixed at 50}
+%    \begin{macrocode}
+    \PositionY = 50
+    \SetToHalf\PositionX\cnt@hoffset
+    \Identify{1}
+    \InsideHArrow\cnt@hoffset
+%    \end{macrocode}
+%
+%
+%    The width of the margin.
+% \changes{v1.2}{1998/04/13}{The direction of the arrows should be
+%    switched by the sign of \cs{oddsidemargin}}
+%    \begin{macrocode}
+    \SetToQuart\PositionY\cnt@textheight
+    \advance\PositionY by \ref@body
+    \ifnum\ref@marginwidth > 0
+      \OutsideHArrow\ref@margin\ref@marginwidth{20}
+      \PositionX = \cnt@hoffset
+    \else
+      \OutsideHArrow\cnt@hoffset{-\ref@marginwidth}{20}
+      \PositionX = \ref@margin
+    \fi
+    \advance\PositionX by -30
+    \Identify{3}
+%    \end{macrocode}
+%
+%    the |\marginparwidth|,
+%    \begin{macrocode}
+    \SetToQuart\PositionY\cnt@textheight
+    \advance\PositionY by \ref@body
+%    \end{macrocode}
+%    This arrow has to be bit below the one for the |\oddsidemargin|
+%    or\\ |\evensidemargin|.
+%    \begin{macrocode}
+    \advance\PositionY by 30
+    \SetToHalf\PositionX\cnt@marginparwidth
+    \advance\PositionX by \ref@marginpar
+    \Identify{10}
+    \InsideHArrow\cnt@marginparwidth
+%    \end{macrocode}
+%
+%
+%    The |\marginparsep|, this depends on single or double sided
+%    printing.
+%    \begin{macrocode}
+    \advance\PositionY by 30
+    \if@twoside
+%    \end{macrocode}
+%
+%    Twosided mode, reversemargin;
+% \changes{v1.1b}{1994/03/23}{\cs{OutSideHArrow} should be
+%    \cs{OutsideHArrow}}
+% \changes{v1.2}{1998/04/13}{Added check for reversemargin}
+%    \begin{macrocode}
+      \if@reversemargin
+        \ifodd\count\z@
+          \OutsideHArrow\ref@margin\cnt@marginparsep{20}
+          \PositionX = \ref@margin
+        \else
+          \OutsideHArrow\ref@marginpar\cnt@marginparsep{20}
+          \PositionX = \ref@marginpar
+        \fi
+      \else
+%    \end{macrocode}
+%    Not reversemargin;
+%    \begin{macrocode}
+        \ifodd\count\z@
+          \OutsideHArrow\ref@marginpar\cnt@marginparsep{20}
+          \PositionX = \ref@marginpar
+        \else
+          \OutsideHArrow\ref@margin\cnt@marginparsep{20}
+          \PositionX = \ref@margin
+        \fi
+      \fi
+    \else
+%    \end{macrocode}
+%
+%    Single sided mode.
+% \changes{v1.2}{1998/04/13}{Added check for reversemargin}
+%    \begin{macrocode}
+      \if@reversemargin
+        \OutsideHArrow\ref@margin\cnt@marginparsep{20}
+        \PositionX = \ref@margin
+      \else
+        \OutsideHArrow\ref@marginpar\cnt@marginparsep{20}
+        \PositionX = \ref@marginpar
+      \fi
+    \fi
+%    \end{macrocode}
+% \changes{v1.2}{1998/04/13}{The \cs{PositionX} of the label 9 is
+%    changed to the left side of the arrows}
+%    \begin{macrocode}
+    \advance\PositionX by -\cnt@marginparsep
+    \advance\PositionX by -30
+    \Identify{9}
+%    \end{macrocode}
+%
+%    Identify the |\footskip|. The arrow will be located on $1/8$th of
+%    the |\textwidth|.
+% \changes{v1.2}{1998/04/13}{The \cs{PositionY} of the label 11 is
+%    changed to the upper side of the arrows}
+%    \begin{macrocode}
+    \PositionX = \cnt@textwidth
+    \divide\PositionX by 8
+    \advance\PositionX by \ref@margin
+    \OutsideVArrow\ref@foot\cnt@footskip{20}{20}
+    \PositionY = \ref@foot
+    \advance\PositionY by \cnt@footskip
+    \advance\PositionY by 30
+    \Identify{11}
+%    \end{macrocode}
+%
+%    Identify the |\voffset|. The arrow will be located a bit to the
+%    left of the edge of the paper.
+%    \begin{macrocode}
+    \PositionX = \cnt@paperwidth
+    \advance\PositionX by -50
+    \PositionY = \cnt@paperheight
+    \ExtraYPos = \PositionY
+    \advance\ExtraYPos by -\cnt@voffset
+    \advance\PositionY by \cnt@voffset
+    \divide\PositionY by \tw@
+    \Identify{2}
+    \InsideVArrow\ExtraYPos
+%    \end{macrocode}
+%
+%    Identify |\topmargin|, |\headheight| and |\headsep|.
+%
+%    The arrows will be located on $1/8$th of the |\textwidth|, with
+%    intervals of the same size, stored in |\Interval|.
+%    \begin{macrocode}
+    \Interval = \cnt@textwidth
+    \divide\Interval by 8
+    \PositionX = \ref@margin
+    \advance\PositionX by \Interval
+%    \end{macrocode}
+%    First the |\topmargin|. If |\topmargin| has a positive value, the
+%    arrow is upward. Otherwise, it is downward. The number label is
+%    always placed at the base of the arrow.
+% \changes{v1.2}{1998/04/13}{The direction of the arrows should be
+%    switched by the sign of \cs{topmargin}}
+%    \begin{macrocode}
+    \ifnum\cnt@topmargin > \z@
+      \ExtraYPos = \ref@head
+      \advance\ExtraYPos\cnt@headheight
+      \OutsideVArrow\ExtraYPos\cnt@topmargin{20}{20}
+      \PositionY = \ExtraYPos
+      \advance\PositionY by \cnt@topmargin
+    \else
+      \ExtraYPos = \cnt@voffset
+      \OutsideVArrow\ExtraYPos{-\cnt@topmargin}{20}{20}
+      \PositionY = \ExtraYPos
+      \advance\PositionY by -\cnt@topmargin
+    \fi
+    \advance\PositionY by 30
+    \Identify{4}
+    \advance\PositionX by \Interval
+%    \end{macrocode}
+%    Then the |\headheight|
+% \changes{v1.2}{1998/04/13}{The \cs{PositionY} of the label 5 is
+%    fixed}
+%    \begin{macrocode}
+    \OutsideVArrow\ref@head\cnt@headheight{20}{20}
+    \PositionY = \ref@head
+    \advance\PositionY by \cnt@headheight
+    \advance\PositionY by 30
+    \Identify{5}
+    \advance\PositionX by \Interval
+%    \end{macrocode}
+%    and finally the |\headsep|
+% \changes{v1.2}{1998/04/13}{The \cs{PositionY} of the label 6 is
+%    fixed}
+%    \begin{macrocode}
+    \ExtraYPos=\ref@body
+    \advance\ExtraYPos\cnt@textheight
+    \OutsideVArrow\ExtraYPos\cnt@headsep{20}{20}
+    \PositionY = \ref@body
+    \advance\PositionY by \cnt@textheight
+    \advance\PositionY by -30
+    \Identify{6}
+%    \end{macrocode}
+%
+%    Here we can end the picture environment and insert a little
+%    space.
+%    \begin{macrocode}
+  \end{picture}
+
+  \medskip
+%    \end{macrocode}
+%
+%    Below the picture we put a table to show the actual values of the
+%    parameters.  Note that fractional points are truncated, i.e.,
+%    \texttt{72.27pt} is displayed as \texttt{72pt}
+%
+%    The table is typeset inside a box with a depth of 0 to always
+%    keep it on the same page as the picture.
+% \changes{v1.1b}{1994/03/23}{Showing oddside and evenside margins was
+%    defective}
+% \changes{v1.1c}{1994/07/14}{in compatibility mode \cs{footnotesize}
+%    calls \cs{normalfont}; therefore we need to switch to a tt font
+%    later}
+% \changes{v1.1f}{1995/03/14}{introduced \cs{notshown}}
+%    \begin{macrocode}
+  \vtop to 0pt{%
+    \@minipagerestore\footnotesize\ttfamily
+    \begin{tabular}{@{}rl@{\hspace{20pt}}rl}
+      1 & \oneinchtext\ + \LayOutbs\texttt{hoffset}
+        & 2 & \oneinchtext\ + \LayOutbs\texttt{voffset} \\
+      3 & \if@twoside
+            \ifodd\count\z@ \Show{cnt}{oddsidemargin}
+            \else \Show{cnt}{evensidemargin}
+            \fi
+          \else
+            \Show{cnt}{oddsidemargin}
+          \fi                    & 4 & \Show{cnt}{topmargin} \\
+      5 & \Show{cnt}{headheight} & 6 & \Show{cnt}{headsep} \\
+      7 & \Show{cnt}{textheight} & 8 & \Show{cnt}{textwidth} \\
+      9 & \Show{cnt}{marginparsep}&10& \Show{cnt}{marginparwidth} \\
+      11& \Show{cnt}{footskip}   &   & \Show{cnt}{marginparpush}
+       \rlap{(\notshown)}\\
+        & \Show{ref}{hoffset}    &   & \Show{ref}{voffset} \\
+        & \Show{cnt}{paperwidth} &   & \Show{cnt}{paperheight} \\
+
+  \end{tabular}\vss}
+%    \end{macrocode}
+%    When the option \Lopt{verbose} was used the following lines will
+%    show dimensions on the terminal.
+%    \begin{macrocode}
+  \Type{ref}{hoffset}
+  \Type{ref}{voffset}
+  \Type{cnt}{textheight}
+  \Type{cnt}{textwidth}
+%    \end{macrocode}
+%    Finally we start a new page.
+%    \begin{macrocode}
+  \newpage
+}
+%</package>
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \Finale
+\endinput
diff --git a/macros/latex-dev/required/tools/layout.pdf b/macros/latex-dev/required/tools/layout.pdf
new file mode 100644
index 0000000000..2c06d2b63c
--- /dev/null
+++ b/macros/latex-dev/required/tools/layout.pdf
diff --git a/macros/latex-dev/required/tools/longtable.dtx b/macros/latex-dev/required/tools/longtable.dtx
new file mode 100644
index 0000000000..9a3b5c03b8
--- /dev/null
+++ b/macros/latex-dev/required/tools/longtable.dtx
@@ -0,0 +1,2154 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: longtable.dtx Copyright (C) 1990-2019 David Carlisle
+%
+%<*dtx>
+          \ProvidesFile{longtable.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}[1995/06/01]
+%<package>\ProvidesPackage{longtable}
+%<driver> \ProvidesFile{longtable.drv}
+% \fi
+%         \ProvidesFile{longtable.dtx}
+          [2019/02/06 v4.12 Multi-page Table package (DPC)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{longtable}
+\begin{document}
+\DocInput{longtable.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{longtable.dtx}
+% \title{The \textsf{longtable} package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{David Carlisle\thanks{The new algorithm for aligning `chunks'
+% of a table used in version 4 of this package was devised coded
+% and documented by David Kastrup.}}
+% \date{\filedate}
+%
+% \let\package\textsf
+% \let\env\textsf
+% \providecommand\finalclearpage{\clearpage}
+%
+%  \MaintainedByLaTeXTeam{tools}
+%  \maketitle
+%
+% \begin{abstract}
+%  This package defines the \env{longtable} environment, a multi-page
+%  version of \env{tabular}.
+% \end{abstract}
+%
+% \DeleteShortVerb{\|}
+% \MakeShortVerb{\"}
+%
+% \changes{v0.00}{1989/11/06}
+%    {`Version 0' distributed as longtab.sty
+%      always used just one chunk for the whole table}
+%
+% \changes{v1.00}{1990/12/20}
+%    {Initial version}
+%
+% \changes{v2.00}{1991/06/17}
+%    {Support NFSS and array.sty}
+%
+% \changes{v3.00}{1992/03/16}
+%    {New implementation. tables may now start anywhere on the page.}
+%
+% \changes{v3.01}{1992/04/06}
+%    {(Michel Goossens) If a chunk ends on a line in which the first
+%     entry is empty, weird errors occur. Added special begin and end
+%     groups, (\cs{ifnum}0 ) stuff as  explained in Appendix D.}
+%
+% \changes{v3.02}{1992/04/09}
+%    {(Michel Goossens) Longtable fails if the table counter is reset
+%     during a document. Now use an internal counter, but still
+%     increment table so \cs{caption} and \cs{label} work out right.}
+%
+% \changes{v3.03}{1992/06/25}
+%    {Add \cs{@ifundefined\{reset@font\}} so that the documentation may
+%     be processed with old versions of \LaTeX.}
+% \changes{v3.03}{1992/06/25}
+%    {Modify the treatment of \cs{d@llar} to match the new versions of
+%     Mittelbach's array.sty (array.sty v2.0h)}
+%
+% \changes{v3.04}{1992/11/12}
+%    {(Jean-Pierre Drucbert) Longtable failed when used with
+%     \cs{includeonly}.}
+% \changes{v3.04}{1992/11/12}
+%    {Fix bug which stopped \cs{kill} working correctly in headings.}
+% \changes{v3.04}{1992/11/12}
+%    {(Graham Gough) Made \cs{setlongtables} issue a warning message.}
+% \changes{v3.04}{1992/11/12}
+%    {(Sebastian Rahtz) longtable ran out of memory on really long
+%     tables. Another bug introduced in V3.}
+%
+% \changes{v3.05}{1992/11/20}
+%   {(Juergen Peus) Table was hard coded into the captions, Now the
+%     captions use \cs{fnum@table}, so \cs{tablename} will be used.}
+%
+% \changes{v3.06}{1993/01/21}
+%    {(Ingo Hoffmann) longtable fails with letter style.
+%     The table counter is not defined, and the .aux file is not used in
+%     the same way. This version will use a .lta file for letter style.}
+%
+% \changes{v3.07}{1993/06/09}
+%    {Allow the \LaTeX\ syntax \cs{setcounter}\{LTchunksize\}\{10\}}
+%
+% \changes{v3.08}{1993/06/09}
+%     {Update for \LaTeXe}
+%
+% \changes{v3.09}{1994/03/15}
+%     {New ltxdoc style}
+%
+% \changes{v3.11}{1994/05/22}
+%      {Option handling added, new style errors and warnings}
+%
+% \changes{v3.12}{1994/06/30}
+%      {Remove special letter class handling from v3.06, not needed for
+%      new letter class}
+%
+% \changes{v4.00}{1996/04/08}
+%      {(DK) New algorithm to align chunks devised and coded by David
+%      Kastrup}
+%
+% \changes{v4.02}{1996/04/16}
+%      {(DPC/DK) documentation improvements}
+%
+% \changes{v4.06}{1997/06/28}
+%      {(DK) new email address}
+%
+%
+%
+% \makeatletter
+% \def\@oddfoot{\normalfont\rmfamily\dotfill Page \thepage\dotfill}
+% \def\@oddhead{\dotfill{\normalfont\ttfamily longtable.sty}\dotfill}
+% \def\ps@titlepage{\let\@oddhead\@empty}
+% \makeatother
+%
+%
+% \setlength\LTleft\parindent
+% \setlength\LTright\fill
+% \setcounter{LTchunksize}{10}
+%
+% \def\v{\char`}
+%
+% ^^A \vbox to 100pt makes the page breaks the same on the first run.
+% \changes{v3.08}{1993/06/09}
+%     {No need to use \cs{vbox} with \LaTeXe\ minipage}
+% \noindent\begin{minipage}[t][130pt]{\textwidth}
+% \listoftables
+% \end{minipage}
+%
+% \section{Introduction}
+%
+% The \package{longtable} package defines a new environment,
+% \DescribeEnv{longtable}
+% \env{longtable}, which has most of the features of the \env{tabular}
+% environment, but produces tables which may be broken by \TeX's
+% standard page-breaking algorithm. It also shares some features with
+% the \env{table} environment. In particular it uses the same counter,
+% \texttt{table}, and has a similar "\caption" command. Also, the
+% standard "\listoftables" command lists tables produced by either the
+% \env{table} or \env{longtable} environments.
+%
+% The following example uses most of the features of the \env{longtable}
+% environment. An edited listing of the input for this example appears
+% in Section~\ref{listing}.
+%
+% \textbf{Note:} Various parts of the following table will
+% \textbf{not} line up correctly until this document has been run
+% through \LaTeX\ several times.  This is a characteristic feature of
+% this package, as described below.
+%
+% \begin{longtable}{@{*}r||p{1in}@{*}}
+% KILLED & LINE!!!! \kill
+% \caption
+% [An optional table caption (used in the list of tables)]
+% {A long table\label{long}}\\
+% \hline\hline
+% \multicolumn{2}{@{*}c@{*}}%
+%      {This part appears at the top of the table}\\
+% \textsc{First}&\textsc{Second}\\
+% \hline\hline
+% \endfirsthead
+% \caption[]{(continued)}\\
+% \hline\hline
+% \multicolumn{2}{@{*}c@{*}}%
+%       {This part appears at the top of every other page}\\
+% \textbf{First}&\textbf{Second}\\
+% \hline\hline
+% \endhead
+% \hline
+% This goes at the&bottom.\\
+% \hline
+% \endfoot
+% \hline
+% These lines will&appear\\
+% in place of the & usual foot\\
+% at the end& of the table\\
+% \hline
+% \endlastfoot
+% \env{longtable}  columns  are specified& in the \\
+% same way as  in the \env{tabular}& environment.\\
+% "@{*}r||p{1in}@{*}"& in this case.\\
+% Each row ends with a& "\\" command.\\
+% The "\\"  command  has an& optional\\
+% argument, just as in& the\\
+%  \env{tabular}&environment.\\[10pt]
+% See the  effect  of "\\[10pt]"&?\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Also  "\hline"  may be used,&  as in \env{tabular}.\\
+% \hline
+% That  was a "\hline"&.\\
+% \hline\hline
+% That  was "\hline\hline"&.\\
+% \multicolumn{2}{||c||}%
+% {This is a \ttfamily\v\\multicolumn\v{2\v}\v{||c||\v}}\\
+% If a  page break  occurs at a "\hline" then& a line is drawn\\
+% at the bottom of one  page  and at the& top of the next.\\
+% \hline
+% The  "[t] [b] [c]"  argument of \env{tabular}& can  not be used.\\
+% The optional argument may be  one of& "[l] [r] [c]"\\
+% to specify whether  the  table  should be& adjusted\\
+% to the  left, right& or centrally.\\
+% \hline\hline
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Some lines may take up a lot of space, like this: &
+%     \raggedleft This last column is a ``p'' column so this
+%     ``row'' of the table can take up several lines. Note however that
+%     \TeX\ will  never break a page within such a row. Page breaks only
+%     occur between rows of the table or at "\hline" commands.
+%     \tabularnewline
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% Lots of lines& like this.\\
+% \hline
+% Lots\footnote{This is a footnote.} of lines& like this.\\
+% Lots   of   lines& like this\footnote{\env{longtable} takes special
+%     precautions, so that footnotes may also be used in `p' columns.}\\
+% \hline
+% Lots of lines& like this.\\
+% Lots of lines& like this.
+% \end{longtable}
+%
+% \section{Chunk Size}
+%
+% \DescribeMacro{LTchunksize}
+% In order to \TeX\ multi-page tables, it is necessary to break up the
+% table into smaller chunks, so that \TeX\ does  not have to keep
+% everything in memory at one time. By default \env{longtable} uses 20
+% rows per chunk, but this can be set by the user, with e.g.,
+% "\setcounter{LTchunksize}{10}".\footnote
+%    {You can also use the plain \TeX\ syntax
+%    {\ttfamily\v\\LTchunksize=10.}}
+% These chunks do not affect page breaking,
+% thus if you are using a \TeX\ with a lot of memory, you can set
+% "LTchunksize" to be several pages of the table. \TeX\ will run
+% faster with a large "LTchunksize". However, if necessary,
+% \env{longtable} can work with "LTchunksize" set to 1, in which case
+% the memory taken up is negligible.
+% Note that if you use the commands for setting the table head or foot
+% (see below), the "LTchunksize" must be at least  as large as the
+% number of rows in each of the head or foot sections.
+%
+% This document specifies "\setcounter{LTchunksize}{10}".  If you look
+% at the previous table, after the \emph{first} run of \LaTeX\  you will
+% see that various parts of the table do not line up.
+% \LaTeX\ will also have printed a warning that the column
+% widths had changed. \env{longtable} writes information onto the
+% ".aux" file, so that it can line up the different chunks.
+% Prior to version~4 of this package, this information was not used
+% unless a "\setlongtables" command was issued,  however, now the
+% information is always used, using a new algorithm\footnote{Due to
+% David Kastrup.} and so "\setlongtables" is no longer needed. It is
+% defined (but does nothing) for the benefit of old documents that
+% use it.
+%
+% \begin{table}
+% \centering
+% \begin{tabular}{||l|l|l||}
+% \hline\hline
+% A&\env{tabular}& environment\\
+% \hline
+% within&a floating&\env{table}\\
+% \hline\hline
+% \end{tabular}
+% \caption{A floating table}
+% \end{table}
+%
+% \section{Captions and Headings}
+%
+% At the start of the table one may specify lines which are to appear at
+% the top of every page (under the headline, but before the other lines
+% of the table).
+% \DescribeMacro{\endhead}
+% The lines are entered as normal, but the last "\\" command is
+% replaced by a "\endhead" command.
+% \DescribeMacro{\endfirsthead}
+% If the first page should have a different heading, then this should be
+% entered in the same way, and terminated with the "\endfirsthead"
+% command. The "LTchunksize" should be at least as large as the
+% number of rows in the heading.
+% \DescribeMacro{\endfoot}
+% There are also "\endfoot" and "\endlastfoot"
+%\DescribeMacro{\endlastfoot}
+% commands which are used in the same way (at the \emph{start} of the
+% table) to specify rows (or an "\hline") to appear at the bottom of
+% each page. In certain situations, you may want to place lines which
+% logically belong in the table body at the end of the \env{firsthead},
+% or the beginning of the \env{lastfoot}. This helps to control which
+% lines appear on the first and last page of the table.
+%
+% \DescribeMacro{\caption}%
+% The "\caption{...}" command is essentially equivalent to\\
+% "\multicolumn{n}{c}{\parbox{\LTcapwidth}{...}}"\\
+% where \texttt{n} is the number of columns of the table. You may set
+% the width of the caption with a command such as
+% "\setlength{\LTcapwidth}{2in}"
+% in the preamble of your document. The default is 4in. "\caption" also
+% writes the information to produce an entry in the list of tables. As
+% with the "\caption" command in the \env{figure} and \env{table}
+% environments, an optional argument specifies the text to appear in the
+% list of tables if this is different from the text to appear in the
+% caption. Thus the caption for table \ref{long} was specified as
+% {\ttfamily
+%  "\caption"[An optional table caption
+%             (used in the list of tables)]\v{A long
+%  table"\label{long}"\v}}.
+%
+% You may wish the caption on later pages to be different to that on the
+% first page. In this case put the "\caption" command in the first
+% heading, and put a subsidiary caption in a "\caption[]" command in
+% the main heading. If the optional argument to "\caption" is empty,
+% no entry is made in the list of tables. Alternatively, if you do not
+% want the table number to be printed each time, use the "\caption*"
+% command.
+%
+% The captions are set based on the code for the \package{article}
+% class.
+% If you have redefined the standard "\@makecaption" command to produce
+% a different format for the captions, you may
+% need to make similar changes to the \package{longtable} version,
+% "\LT@makecaption". See the code section for more details.
+%
+% A more convenient method of customising captions is given by the
+% \package{caption(2)} package, which provides commands for customising
+% captions, and arranges that the captions in standard environments, and
+% many environments provided by packages (including \package{longtable})
+% are modified in a compatible manner.
+%
+% You may use the "\label" command so that you can cross reference
+% \env{longtable}s with "\ref". Note however, that the "\label" command
+% should not be used in a heading that may appear more than once. Place
+% it either in the \env{firsthead}, or in the body of the table. It
+% should not be the \emph{first} command in any entry.
+%
+% \section{Multicolumn entries}
+%
+% The "\multicolumn" command may be used in \env{longtable} in exactly
+% the same way as for \env{tabular}. So you may want to skip this
+% section, which is rather technical, however coping with "\multicolumn"
+% is one of the main problems for an environment such as
+% \env{longtable}. The main effect that a user will see is that
+% certain combinations of "\multicolumn" entries will result in a
+% document needing more runs of \LaTeX\ before the various `chunks' of
+% a table align.
+%
+% The examples in this section are set with "LTchunksize" set to the
+% minimum value of one, to demonstrate the effects when "\multicolumn"
+% entries occur in different chunks.
+%
+% \begin{table}[!htp]
+% \begin{center}
+% \LTchunksize=1
+%  \makeatletter
+%
+%  \global\let\LT@save@row\relax
+%  \let\LT@warn\@gobble
+%  \let\LT@final@warn\relax
+%
+%  \newcommand\ltexample[1]{
+%  \stepcounter{LT@tables}
+%  \expandafter\let\csname LT@\romannumeral\c@LT@tables\endcsname
+%                   \LT@save@row
+%  \addtocounter{LT@tables}{-1}
+%  \begin{longtable}{|c|c|c|}
+%  \caption{A difficult {\cs{multicolumn}} combination:
+%                                pass #1\label{pass#1}}\\
+%    \hline
+%    1&2&3\\
+%    \multicolumn{3}{|c|}{wide multicolumn spanning 1--3}\\
+%    \multicolumn{2}{|c|}{multicolumn 1--2}&3\\
+%    wide 1&2&3\\
+%    \hline
+% \end{longtable}
+% }
+%
+% \ltexample{1}
+%
+% \ltexample{2}
+%
+% \ltexample{3}
+%
+% \ltexample{4}
+%
+% \end{center}
+% \end{table}
+%
+% Consider Table~\ref{pass1}.
+% In the second chunk, \env{longtable}  sees the wide
+% multicolumn entry.  At this point it thinks that the first two
+% columns are very narrow. All
+% the width of the multicolumn entry is assumed to be in the
+% third column. (This is a `feature' of \TeX's primitive "\halign"
+% command.) \env{longtable} then passes the information that there
+% is a wide third column to the later chunks, with the result that the
+% first pass over the table is too wide.
+%
+% If the `saved row' from this first pass was re-inserted into the
+% table on the next pass, the table would line up in two passes, but
+% would be much two wide.
+%
+% \DescribeMacro{\kill}%
+% The solution to this problem used in Versions 1~and~2, was to use a
+% "\kill" line. If a line is "\kill"ed, by using "\kill" rather than
+% "\\" at the end of the line, it is used in calculating
+% column widths, but removed from the final table. Thus entering
+% "\kill"ed copies of the last two rows before the wide multicolumn
+% entry would  mean that "\halign" `saw' the wide entries in the first
+% two columns, and so would not widen the third column by so much to
+% make room for the multicolumn entry.
+%
+% In Version~3, a new solution was introduced. If the saved row in
+% the ".aux" file was not being used, \env{longtable} used a special
+% `draft' form of "\multicolumn", this modified the definition, so the
+% spanning entry was never considered to be wider than the columns it
+% spanned. So after the first pass, the ".aux" file stored the
+% widest normal entry for each column, no column was widened due to
+% "\span"ned columns. By default \env{longtable} ignored the ".aux"
+% file, and so each run of \LaTeX\ was considered a first pass. Once the
+% "\setlongtables" declaration was given, the saved row in the ".aux"
+% file, and the proper definition of "\multicolumn" were used. If any
+% "\multicolumn" entry caused one of the columns to be widened, this
+% information could not be passed back to earlier chunks, and so the
+% table would not correctly line up until the third pass. This algorithm
+% always converged in three passes as described above, but in examples
+% such as the ones in Tables \ref{pass1}--\ref{pass4}, the final
+% widths were not optimal as the width of column~2, which is
+% determined by a "\multicolumn" entry was not known when the final
+% width for column~3 was fixed, due to the fact that \emph{both}
+% "\multicolumn" commands were switched from `draft' mode to `normal'
+% mode at the same time.
+%
+% Version~4 alleviates the problem considerably.
+% The first pass of the table will
+% indeed have the third column much too wide. However, on the next pass
+% \env{longtable} will notice the error and reduce the column width
+% accordingly. If this has to propagate to chunks before the
+% "\multicolumn" one, an additional pass will, of course, be
+% needed. It is possible to construct tables where this rippling up of
+% the correct widths takes several passes to `converge' and produce a
+% table with all chunks aligned. However in
+% order to need many passes one needs to construct a table with
+% many overlapping "\multicolumn" entries, all being wider than the
+% natural widths of the columns they span, and all occurring in
+% different chunks. In the typical case the algorithm will converge
+% after three or four passes, and, the benefits of not needing to edit
+% the document before the final run to add "\setlongtables", and the
+% better choice of final column widths in the case of multiple
+% "\multicolumn" entries  will hopefully more than pay for the extra
+% passes that may possibly be needed.
+%
+% So Table~\ref{pass1} converges after 4~passes, as seen in
+% Table~\ref{pass4}.
+%
+% You can still speed the convergence by introducing judicious "\kill"
+% lines, if you happen to have constellations like the above.
+%
+% If you object even to \LaTeX-ing a file twice, you should
+% make the first line of
+% every \env{longtable} a "\kill" line that contains the widest entry
+% to be used in each column. All chunks will then line up on the first
+% pass.
+%
+% \section{Adjustment}
+%
+% The optional argument of \env{longtable} controls the
+% horizontal alignment of the table. The possible options are "[c]",
+% "[r]" and "[l]", for  centring,
+% right  and left adjustment, respectively.
+% \DescribeMacro{\LTleft}
+% Normally centring is the default, but this document specifies
+% \DescribeMacro{\LTright}
+%\begin{verbatim}
+% \setlength\LTleft\parindent
+% \setlength\LTright\fill
+%\end{verbatim}
+% in the preamble,
+%  which means that the tables are set flush left, but
+% indented by the usual paragraph indentation. Any lengths can be
+% specified for these two parameters, but at least one of them should be
+% a rubber length so that it fills up the width of the page, unless
+% rubber lengths are added between the columns using the
+% "\extracolsep" command.
+% For instance
+%\begin{verbatim}
+%  \begin{tabular*}{\textwidth}{@{\extracolsep{...}}...}
+%\end{verbatim}
+% produces a full width table, to get a similar effect with
+% \env{longtable} specify
+%\begin{verbatim}
+% \setlength\LTleft{0pt}
+% \setlength\LTright{0pt}
+% \begin{longtable}{@{\extracolsep{...}}...}
+%\end{verbatim}
+%
+% \section{Changes}
+%
+% This section highlights the major changes since version~2. A more
+% detailed change log may be produced at the end of the code listing
+% if the "ltxdoc.cfg" file specifies
+%\begin{verbatim}
+%  \AtBeginDocument{\RecordChanges}
+%  \AtEndDocument{\PrintChanges}
+%\end{verbatim}
+%
+% Changes made between versions 2 and 3.
+% \begin{itemize}
+% \item The mechanism for adding the head and foot of the table has been
+% completely rewritten. With this new mechanism, \env{longtable} does
+% not need to issue a "\clearpage" at the start of the table, and so the
+% table may start half way down a page. Also the "\endlastfoot" command
+% which could not safely be implemented under the old scheme, has been
+% added.
+% \item \env{longtable} now issues an error if started in the scope of
+% "\twocolumn", or the \env{multicols} environment.
+% \item The separate documentation file "longtable.tex" has been
+% merged with the package file, "longtable.dtx" using Mittelbach's
+% \package{doc} package.
+% \item Support for footnotes has been added. Note however that
+% "\footnote" will not work in the `head' or `foot' sections of the
+% table. In order to put a footnote in those sections (e.g., inside a
+% caption), use "\footnotemark" at that point, and "\footnotetext"
+% anywhere in the table \emph{body} that will fall on the same page.
+% \item The treatment of "\multicolumn" has changed, making
+% "\kill" lines unnecessary, at the price of sometimes requiring a
+% third pass through \LaTeX.
+% \item The "\newpage" command now works inside a \env{longtable}.
+% \end{itemize}
+%
+% Changes made between versions 3 and 4.
+% \begin{itemize}
+% \item A new algorithm is used for aligning chunks. As well as the
+% widest width in each column, \package{longtable} remembers which
+% chunk produced this maximum. This allows it to check that the
+% maximum is still achieved in later runs. As \package{longtable} can
+% now deal with columns shrinking as the file is edited, the
+% "\setlongtables" system is no longer needed and is disabled.
+%
+% \item An extra benefit of the new algorithm's ability to deal with
+% `shrinking' columns is that it can give better (narrower) column
+% widths in the case of overlapping "\multicolumn" entries in
+% different chunks than the previous algorithm produced.
+%
+% \item The `draft' multicolumn system has been removed, along with
+% related commands such as "\LTmulticolumn".
+%
+% \item The disadvantage of the new algorithm is that it can take more
+% passes. The theoretical maximum is approximately twice the length
+% of a `chain' of columns with overlapping "\multicolumn" entries,
+% although in practice it usually converges as fast as the old
+% version. (Which always converged in three passes once
+% "\setlongtables" was  activated.)
+%
+% \item "\\*" and "\nopagebreak" commands may be used to control page
+%  breaking.
+%
+% \end{itemize}
+%
+%
+% \section{Summary}
+%
+% ^^A Allow the table to stick into the left margin.
+% \setlength{\LTleft}{0pt plus 1fill minus 1fill}
+% \setlength{\LTright}{0pt}
+%
+% \begin{longtable}{@{}l@{\hspace{10pt}}p{.8\linewidth}@{}}
+% \caption[A summary of \env{longtable} commands]%
+%         {\normalsize A summary of \env{longtable} commands}\\
+% \multicolumn{2}{c}{\textbf{Parameters}}\\*
+% \hline
+% "\LTleft"&
+%     Glue to the left of the table.           \hfill("\fill")\\
+% "\LTright"&
+%     Glue to the right of the table.          \hfill("\fill")\\
+% "\LTpre"&
+%     Glue before the the table.      \hfill("\bigskipamount")\\
+% "\LTpost"&
+%     Glue after the the table.       \hfill("\bigskipamount")\\
+% "\LTcapwidth"&
+%     The width of a parbox containing the caption.\hfill(4in)\\
+% "LTchunksize"&
+%     The number of rows per chunk.                 \hfill(20)\\[5pt]
+% \multicolumn{2}{c}{\textbf{Optional
+%      arguments to} \ttfamily\v\\begin\v{longtable\v}}\\*
+% \hline
+% \it none& Position as specified by "\LTleft" and "\LTright".\\
+% "[c]"&   Centre the table.\\
+% "[l]"&   Place the table flush left.\\
+% "[r]"&   Place the table flush right.\\[5pt]
+% \pagebreak[2]
+% \multicolumn{2}{c}{\textbf{Commands
+%                     to end table rows}}\\*
+% \hline
+% "\\"&
+%     Specifies the end of a row\\
+% "\\"\oarg{dim}& Ends row, then adds vertical space
+%     (as in the \env{tabular} environment).\\
+% "\\*"&
+%     The same as "\\" but disallows a page break after the row.\\
+% "\tabularnewline"&
+%     Alternative to "\\" for use in the scope of "\raggedright" and
+%     similar commands that redefine "\\".\\
+% "\kill"&
+%     Row is `killed', but is used in calculating widths.\\
+% "\endhead"&
+%     Specifies rows to appear at the top of every page.\\
+% "\endfirsthead"&
+%     Specifies rows to appear at the top the first page.\\
+% "\endfoot"&
+%     Specifies rows to appear at the bottom of every page.\\
+% "\endlastfoot"&
+%     Specifies rows to appear at the bottom of the last page.\\[5pt]
+% \multicolumn{2}{c}{\textbf{\env{longtable} caption commands}}\\*
+% \hline
+% "\caption"\marg{caption}&
+%     Caption `Table ?: \meta{caption}', and a `\meta{caption}'
+%     entry in the list of tables.\\
+% "\caption"\oarg{lot}\marg{caption}&
+%     Caption `Table ?: \meta{caption}', and a `\meta{lot}'
+%     entry in the list of tables.\\
+% "\caption[]"\marg{caption}&
+%     Caption `Table ?: \meta{caption}',
+%     but no entry in the list of tables.\\
+% "\caption*"\marg{caption}&
+%     Caption `\meta{caption}', but no entry in the list of tables.\\[5pt]
+% \multicolumn{2}{c}{%^^A
+%        \textbf{Commands available at the start of a row}}\\*
+% \hline
+% "\pagebreak"&
+%     Force a page break.\\*
+% "\pagebreak"\oarg{val}& A `hint' between 0 and 4
+%  of the desirability  of a break.\\
+% "\nopagebreak"& Prohibit a page break.\\*
+% "\nopagebreak"\oarg{val}& A `hint' between 0 and 4 of the undesirability
+%    of a break.\\
+% "\newpage"&
+%     Force a page break.\\[5pt]
+% \multicolumn{2}{c}{\textbf{Footnote commands
+%                      available inside \env{longtable}}}\\*
+% \hline
+% "\footnote"&
+%     Footnotes, but may not be used in the table head \& foot.\\*
+% "\footnotemark"&
+%     Footnotemark, may be used in the table head \& foot.\\*
+% "\footnotetext"&
+%     Footnote text, use in the table body.\\[5pt]
+% \multicolumn{2}{c}{\textbf{Setlongtables}}\\
+% \hline
+% "\setlongtables"&  Obsolete command. Does nothing now.
+% \end{longtable}
+%
+%
+% \finalclearpage
+% \section{Verbatim highlights from Table \protect\ref{long}}
+% \label{listing}
+% \begingroup\catcode`\/=0
+% \begin{verbatim}
+% \begin{longtable}{@{*}r||p{1in}@{*}}
+% KILLED & LINE!!!! \kill
+% \caption[An optional table caption /ldots]{A long table\label{long}}\\
+% \hline\hline
+% \multicolumn{2}{@{*}c@{*}}%
+%      {This part appears at the top of the table}\\
+% \textsc{First}&\textsc{Second}\\
+% \hline\hline
+% \endfirsthead
+% \caption[]{(continued)}\\
+% \hline\hline
+% \multicolumn{2}{@{*}c@{*}}%
+%       {This part appears at the top of every other page}\\
+% \textbf{First}&\textbf{Second}\\
+% \hline\hline
+% \endhead
+% \hline
+% This goes at the&bottom.\\
+% \hline
+% \endfoot
+% \hline
+% These lines will&appear\\
+% in place of the & usual foot\\
+% at the end& of the table\\
+% \hline
+% \endlastfoot
+% \env{longtable}  columns  are specified& in the \\
+% same way as  in the \env{tabular}& environment.\\
+% /ldots
+% \multicolumn{2}{||c||}{This is a /ldots}\\
+% /ldots
+% Some lines may take/ldots&
+%     \raggedleft This last column is a ``p'' column/ldots
+%     \tabularnewline
+% /ldots
+% Lots of lines& like this.\\
+% /ldots
+% \hline
+% Lots\footnote{/ldots} of lines& like this.\\
+% Lots   of   lines& like this\footnote{/ldots}\\
+% \hline
+% Lots of lines& like this.\\
+% /ldots
+% \end{longtable}
+% \end{verbatim}
+% \endgroup
+%
+% \StopEventually{}
+%
+% \finalclearpage
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \subsection{Initial code}
+%
+% Before declaring the package options, we must define some defaults
+% here.
+%
+%  \begin{macro}{\LT@err}
+% The error generating command
+%    \begin{macrocode}
+\def\LT@err{\PackageError{longtable}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\LT@warn}
+% The warning generating command
+%    \begin{macrocode}
+\def\LT@warn{\PackageWarning{longtable}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\LT@final@warn}
+% \changes{v4.04}{1996/05/24}
+%      {Macro added}
+% If any \env{longtable}s have not aligned, generate a warning at the
+% end of the run at "\AtEndDocument".
+%    \begin{macrocode}
+\def\LT@final@warn{%
+  \AtEndDocument{%
+    \LT@warn{Table \@width s have changed. Rerun LaTeX.\@gobbletwo}}%
+  \global\let\LT@final@warn\relax}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \subsection{Options}
+%
+% The first two options deal with error handling. They are compatible
+% with the options used by the \texttt{tracefnt} package.
+%
+%  \begin{macro}{errorshow}
+% \emph{Only} show errors on the terminal. `warnings' are just sent to
+% the log file.
+% \changes{v3.14}{1995/04/25}
+%      {Change string from LT to longtable}
+%    \begin{macrocode}
+\DeclareOption{errorshow}{%
+  \def\LT@warn{\PackageInfo{longtable}}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{pausing}
+% \changes{v3.14}{1995/04/25}
+%      {Change string from LT to longtable}
+% \changes{v3.15}{1995/06/15}
+%      {Use single hash for latex/1557}
+% Make every warning message into an error so \TeX\ stops.
+% May be useful for debugging.
+%    \begin{macrocode}
+\DeclareOption{pausing}{%
+  \def\LT@warn#1{%
+    \LT@err{#1}{This is not really an error}}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{set}
+%  \begin{macro}{final}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) make set and final options no op}
+% The next options are just alternative syntax for the
+% "\setlongtables" declaration.
+%    \begin{macrocode}
+\DeclareOption{set}{}
+\DeclareOption{final}{}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%    \begin{macrocode}
+\ProcessOptions
+%    \end{macrocode}
+%
+% \subsection{User Settable Parameters}
+%
+% \begin{macro}{\LTleft}
+% \begin{macro}{\LTright}
+% Glue to the left and right of the table, default "\fill" (ie
+% centred).
+%    \begin{macrocode}
+\newskip\LTleft       \LTleft=\fill
+\newskip\LTright      \LTright=\fill
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LTpre}
+% \begin{macro}{\LTpost}
+% Glue before and after the \env{longtable}.  "\bigskip" by default.
+%    \begin{macrocode}
+\newskip\LTpre        \LTpre=\bigskipamount
+\newskip\LTpost       \LTpost=\bigskipamount
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LTchunksize}
+% Chunk size (The number of rows taken per "\halign"). Default 20.
+%    \begin{macrocode}
+\newcount\LTchunksize \LTchunksize=20
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@LTchunksize}
+% Added in V3.07 to allow the \LaTeX\ syntax
+% "\setcounter{LTchunksize}{10}".
+%    \begin{macrocode}
+\let\c@LTchunksize\LTchunksize
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LTcapwidth}
+% Width of the "\parbox" containing the caption. Default 4in.
+%    \begin{macrocode}
+\newdimen\LTcapwidth  \LTcapwidth=4in
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Internal Parameters}
+%
+% \begin{macro}{\LT@head}
+% \begin{macro}{\LT@firsthead}
+% \begin{macro}{\LT@foot}
+% \begin{macro}{\LT@lastfoot}
+% Boxes for the table head and foot.
+%    \begin{macrocode}
+\newbox\LT@head
+\newbox\LT@firsthead
+\newbox\LT@foot
+\newbox\LT@lastfoot
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LT@cols}
+% Counter for number of columns.
+%    \begin{macrocode}
+\newcount\LT@cols
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@rows}
+% Counter for rows up to chunksize.
+%    \begin{macrocode}
+\newcount\LT@rows
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@LT@tables}
+% Counter for the tables, added in V3.02. Previous versions just used
+% the \LaTeX\ counter "table", but this fails if "table" is
+% reset during a document, eg \package{report} class resets it every
+% chapter.
+%
+% This was changed from "\newcount\LT@tables" in V3.04. \LaTeX\ counters
+% are preserved correctly when "\includeonly" is used. In the rest of
+% the file "\LT@tables" has been replaced by "\c@LT@tables" without
+% further comment.
+%    \begin{macrocode}
+\newcounter{LT@tables}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@LT@chunks}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) Chunk counter added}
+% We need to count through the chunks of our tables from Version~4 on.
+%    \begin{macrocode}
+\newcounter{LT@chunks}[LT@tables]
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@table}
+% \begin{macro}{\fnum@table}
+% \begin{macro}{\tablename}
+% If the "table" counter is not defined (eg in "letter" style), define
+% it. (Added in V3.06.)
+%    \begin{macrocode}
+\ifx\c@table\undefined
+  \newcounter{table}
+  \def\fnum@table{\tablename~\thetable}
+\fi
+\ifx\tablename\undefined
+  \def\tablename{Table}
+\fi
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LT@out}
+% In a normal style, "longtable" uses the ".aux" file to record the
+% column widths. With "letter.sty", use a separate ".lta" file.
+% (Added in V3.06.)
+%
+% Not needed for new letter class.
+%\begin{verbatim}
+%\ifx\startlabels\undefined
+%  \let\@auxout\@auxout
+%\else
+%  {\@input{\jobname.lta}}%
+%  \newwrite\@auxout
+%  \immediate\openout\@auxout=\jobname.lta
+%\fi
+%\end{verbatim}
+% \end{macro}
+%
+% \begin{macro}{\LT@p@ftn}
+% Temporary storage for footnote text in a `p' column.
+%    \begin{macrocode}
+\newtoks\LT@p@ftn
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@end@pen}
+% Special penalty for the end of the table. Done this way to save using
+% up a count register.
+%    \begin{macrocode}
+\mathchardef\LT@end@pen=30000
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The \env{longtable} environment}
+%
+% \begin{macro}{\longtable}
+% Called by "\begin{longtable}". This implementation does not work in
+% multiple column formats. "\par" added at V3.04.
+%    \begin{macrocode}
+\def\longtable{%
+  \par
+  \ifx\multicols\@undefined
+  \else
+     \ifnum\col@number>\@ne
+       \@twocolumntrue
+     \fi
+  \fi
+  \if@twocolumn
+    \LT@err{longtable not in 1-column mode}\@ehc
+  \fi
+  \begingroup
+%    \end{macrocode}
+% Check for an optional argument.
+%    \begin{macrocode}
+  \@ifnextchar[\LT@array{\LT@array[x]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@array}
+% Start setting the alignment.
+% Based on "\@array" from the \LaTeX\ kernel
+% and the \package{array} package.
+%
+% Since Version 3.02, \package{longtable} has used the internal counter
+% "\c@LT@tables". The \LaTeX\ counter "table" is still incremented
+% so that "\caption" works correctly.
+%    \begin{macrocode}
+\def\LT@array[#1]#2{%
+  \refstepcounter{table}\stepcounter{LT@tables}%
+%    \end{macrocode}
+% Set up the glue around the table if an optional argument given.
+%    \begin{macrocode}
+  \if l#1%
+    \LTleft\z@ \LTright\fill
+  \else\if r#1%
+    \LTleft\fill \LTright\z@
+  \else\if c#1%
+    \LTleft\fill \LTright\fill
+  \fi\fi\fi
+%    \end{macrocode}
+% Set up these internal commands for \env{longtable}.
+% \changes{v3.13}{1994/12/08}
+%      {add \cs{tabularnewline}}
+% \changes{v3.14}{1995/04/25}
+%      {(Mike Van Geest) rename \cs{LT@mc} to
+%         \cs{LT@mcol} to allow 1100 tables}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) don't need multicolumn warning}
+%\begin{verbatim}
+%  \global\let\LT@mcw@rn\relax
+%\end{verbatim}
+%    \begin{macrocode}
+  \let\LT@mcol\multicolumn
+%    \end{macrocode}
+% \changes{v3.17}{1996/01/31}
+%      {Reset \cs{hline} and \cs{multicolumn} in nested tabular
+%       and array, for tools/2068}
+% Now redefine "\@tabarray" to restore "\hline" and "\multicolumn" so
+% that arrays and tabulars nested in longtable (or in page headings on
+% longtable pages) work out OK. Saving the original definitions done
+% here so that you can load the \package{array} package before or after
+% \package{longtable}.
+%    \begin{macrocode}
+  \let\LT@@tabarray\@tabarray
+  \let\LT@@hl\hline
+  \def\@tabarray{%
+    \let\hline\LT@@hl
+%    \end{macrocode}
+%\begin{verbatim}
+%    \let\multicolumn\LT@mcol
+%\end{verbatim}
+%    \begin{macrocode}
+    \LT@@tabarray}%
+  \let\\\LT@tabularcr\let\tabularnewline\\%
+  \def\newpage{\noalign{\break}}%
+%    \end{macrocode}
+% \changes{v4.05}{1996/11/12}
+%      {\cs{nopagebreak} and \cs{pagebreak} added}
+% More or less standard definitions, but first start a "\noalign".
+%    \begin{macrocode}
+  \def\pagebreak{\noalign{\ifnum`}=0\fi\@testopt{\LT@no@pgbk-}4}%
+  \def\nopagebreak{\noalign{\ifnum`}=0\fi\@testopt\LT@no@pgbk4}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \let\hline\LT@hline \let\kill\LT@kill\let\caption\LT@caption
+  \@tempdima\ht\strutbox
+%    \end{macrocode}
+%
+% \changes{v4.08}{1998/01/20}
+%      {Move \cs{@endpbox} definition earlier and define \cs{@@endpbox}
+%      and \cs{@@startpbox} for non-array case. tools/2736}
+%    \begin{macrocode}
+  \let\@endpbox\LT@endpbox
+%    \end{macrocode}
+% Set up internal commands according to Lamport or Mittelbach.
+%    \begin{macrocode}
+  \ifx\extrarowheight\@undefined
+%    \end{macrocode}
+% Initialise these commands as in \env{tabular} from the \LaTeX\ kernel.
+%    \begin{macrocode}
+    \let\@acol\@tabacol
+    \let\@classz\@tabclassz \let\@classiv\@tabclassiv
+    \def\@startpbox{\vtop\LT@startpbox}%
+    \let\@@startpbox\@startpbox
+    \let\@@endpbox\@endpbox
+    \let\LT@LL@FM@cr\@tabularcr
+  \else
+%    \end{macrocode}
+% Initialise these commands as in \package{array}. "\d@llar"
+% replaced by "\d@llarbegin" "\d@llarend"  in V3.03 to match
+% \package{array} V2.0h. We do not need to set "\d@llarbegin" and
+% "\d@llarend"  as the \package{array} package gives them the correct
+% values at the top level.
+%    \begin{macrocode}
+    \advance\@tempdima\extrarowheight
+    \col@sep\tabcolsep
+    \let\@startpbox\LT@startpbox\let\LT@LL@FM@cr\@arraycr
+  \fi
+%    \end{macrocode}
+% The rest of this macro is mainly based on \package{array} package, but
+% should work for the standard \env{tabular} too.
+%    \begin{macrocode}
+  \setbox\@arstrutbox\hbox{\vrule
+    \@height \arraystretch \@tempdima
+    \@depth \arraystretch \dp \strutbox
+    \@width \z@}%
+  \let\@sharp##\let\protect\relax
+%    \end{macrocode}
+% Interpret the preamble argument.
+%    \begin{macrocode}
+   \begingroup
+    \@mkpream{#2}%
+%    \end{macrocode}
+% We need to rename "\@preamble" here as F.M.'s scheme uses
+% "\global", and we may need to nest "\@mkpream", eg for
+% "\multicolumn"
+% or an \env{array}.
+% We do not need to worry about nested \env{longtable}s though!
+%    \begin{macrocode}
+    \xdef\LT@bchunk{%
+%    \end{macrocode}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) Increment Chunk counter}
+%    \begin{macrocode}
+       \global\advance\c@LT@chunks\@ne
+       \global\LT@rows\z@\setbox\z@\vbox\bgroup
+%    \end{macrocode}
+% \changes{v4.05}{1996/11/12}
+%      {\cs{LT@setprevdepth} added}
+% The following line was added in v4.05.
+% In order to get the "\penalties" to work at chunk boundaries
+% Need to take more care about where and when "\lineskip" glue
+% is added. The following does nothing at top of table, and in
+% header chunks, but in normal body chunks it sets "\prevdepth"
+% (to 0pt, but any value would do) so that "\lineskip" glue will
+% be added. the important thing to note is that the glue will be
+% added \emph{after} any vertical material coming from "\noalign".
+%    \begin{macrocode}
+       \LT@setprevdepth
+%    \end{macrocode}
+%
+% \changes{v4.10}{2000/10/22}
+%      {\cs{noexpand} added (as in array.sty) for mathtext.sty, CAR}
+%    \begin{macrocode}
+       \tabskip\LTleft \noexpand\halign to\hsize\bgroup
+%       \tabskip\LTleft\halign to\hsize\bgroup
+      \tabskip\z@ \@arstrut \@preamble \tabskip\LTright \cr}%
+  \endgroup
+%    \end{macrocode}
+% Find out how many columns we have (store in "\LT@cols").
+%    \begin{macrocode}
+  \expandafter\LT@nofcols\LT@bchunk&\LT@nofcols
+%    \end{macrocode}
+% Get the saved row from "\LT@i"\ldots"\LT@ix" (from the
+% ".aux"  file), or make a new blank row.
+%    \begin{macrocode}
+  \LT@make@row
+%    \end{macrocode}
+% A few more internal commands for \env{longtable}.
+%    \begin{macrocode}
+  \m@th\let\par\@empty
+  \everycr{}\lineskip\z@\baselineskip\z@
+%    \end{macrocode}
+% Start the first chunk.
+%    \begin{macrocode}
+  \LT@bchunk}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@no@pgbk}
+% \changes{v4.05}{1996/11/12}
+%      {Macro added}
+% Can simplify the standard "\@no@pgbk" as this is vmode only
+% but then need to close the "\noalign".
+%    \begin{macrocode}
+\def\LT@no@pgbk#1[#2]{\penalty #1\@getpen{#2}\ifnum`{=0\fi}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@start}
+% This macro starts the process of putting the table on the current
+% page. It is not called until either a "\\" or "\endlongtable" command
+% ends a chunk, as we do not know until that point which of the four
+% possible head or foot sections have been specified.
+%
+% It begins by redefining itself, so that the table is only started
+% once! Until V3.04, was redefined to "\relax", now use "\endgraf" to
+% force the page-breaker to wake up.
+%    \begin{macrocode}
+\def\LT@start{%
+  \let\LT@start\endgraf
+  \endgraf\penalty\z@\vskip\LTpre
+%    \end{macrocode}
+% Start a new page if there is not enough room for the table head, foot,
+% and one extra line.
+%    \begin{macrocode}
+  \dimen@\pagetotal
+  \advance\dimen@ \ht\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
+  \advance\dimen@ \dp\ifvoid\LT@firsthead\LT@head\else\LT@firsthead\fi
+  \advance\dimen@ \ht\LT@foot
+%    \end{macrocode}
+% \changes{v3.16}{1995/11/09}
+%      {Measure the first line of the table}
+% At this point I used to add "\ht\@arstrutbox" and "\dp\@arstrutbox"
+% as a measure of a row size. However this can fail spectacularly
+% for "p" columns which might be much larger. Previous versions could
+% end up with the table starting with a foot, then a page break then
+% a head \emph{then} a `first head'! So now measure the first line of
+% the table accurately by "\vsplit"ting it out of the first chunk.
+%    \begin{macrocode}
+  \dimen@ii\vfuzz
+  \vfuzz\maxdimen
+    \setbox\tw@\copy\z@
+    \setbox\tw@\vsplit\tw@ to \ht\@arstrutbox
+    \setbox\tw@\vbox{\unvbox\tw@}%
+  \vfuzz\dimen@ii
+  \advance\dimen@ \ht
+        \ifdim\ht\@arstrutbox>\ht\tw@\@arstrutbox\else\tw@\fi
+  \advance\dimen@\dp
+        \ifdim\dp\@arstrutbox>\dp\tw@\@arstrutbox\else\tw@\fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \advance\dimen@ -\pagegoal
+  \ifdim \dimen@>\z@\vfil\break\fi
+%    \end{macrocode}
+% Store height of page minus table foot in  "\@colroom".
+% \changes{v3.14}{1995/05/02}
+%      {Set \cs{@colroom}, for tools/1584}
+%    \begin{macrocode}
+      \global\@colroom\@colht
+%    \end{macrocode}
+% If the foot is non empty, reduce the "\vsize" and "\@colroom"
+% accordingly.
+%    \begin{macrocode}
+  \ifvoid\LT@foot\else
+    \advance\vsize-\ht\LT@foot
+    \global\advance\@colroom-\ht\LT@foot
+    \dimen@\pagegoal\advance\dimen@-\ht\LT@foot\pagegoal\dimen@
+    \maxdepth\z@
+  \fi
+%    \end{macrocode}
+% Put the table head on the page, and then switch to the new output
+% routine.
+% \changes{v4.11}{2004/02/01}
+%      {\cs{nobreak}, for tools/3484}
+%    \begin{macrocode}
+  \ifvoid\LT@firsthead\copy\LT@head\else\box\LT@firsthead\fi\nobreak
+  \output{\LT@output}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endlongtable}
+% Called by "\end{longtable}".
+%    \begin{macrocode}
+\def\endlongtable{%
+%    \end{macrocode}
+% Essentially add a final "\\". But as we now know the number of
+% actual chunks, we first strip away all entries referring to a
+% maximum entry beyond the table (this can only happen if a table has
+% been shortened, or the table numbering has gone awry). In that case
+% we at least start collecting valid new information with the last
+% chunk of this table, by removing the width constraint.
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) use \cs{noalign} to sneak in \cs{LT@entry@chop}}
+%    \begin{macrocode}
+  \crcr
+  \noalign{%
+    \let\LT@entry\LT@entry@chop
+    \xdef\LT@save@row{\LT@save@row}}%
+  \LT@echunk
+  \LT@start
+  \unvbox\z@
+  \LT@get@widths
+%    \end{macrocode}
+% Write the dummy row to the ".aux" file.
+% Since V3.06, use ".lta" for "letter.sty".
+% \changes{v3.12}{1994/06/30}
+%      {Do not write if \cs{nofiles} in operation.}
+%    \begin{macrocode}
+  \if@filesw
+    {\let\LT@entry\LT@entry@write\immediate\write\@auxout{%
+%    \end{macrocode}
+% Since Version 3.02, \package{longtable} has used the internal counter
+% "\c@LT@tables" rather than the \LaTeX\ counter \textsf{table}. This
+% information looks entirely different from version~3
+% information. Still, we don't need to rename the macro name because
+% later code will consider the information to have no columns, and
+% thus will throw the old data away.
+%    \begin{macrocode}
+      \gdef\expandafter\noexpand
+        \csname LT@\romannumeral\c@LT@tables\endcsname
+          {\LT@save@row}}}%
+  \fi
+%    \end{macrocode}
+% At this point used to
+% issue a warning if a "\multicolumn" has been set in draft mode.
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) No need for multicolumn warnings}
+%\begin{verbatim}
+%  \LT@mcw@rn
+%\end{verbatim}
+% If the last chunk has different widths than the first, warn the user.
+% Also trigger a warning to rerun \LaTeX\ at the end of the document.
+% \changes{v4.04}{1996/05/24}
+%      {Use \cs{LT@final@warn}}
+%    \begin{macrocode}
+  \ifx\LT@save@row\LT@@save@row
+  \else
+    \LT@warn{Column \@width s have changed\MessageBreak
+             in table \thetable}%
+    \LT@final@warn
+  \fi
+%    \end{macrocode}
+% Force one more go with the \env{longtable} output routine.
+%    \begin{macrocode}
+  \endgraf\penalty -\LT@end@pen
+%    \end{macrocode}
+% Now close the group to return to the standard routine.
+%    \begin{macrocode}
+  \endgroup
+%    \end{macrocode}
+% Reset "\@mparbottom" to allow marginpars close to the end of the
+% table.\footnote{This can not be the correct. However if it is omitted,
+% there is a problem with marginpars, for example on page~3 of this
+% document. Any Output Routine Gurus out there?}
+%    \begin{macrocode}
+  \global\@mparbottom\z@
+  \pagegoal\vsize
+  \endgraf\penalty\z@\addvspace\LTpost
+%    \end{macrocode}
+% Footnotes. As done in  the \package{multicol} package.
+%    \begin{macrocode}
+  \ifvoid\footins\else\insert\footins{}\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Counting Columns}
+%
+% Columns are counted by examining "\@preamble", rather than simply
+% getting "\@mkpream" to increment the counter as it builds the
+% preamble so that this package works with many of the packages which
+% add extra column specifiers to \LaTeX's standard ones.
+%
+%  Version~1 counted "\@sharp"'s to calculate the number of columns,
+%  this was changed for Version~2 as it does not work with the NFSS. Now
+%  count "&"'s. ("lfonts.new" (and now the Standard \LaTeX\ definition)
+% defines "\@tabclassz" so that "\@sharp" is inside a group.)
+%
+% \begin{macro}{\LT@nofcols}
+% Find the next "&", then look ahead to see what is next.
+%    \begin{macrocode}
+\def\LT@nofcols#1&{%
+  \futurelet\@let@token\LT@n@fcols}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@n@fcols}
+% Add one, then stop at an "\LT@nofcols" or look for the next
+% "&". The "\expandafter" trick was added in Version~3, also the
+% name changed from "\@LT@nofcols" to preserve the "\LT@" naming
+% convention.
+%    \begin{macrocode}
+\def\LT@n@fcols{%
+  \advance\LT@cols\@ne
+  \ifx\@let@token\LT@nofcols
+    \expandafter\@gobble
+  \else
+    \expandafter\LT@nofcols
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The {\ttfamily\bslash\bslash} and \cs{kill} Commands}
+%
+% \begin{macro}{\LT@tabularcr}
+% \changes{v4.05}{1996/11/12}
+%      {Code re-organised for the *-form processing.}
+% The internal definition of "\\".
+% In the "*" form, insert a "\nobreak" after the next "\cr" (or "\crcr").
+%
+% This star form processing was finally added in v4.05. For the previous
+% six or seven years the comment at this point said
+% \begin{quote}\small
+% This definition also accepts "\\*", which acts in the same way as
+% "\\". \env{tabular} does this, but \env{longtable} probably ought to
+% make "\\*" prevent page breaking.
+% \end{quote}
+%
+% "{\ifnum0=`}\fi" added in version 3.01, required if the first entry
+% is empty.
+% The above in fact is not good enough, as with \package{array} package
+% it can introduce a "{}" group in math mode, which changes the spacing.
+% So use the following variant. Added in v3.14.
+% \changes{v3.14}{1995/04/25}
+%      {More fun with \cs{ifnum} cf tools/1571}
+%    \begin{macrocode}
+\def\LT@tabularcr{%
+  \relax\iffalse{\fi\ifnum0=`}\fi
+  \@ifstar
+    {\def\crcr{\LT@crcr\noalign{\nobreak}}\let\cr\crcr
+     \LT@t@bularcr}%
+    {\LT@t@bularcr}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@crcr}
+% \changes{v4.05}{1996/11/12}
+%      {Macro added}
+%    \begin{macrocode}
+\let\LT@crcr\crcr
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@setprevdepth}
+% \changes{v4.05}{1996/11/12}
+%      {Macro added}
+% This will be redefined to set the "\prevdepth"
+%  at the start of a chunk.
+%    \begin{macrocode}
+\let\LT@setprevdepth\relax
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@t@bularcr}
+%    \begin{macrocode}
+\def\LT@t@bularcr{%
+%    \end{macrocode}
+% Increment the counter, and do  \env{tabular}'s "\\" or finish the
+% chunk.\\ The "\expandafter" trick was added in Version~3.
+% Set the "\prevdepth" at the start of a new chunk. (Done here
+% so not set in header chunks).
+%    \begin{macrocode}
+  \global\advance\LT@rows\@ne
+  \ifnum\LT@rows=\LTchunksize
+    \gdef\LT@setprevdepth{%
+      \prevdepth\z@\global
+      \global\let\LT@setprevdepth\relax}%
+    \expandafter\LT@xtabularcr
+  \else
+    \ifnum0=`{}\fi
+    \expandafter\LT@LL@FM@cr
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@xtabularcr}
+% This just looks for an optional argument.
+%    \begin{macrocode}
+\def\LT@xtabularcr{%
+  \@ifnextchar[\LT@argtabularcr\LT@ntabularcr}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@ntabularcr}
+% The version with no optional argument.
+% "\ifnum0=`{\fi}" added in version 3.01. Changed in 3.14.
+%    \begin{macrocode}
+\def\LT@ntabularcr{%
+  \ifnum0=`{}\fi
+  \LT@echunk
+  \LT@start
+  \unvbox\z@
+  \LT@get@widths
+  \LT@bchunk}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@argtabularcr}
+% The version with an optional argument.
+% "\ifnum0=`{\fi}" added in version 3.01. Changed in 3.14.
+%    \begin{macrocode}
+\def\LT@argtabularcr[#1]{%
+  \ifnum0=`{}\fi
+  \ifdim #1>\z@
+    \unskip\@xargarraycr{#1}%
+  \else
+    \@yargarraycr{#1}%
+  \fi
+%    \end{macrocode}
+% Add the dummy row, and finish the "\halign".
+%    \begin{macrocode}
+  \LT@echunk
+  \LT@start
+  \unvbox\z@
+  \LT@get@widths
+  \LT@bchunk}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@echunk}
+% \changes{v4.05}{1996/11/12}
+%      {\cs{unskip} added for pagebreak support}
+% This ends the current chunk, and removes the dummy row.
+%    \begin{macrocode}
+\def\LT@echunk{%
+  \crcr\LT@save@row\cr\egroup
+  \global\setbox\@ne\lastbox
+%    \end{macrocode}
+% The following line was added in v4.05.
+% \package{longtable} relies on "\lineskip" glue (which is 0pt) to
+% provide break points between each row so the table may be split
+%  into pages.
+%
+% Previous releases left the "\lineskip" glue at the end of each chunk
+% that had been added when the dummy row was added. There was no glue
+% at the start of the next chunk as \TeX\ normally does not put
+% "\lineskip" glue at the top of a box. This meant that normally the
+% chunks fitted together perfectly, however "\noalign" material at a
+% chunk boundary came before the first row of the next chunk
+% but after the lineskip glue at the end of this chunk. This is the
+% wrong place, e.g., it means even a "\penalty10000" does not stop a
+% break as the "\lineskip" glue in the previous item on the list
+% provides a legal breakpoint. So now remove the "\lineskip" glue that
+% was before the dummy row and introduce "\LT@setprevdepth" to set the
+% "\prevdepth" at the start of the next chunk, to make sure "\lineskip"
+% glue is added later.
+%    \begin{macrocode}
+    \unskip
+  \egroup}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@entry}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) Macro added}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) Use \cs{ifhmode} trick to determine first entry}
+% We here give the `basic' definition of "\LT@entry", namely that used
+% in alignment templates. It has a "\kern" only if the maximum is
+% imposed from a different chunk.
+% The "\ifhmode" test reveals the first entry, when we don't want to add
+% an "&".
+%    \begin{macrocode}
+\def\LT@entry#1#2{%
+  \ifhmode\@firstofone{&}\fi\omit
+  \ifnum#1=\c@LT@chunks
+  \else
+    \kern#2\relax
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@entry@chop}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) Macro added}
+% This definition for the argument of "\LT@save@row" is used to scrap
+% all those maxima which could not be verified because they occur
+% after the end of the table. This can happen only if a table has been
+% shortened (or the sequencing got mixed up) since the
+% previous run.
+% Note that this is premature: the last chunk still is going to be
+% set, and with the chopped limits.
+%    \begin{macrocode}
+\def\LT@entry@chop#1#2{%
+  \noexpand\LT@entry
+    {\ifnum#1>\c@LT@chunks
+       1}{0pt%
+     \else
+       #1}{#2%
+     \fi}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@entry@write}
+% \changes{v4.07}{1997/10/16}
+%      {Avoid use of percent. tools/2631}
+% To write an entry for the "aux" file, we use a slightly
+% surprising definition which has the sole purpose of avoiding
+% overfull lines (which might break \TeX{}'s limits when reading the
+% "aux" file, probably you'd need to have a few hundred columns before
+% this happened but\ldots).
+%    \begin{macrocode}
+\def\LT@entry@write{%
+  \noexpand\LT@entry^^J%
+  \@spaces}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@kill}
+% This ends the current chunk as above, but strips off two rows, the
+% `dummy row' and the `killed row' before starting the next chunk.
+% Since V3.04, the old chunk is reboxed at the start of the box
+% containing the next chunk. This allows "\kill" to be used in headers,
+% which must be processed in a single box.
+%    \begin{macrocode}
+\def\LT@kill{%
+  \LT@echunk
+  \LT@get@widths
+  \expandafter\LT@rebox\LT@bchunk}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@rebox}
+% Drop the old chunk (box0) back at the top of the new chunk, removing
+% the killed row. This macro added at V3.04.
+%    \begin{macrocode}
+\def\LT@rebox#1\bgroup{%
+  #1\bgroup
+  \unvbox\z@
+  \unskip
+  \setbox\z@\lastbox}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The Dummy Row}
+%
+% The dummy row is kept inside of the macro "\LT@save@row".
+%
+% \begin{macro}{\LT@blank@row}
+% \begin{macro}{\LT@build@blank}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) Macro added}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) Don't mess with \cs{multicolumn} on draft passes}
+% Create a blank row if we are not using the info in the ".aux" file.
+%    \begin{macrocode}
+\def\LT@blank@row{%
+  \xdef\LT@save@row{\expandafter\LT@build@blank
+    \romannumeral\number\LT@cols 001 }}
+%    \end{macrocode}
+% Whoops! What's that supposed to be? A drop-in replacement for the
+% first task of Appendix~D in the \TeX book. The "\romannumeral"
+% produces "\LT@cols" instances of "m" followed by "i". The below
+% macro then replaces the "m"s by appropriate entries.
+%    \begin{macrocode}
+\def\LT@build@blank#1{%
+  \if#1m%
+    \noexpand\LT@entry{1}{0pt}%
+    \expandafter\LT@build@blank
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\LT@make@row}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) New implementation}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) Make this the default behaviour, not needing
+%      \cs{setlongtables}}
+%
+% Prior to version 4, by default did not use information in the
+% ".aux" file but now we can define "\LT@make@row" to use the ".aux"
+% file, even on the `draft' passes.
+%    \begin{macrocode}
+\def\LT@make@row{%
+  \global\expandafter\let\expandafter\LT@save@row
+    \csname LT@\romannumeral\c@LT@tables\endcsname
+  \ifx\LT@save@row\relax
+    \LT@blank@row
+%    \end{macrocode}
+% Now a slightly difficult part comes. Before we decide making the
+% template from the ".aux" file info we check that the number of
+% fields has remained the same. If it hasn't, either the table format
+% has changed, or we have the wrong table altogether. In both cases,
+% we decide to better drop all gathered information and start over.
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) Use \cs{if} test rather than \cs{ifx}\cs{@empty}}
+%
+% The expansion between "!"\ldots"!" below will be empty if the number
+% of "\LT@entry" macros
+% including arguments in "\LT@save@row" is equal to "\LT@cols". If it
+% is not empty, we throw the row away and start from scratch.
+%    \begin{macrocode}
+  \else
+    {\let\LT@entry\or
+     \if!%
+         \ifcase\expandafter\expandafter\expandafter\LT@cols
+         \expandafter\@gobble\LT@save@row
+         \or
+         \else
+           \relax
+         \fi
+        !%
+     \else
+       \aftergroup\LT@blank@row
+     \fi}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\setlongtables}
+% Redefine "\LT@make@row" to use information in the ".aux" file,
+% if there is a saved row for this table with the right number of
+% columns.
+%
+% Since Version 3.02, \package{longtable} has used the internal counter
+% "\c@LT@tables" rather than the \LaTeX\ counter \textsf{table}.
+% The warning message was added at V3.04, as was the "\global", to stop
+% save-stack overflow.
+%
+% Since Version 4.01 "\setlongtables" does nothing as it is not
+% needed, but is defined as "\relax" for the benefit of old documents.
+% \changes{v3.12}{1994/06/30}
+%      {Warning altered to fit line on terminal.}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) make into no op}
+%    \begin{macrocode}
+\let\setlongtables\relax
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@get@widths}
+% This is the heart of \package{longtable}. If it were not for the table
+% head and foot, this macro together with the modified "\\" command
+% would form the basis of quite a simple little package file for long
+% tables. It is closely modelled on the "\endvrulealign" macro of
+% appendix D of the \TeX book.
+%    \begin{macrocode}
+\def\LT@get@widths{%
+%    \end{macrocode}
+% "\global" added at V3.04, to stop save-stack overflow.
+%    \begin{macrocode}
+%    \end{macrocode}
+% Loop through the last row, discarding glue, and saving box widths. At
+% V3.04 changed the scratch box to 2, as the new "\kill" requires that
+% "\box0" be preserved.
+%    \begin{macrocode}
+  \setbox\tw@\hbox{%
+    \unhbox\@ne
+    \let\LT@old@row\LT@save@row
+    \global\let\LT@save@row\@empty
+    \count@\LT@cols
+    \loop
+      \unskip
+      \setbox\tw@\lastbox
+    \ifhbox\tw@
+      \LT@def@row
+      \advance\count@\m@ne
+    \repeat}%
+%    \end{macrocode}
+% Remember the widths if we are in the first chunk.
+%    \begin{macrocode}
+  \ifx\LT@@save@row\@undefined
+    \let\LT@@save@row\LT@save@row
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@def@row}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) New implementation}
+% Add a column to the dummy row. Name changed from "\defLT@save@row"
+% in Version~3, to preserve the "\LT@" naming convention.
+%    \begin{macrocode}
+\def\LT@def@row{%
+%    \end{macrocode}
+% We start by picking the respective entry from our old row.
+% These redefinitions of "\LT@entry" are local to the group started
+% in "\LT@get@widths".
+%    \begin{macrocode}
+  \let\LT@entry\or
+  \edef\@tempa{%
+    \ifcase\expandafter\count@\LT@old@row
+    \else
+      {1}{0pt}%
+    \fi}%
+%    \end{macrocode}
+% Now we tack the right combination in front of "\LT@save@row":
+%    \begin{macrocode}
+  \let\LT@entry\relax
+  \xdef\LT@save@row{%
+    \LT@entry
+    \expandafter\LT@max@sel\@tempa
+    \LT@save@row}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@max@sel}
+% \changes{v4.00}{1996/04/08}
+%      {(DK) macro added}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) minor modifications}
+% And this is how to select the right combination. Note that we take
+% the old maximum information only if the size does not change in
+% \emph{either} direction. If the size has grown, we of course have a
+% new maximum. If the size has shrunk, the old maximum (which was
+% explicitly not enforced because of being in the current chunk) is
+% invalid, and we start with this chunk as the new size. Note that
+% even in the case of equality we \emph{must} use the "\the\wd\tw@"
+% construct instead of "#2" because "#2" might be read in from the
+% file, and so could have "\catcode"~11 versions of "p" and~"t" in~it
+% which we want to be replaced by their `proper' "\catcode"~12 versions.
+%    \begin{macrocode}
+\def\LT@max@sel#1#2{%
+  {\ifdim#2=\wd\tw@
+     #1%
+   \else
+     \number\c@LT@chunks
+   \fi}%
+  {\the\wd\tw@}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The \cs{hline} Command}
+%
+% \begin{macro}{\LT@hline}
+% "\hline" and "\hline\hline" both produce \emph{two} lines.
+% The only difference being the glue and penalties between them.
+% This is so that a page break at a "\hline" produces a line on both
+% pages.\footnote
+% {\env{longtable} has always done this, but perhaps it would be
+% better if hlines were \emph{omitted} at a page break, as the head and
+% foot usually put a hline here anyway.}
+% Also this "\hline" is more like a "\cline{1-\LT@cols}".
+% \env{tabular}'s "\hline" would draw lines the full width of the page.
+%    \begin{macrocode}
+\def\LT@hline{%
+  \noalign{\ifnum0=`}\fi
+    \penalty\@M
+    \futurelet\@let@token\LT@@hline}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@@hline}
+% This code is based on "\cline". Two copies of the line are produced,
+% as described above.
+%    \begin{macrocode}
+\def\LT@@hline{%
+  \ifx\@let@token\hline
+    \global\let\@gtempa\@gobble
+    \gdef\LT@sep{\penalty-\@medpenalty\vskip\doublerulesep}%
+  \else
+    \global\let\@gtempa\@empty
+    \gdef\LT@sep{\penalty-\@lowpenalty\vskip-\arrayrulewidth}%
+  \fi
+  \ifnum0=`{\fi}%
+  \multispan\LT@cols
+     \unskip\leaders\hrule\@height\arrayrulewidth\hfill\cr
+  \noalign{\LT@sep}%
+  \multispan\LT@cols
+     \unskip\leaders\hrule\@height\arrayrulewidth\hfill\cr
+  \noalign{\penalty\@M}%
+  \@gtempa}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Captions}
+%
+% \begin{macro}{\LT@caption}
+% The caption is "\multicolumn{\LT@cols}{c}{"\meta{a parbox with the
+% table's caption}"}"
+%    \begin{macrocode}
+\def\LT@caption{%
+  \noalign\bgroup
+    \@ifnextchar[{\egroup\LT@c@ption\@firstofone}\LT@capti@n}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@c@ption}
+% Caption command (with [optional argument]).  "\protect" added in
+% Version~3. "\fnum@table" added at V3.05.
+% \changes{v3.14}{1995/05/02}
+%      {Call \cs{LT@makecaption} not \cs{LT@mkcaption}}
+% \changes{v3.14}{1995/05/24}
+%      {Add new control argument}
+%    \begin{macrocode}
+\def\LT@c@ption#1[#2]#3{%
+  \LT@makecaption#1\fnum@table{#3}%
+  \def\@tempa{#2}%
+  \ifx\@tempa\@empty\else
+     {\let\\\space
+     \addcontentsline{lot}{table}{\protect\numberline{\thetable}{#2}}}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@capti@n}
+% Caption command (no [optional argument])
+% \changes{v3.14}{1995/05/02}
+%      {Call \cs{LT@makecaptionx} not \cs{LT@mkcaption}}
+% \changes{v3.14}{1995/05/24}
+%      {Call \cs{LT@makecaption} with \cs{@gobble} or \cs{@firstofone}}
+%    \begin{macrocode}
+\def\LT@capti@n{%
+  \@ifstar
+    {\egroup\LT@c@ption\@gobble[]}%
+    {\egroup\@xdblarg{\LT@c@ption\@firstofone}}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\LT@makecaption}
+% Put the caption in a box of width 0pt, so that it never affects the
+% column widths. Inside that is a "\parbox" of width
+% "\LTcapwidth".
+% \changes{v3.14}{1995/05/02}
+%      {Renamed from \cs{LT@mkcaption},
+%       and modified to call \cs{@makecaption}}
+% \changes{v3.14}{1995/05/02}
+%      {Use the first arg to remove counter for star form}
+%    \begin{macrocode}
+\def\LT@makecaption#1#2#3{%
+  \LT@mcol\LT@cols c{\hbox to\z@{\hss\parbox[t]\LTcapwidth{%
+%    \end{macrocode}
+% Based on article class "\@makecaption", "#1" is "\@gobble" in star
+% form, and "\@firstofone" otherwise.
+%    \begin{macrocode}
+    \sbox\@tempboxa{#1{#2: }#3}%
+    \ifdim\wd\@tempboxa>\hsize
+      #1{#2: }#3%
+    \else
+      \hbox to\hsize{\hfil\box\@tempboxa\hfil}%
+    \fi
+    \endgraf\vskip\baselineskip}%
+  \hss}}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{The Output Routine}
+%
+% The method used here for interfacing a special purpose output routine
+% to the standard \LaTeX\ routine is lifted straight out of
+% F.~Mittelbach's \package{multicol} package.
+%
+% \begin{macro}{\LT@output}
+%     Actually this is not so bad, with FM leading the way.
+%    \begin{macrocode}
+\def\LT@output{%
+  \ifnum\outputpenalty <-\@Mi
+    \ifnum\outputpenalty > -\LT@end@pen
+%    \end{macrocode}
+%     If this was a float or a marginpar we complain.
+%    \begin{macrocode}
+      \LT@err{floats and marginpars not allowed in a longtable}\@ehc
+    \else
+%    \end{macrocode}
+% We have reached the end of the table, on the scroll at least,
+%    \begin{macrocode}
+      \setbox\z@\vbox{\unvbox\@cclv}%
+      \ifdim \ht\LT@lastfoot>\ht\LT@foot
+%    \end{macrocode}
+% The last foot might not fit, so:\footnote{An alternative would be to
+% vsplit off a bit of the last chunk, so that the last page did not just
+% have head and foot sections, but it is hard to do this in a consistent
+% manner.}
+%    \begin{macrocode}
+        \dimen@\pagegoal
+        \advance\dimen@-\ht\LT@lastfoot
+        \ifdim\dimen@<\ht\z@
+          \setbox\@cclv\vbox{\unvbox\z@\copy\LT@foot\vss}%
+          \@makecol
+          \@outputpage
+          \setbox\z@\vbox{\box\LT@head}%
+%    \end{macrocode}
+% End of "\ifdim\dimen@<\ht\@cclc".
+%    \begin{macrocode}
+        \fi
+%    \end{macrocode}
+% End of "\ifdim \ht\LT@lastfoot > \ht\LT@foot".
+%    \begin{macrocode}
+      \fi
+%    \end{macrocode}
+% Reset "\@colroom".
+% \changes{v3.14}{1995/05/02}
+%      {Reset \cs{@colroom}, for tools/1584}
+%    \begin{macrocode}
+      \global\@colroom\@colht
+      \global\vsize\@colht
+%    \end{macrocode}
+% Put the last page of the table on to the main vertical list.
+%    \begin{macrocode}
+      \vbox
+        {\unvbox\z@\box\ifvoid\LT@lastfoot\LT@foot\else\LT@lastfoot\fi}%
+%    \end{macrocode}
+% End of "\ifnum\outputpenalty > -\LT@end@pen".
+%    \begin{macrocode}
+    \fi
+%    \end{macrocode}
+% Else "\outputpenalty > -\@Mi".
+%    \begin{macrocode}
+  \else
+%    \end{macrocode}
+% If we have not reached the end of the table,
+%    \begin{macrocode}
+    \setbox\@cclv\vbox{\unvbox\@cclv\copy\LT@foot\vss}%
+    \@makecol
+    \@outputpage
+%    \end{macrocode}
+% Reset "\vsize".
+% \changes{v3.14}{1995/05/02}
+%      {Reset \cs{vsize}, for tools/1584}
+%    \begin{macrocode}
+      \global\vsize\@colroom
+%    \end{macrocode}
+% Put the head at the top of the next page.
+% \changes{v4.11}{2004/02/01}
+%      {\cs{nobreak}, for tools/3484}
+%    \begin{macrocode}
+    \copy\LT@head\nobreak
+%    \end{macrocode}
+% End of "\ifnum\outputpenalty <-\@Mi".
+%    \begin{macrocode}
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Commands for the the table head and foot}
+%
+% \begin{macro}{\LT@end@hd@ft}
+% The core of "\endhead" and friends. Store the current chunk in the
+% box specified by "#1". Issue an error if the table has already
+% started. Then start a new chunk.
+%    \begin{macrocode}
+\def\LT@end@hd@ft#1{%
+  \LT@echunk
+%    \end{macrocode}
+% Changed from "\relax" to "\endgraf" at V3.04, see "\LT@start".
+%    \begin{macrocode}
+  \ifx\LT@start\endgraf
+    \LT@err
+     {Longtable head or foot not at start of table}%
+     {Increase LTchunksize}%
+  \fi
+  \setbox#1\box\z@
+  \LT@get@widths
+  \LT@bchunk}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\endfirsthead}
+% \begin{macro}{\endhead}
+% \begin{macro}{\endfoot}
+% \begin{macro}{\endlastfoot}
+% Call "\LT@end@hd@ft" with the appropriate box.
+%    \begin{macrocode}
+\def\endfirsthead{\LT@end@hd@ft\LT@firsthead}
+\def\endhead{\LT@end@hd@ft\LT@head}
+\def\endfoot{\LT@end@hd@ft\LT@foot}
+\def\endlastfoot{\LT@end@hd@ft\LT@lastfoot}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{The \cs{multicolumn} command}
+%
+% Earlier versions needed a special `draft' form of "\multicolumn".
+% This is not needed in version~4, and so these commands have been
+% removed.
+%
+% \begin{macro}{\LTmulticolumn}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) macro removed}
+% \end{macro}
+%
+% \begin{macro}{\LT@mcwarn}
+% \changes{v4.01}{1996/04/11}
+%      {(DPC) macro removed}
+% \end{macro}
+%
+% \subsection{Footnotes}
+%
+% The standard "\footnote" command works in a "c" column, but we
+% need to modify the definition in a "p" column to overcome the
+% extra level of boxing. These macros are based on the \package{array}
+% package, but should be OK for the standard \env{tabular}.
+%
+% \begin{macro}{\LT@startpbox}
+% \changes{v4.09}{1998/05/13}
+%      {Use \cs{setlength}, so that calc extensions apply. tools/2793}
+% Add extra code to switch the definition of "\@footnotetext".
+%    \begin{macrocode}
+\def\LT@startpbox#1{%
+  \bgroup
+%    \end{macrocode}
+% \changes{v4.12}{2019/02/06}{Color group to match array package}
+%    \begin{macrocode}
+    \color@begingroup
+    \let\@footnotetext\LT@p@ftntext
+    \setlength\hsize{#1}%
+    \@arrayparboxrestore
+    \vrule \@height \ht\@arstrutbox \@width \z@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@endpbox}
+% After the parbox is closed, expand "\LT@p@ftn" which will execute a
+% series of\\
+% "\footnotetext["\meta{num}"]{"\meta{note}"}"\\
+% commands. After being lifted out of the parbox, they can migrate on
+% their own from here.
+% \changes{v3.10}{1994/05/15}
+%     {Use \cs{@finalstrut}}
+% \changes{v4.03}{1996/05/07}
+%     {Use \cs{hfil} for tools/2120}
+%    \begin{macrocode}
+\def\LT@endpbox{%
+  \@finalstrut\@arstrutbox
+%    \end{macrocode}
+% \changes{v4.12}{2019/02/06}{Color group to match array package}
+%    \begin{macrocode}
+  \color@endgroup 
+  \egroup
+  \the\LT@p@ftn
+  \global\LT@p@ftn{}%
+  \hfil}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\LT@p@ftntext}
+% Inside the `p' column, just save up the footnote text in a token
+% register.
+%    \begin{macrocode}
+\def\LT@p@ftntext#1{%
+  \edef\@tempa{\the\LT@p@ftn\noexpand\footnotetext[\the\c@footnote]}%
+  \global\LT@p@ftn\expandafter{\@tempa{#1}}}%
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+\endinput
+
diff --git a/macros/latex-dev/required/tools/longtable.ins b/macros/latex-dev/required/tools/longtable.ins
new file mode 100644
index 0000000000..1fc3c12dfa
--- /dev/null
+++ b/macros/latex-dev/required/tools/longtable.ins
@@ -0,0 +1,75 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+
+\generate{\file{longtable.sty}{\from{longtable.dtx}{package}}}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/longtable.pdf b/macros/latex-dev/required/tools/longtable.pdf
new file mode 100644
index 0000000000..87a022140c
--- /dev/null
+++ b/macros/latex-dev/required/tools/longtable.pdf
diff --git a/macros/latex-dev/required/tools/manifest.txt b/macros/latex-dev/required/tools/manifest.txt
new file mode 100644
index 0000000000..8b0f9e32d0
--- /dev/null
+++ b/macros/latex-dev/required/tools/manifest.txt
@@ -0,0 +1,111 @@
+% \iffalse meta-comment
+%
+% Copyright 1993-2016
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file. 
+% 
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+% 
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX 
+% version 2005/12/01 or later.
+% 
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+% 
+% \fi
+%
+% CONTENTS OF THE TOOLS BUNDLE
+% ============================
+
+tools-overview.tex
+        Overview of the content of the tools bundle.
+
+array.dtx
+        Extended versions of the environments array, tabular and tabular*.
+dcolumn.dtx
+        Alignment on `decimal points' in tabular entries. Requires array.
+delarray.dtx
+        Adds `large delimiters' around arrays. Requires array.
+hhline.dtx
+        Finer control over horizontal rules in tables. Requires array.
+longtable.dtx
+        Multipage tables. (Does not require array, but uses the extended
+        features if both are loaded.)  
+tabularx.dtx
+        Defines tabularx environment (similar to tabular*) but modifies
+        column widths, not inter-column space, to achieve a desired
+        table width.
+
+afterpage.dtx
+        Place text after the current page.
+
+bm.dtx
+        Access bold math symbols.
+
+calc.dtx
+        Infix arithmetic expresions. Contributed to the distribution by 
+        Kresten Krab Thorup and Frank Jensen.
+
+enumerate.dtx
+        Extended version of the enumerate environment.
+
+fileerr.dtx
+        Suite of small files which may be used to control TeX's 
+        missing file error loop.
+
+fontsmpl.dtx
+        Package and test file for producing `font samples'
+
+ftnright.dtx
+        Place footnotes in the right hand column in two-column mode.
+
+indentfirst.dtx
+        Indent the first paragraph of sections etc.
+
+layout.dtx
+        Produces an overview of the layout of the current document.
+
+multicol.dtx
+        Typeset text in columns, with the length of the final columns
+        `balanced'.
+
+rawfonts.dtx
+        Preload fonts under the old internal font names of LaTeX2.09.
+        Not recomended for new packages, but may help when updating old
+        files.
+
+shellesc.dtx
+        Unified interface for accessing system commands.
+	
+showkeys.dtx
+        Draft mode showing the `keys' used by \label, \ref, \cite etc.
+
+somedefs.dtx
+       Selective handling of package options. (Used in rawfonts.sty.)
+
+theorem.dtx
+       Flexible definition of `theorem-like' environments.
+
+trace.dtx
+      The package helps to suppress and to control the amount of tracing
+      output (\tracingall) by taming calc and making NFSS less noisy.
+
+varioref.dtx
+       `Smart' handling of page references.
+
+verbatim.dtx
+        Flexible version of verbatim environment.
+
+xr.dtx
+       eXternall References. Extend \ref to access \label commands in
+       other documents.
+
+xspace.dtx
+       Smart space command that avoids the common mistake of missing
+       spaces after command names.
diff --git a/macros/latex-dev/required/tools/multicol-2017-04-11.sty b/macros/latex-dev/required/tools/multicol-2017-04-11.sty
new file mode 100644
index 0000000000..e8558e4ce0
--- /dev/null
+++ b/macros/latex-dev/required/tools/multicol-2017-04-11.sty
@@ -0,0 +1,1042 @@
+%%
+%% This is an old release of `multicol.sty',
+%% 
+%% The source is maintained by the LaTeX Project team and bug
+%% reports for it can be opened at http://latex-project.org/bugs.html
+%% (but please observe conditions on bug reports sent to that address!)
+%% 
+%% Copyright 1993-2016
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file.
+%% 
+%% This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+%% --------------------------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% 
+%% Package `multicol' to use with LaTeX2e
+%% Copyright 1989-2016 Frank Mittelbach
+%%
+%%  In addition to the terms of LPPL any distributed version
+%%  (unchanged or modified) of multicol has to keep the statement
+%%  about the moral obligation for using multicol. In case of major
+%%  changes where this would not be appropriate the author of the
+%%  changed version should contact the copyright holder.
+%%
+%%
+%%  Moral obligation for using multicol:
+%%  ------------------------------------
+%%
+%%  Users of multicol who wish to include or use multicol or a modified
+%%  version in a proprietary and commercially market product are asked
+%%  under certain conditions (see below) for the payment of a license
+%%  fee.  The size of this fee is to be determined, in each instance,
+%%  by the commercial user, depending on his/her judgment of the value of
+%%  multicol for his/her product.
+%%
+%%
+%%  The conditions for this are as follows:
+%%
+%%   The producer of a proprietary and commercially market product
+%%   that involves typesetting using multicol is asked to determine
+%%   the value of a license fee for using multicol if
+%%
+%%   - the product is a document and the producer has decided to
+%%     include multicol to typeset (parts of) the document or has
+%%     directed the author of the document to include multicol (for
+%%     example, by providing a class file to be used by the author)
+%%
+%%   - the product is a LaTeX class or package that includes multicol
+%%
+%%
+%%   There is no moral obligation in case
+%%
+%%   - the product is a document but producer has not directed
+%%     the author to include multicol (in that case the moral obligation
+%%     lies with the author of the document)
+%%
+%%   - the product does not involve typesetting, e.g., consists, for
+%%     example, of distributing multicol and its documentation.
+%%
+%%   - the product is not proprietary, i.e., is made available as free
+%%     software itself (which doesn't prohibit its commercial marketing)
+%%
+%%   - multicol is used for non-commercial purposes
+%%
+%%
+%% Determining a license fee might result in a license fee of zero
+%% (i.e., no payment) in case a producer has determined that the use
+%% of multicol has no enhancing effect on the product. This is a
+%% plausible scenario, i.e., in the above two cases the producer is
+%% only asked to evaluate the value of multicol for the product
+%% not for the payment of a license fee per se (which might or might
+%% not follow from this evaluation).
+%%
+%% The license fee, if any, can be payed either to the LaTeX3 fund
+%% (see ltx3info.txt in the base LaTeX distribution) or to the author of
+%% the program who can be contacted at
+%%
+%%     Frank.Mittelbach@latex-project.org
+%%
+\NeedsTeXFormat{LaTeX2e}[1997/12/01]
+\ProvidesPackage{multicol}
+          [2017/04/11 v1.8q  multicolumn formatting (FMi)]
+%%
+\DeclareOption{twocolumn}
+   {\PackageWarning{multicol}{May not work
+             with the twocolumn option}}
+\newcount\c@tracingmulticols
+\DeclareOption{errorshow}
+    {\c@tracingmulticols\z@}
+\DeclareOption{infoshow}
+    {\c@tracingmulticols\@ne}
+\DeclareOption{balancingshow}
+    {\c@tracingmulticols\tw@}
+\DeclareOption{markshow}
+    {\c@tracingmulticols\thr@@}
+\DeclareOption{debugshow}
+    {\c@tracingmulticols5\relax}
+\let\mc@gridwarn\maxdimen
+\DeclareOption{grid}{\def\mc@gridwarn{\maxdepth}}
+\DeclareOption{colaction}{%
+  \def\mc@col@status@write{%
+         \protected@write\@auxout{}%
+              {\string\mc@col@status
+              {\ifmc@firstcol 1\else 2\fi}}%
+         \mc@firstcolfalse}%
+  \def\mc@lastcol@status@write{%
+         \protected@write\@auxout{}%
+              {\string\mc@col@status{3}}}%
+}
+\let\mc@col@status@write\relax
+\let\mc@lastcol@status@write\relax
+\ProcessOptions
+\def\multicols#1{\col@number#1\relax
+  \ifnum\col@number<\tw@
+     \PackageWarning{multicol}%
+      {Using `\number\col@number'
+       columns doesn't seem a good idea.^^J
+       I therefore use two columns instead}%
+     \col@number\tw@ \fi
+  \ifnum\col@number>10
+     \PackageError{multicol}%
+      {Too many columns}%
+      {Current implementation doesn't
+       support more than 10 columns.%
+       \MessageBreak
+       I therefore use 10 columns instead}%
+     \col@number10 \fi
+     \ifx\@footnotetext\mult@footnotetext\else
+       \let\orig@footnotetext\@footnotetext
+       \let\@footnotetext\mult@footnotetext
+     \fi
+  \@ifnextchar[\mult@cols{\mult@cols[]}}
+\long\def\mult@footnotetext#1{\begingroup
+         \columnwidth\textwidth
+         \orig@footnotetext{#1}\endgroup}
+\def\mult@cols[#1]{\@ifnextchar[%
+  {\mult@@cols{#1}}%
+  {\mult@@cols{#1}[\premulticols]}}
+\def\mult@@cols#1[#2]{%
+  \par
+  \ifinner \@boxedmulticolstrue
+  \else
+    \ifnum \doublecol@number>\z@
+       \@boxedmulticolstrue
+    \fi
+  \fi
+  \mult@info\z@
+      {Starting environment with
+       \the\col@number\space columns%
+        \if@boxedmulticols\MessageBreak
+           (boxed mode)\fi
+      }%
+   \enough@room{#2}%
+   #1\par\addvspace\multicolsep
+   \ifdim \prevdepth = -\@m\p@
+   \else
+     \@tempcnta\prevdepth
+     \@tempcntb\baselineskip
+     \divide\@tempcnta\@tempcntb
+     \advance\@tempcnta\@ne
+     \dimen@\prevdepth
+     \advance\dimen@ -\@tempcnta\baselineskip
+     \advance\dimen@ \topskip
+     \kern-\dimen@
+   \fi
+   \begingroup
+     \prepare@multicols
+     \if@boxedmulticols
+       \setbox\mult@box\vbox\bgroup
+                            \color@setgroup
+     \fi
+     \ignorespaces}
+\newif\if@boxedmulticols
+\@boxedmulticolsfalse
+\newbox\mult@box
+\def\enough@room#1{%
+   \if@boxedmulticols\else
+   \par
+   \bgroup\@nobreakfalse\addpenalty\z@\egroup
+   \page@free \pagegoal
+   \advance \page@free -\pagetotal
+     \@tempskipa#1\relax
+   \mult@info\z@
+       {Current page:\MessageBreak
+        height=%
+        \the\pagegoal: used \the\pagetotal
+        \space -> free=\the\page@free
+        \MessageBreak
+        needed \the\@tempskipa
+              \space(for #1)}%
+   \ifdim \page@free <#1\newpage \fi
+  \fi}
+\def\prepare@multicols{%
+  \multicol@leftmargin\@totalleftmargin
+  \@totalleftmargin\z@
+  \parshape\z@
+  \doublecol@number\col@number
+  \multiply\doublecol@number\tw@
+  \advance\doublecol@number\mult@rightbox
+  \if@boxedmulticols
+    \let\l@kept@firstmark\kept@firstmark
+    \let\l@kept@botmark\kept@botmark
+    \global\let\kept@firstmark\@empty
+    \global\let\kept@botmark\@empty
+  \else
+    \nointerlineskip {\topskip\z@\null}%
+    \output{%
+      \global\setbox\partial@page\vbox
+        {%
+         \ifvoid\partial@page\else
+           \PackageError{multicol}%
+            {Error saving partial page}%
+            {The part of the page before
+             the multicols environment was
+             nearly full with^^Jthe result
+             that starting the environment
+             will produce an overfull
+             page.  Some^^Jtext may be lost!
+             Please increase \premulticols
+             either generally or for this%
+             ^^Jenvironment by specifying a
+             suitable value in the second
+             optional argument to^^Jthe
+             multicols environment.}
+           \unvbox\partial@page
+           \box\last@line
+         \fi
+         \unvbox\@cclv
+         \global\setbox\last@line\lastbox
+        }%
+           \prep@keptmarks
+           \global\let\kept@topmark\firstmark
+          }\eject
+    \advance\@colroom-\ht\partial@page
+    \set@mult@vsize\relax
+    \output{\multi@column@out}%
+    \init@mult@footins
+    \reinsert@footnotes
+   \def\clearpage{%
+     \ifx\@deferlist\@empty\else
+       \PackageError{multicol}%
+          {Deferred floats not cleared}%
+          {A \string\clearpage\space inside multicols acts like
+           \string\newpage\space and doesn't clear floats.\MessageBreak
+           Move it before the multicols environment if you need it.}%
+     \fi
+    \newpage}%
+  \fi
+  \vbadness\@Mi \hbadness5000
+  \tolerance\multicoltolerance
+  \pretolerance\multicolpretolerance
+  \setemergencystretch\col@number\hsize
+  \set@floatcmds
+  \advance\baselineskip\multicolbaselineskip
+  \hsize\linewidth \advance\hsize\columnsep
+  \advance\hsize-\col@number\columnsep
+  \divide\hsize\col@number
+  \full@width\linewidth
+  \linewidth\hsize
+  \columnwidth\hsize
+}
+\def\init@mult@footins{%
+    \multiply\count\footins\col@number
+    \multiply\skip \footins\col@number
+}
+\def\set@mult@vsize#1{%
+    \vsize\@colroom
+    \@tempdima\baselineskip
+    \advance\@tempdima-\topskip
+    \advance\vsize\@tempdima
+    \vsize\col@number\vsize
+    \advance\vsize-\@tempdima
+    \advance\vsize\col@number\baselineskip
+    #1\advance\vsize
+        \c@collectmore\baselineskip}
+\newdimen\multicol@leftmargin
+\def\endmulticols{\par
+  \if@boxedmulticols
+    \remove@discardable@items\color@endgroup\egroup
+    \balance@columns
+    \return@nonemptymark{first}%
+                 \kept@firstmark
+    \return@nonemptymark{bot}%
+                  \kept@botmark
+    \page@sofar
+    \global\let\kept@firstmark
+               \l@kept@firstmark
+    \global\let\kept@botmark
+            \l@kept@botmark
+    \mult@info\tw@
+      {Restore kept marks to\MessageBreak
+       first: \meaning\kept@firstmark
+       \MessageBreak bot\space\space:
+                     \meaning\kept@botmark }%
+  \else
+    \ifdim\pagegoal=\maxdimen
+      \ifvoid\colbreak@box\else
+        \mult@info\@ne{Re-adding forced
+                 break(s) for splitting}%
+        \unvbox\colbreak@box\fi
+    \fi
+   \penalty\z@
+   \output{\balance@columns@out}%
+   \eject
+    \ifvbox\partial@page
+         \unvbox\partial@page\fi
+     \global\let\kept@firstmark\@empty
+     \global\let\kept@botmark\@empty
+     \mult@info\tw@
+       {Make kept marks empty}%
+  \fi
+  \@checkend{multicols}%
+  \endgroup
+  \global\c@unbalance\z@
+  \if@boxedmulticols\else
+    \reinsert@footnotes
+    \ifdim \pagegoal=\maxdimen
+      \global\vsize\@colroom
+    \else
+      \enough@room\postmulticols
+    \fi
+  \fi
+  \addvspace\multicolsep
+ \prevdepth\z@
+  \mult@info\z@
+     {Ending environment
+             \if@boxedmulticols
+                \space(boxed mode)\fi
+              }}
+\newcount\c@unbalance
+\newcount\c@collectmore
+\newcount\doublecol@number
+\newcount\multicoltolerance
+\newcount\multicolpretolerance
+\newdimen\full@width
+\newdimen\page@free
+\newdimen\premulticols
+\newdimen\postmulticols
+\newskip\multicolsep
+\newskip\multicolbaselineskip
+\newbox\partial@page
+\newbox\last@line
+\c@unbalance   = 0
+\c@collectmore = 0
+\multicoltolerance = 9999
+\multicolpretolerance = -1
+\premulticols = 50pt
+\postmulticols= 20pt
+\multicolsep = 12pt plus 4pt minus 3pt
+\multicolbaselineskip=0pt
+\def\process@cols#1#2{\count@#1\relax
+     \loop
+      #2%
+     \advance\count@\tw@
+     \ifnum\count@<\doublecol@number
+   \repeat}
+\def\page@sofar{%
+   \process@cols\mult@rightbox
+       {\ifvoid\count@
+          \setbox\count@\hbox to\hsize{}%
+        \else
+          \wd\count@\hsize
+        \fi}%
+   \count@\col@number \advance\count@\m@ne
+   \mult@info\z@
+    {Column spec: \the\full@width\space = indent
+                  + columns + sep =\MessageBreak
+        \the\multicol@leftmargin\space
+        + \the\col@number\space
+        x \the\hsize\space
+        + \the\count@\space
+        x \the\columnsep
+     }%
+\ifvmode\else\errmessage{Multicol Error}\fi
+   \nointerlineskip
+   \setbox\z@\hbox{p}\global\dimen\tw@\dp\z@
+   \moveright\multicol@leftmargin
+    \hbox to\full@width{%
+       \mc@align@columns
+       \rlap{\phantom p}%
+    }%
+   \prevdepth\z@
+ \kern-\dimen\tw@
+ \ifdim\dimen\tw@ > \mc@gridwarn
+   \PackageWarning{multicol}%
+     {Very deep columns!\MessageBreak
+      Grid alignment might be broken}%
+ \fi
+}
+\def\columnseprulecolor{\normalcolor}
+\def\reinsert@footnotes{\ifvoid\footins\else
+         \insert\footins{}\fi}
+\def\vfilmaxdepth{\vskip \z@ \@plus .0001fil
+                           \@minus \maxdepth}
+\def\multi@column@out{%
+   \ifnum\outputpenalty <-\@M
+    \speci@ls \else
+    \ifvoid\colbreak@box\else
+      \mult@info\@ne{Re-adding forced
+                break(s) for splitting}%
+      \setbox\@cclv\vbox{%
+       \unvbox\colbreak@box
+       \penalty-\@Mv
+       \unvbox\@cclv}%
+    \fi
+   \splittopskip\topskip
+   \splitmaxdepth\maxdepth
+   \boxmaxdepth\maxdepth
+   \dimen@\@colroom
+   \divide\skip\footins\col@number
+   \ifvoid\footins \else
+      \leave@mult@footins
+   \fi
+   \let\ifshr@kingsaved\ifshr@king
+   \ifvbox \@kludgeins
+     \advance \dimen@ -\ht\@kludgeins
+     \ifdim \wd\@kludgeins>\z@
+        \shr@nkingtrue
+     \fi
+   \fi
+   \process@cols\mult@gfirstbox{%
+        \setbox\count@
+            \vsplit\@cclv to\dimen@
+            \set@keptmarks
+            \setbox\count@
+                 \vbox to\dimen@
+                  {\unvbox\count@
+                   \ifshr@nking\vfilmaxdepth\fi}%
+           }%
+   \setbox\mult@rightbox
+       \vsplit\@cclv to\dimen@
+   \set@keptmarks
+   \setbox\mult@rightbox\vbox to\dimen@
+          {\unvbox\mult@rightbox
+           \ifshr@nking\vfilmaxdepth\fi}%
+   \let\ifshr@king\ifshr@kingsaved
+   \ifvoid\@cclv \else
+       \unvbox\@cclv
+       \ifnum\outputpenalty=\@M
+       \else
+          \penalty\outputpenalty
+       \fi
+       \ifvoid\footins\else
+         \PackageWarning{multicol}%
+          {I moved some lines to
+           the next page.\MessageBreak
+           Footnotes on page
+           \thepage\space might be wrong}%
+       \fi
+       \ifnum \c@tracingmulticols>\thr@@
+                    \hrule\allowbreak \fi
+   \fi
+   \ifx\@empty\kept@firstmark
+      \let\firstmark\kept@topmark
+      \let\botmark\kept@topmark
+   \else
+      \let\firstmark\kept@firstmark
+      \let\botmark\kept@botmark
+   \fi
+   \let\topmark\kept@topmark
+   \mult@info\tw@
+        {Use kept top mark:\MessageBreak
+          \meaning\kept@topmark
+         \MessageBreak
+         Use kept first mark:\MessageBreak
+          \meaning\kept@firstmark
+        \MessageBreak
+         Use kept bot mark:\MessageBreak
+          \meaning\kept@botmark
+        \MessageBreak
+         Produce first mark:\MessageBreak
+          \meaning\firstmark
+        \MessageBreak
+        Produce bot mark:\MessageBreak
+          \meaning\botmark
+         \@gobbletwo}%
+   \boxmaxdepth\maxdimen
+   \setbox\@cclv\vbox{\unvbox\partial@page
+                      \page@sofar}%
+   \@makecol\@outputpage
+     \global\let\kept@topmark\botmark
+     \global\let\kept@firstmark\@empty
+     \global\let\kept@botmark\@empty
+     \mult@info\tw@
+        {(Re)Init top mark:\MessageBreak
+         \meaning\kept@topmark
+         \@gobbletwo}%
+   \global\@colroom\@colht
+   \global \@mparbottom \z@
+   \global \@textfloatsheight \z@
+   \process@deferreds
+   \@whilesw\if@fcolmade\fi{\@outputpage
+      \global\@colroom\@colht
+      \process@deferreds}%
+   \mult@info\@ne
+     {Colroom:\MessageBreak
+      \the\@colht\space
+              after float space removed
+              = \the\@colroom \@gobble}%
+    \set@mult@vsize \global
+  \fi}
+\def\leave@mult@footins{%
+   \advance\dimen@-\skip\footins
+   \advance\dimen@-\ht\footins
+}
+\def\speci@ls{%
+ \ifnum\outputpenalty <-\@Mi
+  \ifnum \outputpenalty<-\@MM
+   \PackageError{multicol}{Document end
+           inside multicols environment}\@ehd
+   \@specialoutput
+  \else
+     \ifnum\outputpenalty = -\@Mv
+         \mult@info\@ne{Forced column
+                        break seen}%
+         \global\advance\vsize-\pagetotal
+         \global\setbox\colbreak@box
+           \vbox{%
+              \ifvoid\colbreak@box
+              \else
+                \unvbox\colbreak@box
+                \penalty-\@Mv
+              \fi
+              \boxmaxdepth\maxdepth
+              \setbox\@cclv\vbox{%
+                 \unvbox\@cclv
+                 \remove@discardable@items}%
+              \dimen@\dp\@cclv
+              \unvbox\@cclv
+              \kern-\dimen@
+         }%
+         \reinsert@footnotes
+     \else
+        \PackageWarningNoLine{multicol}%
+           {Floats and marginpars not
+            allowed inside `multicols'
+            environment!}%
+        \unvbox\@cclv\reinsert@footnotes
+       \xdef\@freelist{\@freelist\@currlist}%
+       \gdef\@currlist{}%
+     \fi
+  \fi
+ \else \@doclearpage \fi
+}
+\def\process@deferreds{%
+   \@floatplacement
+   \@tryfcolumn\@deferlist
+   \if@fcolmade\else
+     \begingroup
+    \let\@tempb\@deferlist
+      \gdef\@deferlist{}%
+      \let\@elt\@scolelt
+        \@tempb \endgroup
+   \fi}
+\newif\ifshr@nking
+\def\raggedcolumns{%
+   \@bsphack\shr@nkingtrue\@esphack}
+\def\flushcolumns{%
+   \@bsphack\shr@nkingfalse\@esphack}
+\def\balance@columns@out{%
+   \setbox\mult@box\vbox{%
+       \ifvoid\colbreak@box\else
+         \unvbox\colbreak@box
+         \penalty-\@Mv
+         \mult@info\@ne{Re-adding
+           forced break(s) in balancing}%
+       \fi
+       \unvbox\@cclv
+       \remove@discardable@items
+   }%
+   \balance@columns
+   \iftoo@bad
+     \mult@info\@ne
+        {Balancing failed ...
+         cut a normal page}%
+     \setbox\@cclv\vbox
+         {\vskip\topskip
+          \vskip-\splittopskip
+          \unvbox\mult@box}%
+     \multi@column@out
+   \else
+     \global\vsize\@colroom
+     \global\advance\vsize\ht\partial@page
+     \ifvbox\@kludgeins\insert\@kludgeins
+                        {\unvbox\@kludgeins}\fi
+     \unvbox\partial@page
+     \return@nonemptymark{first}\kept@firstmark
+     \return@nonemptymark{bot}\kept@botmark
+     \page@sofar
+     \penalty\z@
+  \fi
+}
+\def\balance@columns{%
+   \get@keptmarks\mult@box
+   \setbox\mult@box\vbox{%
+        \penalty-\@M
+        \unvbox\mult@box
+        }%
+   \@tempdima\topskip
+   \splittopskip\@tempdima
+       \@plus\multicolundershoot
+       \@minus\multicolovershoot
+   \splitmaxdepth\maxdepth
+   \boxmaxdepth\maxdepth
+   \setbox\@tempboxa\vsplit\mult@box to\z@
+   \@tempdima\ht\mult@box
+   \advance\@tempdima\dp\mult@box
+   \divide\@tempdima\col@number
+   \count@\@tempdima
+   \divide\count@\baselineskip
+   \dimen@\count@\baselineskip
+   \advance\dimen@\topskip
+   \ifdim \dimen@ >\@tempdima
+     \advance\dimen@-\baselineskip
+   \fi
+   \advance\dimen@\c@unbalance\baselineskip
+   \mult@info\@ne
+      {Balance columns\on@line:
+        \ifnum\c@unbalance=\z@\else
+       (off balance=\number\c@unbalance)\fi
+      \@gobbletwo}%
+   \ifnum\dimen@<\topskip
+     \mult@info\@ne
+       {Start value
+          \the\dimen@  \space ->
+          \the\topskip \space (corrected)}%
+     \dimen@\topskip
+   \fi
+   \vbadness\@M
+   \vfuzz \maxdimen
+   \last@try-\p@
+   \loop
+    {\process@cols\mult@grightbox
+           {\global\setbox\count@
+                   \box\voidb@x}}%
+    \global\setbox\mult@grightbox
+           \copy\mult@box
+   \too@badfalse
+   \forcedbreak@leftoverfalse
+   {\process@cols\mult@firstbox{%
+         \global\setbox\count@
+         \vsplit\mult@grightbox to\dimen@
+         \global\setbox\count@
+                 \vbox to\dimen@
+                  {\unvbox\count@}%
+         \ifnum\c@tracingmulticols>\@ne
+           \@tempcnta\count@
+           \advance\@tempcnta-\mult@grightbox
+           \divide\@tempcnta \tw@
+           \message{^^JColumn
+              \number\@tempcnta\space
+               badness: \the\badness\space}%
+         \fi
+         \ifnum\badness>\c@columnbadness
+           \ifnum\c@tracingmulticols>\@ne
+             \message{too bad
+                  (>\the\c@columnbadness)}%
+           \fi
+           \too@badtrue
+         \fi
+                        }}%
+   \global\setbox\mult@grightbox
+      \vbox{\unvbox\mult@grightbox}%
+   \setbox\mult@nat@firstbox
+      \vbox{\unvcopy\mult@firstbox}%
+    \ifnum\c@tracingmulticols>\@ne
+       \message{^^JFirst column
+           = \the\dimen@\space
+           (\the\ht\mult@nat@firstbox)}\fi
+    \ifnum\c@tracingmulticols>\@ne
+      \message{<> last column =
+               \the\ht\mult@grightbox^^J}%
+     \fi
+    \ifdim\ht\mult@grightbox >\dimen@
+      \too@badtrue
+      \ifnum\c@tracingmulticols>\@ne
+         \typeout{Rejected: last
+                 column too large!}%
+      \fi
+    \else
+      \setbox\@tempboxa
+           \copy\mult@grightbox
+      \setbox\z@\vsplit\@tempboxa to\maxdimen
+      \ifvoid\@tempboxa
+        \global\setbox\mult@grightbox
+           \vbox to\dimen@
+              {\unvbox\mult@grightbox}%
+        \ifnum\c@tracingmulticols>\@ne
+          \message{Final badness:
+                   \the\badness}%
+        \fi
+        \ifnum\badness>\c@finalcolumnbadness
+          \global\setbox\mult@grightbox
+           \vbox to\dimen@
+              {\unvbox\mult@grightbox\vfil}%
+           \ifnum\c@tracingmulticols>\@ne
+             \message{ setting natural
+              (> \the\c@finalcolumnbadness)}%
+           \fi
+        \fi
+      \else
+       \@tempdima\@colroom
+       \advance\@tempdima \maxbalancingoverflow
+       \ifdim \dimen@ < \@tempdima
+        \too@badtrue
+         \ifnum\c@tracingmulticols>\@ne
+           \typeout{Rejected: unprocessed
+             forced break(s) in last column!}%
+         \fi
+       \else
+         \forcedbreak@leftovertrue
+         \ifnum\c@tracingmulticols>\@ne
+          \typeout{Failed: columns too large
+            with unprocessed forced break(s)!}%
+         \fi
+       \fi
+      \fi
+    \fi
+    \ifdim\ht\mult@nat@firstbox<\dimen@
+      \ifdim\ht\mult@nat@firstbox>\last@try
+        \too@badtrue
+        \ifnum\c@tracingmulticols>\@ne
+           \typeout{Retry: using natural
+                    height of first column!}%
+        \fi
+        \dimen@\ht\mult@nat@firstbox
+        \last@try\dimen@
+        \advance\dimen@-\p@
+      \fi
+    \fi
+    \iftoo@bad
+      \advance\dimen@\p@
+    \repeat
+    \ifforcedbreak@leftover
+       \too@badtrue
+    \else
+     \if@boxedmulticols\else
+       \ifdim\dimen@>\@colroom
+         \dimen@\@colroom
+       \fi
+     \fi
+     \process@cols\mult@rightbox
+         {\@tempcnta\count@
+          \advance\@tempcnta\@ne
+          \vfuzz\z@
+          \setbox\count@\vbox to\dimen@
+             {%
+              \vskip \z@
+                \@plus-\multicolundershoot
+                \@minus-\multicolovershoot
+              \unvbox\@tempcnta
+              \ifshr@nking\vfilmaxdepth\fi
+             }%
+          \ifnum\badness>\@M
+            \vfuzz\maxdimen % no overfull warning
+            \setbox\@tempboxa \vbox to\dimen@
+                 {\vskip-\maxbalancingoverflow
+                  \unvcopy\count@}%
+            \ifnum\badness>\@M
+              \mult@info\@ne
+                {Balanced column more than
+                  \the\maxbalancingoverflow\space
+                  too large}%
+              \too@badtrue
+            \else
+              \mult@info\@ne
+                {Balanced column
+                 too large, but less than
+                 \the\maxbalancingoverflow}%
+            \fi
+          \fi
+         }%
+   \fi
+}
+\newdimen\maxbalancingoverflow
+\maxbalancingoverflow=12pt
+
+\newbox\mult@rightbox
+\newbox\mult@grightbox
+\newbox\mult@gfirstbox
+\newbox\mult@firstbox
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa
+\let\@tempa\relax
+\@ifundefined{emergencystretch}
+     {\newdimen\emergencystretch}{}
+\def\setemergencystretch#1#2{%
+   \emergencystretch 4pt
+   \multiply\emergencystretch#1}
+
+\def\set@floatcmds{%
+ \let\@dblfloat\@dbflt
+ \def\end@dblfloat{\@endfloatbox
+   \@largefloatcheck
+   \outer@nobreak
+   \ifnum\@floatpenalty<\z@
+     \@cons\@deferlist\@currbox
+   \fi
+   \ifnum\@floatpenalty=-\@Mii
+     \@Esphack
+   \fi}}
+\def\kept@topmark{{}{}}
+\let\kept@firstmark\@empty
+\let\kept@botmark\@empty
+\def\return@nonemptymark#1#2{%
+  \ifx#2\@empty
+  \else
+    \mult@info\tw@
+      {Returned #1 mark:\MessageBreak
+       \meaning#2}%
+    \toks@\expandafter{#2}%
+    \mark{\the\toks@}%
+    \nobreak
+  \fi}
+\def\get@keptmarks#1{%
+  \begingroup
+   \vbadness\@M
+   \setbox#1\copy#1%
+   \setbox#1\vsplit#1to\maxdimen
+   \set@keptmarks
+ \endgroup
+}
+\def\set@keptmarks{%
+   \ifx\kept@firstmark\@empty
+     \expandafter\gdef\expandafter
+        \kept@firstmark
+        \expandafter{\splitfirstmark}%
+     \ifx\kept@firstmark\@empty\else
+       \mult@info\tw@
+         {Set kept first mark:\MessageBreak
+          \meaning\kept@firstmark%
+          \@gobbletwo}%
+     \fi
+   \fi
+   \expandafter\def\expandafter\@tempa
+      \expandafter{\splitbotmark}%
+   \ifx\@tempa\@empty\else
+      \global\let\kept@botmark\@tempa
+      \mult@info\tw@
+        {Set kept bot mark:\MessageBreak
+         \meaning\kept@botmark%
+         \@gobbletwo}%
+   \fi}%
+\def\prep@keptmarks{%
+   \if@boxedmulticols \else
+     \get@keptmarks\partial@page
+   \fi}
+\skip0=0pt
+\edef\the@zero@skip{\the\skip0}
+\def\remove@discardable@items{%
+     \unpenalty
+     \edef\@tempa{\the\lastskip}%
+     \unskip
+     \ifx\@tempa\the@zero@skip
+       \edef\@tempb{\the\lastskip}%
+       \ifx\@tempb\the@zero@skip
+       \else
+         \unskip
+         \ifnum \lastpenalty=\@M
+           \vskip\@tempb\vskip\@tempa\relax
+         \else
+           \remove@discardable@items
+         \fi
+       \fi
+     \else
+       \remove@discardable@items
+     \fi
+}
+\newif\iftoo@bad
+\def\too@badtrue{\global\let\iftoo@bad\iftrue}
+\def\too@badfalse{\global\let\iftoo@bad\iffalse}
+\newif\ifforcedbreak@leftover
+\newcount\c@columnbadness
+\c@columnbadness=10000
+\newcount\c@finalcolumnbadness
+\c@finalcolumnbadness=9999
+
+\newdimen\last@try
+
+\newdimen\multicolovershoot
+\newdimen\multicolundershoot
+\multicolovershoot=0pt
+\multicolundershoot=2pt
+\newbox\mult@nat@firstbox
+\def\mult@info#1#2{%
+  \ifnum\c@tracingmulticols>#1%
+   \GenericWarning
+       {(multicol)\@spaces\@spaces}%
+       {Package multicol: #2}%
+  \fi
+}
+ \@namedef{multicols*}{%
+   \ifinner
+     \PackageWarning{multicol}%
+       {multicols* inside a box does
+        not make sense.\MessageBreak
+        Going to balance anyway}%
+   \else
+     \let\balance@columns@out
+         \multi@column@out
+   \fi
+   \begin{multicols}
+}
+\@namedef{endmulticols*}{%
+   \par
+   \ifdim\lastskip>\z@ \vskip-\lastskip \fi
+   \ifdim \prevdepth>\z@
+     \vskip-\ifdim\prevdepth>\boxmaxdepth
+                  \boxmaxdepth
+            \else \prevdepth \fi
+   \fi
+   \ifshr@nking\else
+     \vfil
+   \fi
+   \end{multicols}}
+\mathchardef\@Mv=10005
+\def\columnbreak{%
+ \ifnum\col@number<\tw@
+  \PackageError{multicol}%
+   {\noexpand\columnbreak outside multicols}%
+   {This command can only be used within
+    a multicols or multicols* environment.}%
+ \else
+  \ifvmode
+    \penalty -\@Mv\relax
+  \else
+    \@bsphack
+    \vadjust{\penalty -\@Mv\relax}%
+    \@esphack
+  \fi
+ \fi}
+\newbox\colbreak@box
+\def\LR@column@boxes{%
+     \process@cols\mult@gfirstbox{%
+       \ifdim\dp\count@>\dimen\tw@
+         \global\dimen\tw@\dp\count@ \fi
+       \mc@col@status@write
+       \box\count@
+       \hss{\columnseprulecolor\vrule
+              \@width\columnseprule}\hss}%
+     \ifdim\dp\mult@rightbox>\dimen\tw@
+       \global\dimen\tw@\dp\mult@rightbox \fi
+     \mc@lastcol@status@write
+     \box\mult@rightbox
+}
+
+\def\RL@column@boxes{%
+     \process@cols\mult@gfirstbox{%
+       \hskip\hsize
+       \hss{\columnseprulecolor\vrule
+              \@width\columnseprule}\hss
+     }%
+     \hskip\hsize
+     \process@cols\mult@gfirstbox{%
+       \ifdim\dp\count@>\dimen\tw@
+         \global\dimen\tw@\dp\count@ \fi
+       \hskip-\hsize
+       \mc@col@status@write
+       \box\count@
+       \hskip-\hsize
+       \hskip-\columnsep
+     }%
+     \ifdim\dp\mult@rightbox>\dimen\tw@
+       \global\dimen\tw@\dp\mult@rightbox \fi
+     \hskip-\hsize
+     \mc@lastcol@status@write
+     \box\mult@rightbox
+     \hskip-\hsize
+     \hskip\full@width
+ }
+\newcommand\RLmulticolcolumns
+    {\let\mc@align@columns
+         \RL@column@boxes}
+\newcommand\LRmulticolcolumns
+    {\let\mc@align@columns
+      \LR@column@boxes}
+\LRmulticolcolumns
+\newcount\mc@col@check@num
+
+\newcommand\docolaction[4][1]{%
+ \ifx\mc@col@status@write\relax
+     \PackageError{multicol}%
+      {Option 'colaction' not selected}%
+      {\string\docolaction\space
+       requires the use of the 'colaction'
+       option on the package}%
+ \fi
+ \global\advance\mc@col@check@num\@ne
+ \edef\mc@col@type{\expandafter\ifx
+   \csname mc@col-\the\mc@col@check@num
+   \endcsname\relax
+                   0\else
+   \csname mc@col-\the\mc@col@check@num
+   \endcsname
+                    \fi}%
+ \ifcase \mc@col@type\relax
+     \ifcase #1\or #2\or#3\or#4\fi
+  \or
+     #2%  % 1 First col
+  \or
+     #3%  % 2 any middle col
+  \or
+     #4%  % 3 last col
+  \else
+    \ERROR
+  \fi
+  \edef\next{\write\@auxout
+     {\string\mc@set@col@status
+      {mc@col-\the\mc@col@check@num}%
+      {\mc@col@type}}}%
+  \next
+}
+\def\mc@col@status#1{%
+    \gdef\mc@curr@col@status{#1}}
+\def\mc@set@col@status#1#2{%
+  \global\expandafter\let\csname #1\endcsname
+                         \mc@curr@col@status}
+\AtEndDocument{\def\mc@set@col@status#1#2{%
+     \ifnum #2=\mc@curr@col@status\else
+       \@tempswatrue
+     \fi}%
+}
+\newif\ifmc@firstcol
+\mc@firstcoltrue
+\endinput
+%%
+%% End of file `multicol.sty'.
diff --git a/macros/latex-dev/required/tools/multicol.dtx b/macros/latex-dev/required/tools/multicol.dtx
new file mode 100644
index 0000000000..d68f471fcd
--- /dev/null
+++ b/macros/latex-dev/required/tools/multicol.dtx
@@ -0,0 +1,4450 @@
+% \iffalse meta-comment
+%
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%
+% \iffalse    This is a METACOMMENT
+%
+%% Package `multicol' to use with LaTeX2e
+%% Copyright 1989-2019 Frank Mittelbach
+%%
+%%  In addition to the terms of LPPL any distributed version
+%%  (unchanged or modified) of multicol has to keep the statement
+%%  about the moral obligation for using multicol. In case of major
+%%  changes where this would not be appropriate the author of the
+%%  changed version should contact the copyright holder.
+%%
+%%
+%%  Moral obligation for using multicol:
+%%  ------------------------------------
+%%
+%%  Users of multicol who wish to include or use multicol or a modified
+%%  version in a proprietary and commercially market product are asked
+%%  under certain conditions (see below) for the payment of a license
+%%  fee.  The size of this fee is to be determined, in each instance,
+%%  by the commercial user, depending on his/her judgment of the value of
+%%  multicol for his/her product.
+%%
+%%
+%%  The conditions for this are as follows:
+%%
+%%   The producer of a proprietary and commercially market product
+%%   that involves typesetting using multicol is asked to determine
+%%   the value of a license fee for using multicol if
+%%
+%%   - the product is a document and the producer has decided to
+%%     include multicol to typeset (parts of) the document or has
+%%     directed the author of the document to include multicol (for
+%%     example, by providing a class file to be used by the author)
+%%
+%%   - the product is a LaTeX class or package that includes multicol
+%%
+%%
+%%   There is no moral obligation in case
+%%
+%%   - the product is a document but producer has not directed
+%%     the author to include multicol (in that case the moral obligation
+%%     lies with the author of the document)
+%%
+%%   - the product does not involve typesetting, e.g., consists, for
+%%     example, of distributing multicol and its documentation.
+%%
+%%   - the product is not proprietary, i.e., is made available as free
+%%     software itself (which doesn't prohibit its commercial marketing)
+%%
+%%   - multicol is used for non-commercial purposes
+%%
+%%
+%% Determining a license fee might result in a license fee of zero
+%% (i.e., no payment) in case a producer has determined that the use
+%% of multicol has no enhancing effect on the product. This is a
+%% plausible scenario, i.e., in the above two cases the producer is
+%% only asked to evaluate the value of multicol for the product
+%% not for the payment of a license fee per se (which might or might
+%% not follow from this evaluation).
+%%
+%% The license fee, if any, can be payed either to the LaTeX3 fund
+%% (see ltx3info.txt in the base LaTeX distribution) or to the author of
+%% the program who can be contacted at
+%%
+%%     Frank.Mittelbach@latex-project.org
+%%
+%<*dtx>
+          \ProvidesFile{multicol.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}[2018-04-01]
+%<package>
+%<package>\providecommand\DeclareRelease[3]{}
+%<package>\providecommand\DeclareCurrentRelease[2]{}
+%<package>
+%<package>\DeclareRelease{}{2017-04-11}{multicol-2017-04-11.sty}
+%<package>\DeclareCurrentRelease{}{2018-04-01}
+%<package>
+%<package>\ProvidesPackage{multicol}
+%<driver> \ProvidesFile{multicol.drv}
+% \fi
+%         \ProvidesFile{multicol.dtx}
+          [2019/03/01 v1.8w  multicolumn formatting (FMi)]
+%
+%
+%%
+%
+% \changes{v1.5n}{1997/06/05}{Applied improvement of documentation,
+%          kindly done by Robin Fairbairns.}
+% \changes{v1.4h}{1992/06/04}{Added mark tracing with
+%                           tracingmulticols$\ge2$}
+% \changes{v1.4a}{1992/02/11}{Added support for multicol in inner mode}
+% \changes{v1.0d}{1989/05/17}{All lines shortened to 72 or less.}
+% \changes{v1.0e}{1989/06/21}{Redefinition of description env. to use
+%                           \cs{descriptionmargin}\quotechar=5pt
+%                           in documentation.}
+% \changes{v1.0f}{1989/07/11}{Changed \cs{z@} to 0pt in redefinition of
+%                           description.}
+% \changes{v1.1a}{1989/09/20}{\cs{multicolssep} changed to \cs{multicolsep}.}
+%
+% \def\description{\list{}{\labelwidth 0pt \leftmargin\descriptionmargin
+%    \itemindent-\leftmargin \let\makelabel\descriptionlabel}}
+% \newdimen\descriptionmargin \descriptionmargin=5pt
+%
+% \DoNotIndex{\@M,\@Mi,\@bsphack,\@cclv,\@colht,\@currlist,\@deferlist}
+% \DoNotIndex{\@elt,\@esphack,\@floatplacement}
+% \DoNotIndex{\@ifundefined,\@ifnextchar,\@makecol}
+% \DoNotIndex{\@ne,\@outputpage,\@scolelt,\@spaces,\@tempb,\@tempcnta}
+% \DoNotIndex{\@width}
+% \DoNotIndex{\addvspace,\advance,\allowbreak}
+% \DoNotIndex{\baselineskip,\begingroup,\box,\columnsep,\copy,\count}
+% \DoNotIndex{\count@,\def,\dimen@,\divide,\docdate}
+% \DoNotIndex{\edef,\eject,\egroup,\else,\endgroup,\endinput}
+% \DoNotIndex{\fi,\fileversion,\filedate}
+% \DoNotIndex{\gdef,\global}
+% \DoNotIndex{\hbox,\hfil,\hrule,\ht,\hss}
+% \DoNotIndex{\ifdim,\ifnum,\ifvoid,\ignorespaces,\insert,\immediate}
+% \DoNotIndex{\let,\loop}
+% \DoNotIndex{\maxdepth,\message,\multiply}
+% \DoNotIndex{\newbox,\newcount,\newdimen,\newskip,\number,\newpage}
+% \DoNotIndex{\outputpenalty,\p@,\penalty}
+% \DoNotIndex{\relax,\repeat,\setbox,\skip,\space,\splitmaxdepth}
+% \DoNotIndex{\splittopskip,\string,\sixt@@n}
+% \DoNotIndex{\the,\thepage,\thr@@,\topskip,\tw@,\typeout}
+% \DoNotIndex{\unvbox,\vbox,\vfill,\vsplit,\voidb@x,\vrule}
+% \DoNotIndex{\write,\wd}
+% \DoNotIndex{\z@}
+%
+% \MakeShortVerb{\|}
+% \newcommand{\mc}{\textsf{multicols}}
+% \newcommand{\TUB}{{\sl TUGboat\/}}
+% \newcommand{\TB}{{\sl\TeX book\/}}
+%
+%
+% \setcounter{StandardModuleDepth}{2}
+% \setcounter{collectmore}{3}
+%
+% \GetFileInfo{multicol.dtx}
+% \title{An environment for multicolumn output\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}%
+%       \thanks{Note: This package is released under terms which affect
+%       its use in commercial applications. Please see the details at
+%       the top of the source file.}}
+% \author{Frank Mittelbach\\
+%       {\rm Email:} see top of the source file}
+% \date{Printed \today}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \begin{abstract}
+%   This article describes the use and the implementation of the \mc{}
+%   environment. This environment allows switching between
+%   one and multicolumn format on the same page. Footnotes are handled
+%   correctly (for the most part), but will be placed at the bottom of
+%   the page and not under each column.  \LaTeX{}'s float mechanism,
+%   however, is partly disabled in this implementation.  At the
+%   moment only page-wide floats (i.e., star-forms) can be used within
+%   the scope of the environment.
+% \end{abstract}
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.8}]
+%    The 1.8 release improves on the balancing approach. If due to a
+%    limited number of break points (e.g., due to large objects) the
+%    balanced columns exceed the available vertical space, then
+%    balancing is canceled and a normal page is produced first. Some
+%    overflow is allowed (controlled by the parameter
+%    |\maxbalancingoverflow| which defaults to 12pt). This ensures
+%    that we only cut a normal page if we get enough material carried
+%    over to next page.
+%
+%    Also added was support for |\enlargethispage|. This means it is
+%    now possible to request a page to be artificially  enlarged or
+%    shortened. Note that if you enlarge pages by more than one line
+%    you may have to increase the \textsf{collectmore} counter value to
+%    ensure that enough material is being picked up.
+%
+%    This command was used on the second page of this manual to shorten
+%    it by one line, in order to get rid of a number of widow lines on
+%    the following pages.
+%
+%   There are also some small enhancements to the balancing algorithm
+%   including a ways to require a minimum number of rows in the result.
+%
+%    Finally, version 1.8 adds the command |\docolaction| to help with
+%   more complicated actions that depend on the current column. This
+%   command expects 3 arguments: code that is executed if we are in
+%   the ``first'' column, code to execute if we end up in any
+%   ``middle'' column (if there are more than two) and finally code to
+%   execute if we are in the ``last'' column. Thus
+%\begin{verbatim}
+%  \docolaction{first}
+%              {middle}{last}
+%\end{verbatim}
+%   would typeset a different word depending the type of column this
+%   code is executed. Using it like this is probably pointless, but
+%   you can imagine applications like writing something into the
+%   nearest margin, etc.
+%
+%   As this feature needs at least two \LaTeX{} runs to produce correct
+%   results and as it adds to the processing complexity it is only
+%   made available if one add the option \texttt{colaction} when
+%   loading the package.
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.7
+%                         (right to left support)}]
+%    The 1.7 release adds support for languages that are typeset
+%    right-to-left. For those languages the order of the columns on the page
+%    also need to be reversed---something that wasn't supported before. The next
+%    paragraph demonstrates the result (as it is typeset as if we are writing
+%    in a left-to-right language--- so read the rightmost column
+%    first). The change is initialized via
+%    |\RLmulticolcolumns| and returning to left-right (default)
+%    is done via |\LRmulticolcolumns|.
+% \end{multicols}
+%
+% \RLmulticolcolumns
+%
+% \begin{multicols}{3}
+%    Right-to-left typesetting will only reverse the column orders. Any
+%    other support needed will have to be provided by other means,
+%    e.g., using appropriate fonts and reversing the writing directions
+%    within the columns. As footnotes are typeset in full measure the
+%    footnote rule needs to be redefined as if they are below a single
+%    column, i.e., using |\textwidth| not |\columnwidth|. For example:
+%\begin{verbatim}
+%\renewcommand \footnoterule{%
+%  \kern-3pt\hbox to\textwidth
+%    {\hskip .6\textwidth
+%     \hrulefill }%
+%  \kern2.6pt}
+%\end{verbatim}
+% \end{multicols}
+%
+% \LRmulticolcolumns
+%
+% \begin{multicols}{3}[\section*{Preface to version 1.5 + 1.6}]
+%   \hbadness=10000
+%   The 1.5 release contains two major changes: \mc{} will now
+%   support up to 10 columns and two more tuning possibilities have
+%   been added to the balancing routine. The balancing routine now
+%   checks the badness
+%   of the resulting columns and rejects solutions that are larger
+%   than a certain threshold.
+%   At the same time \mc{} has been upgraded to run under \LaTeXe{}.
+%
+%   Later changes to 1.5 include |\columnbreak| and |multicols*|.
+%
+%   For version 1.6 micro-spacing around the boxes produced by \mc{}
+%   has been improved to allow for baseline-grid typesetting.
+% \end{multicols}
+%
+%
+% \setcounter{collectmore}{2}
+% \begin{multicols}{3}[\section{Introduction}]
+%   \hbadness=10000
+%   Switching between two-column and one-column layout is possible in
+%   \LaTeX{}, but every use of |\twocolumn| or |\onecolumn|
+%   starts a new page. Moreover, the last page of two-column output
+%   isn't balanced and this often results in an empty, or nearly
+%   empty, right column. When I started to write macros for
+% \textsf{doc.sty} (see ``The \texttt{doc}--Option'', \TUB\
+%   volume 10~\#2, pp.~245--273) I thought that it would be nice to
+%   place the index
+%   on the same page as the bibliography. And balancing the last page
+%   would not only look better, it also would save space; provided of
+%   course that it is also possible to start the next article on the
+%   same page. Rewriting the index environment was comparatively easy,
+%   but the next goal, designing an environment which takes care of
+%   footnotes, floats, etc., was a harder task. It took me a whole
+%   weekend\footnote{I started with the algorithm given in the \TeX
+%   book on page 417. Without this help a weekend would not have been
+%   enough. (This remark was made in the documentation of the initial
+%    release, since then several hundreds more hours went into
+%    improving the original code.)} to get together the few lines of
+%    code below and there is
+%   still a good chance that I missed something after all.
+%
+%   Try it and, hopefully, enjoy it; and {\em please\/} direct bug
+%   reports and suggestions back to Mainz.
+% \end{multicols}
+%
+%
+% \setcounter{collectmore}{0}
+% \begin{multicols}{3}[\section{The User Interface}]
+%   \hbadness=10000
+%   To use the environment one simply says\\*[2mm]
+%     \hspace*{2mm}|\begin{multicols}{|\meta{number}|}|
+%     \hspace*{12mm}\meta{multicolumn text}\\
+%     \hspace*{2mm}|\end{multicols}|\\[2mm]
+%   where \meta{number} is the required number of columns and
+%^^A\meta{multicolumn text}
+%   $\langle${\it multi\-column text\/}$\rangle$ may contain arbitrary
+%   \LaTeX{} commands, except that floats and marginpars are not
+%   allowed in the current implementation\footnote{This is dictated by
+%   lack of time.  To implement floats one has to reimplement the
+%   whole \LaTeX{} output routine.}.
+%
+% \enlargethispage{-1\baselineskip}
+%
+% \DescribeMacro\premulticols
+% As its first action, the \textsf{multicols} environment measures the
+% current page to determine whether there is enough room for some
+% portion of multicolumn output. This is controlled by the
+% \meta{dimen} variable |\premulticols| which can be changed by
+% the user with ordinary \LaTeX{} commands.
+% \DescribeMacro\multicolsep
+% If the space is less than |\premulticols|, a new page is
+% started.  Otherwise, a |\vskip| of |\multicolsep| is
+% added.\footnote{Actually the added space may be less because we use
+% \cs{addvspace} (see the \LaTeX{} manual for further
+% information about this command).}
+%
+% \DescribeMacro\postmulticols
+% When the end of the \mc{} environment is encountered, an
+% analogous mechanism is employed, but now we test whether there is a
+% space larger than |\postmulticols| available. Again we add
+% |\multicolsep| or start a new page.
+%
+% It is often convenient to spread some text over all columns, just
+% before the multicolumn output, without any page break in between. To
+% achieve this the \mc{} environment has an optional second
+% argument which can be used for this purpose. For example, the text
+% you are now reading was started with
+% \begin{verbatim}
+% \begin{multicols}{3}
+%   [\section{The User
+%             Interface}] ...
+%\end{verbatim}
+% If such text is unusually long (or short) the value of
+% |\premulticols| might need adjusting to prevent a bad page
+% break.  We therefore provide a third argument which can be used to
+% overwrite the default value of |\premulticols| just for this
+% occasion. So if you want to combine some longer single column text
+% with a multicols environment you could write
+% \begin{verbatim}
+% \begin{multicols}{3}
+%     [\section{Index}
+%      This index contains ...]
+%     [6cm]
+%  ...
+%\end{verbatim}
+%
+%
+% \DescribeMacro\columnsep
+% The space between columns is controlled by the length parameter
+% |\columnsep|. The width for the individual columns is automatically
+% calculated from this parameter and the current |\linewidth|. In this
+% article a value of \textsf{\the\columnsep} was used.
+%
+%
+% \DescribeMacro\columnseprule
+% Separation of columns with vertical rules is achieved by setting the
+% parameter |\columnseprule| to some positive value.  In this
+% article a value of \textsf{.4pt} was used.
+%
+% \DescribeMacro\columnseprulecolor
+% The color of the rules separating the columns can be specified through
+% |\columnseprulecolor|. The default value is |\normalcolor|.
+%
+% \DescribeMacro\multicolbaselineskip
+% Since narrow columns tend to need adjustments in interline spacing
+% we also provide a \meta{skip} parameter called
+% |\multicolbaselineskip| which is added to the
+% |\baselineskip| parameter inside the \mc{}
+% environment.  Please use this parameter with care or leave it alone;
+% it is intended only for package file designers since even small
+% changes might produce totally unexpected changes to your document.
+%
+%
+%    \subsection{Balancing columns}
+%
+%
+% Besides the previously mentioned parameters, some others are
+% provided to influence the layout of the columns generated.
+%
+% Paragraphing in \TeX{} is controlled by several parameters. One of
+% the most important is called |\tolerance|: this controls the
+% allowed `looseness' (i.e.\ the amount of blank space between words).
+% Its default value is 200 (the \LaTeX{} |\fussy|) which is too
+% small for narrow columns. On the other hand the |\sloppy|
+% declaration (which sets |\tolerance| to $10000=\infty$) is too
+% large, allowing really bad spacing.\footnote{Look at the next
+% paragraph, it was set with the \cs{sloppy} declaration.}
+%
+% \begin{sloppypar}
+% \DescribeMacro\multicoltolerance \DescribeMacro\multicolpretolerance
+%  We therefore use a |\multicoltolerance| parameter for the
+% |\tolerance| value inside the \mc{} environment.  Its default value
+% is 9999 which is less than infinity but `bad' enough for most
+% paragraphs in a multicolumn environment. Changing its value should
+% be done outside the \mc{} environment.  Since |\tolerance| is set
+% to |\multicoltolerance| at the beginning of every \textsf{multicols}
+% environment one can locally overwrite this default by assigning
+% \verb*+\tolerance = +\meta{desired value}. There also exists a
+% |\multicolpretolerance| parameter holding the value for
+% |\pretolerance| within a \mc{} environment. Both parameters are
+% usually used only by package designers.
+% \end{sloppypar}
+%
+% Generation of multicolumn output can be divided into two parts.  In
+% the first part we are collecting material for a page, shipping it
+% out, collecting material for the next page, and so on.  As a second
+% step, balancing will be done when the end of the \mc{} environment
+% is reached.
+% In the first step \TeX{} might consider more material whilst
+% finding the final column content than it actually uses when shipping out the
+% page. This might cause a problem if a footnote is encountered in
+% the part of the input considered, but not used, on the current page.
+% In this case the footnote might show up on the current page, while the
+% footnotemark corresponding to this footnote might be set on the next
+% one.\footnote{The reason behind this behavior is the asynchronous
+%               character of the \TeX{} {\it page\_builder}.
+%               However, this
+%               could be avoided by defining very complicated output
+%               routines which don't use \TeX{} primitives like
+%               \cs{insert} but do everything by hand.
+%               This is clearly beyond the scope of a weekend problem.}
+% Therefore the \mc{} environment gives a warning
+% message\footnote{This message will be generated even if there are no
+% footnotes in this part of the text.} whenever it is unable to use
+% all the material considered so far.
+%
+% If you don't use footnotes too often the chances of something
+% actually going wrong are very slim, but if this happens you can help
+% \TeX{} by using a |\pagebreak| command in the final document.
+% Another way to influence the behavior of \TeX{} in this respect is
+% given by the counter variable `\textsf{collectmore}'. If you use the
+% |\setcounter| declaration to set this counter to \meta{number},
+% \TeX{} will consider \meta{number} more (or less) lines before
+% making its final decision. So a value of $-1$ may solve all your
+% problems at the cost of slightly less optimal columns.
+%
+%
+% In the second step (balancing columns) we have other bells and
+% whistles. First of all you can say |\raggedcolumns| if you
+% don't want the bottom lines to be aligned.
+% The default is |\flushcolumns|, so \TeX{} will normally try to
+% make both
+% the top and bottom baselines of all columns align.
+%
+% If there is only a small amount of material available for balancing
+% then you may end up with very few lines per column. In an extreme
+% case there may be only one line which looks distinctly odd. In that
+% case it might be better to have more material distributed to the
+% earlier columns even if that means that later columns are empty or
+% partially empty. This is controlled through the counter
+% `\textsf{minrows}' (default 1). If set to a higher value then the
+% balancing will have at least that many rows in the first column (and
+% also all further columns until it runs outs of material).
+%          
+% Additionally you can set another counter, the `\textsf{unbalance}'
+% counter, to some positive \meta{number}. This will make all but the
+% right-most column \meta{number} of lines longer than they would
+% normally have been. `Lines' in this context refer to normal text
+% lines (i.e.\ one |\baselineskip| apart); thus, if your columns
+% contain displays,
+% for example, you may need a higher \meta{number}
+% to shift something from one column into another. A negative value can make sense if
+% you have set \textsf{minrows} and want to locally adjust that.
+%
+% Unlike `\textsf{collectmore},' the `\textsf{unbalance}' counter is reset
+% to zero at the end of the environment so it only applies to one
+% \mc{} environment.
+%
+% The two methods may be combined but I suggest using these features
+% only when fine tuning important publications.
+%
+% Two more general tuning possibilities were added with version~1.5.
+% \TeX{} allows to measure the badness of a column in terms of an
+% integer value, where 0 means optimal and any higher value means a
+% certain amount of extra white space. 10000 is considered to be
+% infinitely bad (\TeX{} does not distinguish any further). In addition
+% the special value 100000 means overfull (i.e., the column contains
+% more text than could possibly fit into it).
+%
+% The new release now measures every generated column and ignores
+% solutions where at least one column has a badness being larger than
+% the value of the counter \textsf{columnbadness}. The default value for
+% this counter is 10000, thus \TeX{} will accept all solutions except
+% those being overfull.
+% By setting the counter to a smaller value you can force the algorithm
+% to search for solutions that do not have columns with a lot of white
+% space.
+%
+% However, if the setting is too low, the algorithm may not find any
+% acceptable solution at all and will then finally choose the extreme
+% solution of placing all text into the first column.
+%
+% Often, when columns are balanced, it is impossible to find a solution
+% that distributes the text evenly over all columns. If that is the case
+% the last column usually has less text than the others. In the earlier
+% releases this text was stretched to produce a column with the same
+% height as all others, sometimes resulting in really ugly looking
+% columns.
+%
+% In the new release this stretching is only done if the badness of
+% the final column is not larger than the value of the counter
+% \textsf{finalcolumnbadness}. The default setting is 9999, thus preventing
+% the stretching for all columns that \TeX{} would consider infinitely
+% bad. In that case the final column is allowed to run short which gives
+% a much better result.
+%
+% And there are two more parameters of some experimental nature, one
+% called |\multicolovershoot| the other |\multicolundershoot|.  They
+% control the amount of space a column within the \mc{} environment is
+% allowed to be ``too full'' or ``too short'' without affecting the
+% column badness. They are set to 0pt and 2pt, respectively.
+%
+% Finally, when doing the balancing at the end, columns may become
+% higher than the remaining available space. In that case the
+% algorithm aborts and instead generates a normal page. However, if the
+% amount is not too large, e.g., a line or so, then it might be better to
+% keep everything on the same page instead of starting a new page with
+% just one line after balancing. So the parameter
+% |\maxbalancingoverflow| governs this process: only when the excess
+% gets larger than its value balancing is aborted.
+%
+% \subsection{Not balancing the columns}
+%
+% Although this package was written to solve the problem of balancing
+% columns, I got repeated requests to provide a version where all
+% white space is automatically placed in the last column or
+% columns. Since version v1.5q this now exists: if you use
+% \texttt{multicols*} instead of the usual environment the columns on
+% the last page are not  balanced. Of course, this environment only
+% works on top-level, e.g., inside a box one has to balance to
+% determine a column height in absence of a fixed value.
+%
+%
+% \subsection{Manually breaking columns}
+%
+% Another request often voiced was: ``How do I tell \LaTeX{} that it
+% should break the first column after this particular line?''. The
+% |\pagebreak| command (which works with the two-column option of
+% \LaTeX{}) is of no use here since it would end the collection phase
+% of \mc{} and thus all columns on that page. So with version 1.5u
+% the |\columnbreak| command was added. If used within a paragraph it
+% marks the end of the current line as the desired breakpoint. You can
+% observe its effect on
+% the previous page where three lines of text have been artificially
+% forced into the second column  (resulting in some white
+% space between paragraphs in the first column).
+%
+% \subsection{Floats inside a \mc{} environment}
+%
+% Within the \mc{} environment the usual star float commands are
+% available but their function is somewhat different as in the
+% two-column mode of standard \LaTeX. Stared floats, e.g.,
+% \texttt{figure*}, denote page wide floats that are handled in a similar
+% fashion as normal floats outside the \mc{} environment. However,
+% they will never show up on the page where they are encountered. In
+% other words, one can influence their placement by specifying a
+% combination of \texttt{t}, \texttt{b}, and/or \texttt{p} in their optional
+% argument, but \texttt{h} doesn't work because the first possible place
+% is the top of the next page. One should also note, that this means
+% that their placement behavior is determined by the values of
+% |\topfraction|, etc.\ rather than by |\dbl...|.
+%
+%
+% \subsection{Support for right-to-left typesetting}
+%
+%    In right-to-left typesetting the order of the columns on the page
+%    also need to be reversed, i.e., the first column has to appear on the far
+%    right and the last column on the left. This is supported through the
+%    commands |\RLmulticolcolumns| (switching to right-to-left typesetting)
+%    and |\LRmulticolcolumns| (switching to left-to-right typesetting) the
+%    latter being the default.
+%
+% \subsection{Warnings}
+%
+% Under certain circumstances the use of the \mc{} environment may
+% result in some
+% warnings from \TeX{} or \LaTeX{}. Here is a list
+% of the important ones and the possible cause:
+% \begin{description}
+%
+% \item[] {\hspace*{-\labelsep}\tt Underfull \string\hbox\space
+%  (badness ...)}
+%
+%  As the columns are often very narrow \TeX{} wasn't able to find a
+%  good way to break the paragraph. Underfull denotes a loose line but
+%  as long as the badness value is below $10000$ the result is probably
+%  acceptable.
+%
+% \item[]
+% {\hspace*{-\labelsep}\tt Underfull \string\vbox\space ...  while
+%  \string\output\space is active}
+%
+%  If a column contains a character with an unusual depth, for
+%  example a `(', in the bottom line then this message may show up. It
+%  usually has no significance as long as the value is not more than a
+%  few points.
+%
+% \item[] {\hspace*{-\labelsep}\tt LaTeX Warning: I moved some lines
+%  to the next page}
+%
+%  As mentioned above, \mc{} sometimes screws up the footnote
+%  numbering. As a precaution, whenever there is a footnote on a
+%  page where \mc{} had to leave a remainder for the following
+%  page this warning appears. Check the footnote numbering on this
+%  page. If it turns out that it is wrong, you have to manually break
+%  the page using |\newpage| or |\pagebreak[..]|.
+%
+% \item[] {\hspace*{-\labelsep}\tt Floats and marginpars not allowed
+%  inside `multicols' environment!}
+%
+%  This message appears if you try to use the |\marginpar| command or
+%  an unstarred version of the \textsf{figure} or \textsf{table} environment.
+%  Such floats will disappear!
+%
+% \item[] {\hspace*{-\labelsep}\tt Very deep columns!
+%          Grid alignment might be broken}
+%
+% This message can only appear if the option \texttt{grid} was
+%    chosen. In that case it will show up if a column has a very large
+%    depth so that \mc{} is unable to back up to its baseline. This
+%    is only relevant if one tries to produce a document where all
+%    text lines are aligned at an invisible grid, something that
+%    requires careful adjustment of many parameters and macros, e.g.,
+%    heading definitions.
+%
+% \end{description}
+%
+%
+% \subsection{Tracing the output}
+%
+% To understand the reasoning behind the decisions \TeX{} makes when
+% processing a \mc{} environment, a tracing mechanism is provided.
+% If you set the counter `\texttt{tracingmulticols}'
+% to a positive \meta{number} you then
+% will get some tracing information on the terminal and in the
+% transcript file:
+% \begin{description}
+% \item[$\meta{number}=1$.]  \TeX{} will now tell you, whenever it
+%    enters or leaves a \mc{} environment, the number of columns it
+%    is working on and its decision about starting a new page before
+%    or after the environment.
+% \item[$\meta{number}=2$.]
+%    In this case you also get information from the balancing routine:
+%    the heights tried for the left and right-most columns,
+%    information about shrinking if the |\raggedcolumns|
+%    declaration is in force and the value of the `\textsf{unbalance}'
+%    counter if positive.
+% \item[$\meta{number}= 3$.]  Setting \meta{number}\pagebreak[2] to
+%    this value will additionally trace the mark handling
+%    algorithm. It will show what marks are found, what marks are
+%    considered, etc. To fully understand this information you will
+%    probably have to read carefully trough the implementation.
+% \item[$\meta{number}\geq 4$.]  Setting \meta{number}\pagebreak[2] to
+%    such a high value will additionally place an |\hrule| into your
+%    output, separating the part of text which had already been
+%    considered on the previous page from the rest.  Clearly this
+%    setting should {\em not\/} be used for the final output.  It will
+%    also activate even more debugging code for mark handling.
+% \end{description}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{3}[\section{Prefaces to older versions}
+%                      \subsection{Preface to version 1.4}]
+%   \hbadness=10000
+%   Beside fixing some bugs as mentioned in the \textsf{multicol.bug} file
+%   this new release enhances the \mc{} environment by allowing for
+%   balancing in arbitrary contexts. It is now, for example, possible
+%   to balance text within a \mc{} or a \textsf{minipage} as shown in
+%   \ref{tab:newcmds} where a \textsf{multicols} environment within a
+%   \textsf{quote} environment was used. It is now even possible to nest
+%   \mc{} environments.
+%
+%   The only restriction to such inner \mc{} environments (nested, or
+%   within \TeX's internal vertical mode) is that such variants will
+%   produce a box with the balanced material in it, so that they can
+%   not be broken across pages or columns.
+%
+%   Additionally I rewrote the algorithm for balancing so that it will
+%   now produce slightly better results.
+%
+%   I updated the source documentation but like to apologize in
+%   advance for some `left over' parts that slipped through the
+%   revision.
+%
+%   A note to people who like to improve the balancing algorithm of
+%   \mc{}: The balancing routine is now placed into a single macro
+%   which is called |\balance@columns|. This means that one can easily
+%   try different balancing routines by rewriting this macro. The
+%   interface for it is explained in table \ref{tab:balance}. There are
+%   several improvements possible, one can think of integrating the
+%   |\badness| function of \TeX3, define a faster algorithm for finding
+%   the right column height, etc. If somebody thinks he/she has an
+%   enhancement I would be pleased to learn about it. But please obey
+%   the copyright notice and don't change \textsf{multicol.dtx} directly!
+%   \begin{table*}
+%    \begin{quote}
+%    \begin{multicols}{2}
+%     \raggedcolumns
+%     The macro |\balance@columns| that contains the code for balancing
+%     gathered material is a macro without parameters. It assumes that
+%     the material for balancing is stored in the box |\mult@box| which
+%     is a |\vbox|. It also ``knows'' about all parameters set up by the
+%     \mc{} environment, like |\col@number|, etc. It can also assume
+%     that |\@colroom| is the still available space on the current page.
+%
+%     When it finishes it must return the individual columns in boxes
+%     suitable for further processing with |\page@sofar|. This means
+%     that the left column should be stored in box register
+%     |\mult@gfirstbox|, the next
+%     in register |\mult@firstbox|${}+2$, \ldots,
+%     only the last one as an exception in
+%     register |\mult@grightbox|. Furthermore it has to set up
+%     the two macros
+%     |\kept@firstmark| and |\kept@botmark| to hold the values for the
+%     first and bottom mark as found in the individual columns. There
+%     are some helper functions defined in section \ref{sec:v14} which
+%     may be used for this. Getting the marks right ``by hand'' is
+%     non-trivial and it may pay off to first take a look at the
+%     documentation and implementation of |\balance@columns| below
+%     before trying anew.
+%    \end{multicols}
+%    \end{quote}
+%    \vspace*{-3ex}
+%    \vspace*{-0ex}
+%    \caption{Interface description for \cs{balance@columns}}
+%    \label{tab:balance}
+%   \end{table*}
+% \end{multicols}
+%
+% \begin{multicols}{3}[\subsection{Preface to version 1.2}]
+%   \hbadness=10000
+%   After the article about the \mc{} environment was published in
+%   \TUB\ 10\#3, I got numerous requests for these macros. However, I
+%   also got a changed version of my style file, together with a
+%   letter asking me if I would include the changes to get better
+%   paragraphing results in the case of narrow lines. The main
+%   differences to my original style option were additional parameters
+%   (like |\multicoladjdemerits| to be used for |\adjdemerits|, etc.)
+%   which would influence the line breaking algorithm.
+%
+%   But actually resetting such parameters to zero or even worse to a
+%   negative value won't give better line breaks inside the \mc{}
+%   environment. \TeX{}s line breaking algorithm will only look at
+%   those possible line breaks which can be reached without a badness
+%   higher than the current value of |\tolerance| (or |\pretolerance|
+%   in the first pass). If this isn't possible, then, as a last
+%   resort, \TeX{} will produce overfull boxes. All those (and only
+%   those) possible break points will be considered and finally the
+%   sequence which results in the fewest demerits will be chosen. This
+%   means that a value of $-1000$ for |\adjdemerits| instructs \TeX{}
+%   to prefer visibly incompatible lines instead of producing better
+%   line breaks.
+%
+%   However, with \TeX{} 3.0 it is possible to get decent line breaks
+%   even in small columns by setting |\emergencystretch| to an
+%   appropriate value. I implemented a version which is capable of
+%   running both in the old and the new \TeX{} (actually it will
+%   simply ignore the new feature if it is not available). The
+%   calculation of |\emergencystretch| is probably incorrect. I
+%   made a few tests but of course one has to have much more experience
+%   with the new possibilities to achieve the maximum quality.
+%
+%   Version 1.1a had a nice `feature': the penalty for using the
+%   forbidden floats was their ultimate removal from \LaTeX{}s
+%   |\@freelist| so that after a few |\marginpar|s inside the \mc{}
+%   environment floats where disabled forever.  (Thanks to Chris
+%   Rowley for pointing this out.) I removed this misbehavior and at
+%   the same time decided to allow at least floats spanning all
+%   columns, e.g., generated by the |figure*| environment.  You can
+%   see the new functionality in table~\ref{tab:newcmds} which was
+%   inserted at this very point.
+%   \begin{table*}
+%    \small
+%    \setlength{\multicolsep}{0pt}
+%    \begin{quote}
+%     \begin{multicols}{2}
+%      |\setemergencystretch|: This is a hook for people who like
+%      to play around. It is supposed to set the
+%      |\emergencystretch| \meta{dimen} register provided in the
+%      new \TeX{} 3.0. The first argument is the number of columns and
+%      the second one is the current |\hsize|. At the moment the
+%      default definition is $4\texttt{pt} \times |#1|$, i.e.\ the
+%      |\hsize| isn't used at all. But maybe there are better
+%      formulae.
+%
+%      \setlength{\emergencystretch}{20pt} |\set@floatcmds|: This is
+%      the hook for the experts who like to implement a full float
+%      mechanism for the \mc{} environment. The |@| in the name
+%      should signal that this might not be easy.
+%    \end{multicols}
+%   \end{quote}
+%   \vspace*{-1ex}
+%   \vspace*{-0ex}
+%   \caption[]{The new commands of \textsf{multicol.sty} version 1.2.
+%            Both commands might be removed if good solutions to these
+%            open problems are found. I hope that these commands will
+%            prevent that nearly identical style files derived from
+%            this one are floating around.}
+%   \label{tab:newcmds}
+%   \end{table*}
+%   However single column floats are still forbidden and I don't think
+%   I will have time to tackle this problem in the near future. As an
+%   advice for all who want to try: wait for \TeX{} 3.0. It has a few
+%   features which will make life much easier in multi-column
+%   surroundings. Nevertheless we are working here at the edge of
+%   \TeX{}s capabilities, really perfect solutions would need a
+%   different approach than it was done in \TeX{}s page builder.
+%
+%   The text below is nearly unchanged, I only added documentation at
+%   places where new code was added.
+% \end{multicols}
+%
+% \changes{v1.5l}{1996/01/13}{Try hard to explain unresolved reference
+%                that happens if \cs{OnlyDescription} is used}
+%
+% \StopEventually{\PrintIndex \PrintChanges
+%   \ifx\Finale\relax
+%    \typeout{**********************************}
+%    \typeout{* Info: Typesetting this document with
+%                     \protect\OnlyDescription\space will}
+%    \typeout{* Info: result in one unresolved
+%                     reference to `sec:v14'.}
+%    \typeout{* Info: --- tough, it's just not there in this case!}
+%    \typeout{**********************************}
+%   \fi
+%  }
+%
+%
+% \begin{multicols}{2}[\section{The Implementation}
+%         We are now switching to two-column output to show the
+%         abilities of this environment (and bad layout decisions).
+%      \subsection{The documentation driver file}
+%         ][10\baselineskip]
+%
+%   \hbadness=10000
+%
+%
+% The next bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the \texttt{docstrip} program.
+% Since this is the first code in this file one can produce the
+% documentation
+% simply by running \LaTeX{} on the \texttt{.dtx} file.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+%    \end{macrocode}
+%    We use the \texttt{balancingshow} option when loading \mc{} so
+%    that full tracing is produced. This has to be done before the
+%    \texttt{doc} package is loaded, since \texttt{doc} otherwise
+%    requires \mc{} without any options.
+%    \begin{macrocode}
+\usepackage{multicol}[1999/05/25]
+\usepackage{doc}
+%    \end{macrocode}
+%    First we set up the page layout suitable for
+%    this article.
+%    \begin{macrocode}
+\setlength{\textwidth}{39pc}
+\setlength{\textheight}{54pc}
+\setlength{\parindent}{1em}
+\setlength{\parskip}{0pt plus 1pt}
+\setlength{\oddsidemargin}{0pc}
+\setlength{\marginparwidth}{0pc}
+\setlength{\topmargin}{-2.5pc}
+\setlength{\headsep}{20pt}
+\setlength{\columnsep}{1.5pc}
+%    \end{macrocode}
+%    We want a rule between columns.
+%    \begin{macrocode}
+\setlength\columnseprule{.4pt}
+%    \end{macrocode}
+%    We also want to ensure that a new \mc{} environment finds enough
+%    space at the bottom of the page.
+%    \begin{macrocode}
+\setlength\premulticols{6\baselineskip}
+%    \end{macrocode}
+%    When balancing columns we disregard solutions that
+%    are too bad. Also, if the last column is too bad
+%    we typeset it without stretch.
+%    \begin{macrocode}
+\setcounter{columnbadness}{7000}
+\setcounter{finalcolumnbadness}{7000}
+%    \end{macrocode}
+%    The index is supposed to come out in four columns.
+%    And we don't show macro names in the margin.
+%    \begin{macrocode}
+\setcounter{IndexColumns}{4}
+\let\DescribeMacro\SpecialUsageIndex
+\let\DescribeEnv\SpecialEnvIndex
+\renewcommand\PrintMacroName[1]{}
+\CodelineIndex
+%\DisableCrossrefs           % Partial index
+\RecordChanges               % Change log
+%    \end{macrocode}
+%    Line numbers are very small for this article.
+%    \begin{macrocode}
+\renewcommand{\theCodelineNo}
+  {\scriptsize\rm\arabic{CodelineNo}}
+\settowidth\MacroIndent{\scriptsize\rm 00\ }
+
+\begin{document}
+  \typeout
+   {****************************************
+ ^^J* Expect some Under- and overfull boxes.
+ ^^J****************************************}
+   \DocInput{multicol.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Identification and
+%                      option processing}]
+%
+%
+% We start by identifying the package. Since it makes use of features
+% only available in \LaTeXe{} we ensure that this format is available.
+% (Now this is done earlier in the file.)
+%    \begin{macrocode}
+%<*package>
+% \NeedsTeXFormat{LaTeX2e}
+% \ProvidesPackage{multicol}[..../../..
+%    v... multicolumn formatting]
+%    \end{macrocode}
+%
+%^^A \subsection{Option processing}
+%
+%    Next we declare options supported by \mc{}. Two-column mode
+%    and \mc{} do not work together so we warn about possible
+%    problems. However, since you can revert to |\onecolumn|
+%    in which case \mc{} does work, we don't make this an error.
+%    \begin{macrocode}
+\DeclareOption{twocolumn}
+   {\PackageWarning{multicol}{May not work
+             with the twocolumn option}}
+%    \end{macrocode}
+%    Tracing is done using a counter. However
+%    it is also possible to invoke the tracing
+%    using the options declared below.
+%    \begin{macrocode}
+\newcount\c@tracingmulticols
+\DeclareOption{errorshow}
+    {\c@tracingmulticols\z@}
+\DeclareOption{infoshow}
+    {\c@tracingmulticols\@ne}
+\DeclareOption{balancingshow}
+    {\c@tracingmulticols\tw@}
+\DeclareOption{markshow}
+    {\c@tracingmulticols\thr@@}
+\DeclareOption{debugshow}
+    {\c@tracingmulticols5\relax}
+%    \end{macrocode}
+%    The next option is intended for typesetting on a |\baselineskip|
+%    grid. Right now it doesn't do anything other than warning if it
+%    thinks that the grid got lost.
+% \changes{v1.6a}{2003/03/15}{New option grid}
+%    \begin{macrocode}
+\let\mc@gridwarn\maxdimen
+\DeclareOption{grid}{\def\mc@gridwarn{\maxdepth}}
+%    \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%    Next option enables the |\docolaction| command. As this changes
+%   the \texttt{.aux} file content this is not automatically enabled.
+%    \begin{macrocode}
+\DeclareOption{colaction}{%
+  \def\mc@col@status@write{%
+         \protected@write\@auxout{}%
+              {\string\mc@col@status
+              {\ifmc@firstcol 1\else 2\fi}}%
+         \mc@firstcolfalse}%
+  \def\mc@lastcol@status@write{%
+         \protected@write\@auxout{}%
+              {\string\mc@col@status{3}}}%
+}
+\let\mc@col@status@write\relax
+\let\mc@lastcol@status@write\relax
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ProcessOptions
+%    \end{macrocode}
+%
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Starting and
+%                      Ending the \mc{} Environment}]
+%
+% \begin{macro}{\multicols}
+%    As mentioned before, the \mc{} environment has one mandatory
+%    argument (the number of columns) and up to two optional ones.  We
+%    start by reading the number of columns into the |\col@number|
+%    register.
+%    \begin{macrocode}
+\def\multicols#1{\col@number#1\relax
+%    \end{macrocode}
+%    If the user forgot the argument, \TeX{} will complain about a
+%    missing number at this point. The error recovery mechanism will
+%    then use zero, which isn't a good choice in this case. So we
+%    should now test whether everything is okay. The minimum is two
+%    columns at the moment.
+% \changes{v1.3b}{1990/10/09}{Minimum of two columns}
+%    \begin{macrocode}
+  \ifnum\col@number<\tw@
+     \PackageWarning{multicol}%
+      {Using `\number\col@number'
+       columns doesn't seem a good idea.^^J
+       I therefore use two columns instead}%
+     \col@number\tw@ \fi
+%    \end{macrocode}
+%    We have only enough box registers for ten columns, so we need to
+%    check that the user hasn't asked for more.
+% \changes{v1.4k}{1992/06/27}{Maximum of 5 columns (temp)}
+% \changes{v1.5a}{1992/11/04}{Allow 10 columns again}
+%    \begin{macrocode}
+  \ifnum\col@number>10
+     \PackageError{multicol}%
+      {Too many columns}%
+      {Current implementation doesn't
+       support more than 10 columns.%
+       \MessageBreak
+       I therefore use 10 columns instead}%
+     \col@number10 \fi
+%    \end{macrocode}
+%    Within the environment we need a special version of the
+%    kernel |\@footnotetext| command since the original sets the
+%    the |\hsize| to |\columnwidth| which is not correct in the
+%    multicol environment. Here |\columnwidth| refers to the width of
+%    the individual column and the footnote should be in |\textwidth|.
+%    Since |\@footnotetext| has a different definition inside a
+%    minipage environment we do not redefine it directly. Instead we
+%    locally set |\columnwidth| to |\textwidth| and call the original
+%    (current) definition stored in |\orig@footnotetext|.
+% \changes{v1.5p}{1997/12/14}{Redefinition of \cs{@footnotetext}
+%                           only within env pr/2689.}
+% \changes{v1.5r}{1998/08/17}{Use \cs{@footnotetext} but with
+%                             local change to \cs{columnwidth}.}
+% \changes{v1.5w}{1999/10/21}{Make \cs{@footnotetext} long to allow
+%                             multi-paragraph footnotes.}
+%    If the \mc{} environment is nested inside another \mc{}
+%    environment then the redefinition has already happened. So be
+%    better test for this situation. Otherwise, we will get a \TeX{}
+%    stack overflow as this would generate a self-referencing definition.
+% \changes{v1.6e}{2004/02/14}{Avoid self-referencing definition of
+%    \cs{@footnotetext} (pr/3618)}.
+%    \begin{macrocode}
+     \ifx\@footnotetext\mult@footnotetext\else
+       \let\orig@footnotetext\@footnotetext
+       \let\@footnotetext\mult@footnotetext
+     \fi
+%    \end{macrocode}
+%    Now we can safely look for the optional arguments.
+%    \begin{macrocode}
+  \@ifnextchar[\mult@cols{\mult@cols[]}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\mult@footnotetext}
+%
+%    \begin{macrocode}
+\long\def\mult@footnotetext#1{\begingroup
+         \columnwidth\textwidth
+         \orig@footnotetext{#1}\endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mult@cols}
+%    The |\mult@cols| macro grabs the first optional argument
+%    (if any) and looks for the second one.
+%    \begin{macrocode}
+\def\mult@cols[#1]{\@ifnextchar[%
+%    \end{macrocode}
+%    This argument should be a \meta{dimen} denoting the minimum free
+%    space needed on the current page to start the environment. If the
+%    user didn't supply one, we use |\premulticols| as a
+%    default.
+%    \begin{macrocode}
+  {\mult@@cols{#1}}%
+  {\mult@@cols{#1}[\premulticols]}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\mult@@cols}
+%    After removing all arguments from the input we are able
+%    to start with |\mult@@cols|.
+%    \begin{macrocode}
+\def\mult@@cols#1[#2]{%
+%    \end{macrocode}
+%    First thing we do is to decide whether or not this is an
+%    unbounded multicols environment, i.e. one that may split across
+%    pages, or one that has to be typeset into a box. If we are in
+%    \TeX's ``inner'' mode (e.g., inside a box already) then we have a
+%    boxed version of multicols therefore we set the |@boxedmulticols|
+%    switch to true.  The \mc{} should start in vertical mode. If we
+%    are not already there we now force it with |\par| since otherwise
+%    the test for ``inner'' mode wouldn't show if we are in a box.
+% \changes{v1.4f}{1992/04/28}{\cs{par} added to allow for correct inner test}
+%    \begin{macrocode}
+  \par
+  \ifinner \@boxedmulticolstrue
+%    \end{macrocode}
+%    Otherwise we check |\doublecol@number|. This counter is zero
+%    outside a multicols environment but positive inside (this happens
+%    a little later on). In the second case we need to process the
+%    current multicols also in ``boxed mode'' and so change the switch
+%    accordingly.
+%    \begin{macrocode}
+  \else
+    \ifnum \doublecol@number>\z@
+       \@boxedmulticolstrue
+    \fi
+  \fi
+%    \end{macrocode}
+%    Then we look to see if statistics are requested:
+%    \begin{macrocode}
+  \mult@info\z@
+      {Starting environment with
+       \the\col@number\space columns%
+%    \end{macrocode}
+%    In boxed mode we add some more info.
+% \changes{v1.4f}{1992/04/28}{\cs{on@line} added to tracing info}
+%    \begin{macrocode}
+        \if@boxedmulticols\MessageBreak
+           (boxed mode)\fi
+      }%
+%    \end{macrocode}
+%    Then we measure the current page to see whether a useful portion
+%    of the multicolumn environment can be typeset.  This routine
+%    might start a new page.
+% \changes{v1.4a}{1992/02/14}{Forgotten braces added}
+%    \begin{macrocode}
+   \enough@room{#2}%
+%    \end{macrocode}
+%    Now we output the first argument and produce vertical space
+%    above the columns. (Note that this argument corresponds to the
+%    first optional argument of the \textsf{multicols} environment.)
+%    For many releases this argument was typeset in a group to get
+%    a similar effect as |\twocolumn[..]| where the argument is
+%    also implicitly surrounded by braces. However, this conflicts
+%    with local changes done by things like sectioning commands (which
+%    account for the majority of commands used in that argument)
+%    messing up vertical spacing etc.\ later in the document so that
+%    from version v1.5q on this argument is again typeset at the outer
+%    level.
+% \changes{v1.4e}{1992/03/16}{Typeset optional arg inside group}
+% \changes{v1.5q}{1998/01/19}{And removed the group again six years later}
+%    \begin{macrocode}
+   #1\par\addvspace\multicolsep
+%    \end{macrocode}
+%    When the last line of a paragraph had a positive depth then this
+%    depth normally taken into account by the baselineskip calculation
+%    for the next line. However, the columns produced by a following
+%    \texttt{multicol} are rigid and thus the distance from the
+%    baseline of a previous text line to the first line in a
+%    \texttt{multicol} would differ depending on the depth of the
+%    previous line. To account for this we add a negative space unless
+%    the depth is \texttt{-1000pt} which signals something special to
+%    \TeX and is not supposed to be a real depth.
+% \changes{v1.5z1}{2003/02/17}{Add a kern to cancel potential depth of
+%    previous line}
+%    \begin{macrocode}
+   \ifdim \prevdepth = -\@m\p@
+   \else
+%    \end{macrocode}
+%    The actual generation of this corrective space is a little bit
+%    more complicated as it doesn't make sense to always back up to
+%    the previous baseline (in case an object with a very large depth
+%    was placed there, e.g., a centered tabular). So we only back up
+%    to the extend that we are within the |\baselineskip| grid. We
+%    know that the box produced by \mc{} has |\topskip| at its top so
+%    that also needs to be taken into account.
+% \changes{v1.6a}{2003/03/15}{Adjust spacing}
+%    \begin{macrocode}
+     \@tempcnta\prevdepth
+     \@tempcntb\baselineskip
+     \divide\@tempcnta\@tempcntb
+     \advance\@tempcnta\@ne
+     \dimen@\prevdepth
+     \advance\dimen@ -\@tempcnta\baselineskip
+     \advance\dimen@ \topskip
+     \kern-\dimen@
+   \fi
+%    \end{macrocode}
+%    We start a new grouping level to hide all subsequent changes
+%    (done in |\prepare@multicols| for example).
+%    \begin{macrocode}
+   \begingroup
+     \prepare@multicols
+%    \end{macrocode}
+%    If we are in boxed mode we now open a box to typeset all material
+%    from the multicols body into it, otherwise we simply go ahead.
+% \changes{v1.4g}{1992/05/07}{\cs{global} was probably wrong but at least
+%                           unnecessary}
+%    \begin{macrocode}
+     \if@boxedmulticols
+       \setbox\mult@box\vbox\bgroup
+%    \end{macrocode}
+%
+% \changes{v1.8c}{2013/11/03}{Add \cs{color@setgroup} to prevent color leak}
+%    \begin{macrocode}
+                            \color@setgroup
+%    \end{macrocode}
+% \changes{v1.5?}{1994/?/?}{Penalty moved to later point}
+%    We may have to reset some parameters at this point,
+%    perhaps |\@parboxrestore|
+%    would be the right action but I leave it for the moment.
+% \changes{v1.4l}{1992/08/17}{\cs{@totalleftmargin} now in
+%                             \cs{prepare@multicols}}
+%    \begin{macrocode}
+     \fi
+%    \end{macrocode}
+%    We finish by suppressing initial spaces.
+%    \begin{macrocode}
+     \ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\if@boxedmulticols}
+%    Here is the switch and the box for ``boxed'' multicols code.
+%    \begin{macrocode}
+\newif\if@boxedmulticols
+\@boxedmulticolsfalse
+\newbox\mult@box
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\enough@room}
+% \changes{v1.0c}{1989/05/12}{Penalty 0 added to empty the contribution
+%                           list.}
+%    The |\enough@room| macro used
+%    above isn't perfect but works reasonably well in this context. We
+%    measure the free space on the current page by subtracting
+%    |\pagetotal| from |\pagegoal|. This isn't entirely
+%    correct since it doesn't take the `shrinking' (i.e.\
+%    |\pageshrink|) into account.  The `recent contribution list'
+%    might be nonempty so we start with |\par| and an explicit
+%    |\penalty|.\footnote{See the documentation of
+%    \cs{endmulticols} for further details.}
+%    Actually, we use |\addpenalty| to ensure that a following
+%    |\addvspace| will `see' the vertical space that might be
+%    present.
+%    The use of |\addpenalty| will have the effect that all items from
+%    the recent contributions will be moved to the main vertical list
+%    and the |\pagetotal| value will be updated correctly. However,
+%    the penalty will be placed in front of any dangling glue item
+%    with the result that the main vertical list may already be
+%    overfull even if \TeX{} is not invoking the output routine.
+% \changes{v1.3b}{1990/10/09}{Do \cs{penalty} with \cs{addpenalty}}
+% \changes{v1.4e}{1992/03/16}{But ignore \cs{@nobreak} in \cs{addpenalty}}
+%    \begin{macrocode}
+\def\enough@room#1{%
+%    \end{macrocode}
+%    Measuring makes only sense when we are not in ``boxed mode'' so
+%    the routine does nothing if the switch is true.
+%    \begin{macrocode}
+   \if@boxedmulticols\else
+   \par
+%    \end{macrocode}
+%    \label{mac:enoughroom}
+%    To empty the contribution list the first release contained a
+%    penalty zero but this had the result that |\addvspace| couldn't
+%    detect preceding glue. So this was changed to |\addpenalty|. But
+%    this turned out to be not enough as |\addpenalty| will not add a
+%    penalty when |@nobreak| is true. Therefore we force this switch
+%    locally to false. As a result there may be a break between
+%    preceding text and the start of a multicols environment, but this
+%    seems acceptable since there is the optional argument for exactly
+%    this reason.
+%    \begin{macrocode}
+   \bgroup\@nobreakfalse\addpenalty\z@\egroup
+   \page@free \pagegoal
+   \advance \page@free -\pagetotal
+%    \end{macrocode}
+%    To be able to output the value we need to assign it to a register
+%    first since it might be a register (default) in which case we
+%    need to use |\the| or it might be a plain value in which case
+%    |\the| would be wrong.
+% \changes{v1.5e}{1994/05/26}{Assign arg to skip register to be able
+%                             to output value}
+%    \begin{macrocode}
+     \@tempskipa#1\relax
+%    \end{macrocode}
+%    Now we test whether tracing information is required:
+%    \begin{macrocode}
+   \mult@info\z@
+       {Current page:\MessageBreak
+        height=%
+        \the\pagegoal: used \the\pagetotal
+        \space -> free=\the\page@free
+        \MessageBreak
+        needed \the\@tempskipa
+              \space(for #1)}%
+%    \end{macrocode}
+%    Our last action is to force a page break if there isn't enough
+%    room left.
+%    \begin{macrocode}
+   \ifdim \page@free <#1\newpage \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\prepare@multicols}
+%    When preparing for multicolumn output several things must
+%    be done.
+%    \begin{macrocode}
+\def\prepare@multicols{%
+%    \end{macrocode}
+%    We start saving the current |\@totalleftmargin| and then
+%    resetting the |\parshape| in case we are inside some list
+%    environment. The correct indentation for the \mc{} environment in
+%    such a case will be produced by moving the result to the right by
+%    |\multicol@leftmargin| later on. If we would use the value of of
+%    |\@totalleftmargin| directly then lists inside the \mc{}
+%    environment could cause a shift of the output.
+% \changes{v1.4l}{1992/08/17}{saved \cs{@totalleftmargin}}
+%    \begin{macrocode}
+  \multicol@leftmargin\@totalleftmargin
+  \@totalleftmargin\z@
+  \parshape\z@
+%    \end{macrocode}
+%    We also set the register |\doublecol@number| for later use.  This
+%    register should contain $2\times |\col@number|$.  This is also an
+%    indicator that we are within a \mc{} environment as mentioned
+%    above.
+% \changes{v1.5a}{1992/11/04}{Add offset to \cs{doublecolnumber}}
+%    \begin{macrocode}
+  \doublecol@number\col@number
+  \multiply\doublecol@number\tw@
+  \advance\doublecol@number\mult@rightbox
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+  \if@boxedmulticols
+    \let\l@kept@firstmark\kept@firstmark
+    \let\l@kept@botmark\kept@botmark
+    \global\let\kept@firstmark\@empty
+    \global\let\kept@botmark\@empty
+  \else
+%    \end{macrocode}
+%    We add an empty box to the main vertical list to ensure that we
+%    catch any insertions (held over or inserted at the top of the
+%    page). Otherwise it might happen that the |\eject| is discarded
+%    without calling the output routine. Inside the output routine we
+%    remove this box again.  Again this code applies only if we are on
+%    the main vertical list and not within a box.
+%    However, it is not enough to turn off interline spacing, we also
+%    have to clear |\topskip| before adding this box, since |\topskip|
+%    is always inserted before the first box on a page which would
+%    leave us with an extra space of |\topskip| if \mc{} start on a
+%    fresh sheet.
+% \changes{v1.3c}{1991/03/03}{\cs{null} inserted and removed in output}
+% \changes{v1.4a}{1992/02/11}{Conditional code for boxed mode added.}
+% \changes{v1.4o}{1992/11/22}{\cs{topskip} locally zeroed.}
+%    \begin{macrocode}
+    \nointerlineskip {\topskip\z@\null}%
+    \output{%
+      \global\setbox\partial@page\vbox
+        {%
+%    \end{macrocode}
+%    Now we have to make sure that we catch one special situation which
+%    may result in loss of text! If the user has a huge amount of
+%    vertical material within the first optional argument that is larger
+%    then |\premulticols| and we are near the bottom of the page then it
+%    can happen that not the |\eject| is triggering this special output
+%    routine but rather the overfull main vertical list.  In that case
+%    we get another breakpoint through the |\eject| penalty. As a result
+%    this special output routine would be called twice and the contents
+%    of |\partial@page|, i.e.\ the material before the \mc{}
+%    environment gets lost. There are several solutions to avoid this
+%    problem, but for now we will simply detect this and inform the user
+%    that he/she has to enlarge the |\premulticols| by using a suitable
+%    value for the second argument.
+% \changes{v1.4a}{1992/02/11}{Checking for text losses.}
+%    \begin{macrocode}
+%<*check>
+         \ifvoid\partial@page\else
+           \PackageError{multicol}%
+            {Error saving partial page}%
+            {The part of the page before
+             the multicols environment was
+             nearly full with^^Jthe result
+             that starting the environment
+             will produce an overfull
+             page.  Some^^Jtext may be lost!
+             Please increase \premulticols
+             either generally or for this%
+             ^^Jenvironment by specifying a
+             suitable value in the second
+             optional argument to^^Jthe
+             multicols environment.}
+           \unvbox\partial@page
+           \box\last@line
+         \fi
+%</check>
+         \unvbox\@cclv
+         \global\setbox\last@line\lastbox
+        }%
+%    \end{macrocode}
+%    Finally we need to record the marks that are present within the
+%    |\partial@page| so that we can construct correct first and bottom
+%    marks later on. This is done by the following code.
+% \changes{v1.4a}{1992/02/14}{kept marks initiated}
+%    \begin{macrocode}
+           \prep@keptmarks
+%    \end{macrocode}
+%    Finally we have to initialize |\kept@topmark| which should
+%    ideally be initialized with the mark that is current on ``top''
+%    of this page. Unfortunately we can't use |\topmark| because this
+%    register will not always contain what its name promises because
+%    \LaTeX{} sometimes calls the output routine for float
+%    management.\footnote{During such a call the \cs{botmark}
+%    gets globally copied to \cs{topmark} by the \TeX{}
+%    program.} Therefore we use the second best solution by
+%    initializing it with |\firstmark|. In fact, for our purpose this
+%    doesn't matter as we use |\kept@topmark| only to initialize
+%    |\firstmark| and |\botmark| of a following page if we don't find
+%    any marks on the current one.
+% \changes{v1.4i}{1992/06/18}{\cs{kept@topmark} initialized.}
+%    \begin{macrocode}
+           \global\let\kept@topmark\firstmark
+          }\eject
+%    \end{macrocode}
+%    The next thing to do is to assign a new value to |\vsize|.
+%    \LaTeX{} maintains the free room on the page (i.e.\ the page
+%    height without the space for already contributed floats) in the
+%    register |\@colroom|. We must subtract the height of
+%    |\partial@page| to put the actual free room into this
+%    variable.
+%    \begin{macrocode}
+    \advance\@colroom-\ht\partial@page
+%    \end{macrocode}
+%    Then we have to calculate the |\vsize| value to use during column
+%    assembly. |\set@mult@vsize| takes an argument which allows to
+%    make the setting local (|\relax|) or global (|\global|). The
+%    latter variant is used inside the output routine below. At this
+%    point here we have to make a local change to |\vsize| because we
+%    want to get the original value for |\vsize| restored in case
+%    this \mc{} environment ends on the same page where it has started.
+% \changes{v1.4p}{1992/11/26}{Use different \cs{vsize} setting}
+% \changes{v1.4p}{1992/11/26}{Code moved to \cs{set@mult@vsize}}
+%    \begin{macrocode}
+    \set@mult@vsize\relax
+%    \end{macrocode}
+%    Now we switch to a new |\output| routine which will be used
+%    to put the gathered column material together.
+%    \begin{macrocode}
+    \output{\multi@column@out}%
+%    \end{macrocode}
+%    Finally we handle the footnote insertions. We have to multiply
+%    the magnification factor and the extra skip by the number of
+%    columns since each footnote reduces the space for every column
+%    (remember that we have page-wide footnotes).  If, on the other
+%    hand, footnotes are typeset at the very end of the document, our
+%    scheme still works since |\count\footins| is zero then, so it
+%    will not change.
+%    To allow even further customization the setting of the |\footins|
+%    parameters is done in a separate macro.
+% \changes{v1.5?}{1994/?/?}{Use \cs{init@mult@footins}}
+%    \begin{macrocode}
+    \init@mult@footins
+%    \end{macrocode}
+%    For the same reason (page-wide footnotes), the \meta{dimen}
+%    register controlling the maximum space used for footnotes isn't
+%    changed.  Having done this, we must reinsert all the footnotes
+%    which are already present (i.e.\ those encountered when the
+%    material saved in |\partial@page| was first processed). This
+%    will reduce the free space (i.e.\ |\pagetotal|) by the
+%    appropriate amount since we have changed the magnification
+%    factor, etc.\ above.
+%    \begin{macrocode}
+    \reinsert@footnotes
+%    \end{macrocode}
+%    Inside \mc{} a |\clearpage| is fairly useless as we aren't supporting
+%    floats. In fact, it can cause harm as it doesn't know about the
+%    |\partial@page| and may therefore result in making columns too long.
+%    So we change that to behave like |\newpage| but also check if there
+%    are any deferred floats. If so, perhaps the user tried to place them through
+%    that |\clearpage| (but that needs to be done before starting the \mc{}
+%    environment.
+% \changes{v1.8q}{2017/04/11}{Make \cs{clearpage} behave like \cs{newpage} (pr/4511)}
+%    \begin{macrocode}
+   \def\clearpage{%
+     \ifx\@deferlist\@empty\else
+       \PackageError{multicol}%
+          {Deferred floats not cleared}%
+          {A \string\clearpage\space inside multicols acts like
+           \string\newpage\space and doesn't clear floats.\MessageBreak
+           Move it before the multicols environment if you need it.}%
+     \fi
+    \newpage}%
+%    \end{macrocode}
+%    All the code above was only necessary for the unrestricted \mc{}
+%    version, i.e.\ the one that allows page breaks. If we are within
+%    a box there is no point in setting up special output routines or
+%    |\vsize|, etc.
+%    \begin{macrocode}
+  \fi
+%    \end{macrocode}
+%    But now we are coming to code that is necessary in all cases.  We
+%    assign new values to |\vbadness|, |\hbadness| and |\tolerance|
+%    since it's rather hard for \TeX{} to produce `good' paragraphs
+%    within narrow columns.
+% \changes{v1.2a}{1990/02/05}{\cs{vbadness} 10001 now.}
+%    \begin{macrocode}
+  \vbadness\@Mi \hbadness5000
+  \tolerance\multicoltolerance
+%    \end{macrocode}
+%    Since nearly always the first pass will fail we ignore it
+%    completely telling \TeX{} to hyphenate directly.  In fact, we now
+%    use another register to keep the value for the multicol
+%    pre-tolerance, so that a designer may allow to use
+%    |\pretolerance|.
+% \changes{v1.2a}{1990/02/05}{\cs{pretolerance} -1 because it nearly never
+%                            succeeds.}
+% \changes{v1.4e}{1992/03/20}{Using}
+%    \begin{macrocode}
+  \pretolerance\multicolpretolerance
+%    \end{macrocode}
+%    For use with the new \TeX{} we set |\emergencystretch| to
+%    $|\col@number| \times 4pt$. However this is only a guess
+%    so at the moment this is done in a macro
+%    |\setemergencystretch| which gets the current |\hsize|
+%    and the number of columns as arguments. Therefore users are able
+%    to figure out their own formula.
+% \changes{v1.2a}{1990/02/05}{\cs{setemergencystretch} added.}
+%    \begin{macrocode}
+  \setemergencystretch\col@number\hsize
+%    \end{macrocode}
+%    Another hook to allow people adding their own extensions without
+%    making a new package is |\set@floatcmds| which handles any
+%    redefinitions of \LaTeX{}s internal float commands to work with
+%    the \mc{} environment. At the moment it is only used to redefine
+%    |\@dblfloat| and |\end@dblfloat|.
+% \changes{v1.2a}{1990/02/05}{\cs{set@floatcmds} added.}
+%    \begin{macrocode}
+  \set@floatcmds
+%    \end{macrocode}
+%    Additionally, we advance |\baselineskip| by
+%    |\multicolbaselineskip| to allow corrections for narrow
+%    columns.
+%    \begin{macrocode}
+  \advance\baselineskip\multicolbaselineskip
+%    \end{macrocode}
+% \changes{v1.0e}{1989/06/21}{\cs{textwidth} changed to \cs{linewidth}.}
+% \changes{v1.0e}{1989/06/21}{So this file will
+%                           work with the `twocolumn' command.}
+%    The |\hsize| of the columns is given by the formula:
+%    \[
+%       { |\linewidth| - (|\col@number|-1)
+%                             \times
+%                             |\columnsep|
+%        \over
+%        |\col@number|}
+%    \]
+%    The formula above has changed from release to release. We now
+%    start with the current value of |\linewidth| so that the column
+%    width is properly calculated when we are inside a minipage or a
+%    list or some other environment.
+%    This will be achieved with:
+%    \begin{macrocode}
+  \hsize\linewidth \advance\hsize\columnsep
+  \advance\hsize-\col@number\columnsep
+  \divide\hsize\col@number
+%    \end{macrocode}
+%    We also set |\linewidth| and |\columnwidth| to |\hsize| In the past
+%    |\columnwidth| was left unchanged. This is inconsistent,
+%    but |\columnwidth| is used only by floats (which
+%    aren't allowed in their current implementation) and by the
+%    |\footnote| macro. Since we want page-wide
+% footnotes\footnote{I'm not sure that I really want page-wide
+%                       footnotes. But balancing of the last page can
+%                       only be achieved with this approach or with a
+%                       multi-path algorithm which is complicated and
+%                       slow. But it's a challenge to everybody to
+%                       prove me wrong!  Another possibility is to
+%                       reimplement a small part of the {\it
+%                       fire\_up\/} procedure in \TeX{} (the program).
+%                       I think that this is the best solution if you
+%                       are interested in complex page makeup, but it
+%                       has the disadvantage that the resulting
+%                       program cannot be called \TeX{} thereafter.}
+%    this simple trick saved us from rewriting the |\footnote|
+%    macros. However, some applications referred to |\columnwidth| as
+%    the ``width of the current column'' to typeset displays
+%    (the \texttt{amsmath} package, for example) and to allow the use
+%    of such applications together with \texttt{multicol} this is now
+%    changed.
+%
+%    Before we change |\linewidth| to the new value we record its old
+%    value in some register called |\full@width|. This value is
+%    used later on when we package all columns together.
+% \changes{v1.0e}{1989/06/21}{Setting of \cs{columnwidth} removed.}
+% \changes{v1.5o}{1997/11/16}{Setting of \cs{columnwidth} added again
+%                           pr/2664.}
+%    \begin{macrocode}
+  \full@width\linewidth
+  \linewidth\hsize
+  \columnwidth\hsize
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\init@mult@footins}
+%    This macro is used to set up the parameters associated
+%    with footnote floats. It can be redefined by applications that
+%    require different amount of spaces when typesetting footnotes.
+%    \begin{macrocode}
+\def\init@mult@footins{%
+    \multiply\count\footins\col@number
+    \multiply\skip \footins\col@number
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%  \begin{macro}{\set@mult@vsize}
+%
+%    Since we have to set |\col@umber| columns on one page,
+%    each with a height of |\@colroom|, we have to assign
+%    $
+%      |\vsize|  = |\col@number| \times |\@colroom|
+%    $
+%    in order to collect enough material before entering the
+%    |\output| routine again. In fact we have to add another
+%    $
+%       (|\col@number|-1) \times (|\baselineskip|-|\topskip|)
+%    $
+%    if you think about it.
+% \changes{v1.4p}{1992/11/26}{Macro added.}
+%    \begin{macrocode}
+\def\set@mult@vsize#1{%
+    \vsize\@colroom
+    \@tempdima\baselineskip
+    \advance\@tempdima-\topskip
+    \advance\vsize\@tempdima
+    \vsize\col@number\vsize
+    \advance\vsize-\@tempdima
+%    \end{macrocode}
+%    But this might not be enough since we use |\vsplit| later to
+%    extract the columns from the gathered material. Therefore we add
+%    some `extra lines,' one for each column plus a corrective action
+%    depending on the value of the `\texttt{collectmore}' counter.
+%    The final value is assigned globally if |#1| is |\global| because
+%    we want to use this macro later inside the output routine too.
+% \changes{v1.6c}{2003/04/08}{Collect one line per column more}
+%    \begin{macrocode}
+    \advance\vsize\col@number\baselineskip
+    #1\advance\vsize
+        \c@collectmore\baselineskip}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\multicol@leftmargin}
+%    Here is the dimen register we need for saving away the outer
+%    value of |\@totalleftmargin|.
+%    \begin{macrocode}
+\newdimen\multicol@leftmargin
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\@Mvi}
+%    In versions prior to 1.8r the balancing at the end of the
+%   environment was done by changing the output routine from
+%   |\multi@column@out| to |\balance@column@out|. As it turned out
+%   that this has a couple of issues when the last columns should not
+%   be balanced after all (for example because they contained several
+%   |\columnbreak| commands we now stay with one output routine for
+%   the environment and only signal that we reached the end of the
+%   environment by marking it with a special penalty that we can check
+%   for later.
+% \changes{v1.8r}{2018/01/28}{Macro added}
+%    \begin{macrocode}
+\mathchardef\@Mvi=10006  % 10005 is \columnbreak
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \begin{macro}{\endmulticols}
+%    When the end of the \mc{} environment is sensed we have to
+%    balance the gathered material. Depending on whether or not we are
+%    inside a boxed multicol different things must happen. But first
+%    we end the current paragraph with a |\par| command.
+%    \begin{macrocode}
+\def\endmulticols{\par
+  \if@boxedmulticols
+%    \end{macrocode}
+%    In boxed mode we have to close the box in which we have gathered
+%    all material for the columns. But before we do this we need to
+%    remove any space at the end of the box as we don't want to use
+%    this in balancing. Because of the |\color@endgroup| this can't be
+%    done later in |\balance@columns| as the color command will hide
+%    it. 
+% \changes{v1.8c}{2013/11/03}{Add \cs{color@endgroup} to prevent color leak}
+% \changes{v1.8f}{2014/06/19}{Discard spaces before adding \cs{color@endgroup}}
+%    \begin{macrocode}
+    \remove@discardable@items\color@endgroup\egroup
+%    \end{macrocode}
+%    Now we call |\balance@columns| the routine that balances material
+%    stored in the box |\mult@box|.
+% \changes{v1.5?}{1994/?/?}{Splitting off zero box moved to
+%                           \cs{balance@columns}}
+%    \begin{macrocode}
+    \balance@columns
+%    \end{macrocode}
+%    After balancing the result has to be returned by the command
+%    |\page@sofar|. But before we do this we reinsert any marks found
+%    in box |\mult@box|.
+%    \begin{macrocode}
+    \return@nonemptymark{first}%
+                 \kept@firstmark
+    \return@nonemptymark{bot}%
+                  \kept@botmark
+    \page@sofar
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \global\let\kept@firstmark
+               \l@kept@firstmark
+    \global\let\kept@botmark
+            \l@kept@botmark
+%<*marktrace>
+    \mult@info\tw@
+      {Restore kept marks to\MessageBreak
+       first: \meaning\kept@firstmark
+       \MessageBreak bot\space\space:
+                     \meaning\kept@botmark }%
+%</marktrace>
+%    \end{macrocode}
+%    This finishes the code for the ``boxed'' case.
+%    \begin{macrocode}
+  \else
+%    \end{macrocode}
+%    If there was a |\columnbreak| on the very last line all material
+%    will have been moved to the |\colbreak@box|. Thus the the galley
+%    will be empty and no output routine gets called so that the text
+%    is lost. To avoid this problem (though unlikely) we check if the
+%    current galley is empty and the |\colbreak@box| contains text and
+%    if so return that to the galley. If the galley is non-empty any
+%    material in  |\colbreak@box| is added in the output routine since
+%    it needs to be put in front.
+% \changes{v1.6d}{2003/04/17}{Catch problem with \cs{columnbreak} in
+%    last line}
+%    \begin{macrocode}
+    \ifdim\pagegoal=\maxdimen
+      \ifvoid\colbreak@box\else
+        \mult@info\@ne{Re-adding forced
+                 break(s) for splitting}%
+        \unvbox\colbreak@box\fi
+    \fi
+%    \end{macrocode}
+%    If we are in an unrestricted \mc{} environment we end the current
+%    paragraph above with |\par| but this isn't sufficient since \TeX{}s
+%    {\it page\_builder} will not totally empty the contribution
+%    list.\footnote{This once caused a puzzling bug where some of the
+%    material was balanced twice, resulting in some overprints.  The
+%    reason was the \cs{eject} which was placed at the end of
+%    the contribution list. Then the {\it page\_builder} was called
+%    (an explicit \cs{penalty} will empty the contribution
+%    list), but the line with the \cs{eject} didn't fit onto
+%    the current page.  It was then reconsidered after the output
+%    routine had ended, causing a second break after one line.}
+%    Therefore we must also add an explicit |\penalty|.  Now the
+%    contribution list will be emptied and, if its material doesn't
+%    all fit onto the current page then the output routine will be
+%    called before we change it.
+% \changes{v1.3b}{1990/10/09}{Do \cs{penalty} with \cs{addpenalty}}
+% \changes{v1.4e}{1992/03/16}{But ignore \cs{@nobreak} in \cs{addpenalty}}
+% \changes{v1.5c}{1993/04/18}{Again use \cs{penalty}}
+%    At this point we need to use |\penalty| not |\addpenalty| to
+%    ensure that a) the recent contributions are emptied and b) that
+%    the very last item on the main vertical list is a valid break
+%    point so that \TeX{} breaks the page in case it is overfull.
+%    \begin{macrocode}
+    \penalty\z@
+%    \end{macrocode}
+%    Now it's safe to call the output routine in order to balance
+%    the columns. We do this by calling it with a special penalty.
+% \changes{v1.8r}{2018/01/28}{Use special penalty to signal end of environment}
+%    \begin{macrocode}
+    \penalty-\@Mvi
+%    \end{macrocode}
+%    If the \mc{} environment body was completely empty or if a
+%    multi-page \mc{} just ends at a page boundary we have the unusual
+%    case that the |\eject| will have no effect (since the main
+%    vertical list is empty)---thus no output routine is called at
+%    all. As a result the material preceding the \mc{} (stored in
+%    |\partial@page| will get lost if we don't put this back by hand.
+% \changes{v1.4m}{1992/09/04}{Check \cs{partial@page} being emptied}
+%    \begin{macrocode}
+    \ifvbox\partial@page
+         \unvbox\partial@page\fi
+%    \end{macrocode}
+%    After the output routine has acted we restore
+%    the kept marks to their initial value.
+%    \begin{macrocode}
+     \global\let\kept@firstmark\@empty
+     \global\let\kept@botmark\@empty
+%<*marktrace>
+     \mult@info\tw@
+       {Make kept marks empty}%
+%</marktrace>
+  \fi
+%    \end{macrocode}
+%    The output routine above will take care of the |\vsize| and
+%    reinsert the balanced columns, etc. But it can't reinsert the
+%    |\footnotes| because we first have to restore the
+%    |\footins| parameter since we are returning to one column
+%    mode. This will be done in the next line of code; we simply close
+%    the group started in |\multicols|.
+%
+%    To fix an obscure bug which is the result of the current
+%    definition of the |\begin| \ldots\ |\end| macros, we check that
+%    we are still (logically speaking) in the \mc{} environment. If,
+%    for example, we forget to close some environment inside the
+%    \mc{} environment, the following |\endgroup| would be
+%    incorrectly considered to be the closing of this environment.
+% \changes{v1.3c}{1991/03/14}{Check closing env.}
+%    \begin{macrocode}
+  \@checkend{multicols}%
+  \endgroup
+%    \end{macrocode}
+%    We also set the `\textsf{unbalance}' counter to its default. This is
+%    done globally since \LaTeX{} counters are always changed this
+%    way.\footnote{Actually, we are still in a group started by the
+%    \cs{begin} macro, so \cs{global} must be used
+%    anyway.}
+%    \begin{macrocode}
+  \global\c@unbalance\z@
+%    \end{macrocode}
+%    Now it's time to return any footnotes if we are in unrestricted
+%    mode. In boxed mode footnotes are kept inside, but in that case
+%    we have to write another column status into the \texttt{.aux}
+%    file to support \cs{docolaction} in case we have nested
+%    environments.
+% \changes{v1.8s}{2018/04/20}{Support for \cs{docolaction} (issue/39)}
+%    \begin{macrocode}
+  \if@boxedmulticols
+    \mc@col@status@write
+  \else
+    \reinsert@footnotes
+%    \end{macrocode}
+%    We also take a look at the amount of free space on the current
+%    page to see if it's time for a page break.  The vertical space
+%    added thereafter will vanish if |\enough@room| starts a new
+%    page.
+%
+%    But there is one catch. If the |\end{multicols}| is at the top of
+%    which can happen if there is a break point just before it (such
+%    as end ending environment) which was chosen. In that case we
+%    would do the next page using the internal |\vsize| for multicol
+%    collection which is a disaster. So we better catch this
+%    case. Fortunately we can detect it by looking at |\pagegoal|.
+% \changes{v1.5x}{2000/05/05}{Detect and fix problem if a multicols
+%    ends at the top of a page}
+%    \begin{macrocode}
+    \ifdim \pagegoal=\maxdimen
+      \global\vsize\@colroom
+    \else
+      \enough@room\postmulticols
+    \fi
+  \fi
+  \addvspace\multicolsep
+%    \end{macrocode}
+%    There is one more thing to do: the balanced result of the
+%   environment is supposed to have a |\prevdepth| of zero as we
+%   backed up by its real prevdepth within |\page@sofar|. However if
+%   the balancing happened in the output routine then \TeX{} reverts
+%   to the |\prevdepth| that was current before the OR once the OR has
+%   finished. In short |\prevdepth| is something you can't set
+%   globally it is alway local to the current list being built. Thus
+%   we need to set it back to zero here to avoid incorrect spacing.
+% \changes{v1.8h}{2014/09/12}{Set \cs{prevdepdth} for current vlist
+%   when returning from multicols environment}
+%    \begin{macrocode}
+ \prevdepth\z@
+%    \end{macrocode}
+%    If statistics are required we finally report that we have
+%    finished everything.
+%    \begin{macrocode}
+  \mult@info\z@
+     {Ending environment
+             \if@boxedmulticols
+                \space(boxed mode)\fi
+              }}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\c@unbalance}
+% \SpecialMainIndex{\c@collectmore}
+% \SpecialMainIndex{\col@number}
+% \SpecialMainIndex{\doublecol@number}
+% \SpecialMainIndex{\premulticols}
+% \SpecialMainIndex{\multicoltolerance}
+% \SpecialMainIndex{\multicolpretolerance}
+% \SpecialMainIndex{\page@free}
+% \SpecialMainIndex{\premulticols}
+% \SpecialMainIndex{\postmulticols}
+% \SpecialMainIndex{\multicolsep}
+% \SpecialMainIndex{\multicolbaselineskip}
+% \SpecialMainIndex{\partial@page}
+%    Let us end this section by allocating all the registers used so
+%    far.
+%    \begin{macrocode}
+\newcount\c@unbalance
+\newcount\c@collectmore
+%    \end{macrocode}
+%    In the new \LaTeX{} release |\col@number| is already allocated by
+%    the kernel, so we don't allocate it again.
+%    \begin{macrocode}
+%\newcount\col@number
+\newcount\doublecol@number
+\newcount\multicoltolerance
+\newcount\multicolpretolerance
+\newdimen\full@width
+\newdimen\page@free
+\newdimen\premulticols
+\newdimen\postmulticols
+\newskip\multicolsep
+\newskip\multicolbaselineskip
+\newbox\partial@page
+\newbox\last@line
+%    \end{macrocode}
+%    And here are their default values:
+%    \begin{macrocode}
+\c@unbalance   = 0
+\c@collectmore = 0
+%    \end{macrocode}
+%    To allow checking whether some macro is used within the \mc{}
+%    environment the counter |\col@number| gets a default of |1|
+%    outside the the environment.
+% \changes{v1.3d}{1991/10/23}{\cs{col@number} set to one}
+% \changes{v1.8o}{2016/02/08}{\cs{col@number} already initialized in the 
+%    kernel, so not initializing it in the package 
+%    in case the document is in two-column (pr/4435)}
+%    \begin{macrocode}
+%\col@number = 1
+\multicoltolerance = 9999
+\multicolpretolerance = -1
+\premulticols = 50pt
+\postmulticols= 20pt
+\multicolsep = 12pt plus 4pt minus 3pt
+\multicolbaselineskip=0pt
+%    \end{macrocode}
+% \end{macro}
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{The output routines}]
+%
+% We first start with some simple macros. When typesetting the page we
+% save the columns either in the box registers 0, 2, 4,\ldots\
+% (locally) or 1, 3, 5,\ldots\ (globally). This is \PlainTeX{} policy
+% to avoid an overflow of the save stack.
+%
+% \begin{macro}{\process@cols}
+%    Therefore we define a |\process@cols| macro to help us in
+%    using these registers in the output routines below. It has two
+%    arguments: the first one is a number; the second one is the
+%    processing information.  It loops starting with |\count@=#1|
+%    (|\count@| is a scratch register defined in \PlainTeX),
+%    processes argument |#2|, adds two to |\count@|,
+%    processes argument |#2| again, etc.\ until |\count@| is
+%    higher than |\doublecol@number|.  It might be easier to
+%    understand it through an example, so we define it now and
+%    explain its usage afterwards.
+%    \begin{macrocode}
+\def\process@cols#1#2{\count@#1\relax
+     \loop
+%<*debug>
+     \typeout{Looking at box \the\count@}
+%</debug>
+      #2%
+     \advance\count@\tw@
+     \ifnum\count@<\doublecol@number
+   \repeat}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\page@sofar}
+%    We now define |\page@sofar| to give an example of the
+%    |\process@cols| macro. |\page@sofar| should output everything
+%    prepared by the balancing routine |\balance@columns|.
+%    \begin{macrocode}
+\def\page@sofar{%
+%    \end{macrocode}
+%    |\balance@columns| prepares its output in the even numbered
+%    scratch box registers.
+%    Now we output the columns gathered assuming that they are saved
+%    in the box registers 2 (left column), 4 (second column), \ldots\
+%    However, the last column (i.e.\ the right-most) should be saved in
+%    box register 0.\footnote{You will see the reason for this numbering
+%                             when we look at the output routines
+%                             \cs{multi@column@out} and
+%                             \cs{balance@columns@out}.}
+%    First we ensure that the columns have equal width. We use
+%    |\process@cols| for this purpose, starting with
+%    $|\count@|=|\mult@rightbox|$. Therefore |\count@| loops through
+%    |\mult@rightbox|, $|\mult@rightbox| + 2$,\ldots
+%                                  (to |\doublecol@number|).
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+%    \begin{macrocode}
+   \process@cols\mult@rightbox
+%    \end{macrocode}
+%    We have to check if the box in question is void, because the
+%    operation |\wd|\meta{number} on a void box will \emph{not} change
+%    its dimension (sigh).
+% \changes{v1.5h}{1994/08/26}{Check for void boxes}
+% \changes{v1.5i}{1994/10/02}{But don't remove original code.}
+%    \begin{macrocode}
+       {\ifvoid\count@
+          \setbox\count@\hbox to\hsize{}%
+        \else
+          \wd\count@\hsize
+        \fi}%
+%    \end{macrocode}
+%    Now we give some tracing information.
+% \changes{v1.4l}{1992/08/17}{use \cs{multicol@leftmargin} instead of
+%                           \cs{@totalleftmargin}}
+% \changes{v1.6b}{2003/03/15}{Different info display}
+%    \begin{macrocode}
+   \count@\col@number \advance\count@\m@ne
+   \mult@info\z@
+    {Column spec: \the\full@width\space = indent
+                  + columns + sep =\MessageBreak
+        \the\multicol@leftmargin\space
+        + \the\col@number\space
+        x \the\hsize\space
+        + \the\count@\space
+        x \the\columnsep
+     }%
+%    \end{macrocode}
+%    At this point we should always be in vertical mode.
+%    \begin{macrocode}
+\ifvmode\else\errmessage{Multicol Error}\fi
+%    \end{macrocode}
+%    Now we put all columns together in an |\hbox| of width
+%    |\full@width| (shifting it by |\multicol@leftmargin| to the right
+%    so that it will be placed correctly if we are within a list
+%    environment)
+%    and separating the columns with a rule if desired.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.5z}{2000/07/10}{Ensure that column rule has always
+%                             \cs{normalcolor}}
+% \changes{v1.6f}{2006/09/19}{Make the color of the rule a hook}
+% \changes{v1.4l}{1992/08/17}{use \cs{multicol@leftmargin} instead of
+%                           \cs{@totalleftmargin}}
+%
+%    The box containing the columns has  a large height and thus will
+%    always result in using |\lineskip| if the normal |\baselineskip|
+%    calculations are used. We therefore better cancel that process.
+% \changes{v1.5z1}{2003/02/17}{Suppress interline glue at this point}
+%    \begin{macrocode}
+   \nointerlineskip
+%    \end{macrocode}
+%    As mentioned earlier we want to have the reference point of the
+%    box we put on the page being at the baseline of the last line of
+%    the columns but we also want to ensure that the box has no depth
+%    so that any following skip is automatically starting from that
+%    baseline.
+%    We achieve this by recording the depths of all columns and then
+%    finally backing up by the maximum. (perhaps a simpler method
+%    would be to assemble the box in a register and set the depth of
+%    that box to zero (not checked).
+%
+%    We need a global scratch register for this; using standard \TeX{}
+%    conventions we choose |\dimen2| and initialize it with the depth
+%    of the character ``p'' since that is one of the depths that
+%    compete for the maximum.
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+%    \begin{macrocode}
+   \setbox\z@\hbox{p}\global\dimen\tw@\dp\z@
+   \moveright\multicol@leftmargin
+    \hbox to\full@width{%
+%    \end{macrocode}
+%    If the document is written in a language that is typeset right-to-left
+%    then, of course, the multicol columns should be also typeset
+%    right-to-left. To support this we call |\mc@align@columns| which
+%    with execute different code depending on the typesetting direction.
+% \changes{v1.7b}{2011/12/18}{RL language support fixed}
+%    \begin{macrocode}
+       \mc@align@columns
+%    \end{macrocode}
+%    The depths of the columns depend on their last lines. To ensure
+%    that we will always get a similar look as far as the rules are
+%    concerned we force the depth to be at least the depth of a
+%    letter~`p' (which is what we set |\dimen2| to above).
+%    \begin{macrocode}
+       \rlap{\phantom p}%
+    }%
+%    \end{macrocode}
+%    The processed material might consist of a last line with a
+%    descender in which case the |\prevdepth| will be
+%    non-zero. However, this material is getting reformatted now so
+%    that this value is likely to be wrong. We therefore normalize the
+%    situation by pretending that the depth is zero. However, if |\page@sofar|
+%   is being called inside the OR then setting |\prevdepth| here has
+%   no long-lasting effect, we therefore have to repeat this once we
+%   return to the main vertical list. Here we set it only for those
+%   cases where the command is used within a list and then followed by
+%   something else.
+% \changes{v1.8g}{2014/08/24}{Resetting \cs{prevdepth} in the right place}
+%    \begin{macrocode}
+   \prevdepth\z@
+%    \end{macrocode}
+%    Now after typesetting the box we back up to its baseline by using
+%    the value stored in |\dimen2| (which will hold the largest depth
+%    found on any column).
+% \changes{v1.8g}{2003/03/15}{Now adjusting \cs{prevdepth}}
+%    \begin{macrocode}
+ \kern-\dimen\tw@
+%    \end{macrocode}
+%    However, in case one of the columns was unusually deep \TeX{} may
+%    have tried some corrective actions in which case backing up by
+%    the saved value will not bring us back to the baseline. A good
+%    indication for this is a depth of |\maxdepth| though it is not an
+%    absolute proof. If the option \texttt{grid} is used
+%    |\mc@gridwarn| will expand to this, otherwise to |\maxdimen| in
+%    which case this warning will not show up.
+% \changes{v1.8g}{2014/08/24}{Warn if value is exceeded not when equal}
+%    \begin{macrocode}
+ \ifdim\dimen\tw@ > \mc@gridwarn
+   \PackageWarning{multicol}%
+     {Very deep columns!\MessageBreak
+      Grid alignment might be broken}%
+ \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\columnseprulecolor}
+% \changes{v1.6f}{2006/09/19}{Make the color of the rule a hook}
+%    By default the vertical rule between columns will be in |\normalcolor|.
+%    \begin{macrocode}
+\def\columnseprulecolor{\normalcolor}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\reinsert@footnotes}
+%    Before we tackle the bigger output routines we define just one
+%    more macro which will help us to find our way through the
+%    mysteries later. |\reinsert@footnotes| will do what its name
+%    indicates: it reinserts the footnotes present in
+%    |\footinbox| so that they will be reprocessed by \TeX{}'s
+%    {\it page\_builder}.
+%
+%    Instead of actually reinserting the footnotes we insert an empty
+%    footnote. This will trigger insertion mechanism as well and since
+%    the old footnotes are still in their box and we are on a fresh page
+%    |\skip| |footins| should be correctly taken into account.
+% \changes{v1.3c}{1990/03/03}{\cs{unbox}ing avoided.}
+%    \begin{macrocode}
+\def\reinsert@footnotes{\ifvoid\footins\else
+         \insert\footins{}\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\vfilmaxdepth}
+%    This curious definition is used as the space at the bottom of a
+%   column if we implement |\raggedcolumns|. Normally one only appends
+%   |\vfill| in that case but this is actually wrong for columns that
+%   are more or less full: by adding a glue at the bottom such a
+%   column doesn't have any depth any more but without it the material
+%   would be allowed a depth of |\maxdepth|. So we allow shrinking by
+%   that amount. This only makes a difference if the box would
+%   otherwise become overfull and shrinking never exceeds the
+%   specified value, so we should be fine. 
+% \changes{v1.8h}{2014/09/12}{Macro added  (pr/4395)}
+% \changes{v1.8j}{2015/03/07}{Use only `0.0001fil' for stretching}
+%    \begin{macrocode}
+\def\vfilmaxdepth{\vskip \z@ \@plus .0001fil 
+                           \@minus \maxdepth}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\multi@column@out}
+%    Now we can't postpone the difficulties any longer.  The
+%    |\multi@column@out| routine will be called in two situations.
+%    Either the page is full (i.e., we have collected enough material
+%    to generate all the required columns) or a float or marginpar or
+%    a |\clearpage| is
+%    sensed.  In the latter case the |\outputpenalty| is less
+%    than $-10000$, otherwise the penalty which triggered the output
+%    routine is higher.  Therefore it's easy to distinguish both
+%    cases: we simply test this register.
+% \changes{v1.5c}{1993/04/18}{Support \cs{clearpage}}
+%    \begin{macrocode}
+\def\multi@column@out{%
+   \ifnum\outputpenalty <-\@M
+%    \end{macrocode}
+%    If this was a |\clearpage|, a float or a marginpar we call
+%    |\speci@ls|
+%    \begin{macrocode}
+    \speci@ls \else
+%    \end{macrocode}
+%    otherwise we construct the final page.
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for
+%                             column break support}
+%    For the next block of code see comments in section~\ref{sec:colbreak}.
+%    \begin{macrocode}
+    \ifvoid\colbreak@box\else
+      \mult@info\@ne{Re-adding forced
+                break(s) for splitting}%
+      \setbox\@cclv\vbox{%
+       \unvbox\colbreak@box
+       \penalty-\@Mv
+       \unvbox\@cclv}%
+    \fi
+%    \end{macrocode}
+%    Let us now consider the
+%    normal case. We have to |\vsplit| the columns from the
+%    accumulated material in box 255.  Therefore we first assign
+%    appropriate values to |\splittopskip| and |\splitmaxdepth|.
+%    \begin{macrocode}
+   \splittopskip\topskip
+   \splitmaxdepth\maxdepth
+%    \end{macrocode}
+%    We also need to restrict |\boxmaxdepth| so that re-boxing is not
+%    generating boxes with arbitrary depth.   
+% \changes{v1.8j}{2015/03/07}{Set \cs{boxmaxdepth}}
+%    \begin{macrocode}
+   \boxmaxdepth\maxdepth
+%    \end{macrocode}
+%    Then we calculate the current column height (in |\dimen@|).
+%    Note that the height of |\partial@page| is already
+%    subtracted from |\@colroom| so we can use its value as a
+%    starter.
+%    \begin{macrocode}
+   \dimen@\@colroom
+%    \end{macrocode}
+%    But we must also subtract the space occupied by footnotes on the
+%    current page. Note that we first have to reset the skip register
+%    to its normal value.
+%    Again, the actual action is carried out in a utility macro, so that
+%    other applications can modify it.
+% \changes{v1.5?}{1994/?/?}{Use \cs{leave@mult@footins}}
+%    \begin{macrocode}
+   \divide\skip\footins\col@number
+   \ifvoid\footins \else
+      \leave@mult@footins
+   \fi
+%    \end{macrocode}
+%    And there is one more adjustment that we have to make: if the
+%    user has issue a |\enlargethispage| command then the height the
+%    |\@kludgeins| box will be the negation of the size by which the
+%    page should be enlarged. If the star form of this command has
+%    been used then we also need to shrink the resulting column.
+
+%    That local change will be reverted at the end of the output
+%   routine So for the next page the original state will be
+%   reestablished. However, in theory there is a possibility to sneak
+%   in a whole multicols environment into the running header
+%   definition. If that happens then it will also be affected by this
+%   change---too bad I think.   
+% \changes{v1.8a}{2011/12/20}{Support for \cs{enlargethispage}}
+% \changes{v1.8v}{2018/12/27}{Removed dead code, the case where this
+%   can go wrong is too obscure to worry about it (gh/101)}
+%    \begin{macrocode}
+   \ifvbox \@kludgeins
+     \advance \dimen@ -\ht\@kludgeins
+%    \end{macrocode}
+%    The star form of  |\enlargethispage| makes the width of the box
+%    greater than zero (sneaky isn't it?).
+%    \begin{macrocode}
+     \ifdim \wd\@kludgeins>\z@
+        \shr@nkingtrue
+     \fi
+   \fi
+%    \end{macrocode}
+%    Now we are able to |\vsplit| off all but the last column.
+%    Recall that these columns should be saved in the box registers 2,
+%    4,\ldots\ (plus offset).
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+%    \begin{macrocode}
+   \process@cols\mult@gfirstbox{%
+        \setbox\count@
+            \vsplit\@cclv to\dimen@
+%    \end{macrocode}
+%    After splitting we update the kept marks.
+%    \begin{macrocode}
+            \set@keptmarks
+%    \end{macrocode}
+%    If |\raggedcolumns| is in force we add a |vfill| at the bottom by
+%    unboxing the split box.
+%    But we need to unbox anyway to ensure that at the end of the box
+%    we do not have unwanted space. This can sneak in in certain
+%    situations, for example, if two lists follow each other and we
+%    break between them. While such space is usually zero it still has
+%    an effect because it hides depth of the last line in the column
+%    and that will result in incorrect placement.
+% \changes{v1.3c}{1990/03/03}{\cs{unbox}ing avoided.}
+% \changes{v1.8b}{2013/08/28}{And 20odd years later conclude that
+%         this was wrong and unboxing is always needed.}
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+%                             end of split boxes}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8k}{2015/03/22}{\cs{remove@discardable@items} removed}
+%    \begin{macrocode}
+            \setbox\count@
+                 \vbox to\dimen@
+                  {\unvbox\count@
+                   \ifshr@nking\vfilmaxdepth\fi}%
+           }%
+%    \end{macrocode}
+%    Then the last column follows.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+%                             end of split boxes}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8k}{2015/03/22}{\cs{remove@discardable@items} removed}
+%    \begin{macrocode}
+   \setbox\mult@rightbox
+       \vsplit\@cclv to\dimen@
+   \set@keptmarks
+   \setbox\mult@rightbox\vbox to\dimen@
+          {\unvbox\mult@rightbox
+           \ifshr@nking\vfilmaxdepth\fi}%
+%    \end{macrocode}
+%    Having done this we hope that box 255 is emptied. If not, we
+%    reinsert its contents.
+% \changes{v1.8a}{2011/12/20}{Only re-add output penalty if it was
+%    explicitly set}
+%    \begin{macrocode}
+   \ifvoid\@cclv \else
+       \unvbox\@cclv
+       \ifnum\outputpenalty=\@M
+       \else
+          \penalty\outputpenalty
+       \fi
+%    \end{macrocode}
+%    In this case a footnote that happens to fall into the leftover
+%    bit will be typeset on the wrong page. Therefore we warn the user
+%    if the current page contains footnotes. The older versions of
+%    \mc{} produced this warning regardless of whether or not
+%    footnotes were present, resulting in many unnecessary warnings.
+% \changes{v1.3c}{1991/02/17}{Check if footnotes are actually present
+%                           before issuing a warning.}
+%    \begin{macrocode}
+       \ifvoid\footins\else
+         \PackageWarning{multicol}%
+          {I moved some lines to
+           the next page.\MessageBreak
+           Footnotes on page
+           \thepage\space might be wrong}%
+       \fi
+%    \end{macrocode}
+%    If the `\textsf{tracingmulticols}' counter is 4 or higher we also
+%    add a rule.
+%    \begin{macrocode}
+       \ifnum \c@tracingmulticols>\thr@@
+                    \hrule\allowbreak \fi
+   \fi
+%    \end{macrocode}
+%    To get a correct marks for the current page we have to (locally)
+%    redefine |\firstmark| and |\botmark|.
+%    If |\kept@firstmark| is non-empty then |\kept@botmark| must be
+%    non-empty too so we can use their values. Otherwise we use the
+%    value of |\kept@topmark| which was first initialized when we
+%    gathered the |\partical@page| and later on was updated to the
+%    |\botmark| for the preceding page.
+%
+% \changes{v1.4a}{1992/02/14}{\cs{botmark} set to \cs{splitbotmark}}
+%    \begin{macrocode}
+   \ifx\@empty\kept@firstmark
+      \let\firstmark\kept@topmark
+      \let\botmark\kept@topmark
+   \else
+      \let\firstmark\kept@firstmark
+      \let\botmark\kept@botmark
+   \fi
+%    \end{macrocode}
+%    We also initialize |\topmark| with |\kept@topmark|. This will make
+%    this mark okay for all middle pages of the \mc{} environment.
+% \changes{v1.5d}{1993/09/15}{reinit \cs{topmark}}
+%    \begin{macrocode}
+   \let\topmark\kept@topmark
+%<*marktrace>
+   \mult@info\tw@
+        {Use kept top mark:\MessageBreak
+          \meaning\kept@topmark
+         \MessageBreak
+         Use kept first mark:\MessageBreak
+          \meaning\kept@firstmark
+        \MessageBreak
+         Use kept bot mark:\MessageBreak
+          \meaning\kept@botmark
+        \MessageBreak
+         Produce first mark:\MessageBreak
+          \meaning\firstmark
+        \MessageBreak
+        Produce bot mark:\MessageBreak
+          \meaning\botmark
+         \@gobbletwo}%
+%</marktrace>
+%    \end{macrocode}
+%    With a little more effort we could have done better. If we had,
+%    for example, recorded the shrinkage of the material in
+%    |\partial@page| it would be now possible to try higher
+%    values for |\dimen@| (i.e.\ the column height) to overcome
+%    the problem with the nonempty box 255. But this would make the
+%    code even more complex so I skipped it in the current
+%    implementation.
+%
+%    Now we use \LaTeX{}'s standard output
+%    mechanism.\footnote{This will produce a lot of overhead since both
+%                       output routines are held in memory. The correct
+%                       solution would be to redesign the whole output
+%                       routine used in \LaTeX.}
+%    Admittedly this is a funny way to do it.
+%
+%    Within the OR |\boxmaxdepth| needs to be unrestricted so we set it back
+%    now as it was changed above.
+% \changes{v1.8p}{2016/04/07}{Reset \cs{boxmaxdepth}} 
+%    \begin{macrocode}
+   \boxmaxdepth\maxdimen
+   \setbox\@cclv\vbox{\unvbox\partial@page
+                      \page@sofar}%
+%    \end{macrocode}
+%    The macro |\@makecol| adds all floats assigned for the current
+%    page to this page.  |\@outputpage| ships out the resulting box.
+%    Note that it is just possible that such floats are present even
+%    if we do not allow any inside a \mc{} environment.
+%    \begin{macrocode}
+   \@makecol\@outputpage
+%    \end{macrocode}
+%    After the page is shipped out we have to prepare the kept marks
+%    for the following page. |\kept@firstmark| and |\kept@botmark|
+%    reinitialized by setting them to |\@empty|.  The value of
+%    |\botmark| is then assigned to |\kept@topmark|.
+% \changes{v1.4g}{1992/06/03}{Only change \cs{kept@topmark} if
+%                            \cs{kept@botmark} non-empty}
+% \changes{v1.4i}{1992/06/18}{Set \cs{kept@topmark} to \cs{botmark}}
+%    \begin{macrocode}
+     \global\let\kept@topmark\botmark
+     \global\let\kept@firstmark\@empty
+     \global\let\kept@botmark\@empty
+%<*marktrace>
+     \mult@info\tw@
+        {(Re)Init top mark:\MessageBreak
+         \meaning\kept@topmark
+         \@gobbletwo}%
+%</marktrace>
+%    \end{macrocode}
+%    Now we reset |\@colroom| to |\@colht| which is \LaTeX's
+%    saved value of |\textheight|.
+%    We also have to reset the recorded position of the last
+%   |\marginpar| as well as the recorded size of in-text floats 
+%    as we are now on a new page.
+% \changes{v1.8d}{2014/04/23}{Reset \cs{@mparbottom} after page finishes}
+% \changes{v1.8n}{2015/08/19}{Reset \cs{@textfloatsheight} after page finishes}
+%    \begin{macrocode}
+   \global\@colroom\@colht
+   \global \@mparbottom \z@
+   \global \@textfloatsheight \z@
+%    \end{macrocode}
+%    Then we process deferred floats waiting for their chance to be
+%    placed on the next page.
+%    \begin{macrocode}
+   \process@deferreds
+   \@whilesw\if@fcolmade\fi{\@outputpage
+      \global\@colroom\@colht
+      \process@deferreds}%
+%    \end{macrocode}
+%    If the user is interested in statistics we inform him about the
+%    amount of space reserved for floats.
+%    \begin{macrocode}
+   \mult@info\@ne
+     {Colroom:\MessageBreak
+      \the\@colht\space
+              after float space removed
+              = \the\@colroom \@gobble}%
+%    \end{macrocode}
+%    Having done all this we must prepare to tackle the next page.
+%    Therefore we assign a new value to |\vsize|.  New, because
+%    |\partial@page| is now empty and |\@colroom| might be
+%    reduced by the space reserved for floats.
+% \changes{v1.4p}{1992/11/26}{Use different \cs{vsize} setting}
+%    \begin{macrocode}
+    \set@mult@vsize \global
+%    \end{macrocode}
+%    The |\footins| skip register will be adjusted when the output
+%    group is closed.
+% \changes{v1.3c}{1991/03/03}{Unnecessary code removed}
+%    \begin{macrocode}
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\leave@mult@footins}
+%    This macro is used to subtract the amount of space
+%    occupied by footnotes for the current space from the
+%    space available for the current column. The space current column
+%    is stored in |\dimen@|. See above for the description of the default
+%    action.
+% \changes{v1.5?}{1994/?/?}{Macro added}
+%    \begin{macrocode}
+\def\leave@mult@footins{%
+   \advance\dimen@-\skip\footins
+   \advance\dimen@-\ht\footins
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\speci@ls}
+%    We left out two macros: |\process@deferreds| and
+%    |\speci@ls|.
+% \changes{v1.5c}{1993/04/18}{Support \cs{clearpage}}
+%    \begin{macrocode}
+\def\speci@ls{%
+ \ifnum\outputpenalty <-\@Mi
+%    \end{macrocode}
+%    If the document ends in the middle of a multicols environment, e.g.,
+%    if the user forgot the |\end{multicols}|, \TeX{} adds a very
+%    negative penalty to the end of the galley which is intended to signal
+%    the output routine that it is time to prepare for shipping out
+%    everything remaining. Since inside multicols the output routine of
+%    \LaTeX{} is disabled sometimes we better check for this case: if we
+%    find a very negative penalty we produce an error message and run
+%    the default output routine for this case.
+% \changes{v1.5s}{1998/09/10}{check for \cs{stop} penalty pr/2873}
+%    \begin{macrocode}
+  \ifnum \outputpenalty<-\@MM
+   \PackageError{multicol}{Document end
+           inside multicols environment}\@ehd
+   \@specialoutput
+  \else
+%    \end{macrocode}
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for
+%                             column break support}
+%    For the next block of code see comments in section~\ref{sec:colbreak}.
+%    \begin{macrocode}
+     \ifnum\outputpenalty = -\@Mv
+         \mult@info\@ne{Forced column
+                        break seen}%
+         \global\advance\vsize-\pagetotal
+         \global\setbox\colbreak@box
+           \vbox{%
+              \ifvoid\colbreak@box
+              \else
+                \unvbox\colbreak@box
+                \penalty-\@Mv
+              \fi
+%    \end{macrocode}
+%    As this is the place of a forced break we now remove vertical
+%   white space just in front of it (or some of it at least) as it is
+%   quite likely that the break is not exactly in the right place,
+%   e.g., after a display environment (if LaTeX would break here by
+%   its own it would break before the space following the display).
+%
+%   Thus we rebox box 255 once (using |\maxdepth| and calling
+%   |\remove@discardable@items| inside). The depth of 255 will then
+%   give us the depth the box would have had if it would have been a
+%   natural break. We then unbox 255 to get it into the
+%   |\colbreak@box| and then back up by this depth. This will position
+%   the bottom of the box at its natural baseline which is useful for
+%   balancing later on.
+% \changes{v1.8k}{2015/03/21}{Remove discardable items just before a
+%   forced break}
+%    \begin{macrocode}
+              \boxmaxdepth\maxdepth
+              \setbox\@cclv\vbox{%
+                 \unvbox\@cclv
+                 \remove@discardable@items}%
+              \dimen@\dp\@cclv
+              \unvbox\@cclv
+              \kern-\dimen@
+         }%
+         \reinsert@footnotes
+     \else
+%    \end{macrocode}
+%    Another special case is reaching the end of the \mc{}
+%    environment which is signaled by |-\@Mvi|.
+% \changes{v1.8r}{2018/01/28}{Handling end of env through special penalty}
+%    \begin{macrocode}
+       \ifnum\outputpenalty = -\@Mvi
+         \mult@info\@ne{End penalty of multicols seen}%
+%    \end{macrocode}
+%    If we are at this point then have have to run the balancing code
+%    (which was previously its own output routine). First we pretend
+%    that we had a normal forced breakpoint and then call
+%    |\balance@column@out|. The latter may be let to |\multi@column@out|
+%    if we are inside \texttt{multicols*} in which case we would get a loop
+%    if the |\outputpenalty| is not changed---this could be cleaned up
+%    in a better way; basically it is like this, because of the older
+%    code was using different ORs and I simply reused most of it.
+%    \begin{macrocode}
+         \outputpenalty\@M   % pretend we had a natural forced break
+         \balance@columns@out
+       \else
+%    \end{macrocode}
+%    If we encounter a float or a marginpar in the current
+%    implementation we simply warn the user that this is not allowed.
+%    Then we reinsert the page and its footnotes.
+%    \begin{macrocode}
+        \PackageWarningNoLine{multicol}%
+           {Floats and marginpars not
+            allowed inside `multicols'
+            environment!}%
+        \unvbox\@cclv\reinsert@footnotes
+%    \end{macrocode}
+%    Additionally we empty the |\@currlist| to avoid later error
+%    messages when the \LaTeX{} output routine is again in force.
+%    But first we have to place the boxes back onto the
+%    |\@freelist|. (|\@elt|s default is |\relax| so
+%    this is possible with |\xdef|.)
+% \changes{v1.2a}{1990/02/05}{Float boxes freed.}
+%    \begin{macrocode}
+        \xdef\@freelist{\@freelist\@currlist}%
+        \gdef\@currlist{}%
+      \fi
+    \fi
+  \fi
+%    \end{macrocode}
+%    If the penalty is $-10001$ it will come from a |\clearpage| and
+%    we will execute |\@doclearpage| to get rid of any deferred
+%    floats.
+%    \begin{macrocode}
+ \else \@doclearpage \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\process@deferreds}
+%    |\process@deferreds| is a simplified version of \LaTeX{}'s
+%    |\@startpage|.  We first call the macro
+%    |\@floatplacement| to save the current user parameters in
+%    internal registers.  Then we start a new group and save the
+%    |\@deferlist| temporarily in the macro |\@tempb|.
+%    \begin{macrocode}
+\def\process@deferreds{%
+   \@floatplacement
+   \@tryfcolumn\@deferlist
+   \if@fcolmade\else
+     \begingroup
+    \let\@tempb\@deferlist
+%    \end{macrocode}
+%    Our next action is to (globally) empty |\@deferlist| and
+%    assign a new meaning to |\@elt|.  Here |\@scolelt| is a
+%    macro that looks at the boxes in a list to decide whether they
+%    should be placed on the next page (i.e.\ on |\@toplist| or
+%    |\@botlist|) or should wait for further processing.
+%    \begin{macrocode}
+      \gdef\@deferlist{}%
+      \let\@elt\@scolelt
+%    \end{macrocode}
+%    Now we call |\@tempb| which has the form
+%    \begin{center}
+%      |\@elt|\meta{box register}|\@elt|^^A
+%                        \meta{box register}\ldots{}
+%    \end{center}
+%    So |\@elt| (i.e.\ |\@scolelt|) will distribute the
+%    boxes to the three lists.
+%    \begin{macrocode}
+        \@tempb \endgroup
+   \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{ifshr@nking}
+% \begin{macro}{\raggedcolumns}
+% \begin{macro}{\flushcolumns}
+% \changes{v1.1a}{1989/09/20}{\cs{flushedcolumns} renamed to \cs{flushcolumns}.}
+%    The |\raggedcolumns| and |\flushcolumns|
+%    declarations are defined with the help of a new |\if...|
+%    macro.
+%    \begin{macrocode}
+\newif\ifshr@nking
+%    \end{macrocode}
+%    The actual definitions are simple: we just switch to \textsf{true}
+%    or \textsf{false} depending on the desired action. To avoid extra
+%    spaces in the output we enclose these changes in
+%    |\@bsphack|\ldots{}\allowbreak|\@esphack|.
+%    \begin{macrocode}
+\def\raggedcolumns{%
+   \@bsphack\shr@nkingtrue\@esphack}
+\def\flushcolumns{%
+   \@bsphack\shr@nkingfalse\@esphack}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\balance@columns@out}
+%    Now for the last part of the show: the column balancing output
+%    routine.  Since this code is called with an explicit penalty
+%    (|\eject|) there is no need to check for something special (eg
+%    floats).  We start by balancing the material gathered.
+%    \begin{macrocode}
+\def\balance@columns@out{%
+%    \end{macrocode}
+%    For this we need to put the contents of box 255 into |\mult@box|.
+% \changes{v1.5u}{1999/05/25}{Support \cs{columnbreak}}
+% \changes{v1.5v}{1999/07/18}{Added debug statements for column break
+%   support} For the next block of code see also comments in
+%   section~\ref{sec:colbreak}.  All forced breaks except the last are
+%   inside |\colbreak@box| so all we have to do is to concatenate this
+%   box with box |\@cclv| and put a penalty in between. Here we test if
+%   |\colbreak@box| is void so that the message is only generated if
+%   we really add forced breaks and the penalty.
+% \changes{v1.8k}{2015/03/21}{Use \cs{@Mv} and not \cs{break} in case
+%   this forced break is not used on this page}
+%    \begin{macrocode}
+   \setbox\mult@box\vbox{%
+       \ifvoid\colbreak@box\else
+         \unvbox\colbreak@box
+         \penalty-\@Mv
+         \mult@info\@ne{Re-adding
+           forced break(s) in balancing}%
+       \fi
+       \unvbox\@cclv
+%    \end{macrocode}
+%    The last column again is a forced break, so here we discard white
+%   space as well as that is normally unwanted.
+% \changes{v1.8k}{2015/03/21}{Add \cs{remove@discardable@items} at the
+%   end of the last column when balancing.}
+%    \begin{macrocode}
+       \remove@discardable@items
+   }%
+   \balance@columns
+%    \end{macrocode}
+%    If during balancing the columns got too long the flag
+%    |\iftoo@bad| is set to true.
+% \changes{v1.8a}{2011/12/20}{Balancing concept improved}
+%    \begin{macrocode}
+   \iftoo@bad
+     \mult@info\@ne
+        {Balancing failed ...
+         cut a normal page}%
+%    \end{macrocode}
+%    In that case we put the material back in box 255 so that we can
+%    cut a normal page. The curious set of
+%    |\vskip|s we add is necessary to  cancel out the |\splittopskip|
+%    that got added for balancing.
+%    \begin{macrocode}
+     \setbox\@cclv\vbox
+         {\vskip\topskip
+          \vskip-\splittopskip
+          \unvbox\mult@box
+%    \end{macrocode}
+%    We also have to re-add the end of environment penalty since after
+%    this page we may want  balance the remaining material.
+% \changes{v1.8r}{2018/01/28}{Re-add the final penalty}
+%    \begin{macrocode}
+          \penalty-\@Mvi
+         }%
+%    \end{macrocode}
+%    We then call the standard multicol output routine which will
+%    produce a normal page for us (remember we are still within the
+%    OR so some part of the code in |\multi@column@out| is actually not
+%    doing anything---perhaps this should be cleaned up at some point).
+%    This also means that if there was an |\enlargethispage| present
+%    it will apply to this page as |\multi@column@out| will look at
+%    the status of |\@kludgeins|.
+%    \begin{macrocode}
+     \multi@column@out
+%    \end{macrocode}
+%    Because balancing made the columns too long we are sure that there
+%    will be some material remaining which was put back onto the main
+%    vertical list by |\multi@column@out|. This will also put the
+%    explicit |\eject| penalty back so the current
+%    |\balance@columns@out| output routine will be called again (so we
+%    better do not add another penalty or else the OR will be called
+%    twice and we may get scrambled results).
+% \changes{v1.8k}{2015/03/21}{No additional penalty here}
+%    \begin{macrocode}
+   \else
+%    \end{macrocode}
+%    If the balancing went ok, we are in the position
+%    to apply |\page@sofar|.  But first we have to set |\vsize| to a
+%    value suitable for one column output.
+%    \begin{macrocode}
+     \global\vsize\@colroom
+     \global\advance\vsize\ht\partial@page
+%    \end{macrocode}
+%    We also have to look at |\@kludgeins| and generate a new
+%    |\insert| in case there was one present due to an
+%    |\enlargethispage| command.
+% \changes{v1.8a}{2011/12/20}{Support for \cs{enlargethispage}}
+%    \begin{macrocode}
+     \ifvbox\@kludgeins\insert\@kludgeins
+                        {\unvbox\@kludgeins}\fi
+%    \end{macrocode}
+%    Then we |\unvbox| the |\partial@page| (which may be void if we
+%    are not processing the first page of this \mc{} environment.
+%    \begin{macrocode}
+     \unvbox\partial@page
+%    \end{macrocode}
+%    Then we return the first and bottom mark and the gathered
+%    material to the main vertical list.
+%    \begin{macrocode}
+     \return@nonemptymark{first}\kept@firstmark
+     \return@nonemptymark{bot}\kept@botmark
+     \page@sofar
+%    \end{macrocode}
+%    We need to add a penalty at this point which allows to break at
+%    this point since calling the output routine may have removed the
+%    only permissible break point thereby ``glueing'' any following
+%    skip to the balanced box. In case there are any weird settings
+%    for |\multicolsep| etc. this could produce funny results.
+%  \changes{v1.5c}{1993/04/18}{added penalty at output routine exit}
+%    \begin{macrocode}
+     \penalty\z@
+  \fi
+}
+%    \end{macrocode}
+%    As we already know, reinserting of footnotes will be done in the
+%    macro |\endmulticols|.
+% \end{macro}
+%
+%
+%  \begin{macro}{\balance@columns}
+%    This macro now does the actual balancing.
+%    \begin{macrocode}
+\def\balance@columns{%
+%    \end{macrocode}
+%    We start by setting the kept marks by updating them with any
+%    marks from this box. This has to be done \emph{before} we add a
+%    penalty of $-10000$ to the top of the box, otherwise only an
+%    empty box will be considered.
+% \changes{v1.5h}{1994/08/26}{Get kept marks first}
+%    \begin{macrocode}
+   \get@keptmarks\mult@box
+%    \end{macrocode}
+%    We then continue by resetting trying to remove any discardable
+%    stuff at the end of |\mult@box|. This is rather experimental.  We
+%    also add a forced break point at the very beginning, so that we
+%    can split the box to height zero later on, thereby adding a known
+%    |\splittopskip| glue at the beginning.
+% \changes{v1.8k}{2015/03/21}{\cs{remove@discardable@items} removed}
+%    \begin{macrocode}
+   \setbox\mult@box\vbox{%
+        \penalty-\@M
+        \unvbox\mult@box
+        }%
+%    \end{macrocode}
+%    Then follow values assignments to get the |\vsplit|ting right.
+%    We use the natural part of |\topskip| as the natural part for
+%    |\splittopskip| and allow for a bit of undershoot and overshoot
+%    by adding some stretch and shrink.
+% \changes{v1.5?}{1994/?/?}{Allow columns to come out a bit long or short}
+%    \begin{macrocode}
+   \@tempdima\topskip
+   \splittopskip\@tempdima
+       \@plus\multicolundershoot
+       \@minus\multicolovershoot
+   \splitmaxdepth\maxdepth
+%    \end{macrocode}
+%   We also have to set |\boxmaxdepth| which normally allows to
+%   build boxes with arbitrary depth, but as we are building text
+%   columns we really want to restrict the depth. This is necessary as
+%   we sometimes rebox the boxes generated by |\vsplit| and then the
+%   restriction posed by |\splitmaxdepth|  gets lost.
+% \changes{v1.8h}{2014/09/12}{All column boxes should obey
+%   \cs{maxdepth}  (pr/4395)}
+%    \begin{macrocode}
+   \boxmaxdepth\maxdepth
+%    \end{macrocode}
+%    The next step is a bit tricky: when \TeX{} assembles material in
+%    a box, the first line isn't preceded by interline glue, i.e.
+%    there is no parameter like |\boxtopskip| in \TeX{}. This means
+%    that the baseline of the first line in our box is at some
+%    unpredictable point depending on the height of the largest
+%    character in this line. But of course we want all columns to
+%    align properly at the baselines of their first lines. For this
+%    reason we have opened |\mult@box| with a |\penalty| \textsf{-10000}.
+%    This will now allow us to split off from |\mult@box| a tiny bit
+%    (in fact nothing since the first possible break-point is the
+%    first item in the box). The result is that |\splittopskip| is
+%    inserted at the top of |\mult@box| which is exactly what we like
+%    to achieve.
+% \changes{v1.5?}{1994/?/?}{Do splitting to zero here}
+%    \begin{macrocode}
+   \setbox\@tempboxa\vsplit\mult@box to\z@
+%    \end{macrocode}
+%    Next we try to find a suitable starting point for the calculation
+%    of the column height.  It should be less than the height finally
+%    chosen, but large enough to reach this final value in only a few
+%    iterations.  The formula which is now implemented will try to
+%    start with the nearest value which is a multiple of
+%    |\baselineskip|. The coding is slightly tricky in \TeX{} and
+%    there are perhaps better ways \ldots
+% \changes{v1.4d}{1992/03/04}{New algorithm for start height}
+%    \begin{macrocode}
+   \@tempdima\ht\mult@box
+   \advance\@tempdima\dp\mult@box
+   \divide\@tempdima\col@number
+%    \end{macrocode}
+%    The code above sets |\@tempdima| to the length of a column if we
+%    simply divide the whole box into equal pieces. To get to the next
+%    lower multiple of |\baselineskip| we convert this dimen to a
+%    number (the number of scaled points) then divide this by
+%    |\baselineskip| (also in scaled points) and then multiply this
+%    result with |\baselineskip| assigning the result to |\dimen@|.
+%    This makes |\dimen@| $\leq$ to |\@tempdimena|.
+%    \begin{macrocode}
+   \count@\@tempdima
+   \divide\count@\baselineskip
+   \dimen@\count@\baselineskip
+%    \end{macrocode}
+%    Next step is to correct our result by taking into account the
+%    difference between |\topskip| and |\baselineskip|. We start by
+%    adding |\topskip|; if this makes the result too large then we
+%    have to subtract one |\baselineskip|.
+%    \begin{macrocode}
+   \advance\dimen@\topskip
+   \ifdim \dimen@ >\@tempdima
+     \advance\dimen@-\baselineskip
+   \fi
+%    \end{macrocode}
+%    As a further restriction we want to see a minimum number of
+%    rows in the balanced result based on the setting of the counter
+%    |minrows|. If the starting value is lower we adjust.
+% \changes{v1.8w}{2019/03/01}{Provide minrows counter for balancing}
+%    \begin{macrocode}
+   \@tempdima\dimexpr
+       \topskip +\c@minrows\baselineskip-\baselineskip\relax
+   \ifnum\dimen@<\@tempdima
+     \mult@info\@ne
+       {Start value
+          \the\dimen@  \space ->
+          \the\@tempdima \space (corrected for minrows)}%
+     \dimen@\@tempdima
+   \fi
+%    \end{macrocode}
+%    At the user's request we start with a higher value (or lower, but
+%    this usually only increases the number of tries).
+%    \begin{macrocode}
+   \advance\dimen@\c@unbalance\baselineskip
+%    \end{macrocode}
+%    We type out statistics if we were asked to do so.
+% \changes{v1.4f}{1992/04/28}{\cs{on@line} added to tracing info}
+%    \begin{macrocode}
+   \mult@info\@ne
+      {Balance columns\on@line:
+        \ifnum\c@unbalance=\z@\else
+       (off balance=\number\c@unbalance)\fi
+      \@gobbletwo}%
+%    \end{macrocode}
+%    But we don't allow nonsense values for a start.
+%    \begin{macrocode}
+   \ifnum\dimen@<\topskip
+     \mult@info\@ne
+       {Start value
+          \the\dimen@  \space ->
+          \the\topskip \space (corrected)}%
+     \dimen@\topskip
+   \fi
+%    \end{macrocode}
+%    Now we try to find the final column height.  We start by setting
+%    |\vbadness| to infinity (i.e.\ $10000$) to suppress
+%    underfull box reports while we are trying to find an acceptable
+%    solution.  We do not need to do it in a group since at the end of
+%    the output routine everything will be restored. The setting of
+%    the final columns will nearly always produce underfull boxes with
+%    badness $10000$ so there is no point in warning the user about
+%    it.
+% \changes{v1.2a}{1990/02/05}{Group around main loop removed.}
+%    \begin{macrocode}
+   \vbadness\@M
+%    \end{macrocode}
+%    We also allow for overfull boxes while we trying to split the
+%    columns. They can easily happen if we have objects with unusual depth. 
+% \changes{v1.8h}{2014/09/12}{Do not report overfull}
+%    \begin{macrocode}
+   \vfuzz \maxdimen
+%    \end{macrocode}
+%    The variable |\last@try| will hold the dimension used in the
+%    previous trial splitting. We initialize it with a negative value.
+% \changes{v1.5?}{1994/?/?}{Initialize \cs{last@try}}
+%    \begin{macrocode}
+   \last@try-\p@
+   \loop
+%    \end{macrocode}
+%    In order not to clutter up \TeX{}'s valuable main memory with
+%    things that are no longer needed, we empty all globally used box
+%    registers. This is necessary if we return to this point after an
+%    unsuccessful trial.  We use |\process@cols| for this purpose,
+%    starting with |\mult@grightbox|.  Note the extra braces around
+%    this macro call.  They are needed since \PlainTeX{}'s
+%    |\loop|\ldots{}\allowbreak|\repeat| mechanism cannot be nested on
+%    the same level of grouping.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+%    \begin{macrocode}
+    {\process@cols\mult@grightbox
+           {\global\setbox\count@
+                   \box\voidb@x}}%
+%    \end{macrocode}
+%    The contents of box |\mult@box| are now copied globally to
+%    box~|\mult@grightbox|.  (This will be the right-most column, as
+%    we shall see later.)
+%    \begin{macrocode}
+    \global\setbox\mult@grightbox
+           \copy\mult@box
+%    \end{macrocode}
+%    We start with the assumption that the trial will be successful.
+%    If we end up with a solution that is too bad we set
+%    |too@bad| to \texttt{true}. We also assume that all forced breaks
+%    (if any) will be used during balancing. If this is not the case
+%    we record this in |forcedbreak@leftover|.
+% \changes{v1.5b}{1992/11/05}{New badness mechanism}
+% \changes{v1.8k}{2015/03/21}{Init \cs{ifforcedbreak@leftover}}
+%    \begin{macrocode}
+%<*badness>
+   \too@badfalse
+   \forcedbreak@leftoverfalse
+%</badness>
+%    \end{macrocode}
+%    Using |\vsplit| we extract the other columns from box register
+%    |\mult@grightbox|.  This leaves box register |\mult@box|
+%    untouched so that we can start over again if this trial was
+%    unsuccessful.
+%    \begin{macrocode}
+   {\process@cols\mult@firstbox{%
+         \global\setbox\count@
+         \vsplit\mult@grightbox to\dimen@
+%    \end{macrocode}
+%    After splitting we need to ensure that there isn't any space at
+%    the bottom, so we rebox once more.
+% \changes{v1.8b}{2013/08/28}{Remove discardable items at the
+%                             end of split boxes}
+% \changes{v1.8k}{2015/03/21}{Do not use \cs{remove@discardable@items}
+%    here}
+%    \begin{macrocode}
+         \global\setbox\count@
+                 \vbox to\dimen@
+                  {\unvbox\count@}%
+%    \end{macrocode}
+%    After every split we check the badness of the resulting column,
+%    normally the amount of extra white in the column.
+%    \begin{macrocode}
+%<*badness>
+         \ifnum\c@tracingmulticols>\@ne
+           \@tempcnta\count@
+           \advance\@tempcnta-\mult@grightbox
+           \divide\@tempcnta \tw@
+           \message{^^JColumn
+              \number\@tempcnta\space
+               badness: \the\badness\space}%
+         \fi
+%    \end{macrocode}
+%    If this badness is larger than the allowed column badness
+%    we reject this solution by setting |too@bad| to \texttt{true}.
+%    \begin{macrocode}
+         \ifnum\badness>\c@columnbadness
+           \ifnum\c@tracingmulticols>\@ne
+             \message{too bad
+                  (>\the\c@columnbadness)}%
+           \fi
+           \too@badtrue
+         \fi
+%</badness>
+                        }}%
+%    \end{macrocode}
+%    There is one subtle point here: while all other constructed boxes
+%    have a depth that is determined by |\splitmaxdepth| and/or
+%   |\boxmaxdepth| the last box
+%    will get a natural depth disregarding the original setting and
+%    the value of |\splitmaxdepth| or |\boxmaxdepth|. This means that
+%    we may end up with a very large depth in box |\mult@grightbox|
+%    which would
+%    make the result of the testing incorrect. So we change the value
+%    by unboxing the box into itself.
+%    \begin{macrocode}
+   \global\setbox\mult@grightbox
+      \vbox{\unvbox\mult@grightbox}%
+%    \end{macrocode}
+%    We also save a copy |\mult@firstbox| at its ``natural'' size
+%    for later use.
+%    \begin{macrocode}
+   \setbox\mult@nat@firstbox
+      \vbox{\unvcopy\mult@firstbox}%
+%    \end{macrocode}
+%    After |\process@cols| has done its job we have the following
+%    situation:
+%    \begin{center}
+%      \begin{tabular}{r@{$\:\:\longleftarrow\:\:$}l}
+%        box |\mult@rightbox| & all material \\
+%        box |\mult@gfirstbox| & first column \\
+%        box |\mult@gfirstbox|${}+2$ & second column \\
+%        \multicolumn{1}{c}{$\vdots$} &
+%        \multicolumn{1}{c}{$\vdots$} \\
+%        box |\mult@grightbox| & last column
+%      \end{tabular}
+%    \end{center}
+%    We report the height of the first column, in brackets
+%    the natural size is given.
+% \changes{v1.5?}{1994/?/?}{Show natural size}
+%    \begin{macrocode}
+    \ifnum\c@tracingmulticols>\@ne
+       \message{^^JFirst column
+           = \the\dimen@\space
+           (\the\ht\mult@nat@firstbox)}\fi
+%    \end{macrocode}
+%    If |\raggedcolumns| is in force older releases of this file also
+%    shrank the first column to its natural height at this point.
+%    This was done so that the first column doesn't run short compared
+%    to later columns but it is actually producing incorrect results
+%    (overprinting of text) in boundary cases, so since version v1.5q
+%    |\raggedcolumns| means allows for all columns to run slightly short.
+% \changes{v1.5q}{1998/01/19}{Do not reset \cs{mult@firstbox} (pr2739)}
+%    \begin{macrocode}
+%    \ifshr@nking
+%      \global\setbox\mult@firstbox
+%             \copy\mult@nat@firstbox
+%    \fi
+%    \end{macrocode}
+%    Then we give information about the last column.\footnote{With
+%    \TeX{} version 3.141 it is now possible to use \LaTeX's
+%    \cs{newlinechar} in the \cs{message} command, but
+%    people with older \TeX{} versions will now get
+%    \texttt{\string^\string^J} instead of a new line on the screen.}
+% \changes{v1.4a}{1992/02/12}{Changed to proper \cs{endlinechar} in\cs{message}}
+%    \begin{macrocode}
+    \ifnum\c@tracingmulticols>\@ne
+      \message{<> last column =
+               \the\ht\mult@grightbox^^J}%
+%    \end{macrocode}
+%    Some tracing code that we don't compile into the production version
+%    unless asked for. It will produce huge listings of the boxes
+%    involved in balancing in the transcript file.
+% \changes{v1.6f}{2004/07/03}{need to use \cs{mult@grightbox} in the loop}
+%    \begin{macrocode}
+%<*debug>
+      \ifnum\c@tracingmulticols>4
+         {\showoutput
+          \batchmode
+          \process@cols\mult@grightbox
+           {\showbox\count@}}%
+          \errorstopmode
+      \fi
+%</debug>
+     \fi
+%    \end{macrocode}
+%    We check whether our trial was successful.  The test used is very
+%    simple: we merely compare the first and the last column.  Thus
+%    the intermediate columns may be longer than the first if
+%    |\raggedcolumns| is used.  If the right-most column is
+%    longer than the first then we start over with a larger value for
+%    |\dimen@|.
+% \changes{v1.3c}{1991/03/03}{\cs{global}\cs{advance} left over from older code}
+%    \begin{macrocode}
+    \ifdim\ht\mult@grightbox >\dimen@
+%    \end{macrocode}
+%    If the height of the last box is too large we mark this trial as
+%    unsuccessful.
+% \changes{v1.5v}{1999/07/18}{Added tracing statements for
+%                             trial unsuccessful}
+%    \begin{macrocode}
+%<*badness>
+      \too@badtrue
+      \ifnum\c@tracingmulticols>\@ne
+         \typeout{Rejected: last
+                 column too large!}%
+      \fi
+    \else
+%    \end{macrocode}
+% \changes{v1.5v}{1999/07/18}{Check last column if it contains forced
+%    break and reject trial if that is the case}
+%
+%    To ensure that there isn't a forced break in the last column we
+%    try to split off a box of size |\maxdimen| from |\mult@grightbox|
+%    (or rather from a copy of it). This should result in a void box
+%    after the split, unless there was a forced break somewhere within
+%    the column in which case the material after the break would have
+%    stayed in the box.
+%    \begin{macrocode}
+      \setbox\@tempboxa
+           \copy\mult@grightbox
+      \setbox\z@\vsplit\@tempboxa to\maxdimen
+      \ifvoid\@tempboxa
+%    \end{macrocode}
+%    Thus if |\@tempboxa| is void we  have a valid solution.
+%    In this case we take a closer
+%    look at the last column to decide if this column should be made
+%    as long as all other columns or if it should be allowed to be
+%    shorter.
+%    For this we first have to rebox the column into a box of the
+%    appropriate height. If tracing is enabled we then display the
+%    badness for this box.
+%    \begin{macrocode}
+        \global\setbox\mult@grightbox
+           \vbox to\dimen@
+              {\unvbox\mult@grightbox}%
+        \ifnum\c@tracingmulticols>\@ne
+          \message{Final badness:
+                   \the\badness}%
+        \fi
+%    \end{macrocode}
+%    We then compare this badness with the allowed badness for the final
+%    column. If it does not exceed this value we use the box, otherwise
+%    we rebox it once more and add some glue at the bottom.
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8j}{2015/03/07}{Use \cs{vfil} in this case}
+%    \begin{macrocode}
+        \ifnum\badness>\c@finalcolumnbadness
+          \global\setbox\mult@grightbox
+           \vbox to\dimen@
+              {\unvbox\mult@grightbox\vfil}%
+           \ifnum\c@tracingmulticols>\@ne
+             \message{ setting natural
+              (> \the\c@finalcolumnbadness)}%
+           \fi
+        \fi
+%    \end{macrocode}
+%    If |\@tempboxa| above was not void our trial was unsuccessful and
+%    we report this fact and try again.
+% \changes{v1.6f}{2004/07/03}{\texttt{/colbreak} guard in the wrong position}
+%    \begin{macrocode}
+      \else
+%    \end{macrocode}
+%    If we have unprocessed forced breaks we normally reiterate with a
+%    larger column size to fit them in eventually. However, if there
+%    are simply too many of them (e.g., 3 forced breaks but only 2
+%    columns to balance) then this will never succeed and and we would
+%    continue growing the columns until we hit the largest possible
+%    column size. So in addition we check how big the column size is
+%    compared to available room and if we exceed this by
+%    |\maxbalancingoverflow| we give up and instead of balancing cut
+%    another normal page. To be indicate this case we set
+%    |forcedbreak@leftover| to true.
+% \changes{v1.8k}{2015/03/21}{Watch out for columns growing too far in
+%    case of forced breaks}
+% \changes{v1.8l}{2015/03/25}{Added additional tracing if column overflows}
+%    \begin{macrocode}
+       \@tempdima\@colroom
+       \advance\@tempdima \maxbalancingoverflow
+       \ifdim \dimen@ < \@tempdima
+        \too@badtrue
+         \ifnum\c@tracingmulticols>\@ne
+           \typeout{Rejected: unprocessed
+             forced break(s) in last column!}%
+         \fi
+       \else
+         \forcedbreak@leftovertrue
+         \ifnum\c@tracingmulticols>\@ne
+          \typeout{Failed: columns too large
+            with unprocessed forced break(s)!}%
+         \fi
+       \fi
+      \fi
+    \fi
+%    \end{macrocode}
+%    If the natural height of the first box is smaller than the
+%    current trial size but is larger than the previous trial size it
+%    is likely that we have missed a potentially better
+%    solution. (This could have happened if for some reason our first
+%    trial size was too high.) In that case we dismiss this trial and
+%    restart using the natural height for the next trial.
+%    \begin{macrocode}
+    \ifdim\ht\mult@nat@firstbox<\dimen@
+      \ifdim\ht\mult@nat@firstbox>\last@try
+        \too@badtrue
+        \ifnum\c@tracingmulticols>\@ne
+           \typeout{Retry: using natural
+                    height of first column!}%
+        \fi
+        \dimen@\ht\mult@nat@firstbox
+        \last@try\dimen@
+        \advance\dimen@-\p@
+      \fi
+    \fi
+%    \end{macrocode}
+%    Finally the switch |too@bad| is tested. If it was made true
+%    either earlier on or due to a rightmost column being too large
+%    we try again with a slightly larger value for |\dimen@|.
+%    \begin{macrocode}
+    \iftoo@bad
+%</badness>
+      \advance\dimen@\p@
+    \repeat
+%    \end{macrocode} 
+%    If we come out of the loop with the switch |forcedbreak@leftover|
+%    set to true then balancing has failed and we should cut a normal
+%    page. We indicate this below with |\too@badtrue| when any of the
+%    columns get too high, so we set this flag here too in order to
+%    get the same processing logic.\footnote{Should get cleaned up as
+%    we now have two different routes to reach this part of the
+%    processing.}
+% \changes{v1.8k}{2015/03/21}{}
+%    \begin{macrocode}
+    \ifforcedbreak@leftover
+       \too@badtrue
+    \else
+%    \end{macrocode}
+%    At that point |\dimen@| holds the height that was determined by
+%    the balancing loop.
+%    If that height for the columns turns out to be larger
+%    than the available space (which is |\@colroom|) we squeeze the
+%    columns into the space assuming that they will have enough
+%    shrinkability to allow this.\footnote{This might be wrong, since
+%    the shrinkability that accounts for the amount of material might
+%    be present only in some columns. But it is better to try then to
+%    give up directly.}
+%    However, this squeezing should only be done if we are balancing
+%    columns on the main galley and \emph{not} if we are building a
+%    boxed multicol (in the latter case the current |\@colroom| is
+%    irrelevant since the produced box might be moved anywhere at a
+%    later stage).
+% \changes{v1.3c}{1991/03/03}{Limit column height to \cs{@colroom}}
+% \changes{v1.5q}{1998/01/19}{Removed setting \cs{dimen@} (pr2739)}
+% \changes{v1.5y}{2000/06/10}{Limit column height only in unrestricted
+%    mode (pr/3212)}
+%    \begin{macrocode}
+     \if@boxedmulticols\else
+       \ifdim\dimen@>\@colroom
+         \dimen@\@colroom
+       \fi
+     \fi
+%    \end{macrocode}
+%    Then we move the contents of the odd-numbered box registers to
+%    the even-numbered ones, shrinking them if requested.
+%    We have to use |\vbox| not |\vtop| (as it was done in
+%    the first versions) since otherwise the resulting boxes will have
+%    no height (\TB\/ page 81). This would mean that extra
+%    |\topskip|  is added when the boxes are returned to the
+%    page-builder via |\page@sofar|.
+% \changes{v1.3a}{1990/05/20}{Changed \cs{vtop} to \cs{vbox}.}
+%    \begin{macrocode}
+     \process@cols\mult@rightbox
+         {\@tempcnta\count@
+          \advance\@tempcnta\@ne
+%    \end{macrocode}
+%    when putting the final column together we want overfull
+%    information:
+%    \begin{macrocode}
+          \vfuzz\z@
+          \setbox\count@\vbox to\dimen@
+             {%
+%    \end{macrocode}
+%
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+%    \begin{macrocode}
+              \vskip \z@
+                \@plus-\multicolundershoot
+                \@minus-\multicolovershoot
+              \unvbox\@tempcnta
+              \ifshr@nking\vfilmaxdepth\fi
+             }%
+%    \end{macrocode}
+%    If the resulting box is overfull there was too much material to
+%    fit into the available space. The question though is how much? If
+%    it wasn't more than |\maxbalancingoverflow| we accept it still to
+%    avoid getting very little material for the next page (which we
+%    would then have difficulties to balance).
+% \changes{v1.8a}{2011/12/20}{Balancing concept improved}
+%    \begin{macrocode}
+          \ifnum\badness>\@M
+            \vfuzz\maxdimen % no overfull warning
+            \setbox\@tempboxa \vbox to\dimen@
+                 {\vskip-\maxbalancingoverflow
+                  \unvcopy\count@}%
+            \ifnum\badness>\@M
+              \mult@info\@ne
+                {Balanced column more than
+                  \the\maxbalancingoverflow\space
+                  too large}%
+%    \end{macrocode}
+%    Fail the balancing attempt:
+%    \begin{macrocode}
+              \too@badtrue
+            \else
+%    \end{macrocode}
+%    Otherwise report that there is a problem but within the accepted
+%    boundary.
+%    \begin{macrocode}
+              \mult@info\@ne
+                {Balanced column
+                 too large, but less than
+                 \the\maxbalancingoverflow}%
+            \fi
+          \fi
+         }%
+%    \end{macrocode}
+%    Finally end the |\ifforcedbreak@leftover| conditional.
+% \changes{v1.8k}{2015/03/21}{Finish the new conditional}
+%    \begin{macrocode}
+   \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \begin{macro}{\maxbalancingoverflow}
+%    Amount that balancing is allowed to overflow the available column
+%    space. We default to 12pt which means about one line in most
+%    layouts.
+% \changes{v1.8a}{2011/12/20}{\cs{maxbalancingoverflow} parameter added}
+%    \begin{macrocode}
+\newdimen\maxbalancingoverflow
+\maxbalancingoverflow=12pt
+%    \end{macrocode}
+%  \end{macro}
+
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{The box allocations}]
+%
+% \begin{macro}{\mult@rightbox}
+% \begin{macro}{\mult@grightbox}
+% \begin{macro}{\mult@firstbox}
+% \begin{macro}{\mult@gfirstbox}
+%    Early releases of these macros used the first box registers
+%    0, 2, 4,\ldots\ for global boxes and 1, 3, 5,\ldots\ for the
+%    corresponding local boxes. (You might still find some traces
+%    of this setup in the documentation, sigh.) This produced a problem
+%    at the moment we had more than 5 columns because then officially
+%    allocated boxes were overwritten by the algorithm.
+%    The new release now uses private box registers
+%    \begin{macrocode}
+\newbox\mult@rightbox
+\newbox\mult@grightbox
+\newbox\mult@gfirstbox
+\newbox\mult@firstbox
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa\newbox\@tempa
+\newbox\@tempa
+\let\@tempa\relax
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{2}[\section{New macros and hacks for version 1.2}]
+%
+% \begin{macro}{\emergencystretch}
+% \begin{macro}{\setemergencystretch}
+%    If we don't use \TeX{} 3.0 |\emergencystretch| is undefined
+%    so in this case we simply add it as an unused \meta{dimen}
+%    register.
+% \changes{v1.4j}{1992/06/25}{Setting of \cs{emergencystretch} on top
+%                  removed.}
+%    \begin{macrocode}
+\@ifundefined{emergencystretch}
+     {\newdimen\emergencystretch}{}
+%    \end{macrocode}
+% \changes{v1.2a}{1990/02/05}{Macro added.}
+%    My tests showed that the following formula worked pretty well.
+%    Nevertheless the |\setemergencystretch| macro also gets
+%    |\hsize| as second argument to enable the user to try
+%    different formulae.
+%    \begin{macrocode}
+\def\setemergencystretch#1#2{%
+   \emergencystretch 4pt
+   \multiply\emergencystretch#1}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+
+
+% \begin{macro}{\set@floatcmds}
+% \changes{v1.2a}{1990/02/05}{Macro added.}
+% \changes{v1.5g}{1994/06/07}{Updated since floats have changed}
+% \changes{v1.5j}{1994/06/07}{Updated since floats have changed again}
+% \changes{v1.5l}{1995/10/19}{Added \cs{@largefloatcheck}}
+% \changes{v1.6g}{2006/02/23}{Added \cs{@minipagefalse}}
+% \changes{v1.6h}{2008/12/05}{Use \cs{@endfloatbox} to better support
+%   the modifications done by the float package}
+%    Even if this should be used as a hook we use a |@| in the
+%    name since it is more for experts.
+%    \begin{macrocode}
+\def\set@floatcmds{%
+ \let\@dblfloat\@dbflt
+ \def\end@dblfloat{\@endfloatbox
+   \@largefloatcheck
+   \outer@nobreak
+%    \end{macrocode}
+%    This is cheap (deferring the floats until after the current page)
+%    but any other solution would go deep into \LaTeX's output
+%    routine and I don't like to work on it until I know which parts
+%    of the output routine have to be reimplemented anyway for
+%    \LaTeX3.
+%    \begin{macrocode}
+   \ifnum\@floatpenalty<\z@
+%    \end{macrocode}
+%    We have to add the float to the |\@deferlist| because we assume
+%    that outside the \mc{} environment we are in one column mode.
+%    This is not entirely correct, I already used the \mc{}
+%    environment inside of \LaTeX{}s |\twocolumn| declaration but it
+%    will do for most applications.
+%    \begin{macrocode}
+     \@cons\@deferlist\@currbox
+   \fi
+   \ifnum\@floatpenalty=-\@Mii
+     \@Esphack
+   \fi}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \end{multicols}
+%
+% \begin{multicols}{2}[\subsection{Maintaining the mark registers}]
+% \label{sec:v14}
+%
+% This section contains the routines that set the marks so that they
+% will be handled correctly. They have been introduced with version~1.4.
+%
+%  \begin{macro}{\kept@topmark}
+% \changes{v1.4h}{1992/06/04}{Init to double brace pair}
+%  \begin{macro}{\kept@firstmark}
+%  \begin{macro}{\kept@botmark}
+%    First thing we do is to reserve three macro names to hold the
+%    replacement text for \TeX's primitives |\firstmark|, |\botmark| and
+%    |\topmark|. We initialize the first two to be empty and
+%    |\kept@topmark| to contain  two empty pair of braces. This is
+%    necessary since |\kept@topmark| is supposed to contain the last
+%    mark from a preceding page and in \LaTeX{} any ``real'' mark must
+%    contain two parts representing left and right mark information.
+%    \begin{macrocode}
+\def\kept@topmark{{}{}}
+\let\kept@firstmark\@empty
+\let\kept@botmark\@empty
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\return@nonemptymark}
+%    Sometimes we want to return the value of a ``kept'' mark into a
+%    |\mark| node on the main vertical list. This is done by the
+%    function |\return@nonemptymark|. As the name suggests it only acts
+%    if the replacement text of the kept mark is non-empty. This is done
+%    to avoid adding an empty mark when no mark was actually present. If
+%    we would nevertheless add such a mark it would be regarded as a
+%    valid |\firstmark| later on.
+%    \begin{macrocode}
+\def\return@nonemptymark#1#2{%
+  \ifx#2\@empty
+  \else
+%    \end{macrocode}
+%    For debugging purposes we take a look at the value of the kept mark
+%    that we are about to return. This code will get stripped out for
+%    production.
+%    \begin{macrocode}
+%<*marktrace>
+    \mult@info\tw@
+      {Returned #1 mark:\MessageBreak
+       \meaning#2}%
+%      \nobreak
+%    \fi
+%</marktrace>
+%    \end{macrocode}
+%    Since the contents of the mark may be arbitrary \LaTeX{} code we
+%    better make sure that it doesn't get expanded any further. (Some
+%    expansion have been done already during the execution of
+%    |\markright| or |\markboth|.) We therefore use the usual mechanism
+%    of a toks register to prohibit expansion.\footnote{Due to the
+%    current definition of \cs{markright} etc.\ it wouldn't
+%    help to define the \cs{protect} command to prohibit
+%    expansion as any \cs{protect} has already vanished due to
+%    earlier expansions.}
+% \changes{v1.4n}{1992/09/10}{Make marks robust}
+% \changes{v1.5t}{1999/03/22}{re-add \cs{mark} command which was commented out
+%       by mistake at some point in 1998 (pr/2978)}
+%    \begin{macrocode}
+    \toks@\expandafter{#2}%
+    \mark{\the\toks@}%
+%    \end{macrocode}
+%    We don't want any breakpoint between such a returned mark and the
+%    following material (which is usually just the box where the mark
+%    came from).
+%    \begin{macrocode}
+    \nobreak
+  \fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\get@keptmarks}
+%    If we have some material in a box register we may want to get the
+%    first and the last mark out of this box. This can be done with
+%    |\get@keptmarks| which takes one argument: the box register number
+%    or its nick name defined by |\newbox|.
+%    \begin{macrocode}
+\def\get@keptmarks#1{%
+%    \end{macrocode}
+%    For debugging purposes we take a look at the current dimensions
+%    of the box since in earlier versions of the code I made some
+%    mistakes in this area.
+%    \begin{macrocode}
+%<*debug>
+      \typeout{Mark box #1 before:
+               ht \the\ht#1, dp \the\dp#1}%
+%</debug>
+%    \end{macrocode}
+%    Now we open a new group and locally copy the box to itself. As a
+%    result any operation, i.e.\ |\vsplit|, will only have a local
+%    effect. Without this trick the box content would get lost up to
+%    the level where the last assignment to the box register was done.
+%    \begin{macrocode}
+  \begingroup
+   \vbadness\@M
+   \setbox#1\copy#1%
+%    \end{macrocode}
+%    Now we split the box to the maximal possible dimension. This
+%    should split off the full contents of the box so that effectively
+%    everything is split off. As a result |\splitfirstmark| and
+%    |\splitbotmark| will contain the first and last mark in the box
+%    respectively.
+%    \begin{macrocode}
+   \setbox#1\vsplit#1to\maxdimen
+%    \end{macrocode}
+%    Therefore we can now set the kept marks which is a global
+%    operation and afterwards close the group. This will restore the
+%    original box contents.
+%    \begin{macrocode}
+   \set@keptmarks
+ \endgroup
+%    \end{macrocode}
+%    For debugging we take again a look at the box dimension which
+%    shouldn't have changed.
+%    \begin{macrocode}
+%<*debug>
+    \typeout{Mark box #1 \space after:
+             ht \the\ht#1, dp \the\dp#1}%
+%</debug>
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\set@keptmarks}
+%    The macro |\set@keptmarks| is responsible for setting
+%    |\kept@firstmark| and |\kept@botmark|, by checking the current
+%    values for |\splitfirstmark| and |\splitbotmark|.
+%    \begin{macrocode}
+\def\set@keptmarks{%
+%    \end{macrocode}
+%    If |\kept@firstmark| is empty we assume that it isn't set. This
+%    is strictly speaking not correct as we loose the ability to have
+%    marks that are explicitly empty, but for standard \LaTeX{}
+%    application it is sufficient. If it is non-empty we don't change
+%    the value---within the output routines it will then be restored
+%    to |\@empty|.
+%    \begin{macrocode}
+   \ifx\kept@firstmark\@empty
+%    \end{macrocode}
+%    We now put the contents of |\splitfirstmark| into
+%    |\kept@firstmark|. In the case that there wasn't any mark at all
+%    |\kept@firstmark| will not change by that operation.
+%    \begin{macrocode}
+     \expandafter\gdef\expandafter
+        \kept@firstmark
+        \expandafter{\splitfirstmark}%
+%    \end{macrocode}
+%    When debugging we show the assignment but only when something
+%    actually happened.
+%    \begin{macrocode}
+%<*marktrace>
+     \ifx\kept@firstmark\@empty\else
+       \mult@info\tw@
+         {Set kept first mark:\MessageBreak
+          \meaning\kept@firstmark%
+          \@gobbletwo}%
+     \fi
+%</marktrace>
+   \fi
+%    \end{macrocode}
+%    We always try to set the bottom mark to the |\splitbotmark| but
+%    of course only when there has been a |\splitbotmark| at all.
+%    Again, we assume that an empty |\splitbotmark| means that the
+%    split off box part didn't contain any marks at all.
+%    \begin{macrocode}
+   \expandafter\def\expandafter\@tempa
+      \expandafter{\splitbotmark}%
+   \ifx\@tempa\@empty\else
+      \global\let\kept@botmark\@tempa
+%<*marktrace>
+      \mult@info\tw@
+        {Set kept bot mark:\MessageBreak
+         \meaning\kept@botmark%
+         \@gobbletwo}%
+%</marktrace>
+   \fi}%
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\prep@keptmarks}
+%    The |\prep@keptmarks| function is used to initialize the kept
+%    marks from the contents of  |\partial@page|, i.e.\ the box that
+%    holds everything from the top of the current page prior to
+%    starting the \mc{} environment. However, such a box is only
+%    available if we are not producing a boxed \mc{}.
+%    \begin{macrocode}
+\def\prep@keptmarks{%
+   \if@boxedmulticols \else
+     \get@keptmarks\partial@page
+   \fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\remove@discardable@items}
+%    There are situations when we may have some space at the end of a
+%    column and this macro here will attempt to get rid of it. The
+%    typical \LaTeX{} sequence is a series of self-canceling glues so
+%    if we remove them recursively we are usually fine.
+%
+%    Special care is needed with handling |\vspace*| as that
+%    corresponds to |\penalty10000|, |\vskip <skip>|, followed by
+%    |\vskip 0pt|. If we see this sequence going backwards in the the
+%    vertical list we assume that this is a ``desired'' space. We
+%    therefore stop the recursion and reinsert the spaces.
+%
+%    As the multicol code sometimes add an explicit penalty at the end
+%    of a column we first attempt to remove it in case it is there.
+% \changes{v1.8m}{2015/03/31}{Another rewrite of
+%     \cs{remove@discardable@items} hopefully okay now}
+%    \begin{macrocode}
+\skip0=0pt
+\edef\the@zero@skip{\the\skip0}
+\def\remove@discardable@items{%
+     \unpenalty
+%    \end{macrocode}
+%    Save a previous skip (if there) and then remove it, we can't
+%    really tell the difference between no skip an a skip of zero but
+%    that's life.
+%    \begin{macrocode}
+     \edef\@tempa{\the\lastskip}%
+%\typeout{s1=\@tempa}%
+     \unskip
+%    \end{macrocode}
+%    If it was a zero skip (or none) we save the next previous skip
+%    (if any).
+%    \begin{macrocode}
+     \ifx\@tempa\the@zero@skip
+       \edef\@tempb{\the\lastskip}%
+%\typeout{s2=\@tempb}%
+%    \end{macrocode}
+%    If this one again was zero (or more likely not there in the first
+%    place) we stop.
+%    \begin{macrocode}
+       \ifx\@tempb\the@zero@skip
+       \else
+%    \end{macrocode}
+%    Otherwise we remove this ``real'' skip. Then we look if it was
+%    preceded by a penalty of 10000 (i.e., a |\nobreak|)
+%    \begin{macrocode}
+         \unskip
+%\typeout{p=\lastpenalty}%
+         \ifnum \lastpenalty=\@M
+%    \end{macrocode}
+%    If so this was a |\vspace*| or something equivalent to
+%    it. Therefore we reintroduce the skips and stop. Otherwise we
+%    recurse.
+%    \begin{macrocode}
+           \vskip\@tempb\vskip\@tempa\relax
+         \else 
+           \remove@discardable@items
+         \fi
+       \fi
+     \else
+%    \end{macrocode}
+%    If the first skip was a non-zero skip we recurse as well.
+%    \begin{macrocode}
+       \remove@discardable@items
+     \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    \begin{macrocode}
+%<*badness>
+\newif\iftoo@bad
+\def\too@badtrue{\global\let\iftoo@bad\iftrue}
+\def\too@badfalse{\global\let\iftoo@bad\iffalse}
+%    \end{macrocode}
+%    
+% \changes{v1.8k}{2015/03/21}{The new switch}
+%    \begin{macrocode}
+\newif\ifforcedbreak@leftover
+%    \end{macrocode}
+%
+%  \begin{macro}{\c@minrows}
+% \changes{v1.8w}{2019/03/01}{Provide minrows counter for balancing}
+%    \begin{macrocode}
+\newcount\c@minrows
+\c@minrows=1
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\c@columnbadness}
+% \begin{macro}{\c@finalcolumnbadness}
+%    \begin{macrocode}
+\newcount\c@columnbadness
+\c@columnbadness=10000
+\newcount\c@finalcolumnbadness
+\c@finalcolumnbadness=9999
+
+\newdimen\last@try
+
+%    \end{macrocode}
+%
+% \changes{v1.5z1}{2003/02/17}{Change wrong default for
+%    \cs{multicolovershoot} to zero (pr/3465).}
+%    \begin{macrocode}
+\newdimen\multicolovershoot
+\newdimen\multicolundershoot
+\multicolovershoot=0pt
+\multicolundershoot=2pt
+\newbox\mult@nat@firstbox
+%</badness>
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%  \begin{macro}{\mult@info}
+%    A helper for producing info messages
+%    \begin{macrocode}
+\def\mult@info#1#2{%
+  \ifnum\c@tracingmulticols>#1%
+   \GenericWarning
+       {(multicol)\@spaces\@spaces}%
+       {Package multicol: #2}%
+  \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+% \end{multicols}
+%
+%
+% \begin{multicols}{2}[\section{Fixing the
+%                        \cs{columnwidth}}]
+%
+%  \begin{macro}{\@footnotetext}
+% \changes{v1.5o}{1997/11/16}{Redefinition added pr/2664.}
+% \changes{v1.5r}{1998/08/17}{Use \cs{@footnotetext} but with
+%                             local change to \cs{columnwidth}.}
+%  \begin{macro}{\mult@footnotetext}
+% \changes{v1.5r}{1998/08/17}{Macro removed again.}
+%    If we store the current column width in |\columnwidth| we have
+%    to redefine the internal |\@footnotetext| macro to use |\textwidth|
+%    for the width of the footnotes rather than using the original
+%    definition.
+%
+%    Starting with version v1.5r this is now done in a way that the original
+%    definition is still used, except that locally |\columnwidth| is set to
+%    |\textwidth|.
+%
+%    This solves two problems: first redefinitions of |\@footnotetext|
+%    done by a class will correctly survive and second if multicols is
+%    used inside a minipage environment the special definition of
+%    |\@footnotetext| in that environment will be picked up and not the
+%    one for the main galley (the latter would result in all footnotes
+%    getting lost in that case).
+%
+%    See the definition of the |\multicols| command further up for the exact
+%    code.
+%  \end{macro}
+%  \end{macro}
+% \end{multicols}
+%
+%
+% \begin{multicols*}{2}[\section{Further extensions}]
+%
+% This section does contain code for extensions added to this package
+% over time. Not all of them may be active, some might sit dormant and
+% wait for being activated in some later release.
+%
+% \subsection{Not balancing the columns}
+%
+%  This is fairly trivial to implement. we just have to disable the
+%  balancing output routine and replace it by the one that ships out
+%  the other pages.
+%
+%  \begin{macro}{\multicols*}
+% \changes{v1.5q}{1998/01/19}{Macro added}
+%  The code for this environment was suggested by Matthias Clasen.
+%    \begin{macrocode}
+%<*nobalance>
+ \@namedef{multicols*}{%
+%    \end{macrocode}
+%    If we are not on the main galley, i.e., inside a box of some
+%    sort, that approach will not work since we don't have a vertical
+%    size for the box so we better warn that we balance anyway.
+%    \begin{macrocode}
+   \ifinner
+     \PackageWarning{multicol}%
+       {multicols* inside a box does
+        not make sense.\MessageBreak
+        Going to balance anyway}%
+   \else
+%    \end{macrocode}
+%    If we aren't balancing we change the |\balance@columns@out| to
+%    work like the normal output routine that cuts normal
+%    pages. However, there is a catch: In case the last page we cut
+%    (after seeing the end of the environment) is actually larger than
+%    a page (for example, if it contains more |\columnbreak| commands
+%    than columns) we end up with some leftover material that is
+%    returned to the main galley, but now the environment end penalty
+%    is missing. So we add another one here too. Of course that
+%    shouldn't be done if there is really only a single final page,
+%    but fortunately in that case we have just finished a page and any
+%    penalty on the recent contributions will be discarded, thus the
+%    extra one is harmless---puh.
+% \changes{v1.8t}{2018/06/26}{Re-add end penalty for
+%    \texttt{multicols*} environment to guard against leftovers (git/53)}
+%    \begin{macrocode}
+     \def\balance@columns@out
+         {\multi@column@out \penalty-\@Mvi }%
+   \fi
+   \begin{multicols}
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\endmulticols*}
+%    When ending the environment we simply end the inner
+%    \texttt{multicols} environment, except that we better also stick
+%    in some stretchable vertical glue so that the last column still
+%    containing text is not vertically stretched out. 
+%
+%    We do this as follows: first we ensure that we are back in vertical mode
+%    and then we cancel out |\lastskip| if it was
+%    positive (in case of a negative glue we assume that it was
+%    deliberate, for a deliberate positive glue one needs to use
+%    |\vspace*|). We can't simply use |\remove@discardable@items| here
+%    as this only works inside boxes but we are here on the main
+%    vertical list.
+%
+%    Then we back up by |\prevdepth| but not more than |\boxmaxdepth|
+%    so that a baseline of the last box is now at the bottom. This way
+%    the material will align properly in case something like |\vfill|
+%    spreads it out after all.
+%    Finally we append |\vfil| to put white space at the bottom of the
+%    column, but we only do this if we aren't anyway doing |\raggedcolumns|.
+% \changes{v1.5q}{1998/01/19}{Macro added}
+% \changes{v1.8h}{2014/09/12}{Use \cs{vfilmaxdepth}}
+% \changes{v1.8i}{2014/10/28}{Add \cs{null} to hide the final fill and only add
+%                             vertical space if not doing \cs{raggedcolumns}}
+% \changes{v1.8j}{2015/03/07}{Redesign the whole approach.}
+% \changes{v1.8k}{2015/03/21}{And a bit more redesign because of the
+%    change in \cs{remove@discardable@items}}
+% \changes{v1.8o}{2016/02/08}{Ensure we are back in vmode before using
+%    \cs{prevdepth} (pr/4448)}
+%    \begin{macrocode}
+\@namedef{endmulticols*}{%
+   \par
+   \ifdim\lastskip>\z@ \vskip-\lastskip \fi
+   \ifdim \prevdepth>\z@
+     \vskip-\ifdim\prevdepth>\boxmaxdepth 
+                  \boxmaxdepth
+            \else \prevdepth \fi
+   \fi
+   \ifshr@nking\else
+     \vfil
+   \fi
+   \end{multicols}}
+%</nobalance>
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \subsection{Manual column breaking} \label{sec:colbreak}
+%
+% The problem with manual page breaks within \mc{} is the fact that
+% during collection of material for all columns a page-forcing penalty
+% (i.e. -10000 or higher) would stop the collecting pass which is not
+% quite what is desired. On the other hand, using a penalty like -9999
+% would mean that there would be occasions where the |\vsplit|ing
+% operations within \mc{} would ignore that penalty and still choose a
+% different break point.
+%
+% For this reason the current implementation
+% uses a completely different approach. In a nutshell it extends the \LaTeX{}
+% output routine handling by introducing an additional penalty flag
+% (i.e., a penalty which is forcing but higher than -10000 so that the
+% output routine can look at this value and thus knows why it has been
+% called).
+%
+% Inside the output routine we test for this value and if it appears
+% we do two things: save the galley up to this point in a special box
+% for later use and reduce the |\vsize| by the height of the material
+% seen. This way the forcing penalty is now hidden in that box and we
+% can restart the collection process for the remaining
+% columns. (This is done in |\speci@ls| above.)
+%
+% In the output routines that do the |\vsplit|ting either for
+% balancing or for a full page we simply combine box~255 with the
+% saved box thus getting a single box for  splitting which now
+% contains forcing breaks in the right positions.
+%
+%
+%  \begin{macro}{\columnbreak}
+% \changes{v1.5u}{1999/05/25}{Macro added}
+%    |\columnbreak| is modeled after |\pagebreak| except that we
+%    generate a penalty -10005.
+%    \begin{macrocode}
+\mathchardef\@Mv=10005
+\def\columnbreak{%
+%    \end{macrocode}
+%    We have to ensure that it is only used within a \mc{}
+%    environment since if that penalty would be seen by the unmodified
+%    \LaTeX{} output routine strange things would happen.
+%    \begin{macrocode}
+ \ifnum\col@number<\tw@
+  \PackageError{multicol}%
+   {\noexpand\columnbreak outside multicols}%
+   {This command can only be used within
+    a multicols or multicols* environment.}%
+ \else
+  \ifvmode
+    \penalty -\@Mv\relax
+  \else
+    \@bsphack
+    \vadjust{\penalty -\@Mv\relax}%
+    \@esphack
+  \fi
+ \fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\colbreak@box}
+% \changes{v1.5u}{1999/05/25}{Macro added}
+%    Need a box to collect the galley up to the column break.
+%    \begin{macrocode}
+\newbox\colbreak@box
+%</package>
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \subsection{Supporting right-to-left languages} \label{sec:RL}
+%
+%
+% \changes{v1.7a}{2010/10/24}{RL language support added}
+% \changes{v1.7b}{2011/12/18}{RL language support fixed}
+%
+%  \begin{macro}{\LR@column@boxes}
+%    |\LR@column@boxes| is called when we are assembling the columns for left
+%    to right typesetting. When we start we are inside an |\hbox| of
+%    full width.
+%    Left to right typesetting is fairly easy, we basically output
+%    each column box intermixed with vertical rules and proper
+%    spacing. As this happens inside a box of a defined width the
+%    rules and the columns automatically get into the right positions.
+%    \begin{macrocode}
+\def\LR@column@boxes{%
+%    \end{macrocode}
+%    We loop through the columns with |\process@cols|
+%    \begin{macrocode}
+     \process@cols\mult@gfirstbox{%
+%    \end{macrocode}
+%    If the depth of the current box is larger than the maximum found
+%    so far in |\dimen2| we update that register for later use.
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+%    \begin{macrocode}
+       \ifdim\dp\count@>\dimen\tw@
+         \global\dimen\tw@\dp\count@ \fi
+%    \end{macrocode}
+%    If the \texttt{colaction} option is given we write out status
+%    information about the current column, otherwise the next command
+%    does nothing.
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%    \begin{macrocode}
+       \mc@col@status@write
+%    \end{macrocode}
+%    The typeset box followed by the column rule material
+%    \begin{macrocode}
+       \box\count@
+       \hss{\columnseprulecolor\vrule
+              \@width\columnseprule}\hss}%
+%    \end{macrocode}
+%    As you will have noticed, we started with box register
+%    |\mult@gfirstbox|  (i.e.\
+%    the left column). So this time |\count@| looped through 2,
+%    4,\ldots\ (plus the appropriate offset).
+%    Finally we add box |\mult@rightbox| and we are done.
+% \changes{v1.5a}{1992/11/04}{New box mechanism}
+% \changes{v1.6a}{2003/03/15}{Preparing for adjusting \cs{prevdepth}}
+%    Again we may have to update |\dimen\tw@|.
+%    \begin{macrocode}
+     \ifdim\dp\mult@rightbox>\dimen\tw@
+       \global\dimen\tw@\dp\mult@rightbox \fi
+%    \end{macrocode}
+%    If the \texttt{colaction} option is given we write out status
+%    information about the last column, otherwise the next command
+%    does nothing.
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%    \begin{macrocode}
+     \mc@lastcol@status@write
+     \box\mult@rightbox
+}
+%    \end{macrocode}
+%  \end{macro}
+
+%  \begin{macro}{\RL@column@boxes}
+%    Assembling the boxes for right to left typesetting is far more
+%    complicated. When I first tried to build a solution for this my
+%    thinking was that all that is necessary to do is to reverse the
+%    order of the columns. But such an approach produces a subtle bug:
+%    If we work this way then the first column put on the page will be
+%    the last column of the text to read. and this means that the
+%    order in which \TeX{} executes write statements or assembles mark
+%    material will not happen in the order of the textual flow. So if,
+%    for example each column contains a section command then these
+%    sections will appear in reverse order in the table of content.
+%
+%    For this reason some amount of gymnastics is needed to add the
+%    columns in their natural flow.
+%    \begin{macrocode}
+\def\RL@column@boxes{%
+%    \end{macrocode}
+%    First step is to put all rules in the right place (without adding
+%    the comes which are instead represented by a space of |\hsize|.
+%    \begin{macrocode}
+     \process@cols\mult@gfirstbox{%
+       \hskip\hsize
+       \hss{\columnseprulecolor\vrule
+              \@width\columnseprule}\hss
+     }%
+     \hskip\hsize
+%    \end{macrocode}
+%    At this point in the code our typesetting reference point is at
+%    the right end of the rightmost column (or rather where that column
+%    should appear).
+%
+%    We are now typesetting all columns by first backing up by their
+%    width (which is |\hsize|) then typesetting the box and then
+%    backing up again, but this time further, i.e., also across the
+%    column separation. That will then enable us to typeset the next
+%    column using the same approach until we are done with all but the
+%    final column.
+%    \begin{macrocode}
+     \process@cols\mult@gfirstbox{%
+       \ifdim\dp\count@>\dimen\tw@
+         \global\dimen\tw@\dp\count@ \fi
+       \hskip-\hsize
+%    \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%    \begin{macrocode}
+       \mc@col@status@write
+       \box\count@
+       \hskip-\hsize
+       \hskip-\columnsep
+     }%
+%    \end{macrocode}
+%    The approach for the final column is similar only that we do not
+%    have to back up over any column gap.
+%    \begin{macrocode}
+     \ifdim\dp\mult@rightbox>\dimen\tw@
+       \global\dimen\tw@\dp\mult@rightbox \fi
+     \hskip-\hsize
+%    \end{macrocode}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%    \begin{macrocode}
+     \mc@lastcol@status@write
+     \box\mult@rightbox
+     \hskip-\hsize
+%    \end{macrocode}
+%    However we do have to move the reference point to its right
+%    place: to make the rules appear at the expected places, we should
+%    get the typesetting position to the far right again. As we at the
+%    moment at the far left we skip to the far right like this:
+%    \begin{macrocode}
+     \hskip\full@width
+ }
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\RLmulticolcolumns}
+%  \begin{macro}{\LRmulticolcolumns}
+%  \begin{macro}{\mc@align@columns}
+%    Macros to switch between left-right and right-left typesetting. In LR
+%    typesetting the |\LR@column@boxes| is used to combine
+%    the columns. When typesetting right to left the |\RL@column@boxes|
+%    is used instead.
+%    \begin{macrocode}
+\newcommand\RLmulticolcolumns
+    {\let\mc@align@columns
+         \RL@column@boxes}
+\newcommand\LRmulticolcolumns
+    {\let\mc@align@columns
+      \LR@column@boxes}
+%    \end{macrocode}
+%    The default is left-to-right:
+%    \begin{macrocode}
+\LRmulticolcolumns
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+% \subsection{Supporting \texttt{\textbackslash docolaction}}
+%
+% \changes{v1.8e}{2014/04/23}{Support \cs{docolaction}}
+%
+%   Whenever we want to do something that depends on the current
+%   column we execute \verb=\docolaction=. This command takes one
+%   optional and three mandatory arguments. The mandatory ones denote
+%   what to do if this is a ``left'', ``middle'', or ``right'' column
+%   and the optional one is simply there to say what to do if we don't
+%   know (default is to use the ``left'' column action in that case).
+%
+%  \begin{macro}{\mc@col@check@num}
+%   We use one counter \verb=\mc@col@check@num= to generate us unique
+%   label names. Each time we execute \verb=\docolaction= we increment
+%   this counter to get a new name.
+%    \begin{macrocode}
+\newcount\mc@col@check@num
+%    \end{macrocode}
+%  \end{macro}
+%
+%   The generated ``labels'' are named
+%\begin{verbatim}
+%\mc@col-\the\mc@col@check@num
+%\end{verbatim}
+%   and they hold as values the
+%   numbers 1, 2, or 3 denoting the current column type.
+
+%  \begin{macro}{\docolaction}
+%
+%    The \verb=\docolaction= scans for a star and optional argument
+%    and 3 mandatory ones, but we do this in chunks (not having xparse
+%    available).
+%
+% \changes{v1.8u}{2018/11/09}{Support star with \cs{docolaction}}
+%    \begin{macrocode}
+\newcommand\docolaction{%
+%    \end{macrocode}
+%    First check is the support is enabled.
+%    \begin{macrocode}
+ \ifx\mc@col@status@write\relax
+     \PackageError{multicol}%
+      {Option 'colaction' not selected}%
+      {\string\docolaction\space
+       requires the use of the 'colaction'
+       option on the package}%
+ \fi
+%    \end{macrocode}
+%    Then prepare \verb=\mc@col@type=.
+%    \begin{macrocode}
+ \global\advance\mc@col@check@num\@ne
+ \edef\mc@col@type{\expandafter\ifx
+   \csname mc@col-\the\mc@col@check@num
+   \endcsname\relax
+                   0\else
+   \csname mc@col-\the\mc@col@check@num
+   \endcsname
+   \fi}%
+%    \end{macrocode}
+%    Finally check for a star, record this information and then call
+%    \verb=\@docolaction= to do the rest.
+%    \begin{macrocode}
+ \@ifstar
+   {\@docolactionstartrue \@docolaction}%
+   {\@docolactionstarfalse\@docolaction}%
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newcommand\@docolaction[4][1]{%
+%    \end{macrocode}
+%    
+%   How does the column number get associated with our label? We
+%   do do this by writing another line into the aux file. Here are the
+%    preparations.
+%    \begin{macrocode}
+ \edef\@docolactioncheck{\write\@auxout
+   {\string\mc@set@col@status
+     {mc@col-\the\mc@col@check@num}%
+     {\mc@col@type}}}%
+%    \end{macrocode}
+%    Where we do the actual \verb=\write= depends on the whether or
+%    not we gave seen a \texttt{*}. If yes, we do it first and then
+%    execute the code argument, otherwise we execute that code first
+%    and check at the point after that.
+%    \begin{macrocode}
+ \if@docolactionstar \@docolactioncheck \fi
+%    \end{macrocode}
+%    We prefix with 0 so that an unknown label (that returns
+%   \verb=\relax=) will result in case 0
+%    \begin{macrocode}
+ \ifcase \mc@col@type\relax
+%    \end{macrocode}
+%    If column is unknown we use the default action or the action
+%   denoted by the optional argument (so that arg can take the value
+%   1, 2, 3).
+%    \begin{macrocode}
+     \ifcase #1\or #2\or#3\or#4\fi
+  \or
+%    \end{macrocode}
+%    Otherwise we know (or think we know) that this is a first, middle,
+%   or last column:
+%    \begin{macrocode}
+     #2%  % 1 First col
+  \or
+     #3%  % 2 any middle col
+  \or
+     #4%  % 3 last col
+  \else
+    \ERRORwrongdefaultgiven
+  \fi
+%    \end{macrocode}
+%    \begin{macrocode}
+ \if@docolactionstar \else \@docolactioncheck \fi
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%    Here is the if used above:
+%    \begin{macrocode}
+\newif\if@docolactionstar
+%    \end{macrocode}
+%    
+%   Because of extra data writing to the aux file the aux file will
+%   now contain something like the following after the document is
+%   processed the first time:
+%\begin{verbatim}
+%\relax
+%\mc@col@status{1}
+%\mc@set@col@status{lcol-1}{0}
+%\mc@col@status{2}
+%\mc@set@col@status{lcol-2}{0}
+%\mc@col@status{3}
+%\mc@set@col@status{lcol-3}{0}
+%\mc@col@status{1}
+%\mc@col@status{2}
+%\mc@col@status{3}
+%\mc@set@col@status{lcol-4}{0}
+%\end{verbatim}
+%   The \verb=\mc@col@status= line denotes the column type and has been
+%   written out just before corresponding the column box was placed
+%   onto the page.
+%   The\verb=\mc@set@col@status= lines have been written out as part
+%   of shipping the column boxes out, e.g.,
+%   \verb=\mc@set@col@status{lcol-1}{0}= was therefore somewhere within
+%   the first column as it appears between \verb=\mc@col@status{1}=
+%   and  \verb=\mc@col@status{2}=
+%   The second argument in that line is the value used in the previous
+%   run (or zero if there was no previous run. We can use this to
+%   determine if a rerun is necessary.
+%
+%   Thus with this knowledge we can set things up to get the labels
+%   working.
+%
+%
+%  \begin{macro}{\mc@col@status}
+%
+%   When the aux file is read in \verb=\mc@col@status= is used to set
+%   \verb=\mc@curr@col@status=:
+%    \begin{macrocode}
+\def\mc@col@status#1{%
+    \gdef\mc@curr@col@status{#1}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%
+%  \begin{macro}{\mc@set@col@status}
+%
+%   And when \verb=\mc@set@col@status= is executed we can simply set
+%   up the label by associating it with the \verb=\mc@curr@col@status=
+%   and ignore the second argument:
+%    \begin{macrocode}
+\def\mc@set@col@status#1#2{%
+  \global\expandafter\let\csname #1\endcsname
+                         \mc@curr@col@status}
+%    \end{macrocode}
+%   The above definition is being used when the \texttt{.aux} file is
+%   read in at the beginning. At the end we need a different
+%   definition to test if another typesetting run is needed. There we
+%   compare the value used in the current run (stored in the second
+%   argument) with the value used on the next run. If those two values
+%   differ we set \verb=@tempswa= to false which will trigger the
+%   ``Label(s) may have changed'' warning.
+%    \begin{macrocode}
+\AtEndDocument{\def\mc@set@col@status#1#2{%
+     \ifnum #2=\mc@curr@col@status\else
+       \@tempswatrue
+     \fi}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{mc@firstcol}
+%   Finally, as part of determining in which column we are, we used a
+%   switch inside |\mc@col@status@write| to determine if we are in the
+%   first column or not.
+%  \begin{macrocode}
+\newif\ifmc@firstcol
+\mc@firstcoltrue
+%    \end{macrocode}
+%  \end{macro}
+% \end{multicols*}
+%
+% \Finale
+%
+\endinput
+
+
diff --git a/macros/latex-dev/required/tools/multicol.ins b/macros/latex-dev/required/tools/multicol.ins
new file mode 100644
index 0000000000..9fd6cbe6e9
--- /dev/null
+++ b/macros/latex-dev/required/tools/multicol.ins
@@ -0,0 +1,77 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+
+\generateFile{multicol.sty}{t}{%
+   \from{multicol.dtx}{package,badness,check,marktrace,nobalance}}
+
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/multicol.pdf b/macros/latex-dev/required/tools/multicol.pdf
new file mode 100644
index 0000000000..e614cb3386
--- /dev/null
+++ b/macros/latex-dev/required/tools/multicol.pdf
diff --git a/macros/latex-dev/required/tools/rawfonts.dtx b/macros/latex-dev/required/tools/rawfonts.dtx
new file mode 100644
index 0000000000..0fd7dd5006
--- /dev/null
+++ b/macros/latex-dev/required/tools/rawfonts.dtx
@@ -0,0 +1,219 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \title{The \textsf{rawfonts} package}
+% \date{v0.01}
+% \author{Alan Jeffrey}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+% \section*{Overview}
+%
+% The |rawfonts| \LaTeXe{} package is used to provide emulation
+% of \LaTeX~2.09 documents which used low-level commands such as
+% |\tenrm|.  If you say:
+% \begin{verbatim}
+%    \usepackage{rawfonts}
+% \end{verbatim}
+% then over sixty fonts such as |\tenrm| will be loaded into \LaTeX.
+% This has a large overhead, for example this document uses:
+% \begin{verbatim}
+%    8221 words of font info for 30 fonts
+% \end{verbatim}
+% but when run with the |rawfonts| package it uses:
+% \begin{verbatim}
+%    19294 words of font info for 73 fonts
+% \end{verbatim}
+% That is |rawfonts| can cause your document to load twice as many
+% fonts.  (This overhead is why \LaTeXe{} does not define |\tenrm| and
+% friends by default.)
+%
+% If you want to only load a small
+% number of fonts, you can use the |only|
+% option, for example to only load |\tenrm| and |\tensf|:
+% \begin{verbatim}
+%    \usepackage[only,tenrm,tensf]{rawfonts}
+% \end{verbatim}
+% The |rawfonts| package is intended mainly for use with \LaTeX~2.09
+% documents, and you might want to have the package loaded every time
+% you use \LaTeXe{} in compatibility mode.  In this case, you should add
+% the line:
+% \begin{verbatim}
+%    \RequirePackage{rawfonts}
+% \end{verbatim}
+% to your |latex209.cfg| \LaTeX~2.09 compatibility configuration file.
+%
+% \StopEventually{}
+%
+% \section*{Implementation}
+%
+% The driver for the documentation you're now reading.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+\begin{document}
+\DocInput{rawfonts.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+% This is a \LaTeXe{} package.
+%    \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{rawfonts}
+   [1994/05/08 Low-level LaTeX 2.09 font compatibility]
+%    \end{macrocode}
+% The |rawfonts| package uses the |somedefs| package.
+%    \begin{macrocode}
+\RequirePackage{somedefs}
+%    \end{macrocode}
+% By default, all the fonts are loaded, but the |only| option says
+% that only the ones specified as options should be.
+%    \begin{macrocode}
+\UseAllDefinitions
+\DeclareOption{only}{\UseSomeDefinitions}
+\DeclareOption*{\UseDefinition{\CurrentOption}}
+\ProcessOptions
+%    \end{macrocode}
+% The rest of the code loads fonts.  Five point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\fivrm}{OT1}{cmr}{m}{n}{\@vpt}}
+\ProvidesDefinition{\DeclareFixedFont{\fivmi}{OML}{cmm}{m}{it}{\@vpt}}
+\ProvidesDefinition{\DeclareFixedFont{\fivsy}{OMS}{cmsy}{m}{n}{\@vpt}}
+\ProvidesDefinition{\DeclareFixedFont{\fivly}{U}{lasy}{m}{n}{\@vpt}}
+%    \end{macrocode}
+% Six point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\sixrm}{OT1}{cmr}{m}{n}{\@vipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sixmi}{OML}{cmm}{m}{it}{\@vipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sixsy}{OMS}{cmsy}{m}{n}{\@vipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sixly}{U}{lasy}{m}{n}{\@vipt}}
+%    \end{macrocode}
+% Seven point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\sevrm}{OT1}{cmr}{m}{n}{\@viipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sevmi}{OML}{cmm}{m}{it}{\@viipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sevsy}{OMS}{cmsy}{m}{n}{\@viipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sevit}{OT1}{cmr}{m}{it}{\@viipt}}
+\ProvidesDefinition{\DeclareFixedFont{\sevly}{U}{lasy}{m}{n}{\@viipt}}
+%    \end{macrocode}
+% Eight point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\egtrm}{OT1}{cmr}{m}{n}{\@viiipt}}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\egtmi}{OML}{cmm}{m}{it}{\@viiipt}}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\egtsy}{OMS}{cmsy}{m}{n}{\@viiipt}}
+\ProvidesDefinition{%
+     \DeclareFixedFont{\egtit}{OT1}{cmr}{m}{it}{\@viiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\egtly}{U}{lasy}{m}{n}{\@viiipt}}
+%    \end{macrocode}
+% Nine point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\ninrm}{OT1}{cmr}{m}{n}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\ninmi}{OML}{cmm}{m}{it}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\ninsy}{OMS}{cmsy}{m}{n}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\ninit}{OT1}{cmr}{m}{it}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\ninbf}{OT1}{cmr}{bx}{n}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\nintt}{OT1}{cmtt}{m}{n}{\@ixpt}}
+\ProvidesDefinition{\DeclareFixedFont{\ninly}{U}{lasy}{m}{n}{\@ixpt}}
+%    \end{macrocode}
+% Ten point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\tenrm}{OT1}{cmr}{m}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tenmi}{OML}{cmm}{m}{it}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tensy}{OMS}{cmsy}{m}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tenit}{OT1}{cmr}{m}{it}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tensl}{OT1}{cmr}{m}{sl}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tenbf}{OT1}{cmr}{bx}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tentt}{OT1}{cmtt}{m}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tensf}{OT1}{cmss}{m}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tenly}{U}{lasy}{m}{n}{\@xpt}}
+\ProvidesDefinition{\DeclareFixedFont{\tenex}{OMX}{cmex}{m}{n}{\@xpt}}
+%    \end{macrocode}
+% Eleven point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\elvrm}{OT1}{cmr}{m}{n}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvmi}{OML}{cmm}{m}{it}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvsy}{OMS}{cmsy}{m}{n}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvit}{OT1}{cmr}{m}{it}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvsl}{OT1}{cmr}{m}{sl}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvbf}{OT1}{cmr}{bx}{n}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvtt}{OT1}{cmtt}{m}{n}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvsf}{OT1}{cmss}{m}{n}{\@xipt}}
+\ProvidesDefinition{\DeclareFixedFont{\elvly}{U}{lasy}{m}{n}{\@xipt}}
+%    \end{macrocode}
+% Twelve point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\twlrm}{OT1}{cmr}{m}{n}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlmi}{OML}{cmm}{m}{it}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlsy}{OMS}{cmsy}{m}{n}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlit}{OT1}{cmr}{m}{it}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlsl}{OT1}{cmr}{m}{sl}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlbf}{OT1}{cmr}{bx}{n}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twltt}{OT1}{cmtt}{m}{n}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlsf}{OT1}{cmss}{m}{n}{\@xiipt}}
+\ProvidesDefinition{\DeclareFixedFont{\twlly}{U}{lasy}{m}{n}{\@xiipt}}
+%    \end{macrocode}
+% Fourteen point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\frtnrm}{OT1}{cmr}{m}{n}{\@xivpt}}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\frtnmi}{OML}{cmm}{m}{it}{\@xivpt}}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\frtnsy}{OMS}{cmsy}{m}{n}{\@xivpt}}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\frtnbf}{OT1}{cmr}{bx}{n}{\@xivpt}}
+\ProvidesDefinition{\DeclareFixedFont{\frtnly}{U}{lasy}{m}{n}{\@xivpt}}
+%    \end{macrocode}
+% Seventeen point:
+%    \begin{macrocode}
+\ProvidesDefinition{%
+                   \DeclareFixedFont{\svtnrm}{OT1}{cmr}{m}{n}{\@xviipt}}
+\ProvidesDefinition{%
+                  \DeclareFixedFont{\svtnmi}{OML}{cmm}{m}{it}{\@xviipt}}
+\ProvidesDefinition{%
+                  \DeclareFixedFont{\svtnsy}{OMS}{cmsy}{m}{n}{\@xviipt}}
+\ProvidesDefinition{%
+                  \DeclareFixedFont{\svtnbf}{OT1}{cmr}{bx}{n}{\@xviipt}}
+\ProvidesDefinition{\DeclareFixedFont{\svtnly}{U}{lasy}{m}{n}{\@xviipt}}
+%    \end{macrocode}
+% Twenty point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\twtyrm}{OT1}{cmr}{m}{n}{\@xxpt}}
+\ProvidesDefinition{\DeclareFixedFont{\twtymi}{OML}{cmm}{m}{it}{\@xxpt}}
+\ProvidesDefinition{\DeclareFixedFont{\twtysy}{OMS}{cmsy}{m}{n}{\@xxpt}}
+\ProvidesDefinition{\DeclareFixedFont{\twtyly}{U}{lasy}{m}{n}{\@xxpt}}
+%    \end{macrocode}
+% Twenty-five point:
+%    \begin{macrocode}
+\ProvidesDefinition{\DeclareFixedFont{\twfvrm}{OT1}{cmr}{m}{n}{\@xxvpt}}
+%    \end{macrocode}
+% That's it.
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
+% \endinput
diff --git a/macros/latex-dev/required/tools/rawfonts.pdf b/macros/latex-dev/required/tools/rawfonts.pdf
new file mode 100644
index 0000000000..316f3b8c76
--- /dev/null
+++ b/macros/latex-dev/required/tools/rawfonts.pdf
diff --git a/macros/latex-dev/required/tools/shellesc.dtx b/macros/latex-dev/required/tools/shellesc.dtx
new file mode 100644
index 0000000000..061ea4457c
--- /dev/null
+++ b/macros/latex-dev/required/tools/shellesc.dtx
@@ -0,0 +1,243 @@
+% \iffalse
+%% Source File: shellesc.dtx
+%% Copyright (C) 2015-2019
+%%
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file.
+%%
+%% This file may be distributed under the terms of the LPPL.
+%% See README for details.
+%
+%<*dtx>
+          \ProvidesFile{shellesc.dtx}
+%</dtx>
+%<package>\ifx\ProvidesPackage\undefined
+%<package>\def\next#1#2[#3]{\wlog{#2 #3}}
+%<package>\ifx\PackageInfo\undefined\def\PackageInfo#1#2{\wlog{#1: #2}}\fi
+%<package>\ifx\PackageWarning\undefined\def\PackageWarning#1#2{\wlog{#1: #2}}\fi
+%<package>\expandafter\next\fi
+%<package>\ProvidesPackage{shellesc}
+%<driver> \ProvidesFile{shellesc.drv}
+% \fi
+%         \ProvidesFile{shellesc.dtx}
+       [2016/06/07 v0.02b unified shell escape interface for LaTeX]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\begin{document}
+\DocInput{shellesc.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{shellesc.dtx}
+%
+% \title{The \textsf{shellesc} Package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{LaTeX3 project}
+% \date{\filedate}
+% \maketitle
+%
+% \changes{v0.1b}{2016/02/02}{Doc typo fixes (JB)}
+% \changes{v0.2a}{2016/06/07}{Improve use with plain TeX}
+% \section{Introduction}
+%
+% 
+% For many years web2c based \TeX\ implementations have used the syntax
+% of the \verb|\write| command to access  system commands by using a
+% special stream 18 (streams above 15 can not be allocated to files in
+% classical \TeX\ so stream 18 would otherwise just print to the
+% terminal).
+%
+% This is a useful extension that did not break the strict rules on
+% extensions in classical \TeX.  This package provides a simple
+% macro level interface hiding the \verb|write18| implementation
+% so a command to remove a file on a unix-like system could be
+% specified  using \verb|\ShellEscape{rm file.txt}| (or \verb|del| in
+% windows). Note that by default system access is not allowed and
+% latex will typically need to be called with the \verb|--shell-escape|
+% command line option.
+%
+% The package may be used with standard \texttt{latex} or
+% \texttt{pdflatex} or \texttt{xetex}, however it is mostly motivated by
+% \texttt{lualatex} as from Lua\TeX~0.87 onwards Lua\TeX\ does \emph{not}
+% support the \verb|\write18| syntax to access system commands: it has
+% 256 write streams and stream 18 can be associated to a file and
+% (without this package) has no special significance. This packge
+% defines the same \verb|\ShellEscape| syntax in Lua\LaTeX, but the
+% implementation is via Lua and the \verb|os.execute| function.
+%
+% \verb|\ShellEscape| in fact corresponds to \verb|\immediate\write18|
+% (or \verb|\directlua|). Very rarely you may need to delay a system
+% command until the current page is output (when page numbers are
+% known) for this classically you could use \verb|\write18| (or
+% (\verb|\latelua|). This package provides \verb|\DelayedShellEscape|
+% as a common syntax for this use.
+%
+% To aid porting existing documents to Lua\TeX~0.87 this package does
+% overload the \verb|\write| command so that
+% \verb|\write18{rm file.txt}|
+% will work with Lua\TeX. Note that the redefinition of \verb|\write|
+% can not detect whether \verb|\immediate| has been used,
+% \verb|\immediate| will work as normal when writing to file streams
+% or the terminal but the special case of stream 18 which is defined to
+% use \verb|os.execute| always uses \verb|\directlua| (so corresponds
+% to \verb|\immediate\write18|. In the rare situations that you need
+% non-immediate \verb|\write18| in a document being ported to current
+% Lua\TeX, you will need to change to use the
+% \verb|\DelayedShellEscape| command.
+% 
+% \section{Implementation}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \subsection{Status Check}
+%
+%
+% \changes{v0.2a}{2016/06/07}{spelling in messages}
+%    \begin{macrocode}
+\ifcase
+  \ifx\pdfshellescape\@undefined
+    \ifx\shellescape\@undefined
+      \ifx\directlua\@undefined
+        \z@
+      \else
+        \directlua{%
+          tex.sprint((status.shell_escape or os.execute()) .. " ")}
+      \fi
+    \else
+      \shellescape
+    \fi
+  \else
+    \pdfshellescape
+  \fi
+  \PackageWarning{shellesc}{Shell escape disabled}
+\or
+  \PackageInfo   {shellesc}{Unrestricted shell escape enabled}
+\else
+  \PackageInfo   {shellesc}{Restricted shell escape enabled}
+\fi
+%    \end{macrocode}
+%
+% \subsection{The shellesc package interface}
+%
+% \begin{macro}{\ShellEscape}
+% Execute the supplied tokens as a system dependent command, assuming 
+% such execution is allowed.
+%    \begin{macrocode}
+\ifx\lastsavedimageresourcepages\@undefined
+  \protected\def\ShellEscape{\immediate\write18 }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\else
+  \protected\def\ShellEscape#1{%
+    \directlua{os.execute("\luaescapestring{#1}")}}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\DelayedShellEscape}
+% \changes{v0.1c}{2016/04/29}{Define \cs{DelayedShellEscape} not \cs{ShellEscape}(UF)}
+% Execute the supplied tokens as a system dependent command, when this
+% node is shipped out with the completed page, assuming 
+% such execution is allowed.
+%    \begin{macrocode}
+\ifx\lastsavedimageresourcepages\@undefined
+  \protected\def\DelayedShellEscape{\relax\write18 }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\else
+  \protected\def\DelayedShellEscape#1{%
+    \latelua{os.execute("\luaescapestring{#1}")}}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \subsection{The write18 package interface}
+%
+% In web2c based engines other than Lua\TeX, |\write18| may be used
+% directly.  The same was true in older LuaTeX, but from version 0.85
+% onwards that is not available.
+%
+% The above |shellesc| package interface is recommended for new code,
+% however for ease of porting existing documents and packages to newer
+% Lua\TeX\ releases, a |\write18| interface is provided here via a
+% call to Lua's |os.execute|.
+%
+% Note that as currently written this always does an \emph{immediate}
+% call to the system.
+%
+% |\immediate| is supported but ignored, |\immediate\write18| and
+% |\write18| both execute immediately. To use a delayed execution at
+% the next shipout, use the |\DelayedShellEscape| command defined
+% above.
+%
+% Note that it would be easy to make |\wriete18| defined here use
+% delayed execution, just use |\DelayedShellEscape| instead of
+% |ShellEscape| in the definition below. However detecting
+% |\immediate| is tricky so the choice here is to always use the
+% immediate form, which is overwhelmingly more commonly used with
+% |\write18|.
+%
+% Stop at this point if not a recent Lua\TeX.
+%    \begin{macrocode}
+\ifx\lastsavedimageresourcepages\@undefined\expandafter\endinput\fi
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\directlua{%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+shellesc = shellesc or {}
+%    \end{macrocode}
+%
+% Lua function to use the token scanner to grab the following \TeX\
+% number, and then test if stream 18 is being used, and then insert an
+% appropriate \TeX\ command to handle the following brace group in
+% each case.
+%    \begin{macrocode}
+local function write_or_execute()
+  local s = token.scan_int()
+  if (s==18) then
+     tex.sprint(\the\numexpr\catcodetable@atletter\relax,
+                "\string\\ShellEscape ")
+  else
+     tex.sprint(\the\numexpr\catcodetable@atletter\relax,
+                "\string\\shellesc@write " .. s)
+  end
+end
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+shellesc.write_or_execute=write_or_execute
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\let\shellesc@write\write
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\protected\def\write{\directlua{shellesc.write_or_execute()}}
+%    \end{macrocode}
+%
+%
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
diff --git a/macros/latex-dev/required/tools/shellesc.pdf b/macros/latex-dev/required/tools/shellesc.pdf
new file mode 100644
index 0000000000..043016f2b9
--- /dev/null
+++ b/macros/latex-dev/required/tools/shellesc.pdf
diff --git a/macros/latex-dev/required/tools/showkeys.dtx b/macros/latex-dev/required/tools/showkeys.dtx
new file mode 100644
index 0000000000..6e2516856d
--- /dev/null
+++ b/macros/latex-dev/required/tools/showkeys.dtx
@@ -0,0 +1,905 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: showkeys.dtx Copyright (C) 1992-1997 David Carlisle
+%% File: showkeys.dtx Copyright (C) 2006-2019 David Carlisle, LaTeX3 Project
+%
+%<*dtx>
+          \ProvidesFile{showkeys.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{showkeys}
+%<driver> \ProvidesFile{showkeys.drv}
+% \fi
+%         \ProvidesFile{showkeys.dtx}
+          [2014/10/28 v3.17 Show cite and label keys (DPC, MH)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage
+%     [notcite,notref,color]
+            {showkeys}
+\setlength{\belowcaptionskip}{\baselineskip}
+\setlength{\abovecaptionskip}{0pt}
+\begin{document}
+\DocInput{showkeys.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{showkeys.dtx}
+% \title{The \textsf{showkeys} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}}
+% \author{David Carlisle \and Morten H\o gholm}
+% \date{\filedate}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+%
+% \changes{v1.01}{1992/08/25}{Initial version}
+% \changes{v1.02}{1994/01/05}
+%         {Fix incorrect initialisation (FGBDA19@CC1.KULEUVEN.AC.BE)}
+% \changes{v2.00}{1994/01/31}{new version for LaTeX2e}
+% \changes{v2.01}{1994/06/30}{Fix \cs{ProvidesPackage} usage.}
+% \changes{v3.00}{1994/09/07}
+%         {Support harvard, varioref and natbib packages,}
+% \changes{v3.02}{1995/03/17}
+%         {Support new AMS files}
+%
+% \section{Introduction}\label{sec:intro}
+%
+% |showkeys.sty| modifies the |\label|, |\ref|, |\pageref|, |\cite|, and
+% |\bibitem| commands so that the `internal' key is printed. The package
+% tries hard to position these labels so that the formatting of the rest
+% of the document is unchanged. |\label| and |\bibitem| cause the
+% key to appear in a box either in the margin, or in a \TeX\ box of zero
+% width, which may possibly over-print other text. The |\ref|,
+% |\pageref| and |\cite| commands print their arguments in small type,
+% raised just above the line, like this: \ref{sec:intro}.
+% This package works with the \textsf{fleqn} option, the packages
+% in the AMS-\LaTeX\ collection, and the \textsf{varioref},
+% \textsf{natbib} and \textsf{harvard} packages.
+%
+% \changes{v2.00}{1992/01/31}
+%         {leqno or ams* may now be loaded after showkeys}
+%
+% \section{Package Options}\label{options}
+% Some people have commented that the printing of the |\ref| and
+% |\cite| keys is less useful than the printing of the |\label| keys
+% and so \textsf{showkeys} now supports two options that can be given
+% in the |\usepackage| command:
+% \begin{description}
+% \item[notref] to stop the redefinition of |\ref| and |\pageref|,
+% and related commands from the \textsf{varioref} package.
+% \item[notcite] to stop the redefinition of |\cite| and related
+% commands from the \textsf{harvard} and \textsf{natbib} packages.
+% \end{description}
+% So if the package is loaded with |\usepackage[notref]{showkeys}|
+% then |\ref| will have its standard definition, but |\label| will
+% print its key argument (usually in the margin).
+%
+% If you find the printed keys distracting, but don't want to use the
+% above options to stop them altogether you may use:
+% \begin{description}
+% \item[color] Print the keys in a distinguishing colour. The default
+%  value is a light grey.
+% \end{description}
+% The colours may be changed by redefining the following two colours
+% after the package is loaded.
+% |refkey| (also used for |\cite|) and
+% |labelkey| (also used for |\bibitem|).
+% The defaults are:
+%\begin{verbatim}
+%  \definecolor{refkey}{gray}{.75}
+%  \definecolor{labelkey}{gray}{.75}
+%\end{verbatim}
+%
+% If this option is used the \textsf{color} package will be loaded.
+%
+% The package accepts two further options.
+% \begin{description}
+% \item[final] to suporess the action of this package, for `final'
+% versions.
+% \item[draft] the normal behaviour of this package.
+% \end{description}
+% Clearly there is not much point in entering the |final| option
+% directly in the |\usepackage| command, as just not loading this
+% package would have the same effect, and execute more quickly,
+% however the |final| option may be useful as it may be used once in
+% the |documentclass| command to affect any number of packages that
+% may be loaded. The |draft| option does not do anything, but is there
+% to honour an informal convention that packages have these options in
+% pairs.
+%
+% You can also control the appearance of the typeset label with the
+% command |\showkeyslabelformat|, which takes one argument. The default is
+% \begin{verbatim}
+% \providecommand*\showkeyslabelformat[1]{%
+%   \fbox{\normalfont\small\ttfamily#1}}
+% \end{verbatim}
+% The command is called inside a group so you can put in local
+% modifications of |\fboxsep|, for instance, without them leaking to
+% the rest of the document.
+%
+%
+% \section{More Examples}\label{examples}
+% The only other similar package that I could find in the macro index,
+% \cite{DMJ:mi}, was |showlabels.sty|, \cite{GN:sl}. After the first
+% draft of this package was written, I found \cite{anon:sk} on my local
+% installation! I think the current package is more robust than
+% \cite{anon:sk}, but I thought that |showkeys| was rather a good name,
+% so I have stolen it for this file.
+%
+% \begin{enumerate}
+% \item \label{e^1}This has |\label| immediately after |\item|.
+% \item This has the |\label| at the end.\label{e^2}
+% \end{enumerate}
+%
+% \[
+% \mbox{A minipage :- }\left\{
+% \begin{minipage}{3in}
+% Within environments like this |minipage|, we cannot use
+% |\marginpar|\footnotemark,
+% so the appearance is slightly different. Here is that |enumerate|
+% environment again:
+%
+% \begin{enumerate}
+% \item \label{m&e^1}This has |\label| immediately after |\item|.
+% \item This has the |\label| at the end.\label{m&e^2}
+% \end{enumerate}
+% \end{minipage}
+% \right.
+% \]
+%
+% Displayed math (without |equation| counter).
+% \[0=0\label{disp}\]
+%
+% Some text referring to the maths on page~\pageref{disp},  and the
+% item~\ref{e^1}.\footnotetext{Actually \texttt{\string\marginpar} is
+% not used at all in this package now.}
+%
+% If |showkeys| thinks that the current environment is going to produce
+% an ``equation number'', then it does not show the label where the
+% |\label| command occurs, but tries to put it in the margin, as shown
+% with equation~\ref{eq:xx}.
+% The package `knows' about the standard |equation| and |eqnarray|
+% environments, and also all the numbered alignment environments offered
+% by the AMS\LaTeX\ package, |amsmath|.
+%
+% ^^A (|amstex.sty| must be loaded before |showkeys.sty|
+% ^^A for this to work.)
+% \changes{v2.00}{1992/01/31}
+%         {leqno or ams* may now be loaded after showkeys}
+%
+% \begin{equation}
+% 1=1\label{eq:xx}
+% \end{equation}
+%
+% \begin{eqnarray}
+% 2&=&2\label{eqnar:a}\\
+% 3&=&3\nonumber\\
+% 4&=&4\label{eqnar:b}
+% \end{eqnarray}
+%
+%
+% \begin{figure}[ht]
+% Within a |figure| environment, the |\label| must not come  before the
+% |\caption| command. If you place |\label| inside the argument of
+% |\caption| the label will be shown like this:
+%
+% \caption{Within the caption argument.\label{cap:a}}
+%
+% If you place |\label| immediately after the |\caption| command it will
+% be shown like this:
+%
+% \caption{Immediately after the caption argument.}\label{cap:b}
+%
+% If you place the |\label| command at some random point after the
+% |\caption| command, it may be shown like:
+%
+% \caption{In vertical mode not immediately after a box.}
+% \vspace{2pt}
+%
+% \label{cap:c}
+% \end{figure}
+%
+%
+% \begin{thebibliography}{9}
+%
+% \bibitem{GN:sl}
+% Gil Neiger, \emph{showlabels.sty},
+% Undated package, similar to this one, but shows labels
+% inline, affecting the formatting of the document.
+%
+% \bibitem{anon:sk}
+% Anonymous, \emph{showkeys.sty},
+% Package, dated 14 May 1988. Very similar to this one,
+% also uses |\marginpar| in outer vertical mode.
+%
+% \bibitem{DMJ:mi}
+% David M. Jones, \emph{\TeX\ Macro Index},
+% A catalogue of \TeX\ macros, including \LaTeX\ packages,
+% available from all good \TeX\ archives.
+%
+% \end{thebibliography}
+%
+% \StopEventually{}
+%
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+%
+% First we handle the options. Normally all related commands are
+% defined to show their `keys'. But since v3.03 one can specify:
+%
+% \texttt{notref} to stop the redefinition of |\ref| (and |\pageref|,
+% and related commands from \textsf{varioref} package),
+%
+% \texttt{notcite} to stop the redefinition of |\cite| and related
+% commands from the \textsf{harvard} and \textsf{natbib} packages.
+%
+% \changes{v3.03}{1995/04/25}
+%      {Add option handling.}
+%    \begin{macrocode}
+\DeclareOption{notref}{\let\SK@ref\@empty}
+\DeclareOption{notcite}{\let\SK@cite\@empty}
+%    \end{macrocode}
+%
+% \begin{macro}{\SK@refcolor}
+% \begin{macro}{\SK@labelcolor}
+% Colour commands. Normally no-op.
+%    \begin{macrocode}
+\let\SK@refcolor\relax
+\let\SK@labelcolor\relax
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \changes{v3.11}{1996/11/01}
+%         {Colour support added, inspired by tools/2297}
+% |color| option loads the \textsf{color} package and defines the
+% colours. Delayed to the end of the  package as package loading not
+% allowed in this option section.
+%    \begin{macrocode}
+\DeclareOption{color}{\AtEndOfPackage{%
+  \RequirePackage{color}%
+  \definecolor{refkey}{gray}{.75}%
+  \definecolor{labelkey}{gray}{.75}%
+  \def\SK@refcolor{\color{refkey}}%
+  \def\SK@labelcolor{\color{labelkey}}}}
+%    \end{macrocode}
+%
+% \changes{v3.04}{1995/10/30}
+%      {final and draft options handling.}
+% \changes{v3.15}{2007/08/07}
+%      {Fix \cs{showkeyslabelformat} for final option PR/3918.}
+% Allow |final| to be specified in the document class options
+% to suppress the loading of this package.
+%    \begin{macrocode}
+\DeclareOption{final}{%
+  \providecommand*\showkeyslabelformat[1]{}%
+  \endinput}
+\DeclareOption{draft}{}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ProcessOptions
+%    \end{macrocode}
+%
+% \changes{v2.00}{1992/01/31}
+%         {\cmd{reset@font} is now standard}
+%
+% \begin{macro}{\SK@label}
+% \begin{macro}{\SK@bibitem}
+% \begin{macro}{\SK@lbibitem}
+% The saved original definitions
+%    \begin{macrocode}
+\let\SK@label\label
+\let\SK@bibitem\@bibitem
+\let\SK@lbibitem\@lbibitem
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\label}
+% \changes{v3.09}{1996/08/30}
+%      {Add extra group so brace hack works. Donald Arseneau tools/2147}
+% The new definition, print the argument, and then do the old
+% definition.
+%    \begin{macrocode}
+\def\label#1{%
+  \@bsphack
+  \SK@\SK@@label{#1}%
+  \begingroup
+    \SK@label{#1}%
+  \endgroup
+  \@esphack}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@bibitem}
+% \begin{macro}{\@lbibitem}
+% \changes{v3.02}{1995/03/17}
+%         {New label code.}
+% For |\bibitem|, position the \textsf{showkeys} code as for a standard
+% list with |\item| and |\label|.
+%    \begin{macrocode}
+\def\@bibitem#1{%
+  \SK@bibitem{#1}\SK@\SK@@label{#1}\ignorespaces}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\@lbibitem[#1]#2{%
+  \SK@lbibitem[{#1}]{#2}\SK@\SK@@label{#2}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\SK@}
+% \changes{v3.07}{1996/05/17}
+%      {use \cs{protected@edef} for tools/2147}
+% Grab hold of |#2| via |\meaning| so characters like |&| and
+% |^| do not cause problems later, and pass the result on to the command
+% |#1|.
+%    \begin{macrocode}
+\def\SK@#1#2{%
+  \protected@edef\@tempa{#2}%
+  \expandafter#1\meaning\@tempa\SK@}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\showkeyslabelformat}
+% \changes{v3.13}{2006/01/09}{Added command}
+%    \begin{macrocode}
+\providecommand*\showkeyslabelformat[1]{%
+  \fbox{\normalfont\small\ttfamily#1}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SK@@label}
+% \changes{v3.13}{2006/01/09}{Do not hardwire label format}
+% Strip off the initial segment of the |\meaning| output, and then put
+% the rest either in a |\marginpar| or in a box of size 0pt,
+% hopefully not disturbing the surrounding text.
+%    \begin{macrocode}
+\def\SK@@label#1>#2\SK@{%
+%    \end{macrocode}
+% Need to work globally as in some cases like alignments, and |fleqn|,
+% the counter will be printed in a different group to the |\label|
+% command.
+%    \begin{macrocode}
+  \gdef\SK@lab{\smash{\SK@labelcolor\showkeyslabelformat{#2}}}%
+  \ifvmode
+    \if@inlabel
+%    \end{macrocode}
+% \changes{v3.02}{1995/03/17}
+%         {New code for `in label' case.}
+% If the |\label| is straight after |\item| (|\bibitem| is handled by
+% this case as well) then the item label has not been added to the page
+% yet. It is hanging around in the box |\@labels| waiting for the
+% paragraph to start. So just need to attach the label to this box.
+%    \begin{macrocode}
+      \global\setbox\@labels\hbox{%
+        \llap{\SK@lab\SK@lab@relax
+              \kern\@totalleftmargin\kern\marginparsep}%
+        \box\@labels}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \else
+%    \end{macrocode}
+% \changes{v3.10}{1996/09/06}
+%      {Save prevdepth and restore later}
+% If we insert a box into the main vertical list, do not want to
+% change |\prevdepth| as that would affect vertical spacing in the
+% document. (The box itself should not cause any difference in break
+% points as there is a node there anyway coming from the |\write| to
+% the aux file.
+%    \begin{macrocode}
+      \dimen@\prevdepth
+      \nointerlineskip
+%    \end{macrocode}
+% The inner vertical mode cases are mainly designed to do the right
+% thing with float captions, but seem to work OK in other cases as well.
+%    \begin{macrocode}
+      \ifinner
+        \skip@\lastskip\unskip
+%    \end{macrocode}
+% In inner vertical mode, attach the label to the right of the
+% immediately preceding box, if it is a box before the current point.
+% Otherwise just put it in a box of zero dimensions, with no interline
+% skip. (This may slightly move the surrounding text (but perhaps not
+% now that |\prevdepth| is restored.)
+% \changes{v3.00}{1994/09/07}
+%      {Back up over a previous skip because of the new
+%       \cs{belowcaptionskip}}
+% \changes{v3.04}{1995/10/30}
+%      {\cs{advance} added, to total two successive skips.}
+% \changes{v3.04}{1995/10/30}
+%      {\cs{nointerlineskip} called before \cs{ifvoid} test, not just
+%      void case}
+% \changes{v3.04}{1995/10/30}
+%      {\cs{marginparskip} added in inner vmode case}
+%    \begin{macrocode}
+        \advance\skip@\lastskip\unskip
+        \setbox\z@\lastbox
+%    \end{macrocode}
+% \changes{v3.10}{1996/09/06}
+%      {Inner vertical mode case, put it in the margin.}
+% \changes{v3.14}{2006/09/25}
+% {The label put in the margin shouldn't make box 255 wider (PR/3884).}
+%    \begin{macrocode}
+        \ifvoid\z@
+          \llap{\SK@lab\SK@lab@relax\kern\marginparsep}%
+        \else
+          \hbox{\box\z@\rlap{\kern\marginparsep\SK@labx}}%
+        \fi
+        \vskip\skip@
+      \else
+%    \end{macrocode}
+% In outer vertical mode, previously used a |\vadjust| at the start of
+% the next  paragraph (and before that used |\marginpar|). These
+% methods sometimes cause extra space, eg if paragraph starts with a
+% math display, so now just insert the box directly, taking care not
+% to change |\prevdepth|.
+% \changes{v3.02}{1995/03/17}
+%         {Use \cs{vadjust} instead of \cs{marginpar}}
+% \changes{v3.10}{1996/09/06}
+%      {Insert the box directly}
+%    \begin{macrocode}
+        \llap{\SK@lab\SK@lab@relax\kern\marginparsep}%
+      \fi
+%    \end{macrocode}
+% Restore |\prevdepth|.
+%    \begin{macrocode}
+      \prevdepth\dimen@
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+    \fi
+  \else
+%    \end{macrocode}
+% If we are in an numbered equation-style environment, do nothing as the
+% code to print the number will also print the label, otherwise just
+% stick the label at the current point, in a box of zero dimensions.
+% \changes{v3.02}{1995/03/17}
+%         {Add \cs{ifmmode} test}
+%    \begin{macrocode}
+    \csname SK@\@currenvir\endcsname
+    \ifSK@equation\else
+      \ifmmode
+        \SK@labx
+      \else
+%    \end{macrocode}
+% Inner horizontal mode. Not much we can do, just stick it here.
+% \changes{v3.03}{1995/04/25}
+%         {Fix inner horizontal mode case (broken in 3.02)}
+%    \begin{macrocode}
+        \ifinner
+          \rlap\SK@lab
+      \else
+%    \end{macrocode}
+% In outer horizontal mode use |\vadjust| to get to the margin.
+% \changes{v3.02}{1995/03/17}
+%         {Use \cs{vadjust} in horizontal mode}
+%    \begin{macrocode}
+          \vadjust{\llap{\SK@lab\kern\marginparsep}}%
+        \fi
+        \SK@lab@relax
+      \fi
+    \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tagform@}
+% \changes{v2.00}{1992/01/31}
+%         {Defer tests to begin document}
+% \changes{v3.02}{1995/03/17}
+%         {Support new AMS files}
+% \begin{macro}{\@eqnnum}
+% \changes{v3.13}{2006/01/09}
+%         {Change to also work correctly for \texttt{leqno} option.}
+% \begin{macro}{\maketag@@@}
+% \changes{v3.13}{2006/01/09}
+%         {Support for \cs{tag*} tools/3693.}
+% Firstly we grab |\@eqnnum|.
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \let\SK@eqnnum\@eqnnum
+%    \end{macrocode}
+% Then check for \textsf{amsmath} where we grab the internal commands
+% |\tagform@| and |\maketag@@@|. Redefine them and redefine |\@eqnnum|
+% as well.
+%    \begin{macrocode}
+  \@ifpackageloaded{amsmath}{%
+    \let\SK@tagform@\tagform@
+    \let\SK@maketag@@@\maketag@@@
+    \iftagsleft@
+      \def\tagform@#1{%
+        \ifx\df@label\@empty
+          \SK@lab@relax
+        \else
+          \expandafter\SK@@label\meaning\df@label\SK@
+        \fi
+        \llap{\SK@lab\kern\marginparsep}%
+        \SK@lab@relax\SK@tagform@{#1}}%
+      \def\maketag@@@#1{%
+        \ifx\df@label\@empty
+          \SK@lab@relax
+        \else
+          \expandafter\SK@@label\meaning\df@label\SK@
+        \fi
+        \llap{\SK@lab\kern\marginparsep}\SK@lab@relax
+        \SK@maketag@@@{#1}%
+      }%
+      \def\@eqnnum{%
+        \llap{\SK@lab\kern\displaywidth\kern\marginparsep}%
+        \SK@lab@relax\SK@eqnnum}%
+    \else
+%    \end{macrocode}
+% Almost the same for tags on the right, except we use |\rlap| and
+% typeset it after the tag.
+%    \begin{macrocode}
+      \def\tagform@#1{%
+        \ifx\df@label\@empty
+          \SK@lab@relax
+        \else
+          \expandafter\SK@@label\meaning\df@label\SK@
+        \fi
+%    \end{macrocode}
+% \changes{v3.08}{1996/07/10}{Missing percent added. /2215}
+%    \begin{macrocode}
+        \SK@tagform@{#1}%
+        \rlap{\kern\marginparsep\SK@lab}\SK@lab@relax}%
+      \def\maketag@@@#1{%
+        \ifx\df@label\@empty
+          \SK@lab@relax
+        \else
+          \expandafter\SK@@label\meaning\df@label\SK@
+        \fi
+        \SK@maketag@@@{#1}%
+        \rlap{\kern\marginparsep\SK@lab}\SK@lab@relax
+      }%
+      \def\@eqnnum{\SK@eqnnum\rlap{\kern\marginparsep\SK@lab}%
+        \SK@lab@relax}%
+    \fi
+  }%
+%    \end{macrocode}
+% If \textsf{amsmath} wasn't loaded we check explicitly if the
+% \texttt{leqno} option was used in |\documentclass| and redefine
+% accordingly.
+%    \begin{macrocode}
+  {%
+    \@ifundefined{ver@leqno.clo}{%
+      \def\@eqnnum{\SK@eqnnum\rlap{\kern\marginparsep\SK@lab}%
+        \SK@lab@relax}%
+    }{%
+      \def\@eqnnum{%
+        \llap{\SK@lab\kern\displaywidth\kern\marginparsep}%
+        \SK@lab@relax\SK@eqnnum}%
+    }%
+  }%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\SK@labx}
+% Print the label, and then globally reset the print command to
+% |\relax|.
+%    \begin{macrocode}
+\def\SK@labx{\rlap\SK@lab\global\let\SK@lab\relax}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SK@lab@relax}
+% Clear the label.
+% \changes{v1.02}{1994/01/05}{Execute to initialise correctly}
+%    \begin{macrocode}
+\def\SK@lab@relax{\global\let\SK@lab\relax}\SK@lab@relax
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SK@equation}
+% \begin{macro}{\SK@eqnarray}
+% The following environments print an equation number, so |\label|
+% should not print its argument at the point where it appears.
+% Note this will fail to show the label if you are in an |eqnarray|
+% environment, and use |\label| together with |\nonumber| This might
+% just about make sense if you are going to use |\pageref|, but that is
+% too bad\ldots
+%    \begin{macrocode}
+\newif\ifSK@equation
+\let\SK@equation\SK@equationtrue
+\let\SK@eqnarray\SK@equationtrue
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\eqnarray}
+% \changes{v3.09}{1996/08/30}
+%      {Fix eqnarray AMS incompatibility. tools/2252}
+% When the AMS packages are loaded |showkeys| assumes environments
+% work `The AMS way' However |eqnarray| (unlike |equation|) is not
+% redefined, so here we need to remove some of the AMS hacks.
+%    \begin{macrocode}
+\toks@\expandafter{\eqnarray}
+\edef\eqnarray{\let\noexpand\tagform@\noexpand\SK@tagform@\the\toks@}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SK@align}
+% \begin{macro}{\SK@alignat}
+% \begin{macro}{\SK@xalignat}
+% \begin{macro}{\SK@xxalignat}
+% \begin{macro}{\SK@gather}
+% \begin{macro}{\SK@multline}
+% \begin{macro}{\SK@flalign}
+% \changes{v3.02}{1995/03/17}
+%         {Add \cs{SK@flalign}}
+% The AMS environments
+%    \begin{macrocode}
+\let\SK@align\SK@equationtrue
+\let\SK@alignat\SK@equationtrue
+\let\SK@xalignat\SK@equationtrue
+\let\SK@xxalignat\SK@equationtrue
+\let\SK@gather\SK@equationtrue
+\let\SK@multline\SK@equationtrue
+\let\SK@flalign\SK@equationtrue
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\SK@align*}
+% \begin{macro}{\SK@alignat*}
+% \begin{macro}{\SK@flalign*}
+% \begin{macro}{\SK@gather*}
+% \begin{macro}{\SK@multline*}
+% \begin{macro}{\SK@equation*}
+% \changes{v3.13}{2006/01/09}
+%         {Add the starred AMS environments for tools/3697.}
+% Starred versions of the AMS environments.
+%    \begin{macrocode}
+\expandafter\let\csname SK@align*\endcsname\SK@equationtrue
+\expandafter\let\csname SK@alignat*\endcsname\SK@equationtrue
+\expandafter\let\csname SK@flalign*\endcsname\SK@equationtrue
+\expandafter\let\csname SK@gather*\endcsname\SK@equationtrue
+\expandafter\let\csname SK@multline*\endcsname\SK@equationtrue
+\expandafter\let\csname SK@equation*\endcsname\SK@equationtrue
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%  \begin{macro}{\SK@def}
+% \changes{v3.05}{1995/11/09}
+%      {Macro added}
+% This macro redefines a command |#1|. The new definition can make use
+% of the old definition as |\SK@|\emph{old name}. If |#1| is really a
+% |\protect|'ed command with the real definition in a `\emph{space}'
+% command then the `space' version is used as the old definition.
+% Need to test this for each command as some package may have changed
+% the status of a command to being `protected'.
+% The new definition is made as if with |\DeclareRobustCommand|, but
+% with |\def| syntax for the argument specification.
+%    \begin{macrocode}
+\def\SK@def#1{%
+  \edef\@tempa{\expandafter\@gobble\string#1}%
+  \@ifundefined{\@tempa\space}%
+    {\expandafter\let\csname SK@\@tempa\endcsname#1}%
+    {\expandafter\let\csname SK@\@tempa\expandafter\endcsname
+                         \csname\@tempa\space\endcsname}%
+  \expandafter\def\expandafter#1\expandafter{%
+        \expandafter\protect\csname\@tempa\space\endcsname}%
+  \expandafter\def\csname\@tempa\space\endcsname}
+%    \end{macrocode}
+%  \end{macro}
+%
+% The next section redefines |\ref| and |\pageref| (unless the
+% \texttt{notref} option was given).
+%    \begin{macrocode}
+\ifx\SK@ref\@empty
+%    \end{macrocode}
+% Even if \texttt{notref} option is used, need to fudge the
+% \textsf{varioref} commands as they use |\label| internally.
+% \changes{v3.04}{1995/10/30}
+%      {improve varioref support in notref option case, for
+%      tools/1744}
+% \changes{v3.13}{2006/01/09}{Updated varioref support, for latex/3373}
+% \changes{v3.15}{2006/06/19}
+%         {Prevent loss of brackets}
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \@ifpackageloaded{varioref}{%
+    \SK@def\@@vpageref#1[#2]#3{{%
+      \let\label\SK@label
+      \SK@@@vpageref{#1}[{#2}]{#3}}}%
+    \def\vr@f#1{%
+      \leavevmode\unskip\vref@space
+      \ref{#1}%
+      {\let\label\SK@label
+      \vpageref[\unskip]{#1}}}%
+  }{}}
+\else
+%    \end{macrocode}
+%
+% \begin{macro}{\ref}
+% \begin{macro}{\pageref}
+% Save the redefinition to |\begin{document}| so that this package can
+% work with packages that redefine |\cite|. Tested with harvard and
+% natbib packages. Also add code at this point to support varioref.
+% \changes{v3.00}{1994/09/07}
+%      {Delay \cs{ref} redefinition.}
+% \changes{v3.03}{1995/04/25}
+%      {Make redefinition conditional on notref option}
+% \changes{v3.15}{2006/06/19}
+%         {Prevent loss of brackets}
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \SK@def\ref#1{\SK@\SK@@ref{#1}\SK@ref{#1}}%
+  \SK@def\pageref#1{\SK@\SK@@ref{#1}\SK@pageref{#1}}%
+%    \end{macrocode}
+% varioref support.
+%    \begin{macrocode}
+  \@ifpackageloaded{varioref}{%
+    \SK@def\@@vpageref#1[#2]#3{{%
+      \let\label\SK@label\let\ref\SK@ref\let\pageref\SK@pageref
+      \leavevmode\unskip\SK@\SK@@ref{#3}\SK@@@vpageref{#1}[{#2}]{#3}}}%
+    \def\vr@f#1{%
+      \leavevmode\unskip\vref@space
+      \ref{#1}%
+      \let\label\SK@label\let\ref\SK@ref\let\pageref\SK@pageref
+      \vpageref[\unskip]{#1}}%
+  }{}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% Now redefine |\cite| unless \texttt{notcite} option given.
+%    \begin{macrocode}
+\ifx\SK@cite\@empty
+%    \end{macrocode}
+% \changes{v3.06}{1995/11/22}
+%         {Fix \cs{harvarditem} support}
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \ifx\HAR@checkdef\@undefined\else
+      \expandafter\let\expandafter
+         \SK@HAR@bi\csname\string\harvarditem\endcsname
+      \expandafter\def\csname\string\harvarditem\endcsname[#1]#2#3#4{%
+        \SK@HAR@bi[{#1}]{#2}{#3}{#4}\SK@\SK@@label{#4}}%
+  \fi}
+\else
+%    \end{macrocode}
+%
+% \begin{macro}{\cite}
+% \changes{v3.00}{1994/09/07}
+%      {Delay \cs{cite} redefinition.}
+% \changes{v3.03}{1995/04/25}
+%      {Make redefinition conditional on notcite option}
+%    \begin{macrocode}
+\AtBeginDocument{%
+  \ifx\HAR@checkdef\@undefined
+%    \end{macrocode}
+% Standard (non-harvard) support, including extra cite commands from
+% \textsf{natbib} and \textsf{cite}.
+% \changes{v3.01}{1994/09/09}
+%         {Add \cs{citefullauthor}}
+% \changes{v3.12}{1997/06/12}
+%         {Support cite package. tools/2490}
+% \changes{v3.17}{2014/04/24}
+%         {redefine \cs{@citex} rather than \cs{cite} for tools/4162}
+%
+% If \textsf{cite} or \textsf{overcite} is being used, redefine |\citen|
+% rather than |\cite| so as not to spoil the space and punctuation
+% calculations done by those packages.
+%    \begin{macrocode}
+    \ifx\citen\@undefined
+      \SK@def\@citex[#1]#2{\SK@citex[{#1}]{#2}}%
+    \else
+      \SK@def\citen#1{\SK@\SK@@ref{#1}\SK@citen{#1}}%
+    \fi
+    \SK@def\citeauthor#1{\SK@\SK@@ref{#1}\SK@citeauthor{#1}}%
+    \SK@def\citefullauthor#1{\SK@\SK@@ref{#1}\SK@citefullauthor{#1}}%
+    \SK@def\citeyear#1{\SK@\SK@@ref{#1}\SK@citeyear{#1}}%
+  \else
+%    \end{macrocode}
+% In the \textsf{harvard} style do \emph{not} redefine individual cite
+% commands. Just redefine one internal command that is used in all the
+% citation forms.
+%    \begin{macrocode}
+    \SK@def\HAR@checkdef#1#2{%
+      \expandafter\SK@\expandafter\SK@@ref\expandafter{#1}%
+      \SK@HAR@checkdef{#1}{#2}}%
+      \expandafter\let\expandafter
+         \SK@HAR@bi\csname\string\harvarditem\endcsname
+%    \end{macrocode}
+% \changes{v3.06}{1995/11/22}
+%         {Fix \cs{harvarditem} support}
+%    \begin{macrocode}
+      \expandafter\def\csname\string\harvarditem\endcsname[#1]#2#3#4{%
+        \SK@HAR@bi[{#1}]{#2}{#3}{#4}\SK@\SK@@label{#4}}%
+  \fi}
+%    \end{macrocode}
+%
+% \changes{v3.17}{2014/04/24}
+%         {Change name, redefine \cs{@citex} rather than \cs{cite} for tools/4162}
+%    \begin{macrocode}
+\def\SK@citex[#1]#2{%
+  \SK@\SK@@ref{#2}\SK@@citex[{#1}]{#2}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\SK@@ref}
+%   This is much simpler than the printing of the label, as we know
+%   that we can be in horizontal mode.
+%   Note extra group for colour safety.
+% \changes{v3.14}{2006/09/25}
+%                {Add fix for pdf\TeX.}
+% \changes{v3.16}{2011/11/24}
+%                {revert change made at v3.14 because of tools/4173}
+%    \begin{macrocode}
+\def\SK@@ref#1>#2\SK@{%
+  \leavevmode\vbox to\z@{{%
+    \vss
+    \SK@refcolor
+    \rlap{\vrule\raise .75em%
+       \hbox{\underbar{\normalfont\footnotesize\ttfamily#2}}}}}}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
diff --git a/macros/latex-dev/required/tools/showkeys.pdf b/macros/latex-dev/required/tools/showkeys.pdf
new file mode 100644
index 0000000000..6b2817a982
--- /dev/null
+++ b/macros/latex-dev/required/tools/showkeys.pdf
diff --git a/macros/latex-dev/required/tools/somedefs.dtx b/macros/latex-dev/required/tools/somedefs.dtx
new file mode 100644
index 0000000000..f73a45b787
--- /dev/null
+++ b/macros/latex-dev/required/tools/somedefs.dtx
@@ -0,0 +1,172 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \title{The \textsf{somedefs} toolkit package}
+% \date{long time ago in a different century\ldots}
+% \author{Alan Jeffrey}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+% \changes{v0.03}{1994/06/01}{Use new style error commands. DPC}
+% \changes{v0.02}{1994/05/10}{Added a \cmd\relax, to stop arguments to
+%    \cmd\newcommand\ being unbraced by \cmd\ProvidesCommand.  Added
+%    an error message for commands which are requested but never
+%    defined.  Spotted by DPC.}
+%
+% \section*{Overview}
+%
+% This is an example `programmers toolkit' package, for use by package
+% writers.  It allows package writers to provide options which switch
+% definitions on and off.  For example, a package |fred| might define a
+% large number of commands, including |\foo| and |\baz|, so:
+% \begin{verbatim}
+%    \usepackage{fred}
+% \end{verbatim}
+% would use a lot of memory, even if |\foo| and |\baz| were the only
+% commands needed.  However, if the author of |fred| used the |somedefs|
+% package, then the user would be able to say:
+% \begin{verbatim}
+%    \usepackage[only,foo,baz]{fred}
+% \end{verbatim}
+% and only the commands |\foo| and |\baz| would be defined.
+%
+% To use the |somedefs| package in your own packages or classes, you
+%  say:
+% \begin{verbatim}
+%    \RequirePackage{somedefs}
+% \end{verbatim}
+% You can then use four new commands:
+% \begin{flushleft}\begin{itemize}
+% \item |\UseAllDefinitions| which says that all the commands in the
+%    file should be defined.
+% \item |\UseSomeDefinitions| which says that only the commands
+%    specified by |\UseDefinition| should be defined.
+% \item |\UseDefinition{|\meta{name}|}| which says that the command
+%    |\name| should be defined.
+% \item |\ProvidesDefinition{|\meta{definition}|}| which provides one
+%    definition, of the form |\definingcommand{\command}...|
+% \end{itemize}\end{flushleft}
+% For example, the package |fred| could say:
+% \begin{verbatim}
+%    \RequirePackage{somedefs}
+%    \UseAllDefinitions
+%    \DeclareOption{only}{\UseSomeDefinitions}
+%    \DeclareOption*{\UseDefinition{\CurrentOption}}
+%    \ProcessOptions
+%    \ProvidesDefinition{\newcommand{\foo}{...}}
+%    \ProvidesDefinition{\newcommand{\baz}{...}}
+% \end{verbatim}
+% One of the commands |\UseAllDefinitions| or |\UseSomeDefinitions|
+% should always be used.  You may have some commands which need other
+% commands, in which case you have to declare the options by hand.  For
+% example, if the command |\bar| needs the command |\foo|, you could
+% say:
+% \begin{verbatim}
+%    \DeclareOption{bar}{\UseDefinition{bar}\UseDefinition{foo}}
+% \end{verbatim}
+% For a longer example of the use of the |somedefs| package, look at the
+% |rawfonts| package.
+%
+% \StopEventually{}
+%
+% \section*{Implementation}
+%
+% The driver for the documentation you're now reading.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+\begin{document}
+\DocInput{somedefs.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+% This is a \LaTeXe{} package.
+%    \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{somedefs}[1994/06/01 v0.03 Toolkit for optional definitions]
+%    \end{macrocode}
+% \begin{macro}{\UseSomeDefinitions}
+% \begin{macro}{\UseAllDefinitions}
+% \begin{macro}{\UseDefinition}
+% \begin{macro}{\ProvidesDefinition}
+% \begin{macro}{\@providesdefinition}
+% \begin{macro}{\@provides@definition}
+% \begin{macro}{\@unprovided@definition}
+%    The package works by having |\UseDefinition{|\meta{name}|}| define
+%    |\name| to be |\@unprovided@definition|.
+%    If |\UseSomeDefinitions| has been called,
+%    then |\ProvidesDefinition| looks to see if |\name|
+%    is |\@unprovided@definition|.  If
+%    |\UseAllDefinitions| has been called, then |\ProvidesDefinition|
+%    does nothing.  If neither has been called, then
+%    |\ProvidesDefinition| produces an error message.
+%    \begin{macrocode}
+\def\UseSomeDefinitions{%
+   \let\ProvidesDefinition\@providesdefinition
+}
+\def\UseAllDefinitions{%
+   \let\ProvidesDefinition\@firstofone
+}
+\def\UseDefinition#1{%
+   \expandafter\let\csname#1\endcsname\@unprovided@definition
+}
+\def\ProvidesDefinition#1{%
+   \PackageError{somedefs}%
+     {No \noexpand\UseSomeDefinitions or \string\UseAllDefinitions}%
+     {The package which used the `somedefs' package has an error.}%
+}
+\def\@providesdefinition#1{\@provides@definition#1\relax
+   \@provides@definition}
+\def\@provides@definition#1#2#3\@provides@definition{%
+   \ifx#2\@unprovided@definition
+      #1#2#3%
+   \fi
+}
+\def\@unprovided@definition{%
+   \PackageError{somedefs}%
+     {Package `somedefs' error: this command was never defined}%
+     {You have requested a command which does not exist.}%
+}
+\@onlypreamble\UseSomeDefinitions
+\@onlypreamble\UseAllDefinitions
+\@onlypreamble\UseDefinition
+\@onlypreamble\ProvidesDefinition
+\@onlypreamble\@providesdefinition
+\@onlypreamble\@provides@definition
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% That's it!
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
+% \endinput
diff --git a/macros/latex-dev/required/tools/somedefs.pdf b/macros/latex-dev/required/tools/somedefs.pdf
new file mode 100644
index 0000000000..b701b5a16e
--- /dev/null
+++ b/macros/latex-dev/required/tools/somedefs.pdf
diff --git a/macros/latex-dev/required/tools/tabularx.dtx b/macros/latex-dev/required/tools/tabularx.dtx
new file mode 100644
index 0000000000..ff8f3cec9a
--- /dev/null
+++ b/macros/latex-dev/required/tools/tabularx.dtx
@@ -0,0 +1,968 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: tabularx.dtx Copyright (C) 1991-1999 2012 2014 2016 2017 David Carlisle
+%
+%<*dtx>
+          \ProvidesFile{tabularx.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{tabularx}
+%<driver> \ProvidesFile{tabularx.drv}
+% \fi
+%         \ProvidesFile{tabularx.dtx}
+          [2016/02/03 v2.11b `tabularx' package (DPC)]
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage[infoshow]{tabularx}
+\begin{document}
+ \DocInput{tabularx.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \changes{v1.00}{1992/01/30}{Initial version.}
+% \changes{v1.01}{1992/07/07}{Re-issue for the new doc and docstrip.}
+% \changes{v1.02}{1992/07/17}{Added some support for \cmd\verb}
+% \changes{v1.03}{1992/08/17}
+%    {Added \cs{ifnum0}!=`\{\cs{fi}\} brackets after report by
+%     Andreas Maassen}
+% \changes{v1.04}{1992/09/02}
+%    {fixed \cmd\verb, and support footnotes.}
+% \changes{v1.05}{1992/11/06}
+%    {preserve all LaTeX counters}
+% \changes{v1.06}{1993/08/02}
+%    {(Martin Schroeder) Support the optional [t] or [b] argument.
+%     Also now works with delarray.sty.}
+% \changes{v1.07}{1993/08/27}
+%    {Modifications to make this style compatible with calc.sty.}
+% \changes{v2.00}{1994/03/14}
+%    {Update to LaTeX2e}
+% \changes{v2.01}{1994/05/22}
+%    {New Tracing format.}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+%
+% \GetFileInfo{tabularx.dtx}
+% \title{The \textsf{tabularx} package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{David Carlisle}
+% \date{\filedate}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+% \DeleteShortVerb{\|}
+% \MakeShortVerb{\"}
+%
+% \begin{abstract}
+% A new environment, {\ttfamily tabularx}, is defined, which takes the
+% same arguments as {\ttfamily tabular*}, but modifies the widths of
+% certain columns, rather than the inter column space, to set a table
+% with the requested total width. The columns that may stretch are
+% marked with the new token {\ttfamily X} in the preamble argument.
+%
+% This package requires the {\ttfamily array} package.
+% \end{abstract}
+%
+% \section{Introduction}
+% This package implements a version of the {\ttfamily tabular}
+% environment in which the widths of certain columns are calculated so
+% that the table is a specified width. Requests for such an
+% environment seem to occur quite regularly in {\ttfamily
+% comp.text.tex}.
+%
+% \DescribeEnv{tabularx}
+% "\begin{tabularx}{"\meta{width}"}["\meta{pos}"]{"\meta{preamble}"}"\\
+% The arguments of "tabularx" are essentially the same as those of
+% the standard "tabular*" environment. However rather than adding space
+% between the columns to achieve the desired width, it adjusts the
+% widths of some of the columns. The columns which are affected by the
+% {\ttfamily tabularx} environment should be denoted with the letter
+% {\ttfamily X} in the preamble argument. The {\ttfamily X} column
+% specification will be converted to  "p{"\meta{some value}"}" once the
+% correct column width has been calculated.
+%
+% \section{Examples}
+%
+% The following table is set with
+% "\begin{tabularx}{250pt}{|c|X|c|X|} ...".
+%
+% \begin{center}
+% \begin{tabularx}{250pt}{|c|X|c|X|}
+% \hline
+% \multicolumn{2}{|c|}{Multicolumn entry!}&
+% THREE&
+% FOUR\\
+% \hline
+% one&
+% \raggedright\arraybackslash The width of this column depends on the
+% width of the table.\footnote
+% {You can now use {\ttfamily \bslash footnote} inside {\ttfamily
+% tabularx}!}&
+% three&
+% \raggedright\arraybackslash Column four will act in the same way as
+% column two, with the same width.\\
+% \hline
+% \end{tabularx}
+% \end{center}
+% If we change the first line to "\begin{tabularx}{300pt}{|c|X|c|X|}" we
+% get:
+% \begin{center}
+% \begin{tabularx}{300pt}{|c|X|c|X|}
+% \hline
+% \multicolumn{2}{|c|}{Multicolumn entry!}&
+% THREE&
+% FOUR\\
+% \hline
+% one&
+% \raggedright\arraybackslash The width of this column depends on the
+% width of the table.&
+% three&
+% \raggedright\arraybackslash Column four will act in the same way as
+% column two, with the same width.\\
+% \hline
+% \end{tabularx}
+% \end{center}
+%
+% \edef\mytt{\expandafter\noexpand\csname
+%             mdseries\endcsname\noexpand\ttfamily}
+% \section{Differences between {\mytt tabularx} and {\mytt tabular*}}
+% These two environments take the same arguments, to produce a table of
+% a specified width. The main differences between them are:
+% \begin{itemize}
+% \item {\ttfamily tabularx} modifies the widths of the \emph{columns},
+% whereas {\ttfamily tabular*} modifies the widths of the inter-column
+% \emph{spaces}.
+% \item {\ttfamily tabular} and {\ttfamily tabular*} environments may be
+% nested with no restriction, however if one {\ttfamily tabularx}
+% environment occurs inside another, then the inner one {\em must\/} be
+% enclosed by "{ }".
+% \item The body of the {\ttfamily tabularx} environment is in fact the
+% argument to a command, and so certain constructions which are not
+% allowed in command arguments (like "\verb") may not be used.\footnote
+% {Since Version 1.02, {\ttfamily\bslash verb and \ttfamily\bslash
+% verb*} may be used, but they may treat spaces incorrectly, and the
+% argument can not contain an unmatched {\ttfamily\char`\{} or
+% {\ttfamily\char`\}}, or a  {\ttfamily\char`\%} character.}
+% \item {\ttfamily tabular*} uses a primitive capability of \TeX\ to
+% modify the inter column space of an alignment. {\ttfamily tabularx}
+% has to set the table several times as it searches for the best column
+% widths, and is therefore much slower. Also the fact that the body is
+% expanded several times may break certain \TeX\ constructs.
+% \end{itemize}
+%
+% \section{Customising the behaviour of {\mytt tabularx}}
+%
+% \subsection{Terminal output}
+% \DescribeMacro{\tracingtabularx}
+% If this declaration is made, say in the document preamble, then all
+% following {\ttfamily tabularx} environments will print information
+% about column widths as they repeatedly re-set the tables to find the
+% correct widths.
+%
+% As an alternative to using the "\tracingtabularx" declaration, either
+% of the options "infoshow" or "debugshow" may be given, either in the
+% "\usepackage" command that loads "tabularx", or as a global option
+% in the "\documentclass" command.
+%
+% \subsection{The environment used to typeset the {\mytt X} columns}
+% By default the {\ttfamily X} specification is turned into
+% "p{"\meta{some value}"}". Such narrow columns often
+% require a special format, this may be achieved using the ">" syntax
+% of {\ttfamily array.sty}. So for example you may give a specification
+% of ">{\small}X". Another format which is useful in narrow columns is
+% ragged right, however \LaTeX's "\raggedright" macro redefines
+% "\\" in a way which conflicts with its use in a tabular or array
+% environments.
+%\DescribeMacro{\arraybackslash}
+% For this reason this package introduces the command "\arraybackslash",
+% this may be used after a "\raggedright", "\raggedleft"  or
+% "\centering" declaration. Thus a {\ttfamily tabularx} preamble may
+% specify\\
+% ">{\raggedright\arraybackslash}X".
+%
+% \DescribeMacro{\newcolumntype}
+% These preamble specifications may of course be saved using the
+% command, "\newcolumntype", defined in {\ttfamily array.sty}. Thus we
+% may say\\
+% "\newcolumntype{Y}{>{\small\raggedright\arraybackslash}X}"\\
+% and then use {\ttfamily Y} in the {\ttfamily tabularx} preamble
+% argument.
+%
+% \DescribeMacro{\tabularxcolumn}
+% The {\ttfamily X} columns are set using the {\ttfamily p} column which
+% corresponds  to "\parbox[t]". You may want them set using, say, the
+% {\ttfamily m} column, which corresponds to "\parbox[c]". It is not
+% possible to change the column type using the ">" syntax, so another
+% system is provided.  "\tabularxcolumn" should be defined to be a macro
+% with one argument, which expands to the {\ttfamily tabular} preamble
+% specification that you want to correspond to {\ttfamily X}. The
+% argument will be replaced by the calculated width of a column.
+%
+% The default is "\newcommand{\tabularxcolumn}[1]{p{#1}}". So we may
+% change this with a command such as:\\
+% "\renewcommand{\tabularxcolumn}[1]{>{\small}m{#1}}"
+%
+% \subsection{Column widths}
+% Normally all {\ttfamily X} columns in a single table are set to the
+% same width, however it is possible to make {\ttfamily tabularx} set
+% them to different widths.
+% A preamble argument of 
+% "{>{\hsize=.5\hsize\linewidth=\hsize}X"\\
+% " >{\hsize=1.5\hsize\linewidth=\hsize}X}"\\
+% specifies two columns, the second will be three times as wide as the
+% first. However if you want to play games like this you should follow
+% the following two rules.
+% \begin{itemize}
+% \item Make sure that the sum of the widths of all the {\ttfamily X}
+% columns is unchanged. (In the above example, the new widths still add
+% up to twice the default width, the same as two standard {\ttfamily X}
+% columns.)
+% \item Do not use "\multicolumn" entries which cross any {\ttfamily X}
+% column.
+% \end{itemize}
+% As with most rules, these may be broken if you know what you are
+% doing.
+%
+% \subsection{If the algorithm fails\ldots}
+% It may be that the widths of the `normal' columns of the table
+% already total more  than the requested total
+% width. \textsf{tabularx} refuses to set the
+% \texttt{X} columns to a negative width, so in this case you get a
+% warning ``X Columns too narrow (table too wide)''.
+%
+% The \texttt{X} columns will in this case be set to a width of 1em
+% and so the table itself will be wider than the requested total width
+% given in the argument to the environment.
+% This behaviour of the package can be customised slightly
+% as noted in the documentation of the code section.
+%
+% \StopEventually{}
+%
+% \section{The Macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \changes{v2.00}{1994/02/07}
+%    {New Option Handling}
+%    \begin{macrocode}
+\DeclareOption{infoshow}{\AtEndOfPackage\tracingtabularx}
+\DeclareOption{debugshow}{\AtEndOfPackage\tracingtabularx}
+\ProcessOptions
+%    \end{macrocode}
+%
+% This requires {\ttfamily array.sty}.
+% \changes{v2.00}{1994/02/07}
+%    {Use LaTeX2e's \cmd{\RequirePackage} to load array}
+%    \begin{macrocode}
+\RequirePackage{array}[1994/02/03]
+%    \end{macrocode}
+%
+% First some registers etc.\ that we need.
+%    \begin{macrocode}
+\newdimen\TX@col@width
+\newdimen\TX@old@table
+\newdimen\TX@old@col
+\newdimen\TX@target
+\newdimen\TX@delta
+\newcount\TX@cols
+\newif\ifTX@
+%    \end{macrocode}
+%
+% Now a trick to get the body of an environment into a token register,
+% without doing any expansion. This does not do any real checking of
+% nested environments, so if you should need to nest one {\ttfamily
+% tabularx} inside another, the inner one must be surrounded by "{ }".
+%
+% \begin{macro}{\tabularx}
+% Prior to v1.06, this macro took two arguments, which were saved in
+% separate registers before the table body was saved by "\TX@get@body".
+% Unfortunately this disables the "[t]" optional argument. Now just save
+% the width specification separately, then clear the token register
+% "\toks@".
+% Finally call "\TX@get@body" to begin saving the body of the table.
+% The "{\ifnum0=`}\fi" was added at v1.03, to allow "tabularx" to appear
+% inside a "\halign".^^A
+% \setbox0=\hbox{\footnotesize"\iffalse{\fi\ifnum0=`}\fi"}^^A
+% \setbox2=\hbox{\footnotesize"\ifnum0=`{}\fi"}^^A
+% \footnote{This adds an extra level of grouping,
+% which is not really needed. Instead, I could use \box0\ here, and
+% \box2\ below, however the code here would then have to be moved after
+% the first line, because of the footnote to page 386 of the \TeX{}Book,
+% and I do not think I should be writing code that is so obscure as to
+% be documented in a footnote in an appendix called ``Dirty Tricks''!}
+%
+% This mechanism of grabbing an environment body does have the
+% disadvantage (shared with the AMS alignment environments) that you
+% can not make extension environments by code such as
+%\begin{verbatim}
+%\newenvironment{foo}{\begin{tabularx}{XX}}{\end{tabularx}}
+%\end{verbatim}
+% as the code is looking for a literal string "\end{tabularx}" to stop
+% scanning. Since version 2.02, one may avoid this problem by using
+% "\tabularx" and "\endtabularx" directly in the definition:
+%\begin{verbatim}
+%\newenvironment{foo}{\tabularx{XX}}{\endtabularx}
+%\end{verbatim}
+% The scanner now looks for the end of the current environment ("foo" in
+% this example.) There are some restrictions on this usage, the
+% principal one being that "\endtabularx" must not be inside any "{ }" pairs
+% ao that the code before "\endtabularx"  may be extracted and added to the table body
+% (prior to version 2.09  "\endtabularx" had to be
+% the \emph{first} token of the `end code' of the environment).
+%    \begin{macrocode}
+\def\tabularx#1{%
+%    \end{macrocode}
+% \changes{v2.02}{1995/03/20}
+%    {New local setting of \cs{TX@}}
+% \changes{v4.09}{1998/05/13}
+%      {Use \cs{setlength}, so that calc extensions apply. tools/2793}
+% Allow "\tabularx" "\endtabularx" (but not "\begin{tabularx}"
+% "\end{tabularx}") to be used in "\newenvironment" definitions.
+%    \begin{macrocode}
+\edef\TX@{\@currenvir}%
+  {\ifnum0=`}\fi
+%    \end{macrocode}
+% "\relax" added at v1.05 so that non-expandable length tokens, like
+% "\textwidth" do not generate an extra space, and an overfull box.
+% "\relax" removed again at v4.09 in favour of "\setlength" so if you
+% use the calc package you can use a width of "(\textwidth-12pt)/2".
+%    \begin{macrocode}
+  \setlength\TX@target{#1}%
+  \TX@typeout{Target width: #1 = \the\TX@target.}%
+  \toks@{}\TX@get@body}
+%    \end{macrocode}
+% \end{macro}
+%
+
+%  \begin{macro}{\endtabularx}
+% This does not do very much\ldots
+% \changes{v2.02}{1995/03/20}
+%    {Macro added}
+%    \begin{macrocode}
+\let\endtabularx\relax
+%    \end{macrocode}
+%  \end{macro}
+%
+% \begin{macro}{\TX@get@body}
+% Place all tokens as far as the first "\end" into a token register.
+% Then call "\TX@find@end" to see if we are at "\end{tabularx}".
+%    \begin{macrocode}
+\long\def\TX@get@body#1\end
+  {\toks@\expandafter{\the\toks@#1}\TX@find@end}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@find@end}
+% If we are at "\end{tabularx}", call "\TX@endtabularx", otherwise
+% add "\end{...}" to the register, and call "\TX@get@body" again.
+%    \begin{macrocode}
+\def\TX@find@end#1{%
+  \def\@tempa{#1}%
+  \ifx\@tempa\TX@\expandafter\TX@endtabularx
+  \else\toks@\expandafter
+    {\the\toks@\end{#1}}\expandafter\TX@get@body\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@find@endtabularxa}
+% \changes{v2.09}{2014/04/22}{macro added}
+% \changes{v2.10}{2014/05/13}{macro modified to test for missing \cs{endtabularx}}
+% \changes{v2.11}{2016/01/03}{Fix to previous change to guard against empty arg 2. (Ulrike Fischer)}
+% split up the end code, and extract the part that lives in the table body.
+%    \begin{macrocode}
+\long\def\TX@find@endtabularxa
+       #1\endtabularx#2\endtabularx#3\TX@find@endtabularxa{%
+  \ifx\TX@#2\relax\else
+  \toks@\expandafter{\the\toks@#1}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TX@find@endtabularxb}
+% \changes{v2.09}{2014/04/22}{macro added}
+% \changes{v2.10}{2014/05/13}{macro modified to test for missing \cs{endtabularx}}
+% split up the end code, and extract the part that lives outside the table body.
+%    \begin{macrocode}
+\long\def\TX@find@endtabularxb
+       #1\endtabularx#2\endtabularx#3\TX@find@endtabularxb{%
+  \ifx\TX@#2%
+    \expandafter\@firstoftwo
+  \else
+     \expandafter\@secondoftwo
+  \fi
+  {#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@find@endtabularxbb}
+% \changes{v2.10}{2014/05/13}{macro added}
+% Helper to avoid needing 15 consecutive "expandafter"
+%    \begin{macrocode}
+\def\TX@find@endtabularxbb{%
+  \expandafter\expandafter\expandafter
+  \TX@find@endtabularxb
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@}
+% The string {\ttfamily tabularx} as a macro for testing with "\ifx".
+%    \begin{macrocode}
+\def\TX@{tabularx}
+%    \end{macrocode}
+% \end{macro}
+%
+% Now that all the parts of the table specification are stored in
+% registers, we can begin the work of setting the table.
+%
+% The algorithm for finding the correct column widths is as follows.
+% Firstly set the table with each {\ttfamily X} column the width of the
+% final table. Assuming that there is at least one {\ttfamily X} column,
+% this will produce a table that is too wide. Divide the excess width by
+% the number of {\ttfamily X} columns, and reduce the column width by
+% this amount. Reset the table. If the table is not now the correct
+% width, a "\multicolumn" entry must be `hiding' one of the {\ttfamily
+% X} columns, and so there is one less {\ttfamily X} column affecting
+% the width of the table. So we reduce by 1 the number of X columns and
+% repeat the process.
+%
+% \begin{macro}{\TX@endtabularx}
+% Although I have tried to make {\ttfamily tabularx} look like an
+% environment, it is in fact a command, all the work is done by this
+% macro.
+%    \begin{macrocode}
+\def\TX@endtabularx{%
+%    \end{macrocode}
+% \changes{v2.09}{2014/04/22}{call to \cs{TX@find@endtabularxa} added}
+% \changes{v2.10}{2014/05/13}{macro modified to test for missing \cs{endtabularx}}
+%    \begin{macrocode}
+   \expandafter\expandafter\expandafter
+     \TX@find@endtabularxa\csname end\TX@\endcsname
+     \endtabularx\TX@\endtabularx\TX@find@endtabularxa
+%    \end{macrocode}
+% Define the {\ttfamily X} column, with an internal version of the
+% "\newcolumntype" command. The "\expandafter" commands enable
+% "\NC@newcol"  to get the {\em expansion} of\\
+% "\tabularxcolumn{\TX@col@width}" as its
+% argument. This will be the definition of an {\ttfamily X} column, as
+% discussed in section 4.
+%    \begin{macrocode}
+  \expandafter\TX@newcol\expandafter{\tabularxcolumn{\TX@col@width}}%
+%    \end{macrocode}
+% Initialise the column width, and the number of {\ttfamily X} columns.
+% The number of {\ttfamily X} columns is set to one, which means that
+% the initial count will be one too high, but this value is decremented
+% before it is used in the main loop.
+%
+% Since v1.02, switch the definition of "\verb".
+%    \begin{macrocode}
+  \let\verb\TX@verb
+%    \end{macrocode}
+% Since v1.05, save the values of all \LaTeX\ counters, the list
+% "\cl@@ckpt" contains the names of all the \LaTeX\ counters that have
+% been defined so far. We expand "\setcounter" at this point, as it
+% results in fewer tokens being stored in "\TX@ckpt", but the actual
+% resetting of the counters occurs when "\TX@ckpt" is expanded after
+% each trial run.
+% Actually since v1.07, use something equivalent to the expansion of the
+% original definition of "\setcounter", so that "tabularx" works in
+% conjunction with "calc.sty".
+%    \begin{macrocode}
+  \def\@elt##1{\global\value{##1}\the\value{##1}\relax}%
+  \edef\TX@ckpt{\cl@@ckpt}%
+  \let\@elt\relax
+  \TX@old@table\maxdimen
+  \TX@col@width\TX@target
+  \global\TX@cols\@ne
+%    \end{macrocode}
+% Typeout some headings (unless this is disabled).
+%    \begin{macrocode}
+  \TX@typeout@
+    {\@spaces Table Width\@spaces Column Width\@spaces X Columns}%
+%    \end{macrocode}%
+% First attempt. Modify the {\ttfamily X} definition to count {\ttfamily
+% X} columns.
+%    \begin{macrocode}
+  \TX@trial{\def\NC@rewrite@X{%
+          \global\advance\TX@cols\@ne\NC@find p{\TX@col@width}}}%
+%    \end{macrocode}
+% Repeatedly decrease column width until table is the correct width,
+% or stops shrinking, or the columns become two narrow.
+% If there are no multicolumn entries, this will only take one attempt.
+%    \begin{macrocode}
+  \loop
+    \TX@arith
+    \ifTX@
+    \TX@trial{}%
+  \repeat
+%    \end{macrocode}
+% One last time, with warnings back on (see appendix D)
+% use {\ttfamily tabular*} to put it in a box of the right size, in case
+% the algorithm failed to find the correct size.
+%
+% Since v1.04, locally make "\footnotetext" save its argument in a token
+% register.
+% Since v1.06, "\toks@" contains the preamble specification,
+% and possible optional argument, as well as the table body.
+%    \begin{macrocode}
+  {\let\@footnotetext\TX@ftntext\let\@xfootnotenext\TX@xftntext
+    \csname tabular*\expandafter\endcsname\expandafter\TX@target
+      \the\toks@
+    \csname endtabular*\endcsname}%
+%    \end{macrocode}
+% Now the alignment is finished, and the "}" has restored the original
+% meaning of "\@footnotetext" expand the register "\TX@ftn" which will
+% execute a series of\\
+% "\footnotetext["\meta{num}"]{"\meta{note}"}"\\
+% commands. We need to be careful about clearing the register as we may
+% be inside a nested {\ttfamily tabularx}.
+%    \begin{macrocode}
+  \global\TX@ftn\expandafter{\expandafter}\the\TX@ftn
+%    \end{macrocode}
+% Now finish off the {\ttfamily tabularx} environment. Note that we need
+% "\end{tabularx}" here as the "\end{tabularx}" in the user's
+% file is never expanded. Now use "\TX@" rather than "tabularx".
+% \changes{v2.02}{1995/03/20}
+%    {Close the environment \cs{TX@} rather than `tabularx'}
+%
+% We also need to finish off the group started by "{\ifnum0=`}\fi" in
+% the macro "\tabularx".
+%    \begin{macrocode}
+  \ifnum0=`{\fi}%
+%    \end{macrocode}
+% \changes{v2.09}{2014/04/22}{call to \cs{TX@find@endtabularxb} added}
+% \changes{v2.10}{2014/05/13}{macro modified to test for missing \cs{endtabularx}}
+%    \begin{macrocode}
+   \expandafter\expandafter\expandafter
+   \TX@find@endtabularxbb
+    \expandafter\end\expandafter{\TX@}%
+    \endtabularx\TX@\endtabularx\TX@find@endtabularxb
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\TX@arith}
+% Calculate the column width for the next try, setting the flag
+% "\ifTX@" to false if the loop should be aborted.
+%    \begin{macrocode}
+\def\TX@arith{%
+  \TX@false
+%    \end{macrocode}
+% \changes{v2.08}{2012/02/06}{Avoid exceeding maxdimen during trials}
+%    \begin{macrocode}
+  \@tempdimb\maxdimen
+  \divide\@tempdimb\TX@cols
+  \ifdim\TX@col@width>\@tempdimb
+    \TX@typeout@{Don't exceed \maxdimen}%
+    \wd\@tempboxa\maxdimen
+  \fi
+  \ifdim\TX@old@table=\wd\@tempboxa
+%    \end{macrocode}
+% If we have reduced the column width, but the table width has not
+% changed, we stop the loop, and output the table (which will cause an
+% over-full alignment) with the previous value of "\TX@col@width".
+%    \begin{macrocode}
+    \TX@col@width\TX@old@col
+    \TX@typeout@{Reached minimum width, backing up.}%
+  \else
+%    \end{macrocode}
+% Otherwise calculate the amount by which the current table is too wide.
+%    \begin{macrocode}
+    \dimen@\wd\@tempboxa
+    \advance\dimen@ -\TX@target
+    \ifdim\dimen@<\TX@delta
+%    \end{macrocode}
+% If this amount is less than "\TX@delta", stop. ("\TX@delta"
+% should be non-zero otherwise we may miss the target due to rounding
+% error.)
+%    \begin{macrocode}
+      \TX@typeout@{Reached target.}%
+    \else
+%    \end{macrocode}
+% Reduce the number of effective {\ttfamily X} columns by one. (Checking
+% that we do not get 0, as this would produce an error later.) Then
+% divide excess width by the number of effective columns, and calculate
+% the new column width. Temporarily store this value (times $-1$) in
+% "\dimen@".
+%    \begin{macrocode}
+      \ifnum\TX@cols>\@ne
+        \advance\TX@cols\m@ne
+      \fi
+      \divide\dimen@\TX@cols
+      \advance\dimen@ -\TX@col@width
+      \ifdim \dimen@ >\z@
+%    \end{macrocode}
+% If the new width would be too narrow, abort the loop. At the moment
+% too narrow, means less than 0\,pt!
+%
+% Prior to v2.03, if the loop was aborted here, the X columns were left
+% with the width of the previous run, but this may make the table far
+% too wide as initial guesses are always too big. Now force to
+% "\TX@error@width" which defaults to be 1em. If you want to
+% get the old behaviour stick\\
+%  "\renewcommand\TX@error@width{\TX@col@width}"\\
+% in a package file loaded after \textsf{tabularx}.
+% \changes{v2.03}{1997/02/20}{Improve warning message and force to 1em.}
+%    \begin{macrocode}
+        \PackageWarning{tabularx}%
+           {X Columns too narrow (table too wide)\MessageBreak}%
+        \TX@col@width\TX@error@width\relax
+      \else
+%    \end{macrocode}
+% Otherwise save the old settings, and set the new column width. Set the
+% flag to true so that the table will be set, and the loop will be
+% executed again.
+%    \begin{macrocode}
+        \TX@old@col\TX@col@width
+        \TX@old@table\wd\@tempboxa
+        \TX@col@width-\dimen@
+        \TX@true
+      \fi
+    \fi
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@error@width}
+% \changes{v2.03}{1997/02/20}{macro added.}
+% \changes{v2.04}{1997/02/26}{spurious brace removed.}
+% If the calculated width is negative, use this instead.
+%    \begin{macrocode}
+\def\TX@error@width{1em}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@delta}
+% Accept a table that is within "\hfuzz" of the correct width.
+%    \begin{macrocode}
+\TX@delta\hfuzz
+%    \end{macrocode}
+% \end{macro}
+%
+% Initialise the {\ttfamily X} column. The definition can be empty here,
+% as it is set for each {\ttfamily tabularx} environment.
+%    \begin{macrocode}
+\newcolumntype{X}{}
+%    \end{macrocode}
+%
+% \begin{macro}{\tabularxcolumn}
+% The default definition of {\ttfamily X} is "p{#1}".
+%    \begin{macrocode}
+\def\tabularxcolumn#1{p{#1}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@newcol}
+% A little macro just used to cut down the number of "\expandafter"
+% commands needed.
+%    \begin{macrocode}
+\def\TX@newcol{\newcol@{X}[0]}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@trial}
+% Make a test run.
+%    \begin{macrocode}
+\def\TX@trial#1{%
+  \setbox\@tempboxa\hbox{%
+%    \end{macrocode}
+% Any extra commands. This is used on the first run to count the number
+% of {\ttfamily X} columns.
+%    \begin{macrocode}
+    #1\relax
+%    \end{macrocode}
+% Since v1.04, make "\footnotetext" gobble its arguments. Also locally
+% clear "\TX@vwarn" so that the warning is generated by the {\ttfamily
+% final} run, and does not appear in the middle of the table if
+% "\tracingtabularx".
+%    \begin{macrocode}
+  \let\@footnotetext\TX@trial@ftn
+  \let\TX@vwarn\@empty
+%    \end{macrocode}
+% Do not nest {\ttfamily tabularx} environments during trial runs. This
+% would waste time, and the global setting of "\TX@cols" would break the
+% algorithm.
+%    \begin{macrocode}
+   \expandafter\let\expandafter\tabularx\csname tabular*\endcsname
+   \expandafter\let\expandafter\endtabularx\csname endtabular*\endcsname
+%    \end{macrocode}
+% Added at v1.05: disable "\write"s during a trial run. This trick is
+% from the \TeX{}Book.\footnote{Actually the \TeX{}Book trick does
+% not work correctly, so changed for v2.05.}
+% \changes{v2.05}{1997/09/18}
+%    {New \cs{write} trick. tools/2607}
+% \changes{v2.07}{1999/01/07}
+%    {Newer \cs{write} trick. tools/2792}
+%    \begin{macrocode}
+   \def\write{\begingroup
+     \def\let{\afterassignment\endgroup\toks@}%
+        \afterassignment\let\count@}%
+%    \end{macrocode}
+% Turn off warnings (see appendix D). Also prevent them being turned
+% back on by setting the parameter names to be registers.
+%    \begin{macrocode}
+    \hbadness\@M
+    \hfuzz\maxdimen
+    \let\hbadness\@tempcnta
+    \let\hfuzz\@tempdima
+%    \end{macrocode}
+% Make the table, and finish the hbox.
+% Since v1.06, "\toks@" contains the preamble specification,
+% and possible optional argument, as well as the table body.
+%    \begin{macrocode}
+    \expandafter\tabular\the\toks@
+    \endtabular}%
+%    \end{macrocode}
+% Since v1.05 reset all \LaTeX\ counters, by executing "\TX@ckpt".
+%    \begin{macrocode}
+  \TX@ckpt
+%    \end{macrocode}
+% Print some statistics.
+% Added "\TX@align" in v1.05, to line up the columns.
+%    \begin{macrocode}
+  \TX@typeout@{\@spaces
+     \expandafter\TX@align
+        \the\wd\@tempboxa\space\space\space\space\space\@@
+     \expandafter\TX@align
+        \the\TX@col@width\space\space\space\space\space\@@
+     \@spaces\the\TX@cols}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@align}
+% Macro added at v1.05, to improve the printing of the tracing info.
+%    \begin{macrocode}
+\def\TX@align#1.#2#3#4#5#6#7#8#9\@@{%
+  \ifnum#1<10 \space\fi
+  \ifnum#1<100 \space\fi
+  \ifnum#1<\@m\space\fi
+  \ifnum#1<\@M\space\fi
+  #1.#2#3#4#5#6#7#8\space\space}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\arraybackslash}
+% "\\" hack.
+% \changes{v2.08}{2012/02/06}{Don't define this if already defined by newer array package and use tabularnewline now this is in 2e.}
+%    \begin{macrocode}
+\ifx\arraybackslash\@undefined
+\def\arraybackslash{\let\\\tabularnewline}
+\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tracingtabularx}
+% Print statistics on column and table widths.
+%    \begin{macrocode}
+\def\tracingtabularx{%
+  \def\TX@typeout{\PackageWarningNoLine{tabularx}}%
+  \def\TX@typeout@##1{\typeout{(tabularx) ##1}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@typeout}
+% The default is to be to be quiet
+%    \begin{macrocode}
+\let\TX@typeout\@gobble
+\let\TX@typeout@\@gobble
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@ftn}
+% A token register for saving footnote texts.
+%    \begin{macrocode}
+\newtoks\TX@ftn
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@ftntext}
+% \begin{macro}{\TX@xftntext}
+% Inside the alignment just save up the footnote text in a token
+% register.
+%    \begin{macrocode}
+\long\def\TX@ftntext#1{%
+  \edef\@tempa{\the\TX@ftn\noexpand\footnotetext
+                    [\the\csname c@\@mpfn\endcsname]}%
+  \global\TX@ftn\expandafter{\@tempa{#1}}}%
+\long\def\TX@xftntext[#1]#2{%
+  \global\TX@ftn\expandafter{\the\TX@ftn\footnotetext[#1]{#2}}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\TX@trial@ftn}
+% On trial runs, gobble footnote texts.
+%    \begin{macrocode}
+\long\def\TX@trial@ftn#1{}
+%    \end{macrocode}
+% \end{macro}
+%
+% This last section was added at Version 1.02. Previous versions
+% documented the fact that "\verb" did not work inside {\ttfamily
+% tabularx}, but that did not stop people using it! This usually put
+% \LaTeX\ into an irrecoverable error position, with error messages that
+% did not mention the cause of the error. The `poor man's "\verb"' (and
+% "\verb*") defined here is based on page 382 of the \TeX{}Book. As
+% explained there, doing verbatim this way means that spaces are not
+% treated correctly, and so "\verb*" may well be useless, however I
+% consider this section of code to be error-recovery, rather than a real
+% implementation of verbatim.
+%
+% The mechanism is quite general, and any macro which wants to allow a
+% form of "\verb" to be used within its argument may
+% "\let\verb=\TX@verb". (Making sure to restore the real definition
+% later!)
+%
+% "\verb" and "\verb*" are subject to the following restrictions:
+% \begin{enumerate}
+% \item Spaces in the argument are not read verbatim, but may be skipped
+%       according to \TeX's usual rules.
+% \item Spaces will be added to the output after control words, even if
+%       they were not present in the input.
+% \item Unless the argument is a single space, any trailing space,
+%       whether in the original argument, or added as in (2),
+%       will be omitted.
+% \item The argument must not end with "\", so "\verb|\|" is not
+%      allowed, however, because of (3), "\verb|\ |" produces
+%      "\".
+% \item The argument must be balanced with respect to "{" and "}". So
+%      "\verb|{|" is not allowed.
+% \item A comment character like "%" will not appear verbatim. It will
+%       act as usual, commenting out the rest of the input line!
+% \item The combinations "?`" and "!`" will appear as
+%       {\ttfamily?`} and {\ttfamily!`} if the {\ttfamily cmtt} font is
+%       being used.
+% \end{enumerate}
+%
+% \begin{macro}{\TX@verb}
+% The internal definition of "\verb". Spaces will be replaced by "~", so
+% for the star-form, "\let" "~" be \verb*| |, which we obtain as
+% "\uppercase{*}". Use "{\ifnum0=`}\fi" rather than "\bgroup" to allow
+% "&" to appear in the argument.
+%    \begin{macrocode}
+{\uccode`\*=`\ %
+\uppercase{\gdef\TX@verb{%
+  \leavevmode\null\TX@vwarn
+  {\ifnum0=`}\fi\ttfamily\let\\\ignorespaces
+  \@ifstar{\let~*\TX@vb}{\TX@vb}}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@vb}
+% Get the `almost verbatim' text using "\meaning". The `"!"' is added to
+% the front of the user supplied text, to ensure that the whole argument
+% does not consist of a single "{ }" group. \TeX\ would strip the outer
+% braces from such a group. The `"!"' will be removed later.
+%
+% Originally I followed Knuth, and had "\def\@tempa{##1}", however this
+% did not allow "#" to appear in the argument. So in v1.04, I changed
+% this to to use a token register, and "\edef". This allows "#" appear,
+% but makes each one appear twice!, so later we loop through, replacing
+% "##" by "#".
+%    \begin{macrocode}
+\def\TX@vb#1{\def\@tempa##1#1{\toks@{##1}\edef\@tempa{\the\toks@}%
+    \expandafter\TX@v\meaning\@tempa\\ \\\ifnum0=`{\fi}}\@tempa!}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@v}
+% Strip the initial segment of the "\meaning", including the `"!"'
+% added earlier.
+%    \begin{macrocode}
+\def\TX@v#1!{\afterassignment\TX@vfirst\let\@tempa= }
+%    \end{macrocode}
+% \end{macro}
+%
+% As explained above we are going to replace "##" pairs by "#". To do
+% this we need non-special "#" tokens.  Make "*" into a parameter
+% token so that we can define macros with arguments. The normal meanings
+% will be restored by the "\endgroup" later.
+%    \begin{macrocode}
+\begingroup
+\catcode`\*=\catcode`\#
+\catcode`\#=12
+%    \end{macrocode}
+%
+% \begin{macro}{\TX@vfirst}
+% As a special case, prevent the first character from being dropped.
+% This makes "\verb*| |" produce \verb*| |. Then call "\TX@v@".
+% This is slightly tricky since v1.04, as I have to ensure that an
+% actual "#" rather than a command "\let" to "#" is passed on if the
+% first character is "#".
+%    \begin{macrocode}
+\gdef\TX@vfirst{%
+  \if\@tempa#%
+    \def\@tempb{\TX@v@#}%
+  \else
+    \let\@tempb\TX@v@
+    \if\@tempa\space~\else\@tempa\fi
+  \fi
+  \@tempb}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@v@}
+% Loop through the "\meaning", replacing all spaces by "~". If the last
+% character is a space it is dropped, so that "\verb*|\LaTeX|" produces
+% "\LaTeX" not \verb*|\LaTeX |. The rewritten tokens are then further
+% processed to replace "##" pairs.
+%    \begin{macrocode}
+\gdef\TX@v@*1 *2{%
+  \TX@v@hash*1##\relax\if*2\\\else~\expandafter\TX@v@\fi*2}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\TX@v@hash}
+% The inner loop, replacing "##" by "#".
+%    \begin{macrocode}
+\gdef\TX@v@hash*1##*2{*1\ifx*2\relax\else#\expandafter\TX@v@hash\fi*2}
+%    \end{macrocode}
+% \end{macro}
+%
+% As promised, we now restore the normal meanings of "#" and "*".
+%    \begin{macrocode}
+\endgroup
+%    \end{macrocode}
+%
+% \begin{macro}{\TX@vwarn}
+% Warn the user the first time this "\verb" is used.
+%    \begin{macrocode}
+\def\TX@vwarn{%
+  \@warning{\noexpand\verb may be unreliable inside tabularx}%
+  \global\let\TX@vwarn\@empty}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+\endinput
diff --git a/macros/latex-dev/required/tools/tabularx.ins b/macros/latex-dev/required/tools/tabularx.ins
new file mode 100644
index 0000000000..06308d7735
--- /dev/null
+++ b/macros/latex-dev/required/tools/tabularx.ins
@@ -0,0 +1,74 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+\generate{\file{tabularx.sty}{\from{tabularx.dtx}{package}}}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/tabularx.pdf b/macros/latex-dev/required/tools/tabularx.pdf
new file mode 100644
index 0000000000..83d15b9119
--- /dev/null
+++ b/macros/latex-dev/required/tools/tabularx.pdf
diff --git a/macros/latex-dev/required/tools/theorem.dtx b/macros/latex-dev/required/tools/theorem.dtx
new file mode 100644
index 0000000000..6f745d016e
--- /dev/null
+++ b/macros/latex-dev/required/tools/theorem.dtx
@@ -0,0 +1,1144 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%
+%%
+%
+%
+\def\FMithmInfo{2014/10/28 v2.2c Theorem extension package (FMi)}
+%
+% \ProvidesFile{theorem.dtx}[\FMithmInfo]
+%\iffalse   % this is a METACOMMENT !
+%%
+%% Package `theorem' to use with LaTeX2e
+%% Copyright (C) 1989-1995 Frank Mittelbach, all rights reserved.
+%<+package>\@ifundefined{theorem@style}{}{\endinput}
+%<+package>\NeedsTeXFormat{LaTeX2e}[1995/06/01]
+%<+package>\ProvidesPackage{theorem}
+%<+package>         [\FMithmInfo]
+%
+% \fi
+%
+% \changes{v1.0}{87/05/07}{First draft.}
+% \changes{v1.0a}{87/05/07}{`thistheoremstyle' added.}
+% \changes{v1.1a}{87/07/29}{New concept: redefine the internal
+%                          \protect\LaTeX{} commands `@xnthm' etc.}
+% \changes{v1.1b}{87/07/31}{`theoremfont' used to specify font.}
+% \changes{v1.2a}{88/01/08}{`@endtheorem' now globally defined.}
+% \changes{v1.2b}{88/01/11}{`newtheorem' only allowed in the preamble.}
+% \changes{v1.3a}{88/02/14}{`theoremfont' now a toks register.}
+%
+% \changes{v2.0a}{88/11/16}{New implementation and new documentation.}
+% \changes{v2.0a}{88/11/16}{No layout changes but internal modifications
+%                           old substyles won't work.}
+% \changes{v2.0b}{89/01/30}{`global' used for all definitions.}
+% \changes{v2.0c}{89/06/15}{Documentation translated to English.
+%                            Thanks to LLL and Nina}
+% \changes{v2.1a}{90/02/15}{Support for new font selection.}
+% \changes{v2.2a}{94/02/03}{Cleanup for LaTeX2e}
+%
+% \DoNotIndex{\@endparenv,\@ifdefinable,\@ifnextchar,\@ifundefined}
+% \DoNotIndex{\@namedef,\@nameuse,\@spaces,\@tempa,\@warning}
+% \DoNotIndex{\ }
+% \DoNotIndex{\begingroup,\bfseries}
+% \DoNotIndex{\csname}
+% \DoNotIndex{\def,\do,\docdate}
+% \DoNotIndex{\endcsname,\endgroup,\endinput,\endtrivlist,\expandafter}
+% \DoNotIndex{\filedate,\fileversion}
+% \DoNotIndex{\gdef,\global}
+% \DoNotIndex{\hbox,\hskip}
+% \DoNotIndex{\ignorespaces,\input,\itshape,\item}
+% \DoNotIndex{\labelsep,\let,\llap}
+% \DoNotIndex{\makeatletter}
+% \DoNotIndex{\noexpand}
+% \DoNotIndex{\refstepcounter,\relax,\rlap}
+% \DoNotIndex{\setlength,\slshape,\space,\string,\strut}
+% \DoNotIndex{\the,\trivlist,\typeout}
+% \DoNotIndex{\vbox}
+% \DoNotIndex{\xdef}
+%
+% \def\deflabel#1{\ttfamily #1\hfill}
+% \def\deflist#1{\begin{list}{}{\settowidth\labelwidth{\ttfamily #1}%
+%                               \setlength\leftmargin\labelwidth
+%                               \addtolength\leftmargin\labelsep
+%                               \let\makelabel\deflabel}}
+% \def\enddeflist{\end{list}}
+% \def\envfont{\normalfont\ttfamily}
+%
+% \MakeShortVerb{\|}
+%
+% \newcommand{\TUB}{{\sl TUGboat\/}}
+%
+% \GetFileInfo{theorem.dtx}
+% \title{An Extension of the
+%        \LaTeX{} theorem environment\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{Frank Mittelbach}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% \begin{abstract}
+%    The macros described in this paper yield an extension of the
+%    \LaTeX{} theorem mechanism. It is designed is to satisfy the
+%    different requirements of various journals. Thus, the
+%    layout of the ``theorems'' can be manipulated by determining a
+%    ``style''. This article describes not only the use, but
+%    also the definition, of the necessary macros.
+% \end{abstract}
+%
+% \section*{Preface to version 2.2}
+%
+% For \LaTeXe{} this package did not need any fundamental changes. I
+% only modified the messages generated so that theorem layout styles
+% will show up with the |\listfiles| command and cleaned the section
+% on the New Font Selection Scheme since this is now included in
+% \LaTeX.
+%
+% \section*{Preface to version 2.1}
+%
+% This version is identical to 2.0g described in \TUB\ 10\#3 except
+% for some internal defaults which are now set depending on the used
+% font selection scheme.
+%
+% This was done to avoid unpleasant surprises if the new font selection
+% scheme is in force. For further details see
+% section~\ref{sec:newfonts} and \cite{bk:GMS94}.
+%
+% \section{Introduction}
+%
+% For our purposes here, ``theorems'' are labelled enunciations,
+% often set off from the main text by extra space and a font change.
+% Theorems, corollaries, conjectures, definitions, and remarks
+% are all instances of ``theorems''.  The ``header'' of these structures
+% is composed of a label (such as \textsc{Theorem} or \textsc{Remark})
+% and a number which serializes an item in the sequence of items
+% with the same label.
+%
+% Shortly after the introduction of \LaTeX{} at the Fachbereich
+% Mathematik in Mainz, the desire to manipulate the layout of
+% ``theorems'' arose.  In Mainz, the following two conventions came
+% into general use:
+% \begin{enumerate}
+%   \item The number of the theorem is shown in the margin.
+%   \item There is a line break at
+%         the end of the theorem header.
+% \end{enumerate}
+%
+% Additionally, some journals require different formats which depend on
+% the ``sort of theorem'': e.g.\ often remarks and definitions are set
+% in |\upshape|, while |\itshape| is employed for main theorems.
+%
+% Confronted with these requirements, a theorem environment was
+% developed in Mainz which allows separate determination of the
+% layout of the ``theorems sets'', comparable to |\pagestyle|.
+%
+%
+% \section{The user interface}
+% \subsection{Defining new theorem sets}
+%
+% \DescribeMacro\newtheorem
+% As in the original \LaTeX{} version, the command |\newtheorem|
+% defines a new ``theorem set'' or ``theorem-like structure''.
+% Two required arguments name the new environment and give the text
+% to be typeset with each instance of the new ``set'', while
+% an optional argument determines how
+% the ``set'' is enumerated:
+% \begin{description}
+%    \item[\ttfamily \bslash newtheorem\{foo\}\{bar\}]
+%       The theorem set {\envfont foo} (whose name is \texttt{bar})
+%       uses its own counter.
+%    \item[\ttfamily \bslash newtheorem\{foo2\}{[foo]}\{bar2\}]
+%       The theorem set {\envfont foo2} (printed name \texttt{bar2})
+%       uses the same counter as the theorem set \texttt{foo}.
+%    \item[\ttfamily \bslash newtheorem\{foo3\}\{bar3\}{[section]}]
+%       The theorem set {\envfont foo3} (printed name \texttt{bar3}) is
+%       enumerated within the counter \texttt{section}, i.e.\ with every
+%       new |\section| the enumeration begins again with 1, and
+%       the enumeration is composed from the section-number and the
+%       theorem counter itself.
+% \end{description}
+%
+% \DescribeMacro\theoremstyle
+% Additionally, the command |\theoremstyle| can define the layout
+% of various, or all, theorem sets.  It should be noted that any
+% theorem set defined by |\newtheorem| is typeset in the
+% |\theoremstyle| that is current at the time of the definition.
+% Thus, the following
+% \begin{verbatim}
+%    \theoremstyle{break}        \newtheorem{Cor}{Corollary}
+%    \theoremstyle{plain}        \newtheorem{Exa}{Example}[section]
+%\end{verbatim}                             ^^A No blank at line start
+% leads to the result that the set {\envfont Cor} is formatted in the
+% style \texttt{break}, while the set {\envfont Exa} and all the
+% following ones are formatted in the style \texttt{plain}, unless
+% another |\theoremstyle| follows.  Since the definitions installed by
+% |\newtheorem| are global, one also can limit |\theoremstyle| locally
+% by grouping braces.
+%
+% \DescribeMacro\theorembodyfont
+% The choice of the font for the theorem body is completely
+% independent of the chosen |\theoremstyle|; this has proven to
+% be very advantageous.  For example,
+% \begin{verbatim}
+%   {\theorembodyfont{\upshape}          \newtheorem{Rem}{Remark}}
+%\end{verbatim}
+% defines a theorem set {\envfont Rem}, which will be set in
+% |\upshape| in the current layout (which in our example is
+% \texttt{plain}).  As with |\theoremstyle|, the |\theorembodyfont|
+% chosen is that current at the time of |\newtheorem|.  If
+% |\theorembodyfont| is not specified or one defines
+% |\theorembodyfont{}|, then the font used will be that defined by the
+% |\theoremstyle|.
+%
+% \DescribeMacro\theoremheaderfont It is also possible to customize
+% the font used for the theorem headers.  This is, however, a global
+% declaration, and therefore there should be at most one
+% |\theoremheaderfont| declaration in the preamble.\footnote{If it is
+% actually necessary to have different header fonts, one has to define
+% new theorem styles (substituting the desired font) or specify the
+% information directly in the \texttt{\bslash newtheorem} declaration
+% (the unclean variant).}
+%
+% \DescribeMacro\theorempreskipamount
+% \DescribeMacro\theorempostskipamount Two additional parameters
+% affect the vertical space around the theorem environments:
+% |\theorempreskipamount| and |\theorempostskipamount| define,
+% respectively, the spacing before and after such an environment.
+% These parameters apply for all theorem sets and can be manipulated
+% with the ordinary length macros.  They are rubber lengths,
+% (`\textsf{skips}'), and therefore can contain \texttt{plus} and
+% \texttt{minus} parts.
+%
+% Since the definition of theorem sets should---most sensibly---be
+% placed in the preamble, we only allow installation there.
+% It is therefore possible to release the memory used here after
+% |\begin{document}|, in order to make room for other
+% applications.
+%
+%
+% \subsection{Existing theorem styles}
+%
+% The following theorem styles exist to date:
+% \begin{deflist}{marginbreak}
+%    \item[plain]
+%       This theorem style emulates the original \LaTeX{} definition,
+%       except that additionally the parameters
+%       |\theorem...skipamount| are used.
+%    \item[break]
+%       In this style, the theorem header is followed by a line
+%       break.
+%    \item[marginbreak]
+%       The theorem number is set in the margin, and there is a line
+%       break as in \texttt{break}.
+%    \item[changebreak]
+%       Like \texttt{break}, but with header number and text
+%       interchanged.
+%    \item[change]
+%       Header number and text are interchanged, without a line break.
+%    \item[margin]
+%       The number is set in the left margin, without a line break.
+% \end{deflist}
+% All styles (except \texttt{plain}) select |\slshape| as the default
+% |\theorembodyfont|.
+%
+%
+% \subsection{Examples}
+%
+% Given the above theorem sets {\envfont Cor}, {\envfont Exa}
+% and {\envfont Rem},
+% suppose that the preamble also contains the declarations:
+% \begin{verbatim}
+%    \theoremstyle{marginbreak}   \newtheorem{Lem}[Cor]{Lemma}
+%    \theoremstyle{change}
+%    \theorembodyfont{\itshape}        \newtheorem{Def}[Cor]{Definition}
+%
+%    \theoremheaderfont{\scshape}
+%\end{verbatim}
+% Then the following are some typical examples of the typeset output
+% resulting from their use.
+%
+% \begin{Cor}
+%    This is a sentence typeset in the theorem environment {\envfont
+%    Cor}.
+% \end{Cor}
+%
+% \begin{Exa}
+%    This is a sentence typeset in the theorem environment {\envfont
+%    Exa}.
+% \end{Exa}
+%
+% \begin{Rem}
+%    This is a sentence typeset in the theorem environment {\envfont
+%    Rem}.
+% \end{Rem}
+%
+% \begin{Lem}[Ben User]
+%    This is a sentence typeset in the theorem environment {\envfont
+%    Lem}.
+% \end{Lem}
+%
+% \begin{Def}[Very impressive Definition]
+%    This is a sentence typeset in the theorem environment {\envfont
+%    Def}.
+% \end{Def}
+%
+% The last two examples show the effect of the optional argument to
+% a theorem environment (it is the text typeset in parentheses).
+%
+%
+% \section{Special Considerations}
+% \label{sec:newfonts}
+%
+% Theoremheader and body are implemented as a unit. This means that
+% the |\theoremheaderfont|  will inherit characteristics of the
+% |\theorembodyfont| in \LaTeXe. Thus, if for example
+% |\theorembodyfont| is |\itshape| and |\theoremheaderfont|
+% is |\bfseries| the font selected for the header will have the
+% characteristics `bold extended italic'. If this is not desired one
+% should set the |\theoremheaderfont| to something like
+% \begin{verbatim}
+%      \theoremheaderfont{\normalfont\bfseries}
+%\end{verbatim}
+% i.e.\ supplying all necessary font information explicitly.
+%
+%
+%
+% \section{Acknowledgements}
+%
+% The publication of this set of macros was only possible with the
+% help of Christina Busse (translating the manuscript into English),
+% Joachim Pense (playing the r\^ole of typist), Chris Rowley
+% (looking everything over) and many others providing useful
+% suggestions.
+%
+% \StopEventually{%
+%    \begin{thebibliography}{9}
+%       \bibitem{bk:GMS94} \textsc{M.~Goossens}, \textsc{F.~Mittelbach}
+%         and \textsc{A.~Samarin}.
+%         \newblock The \LaTeX{} Companion.
+%         \newblock
+%         Addison-Wesley, Reading, Massachusetts, 1994.
+%       \bibitem{latex:source} \textsc{Lamport, Leslie.} \newblock
+%                               \texttt{latex.tex}, version 2.09, date
+%                               Feb. 1990.
+%    \end{thebibliography}
+%    \PrintIndex
+%    \PrintChanges}
+%
+%
+% \section{The documentation driver file}
+%
+% The next bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the
+% \texttt{docstrip} program. Since it is the first code in the file
+% one can alternatively process this file directly with \LaTeXe{} to
+% obtain the documentation.
+%
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+
+\usepackage{theorem}
+
+%<+driver>% The next few lines define theorem sets which are used
+%<+driver>% in the example section of the documentation.
+
+\theoremstyle{break}       \newtheorem{Cor}{Corollary}
+\theoremstyle{plain}       \newtheorem{Exa}{Example}[section]
+{\theorembodyfont{\upshape}\newtheorem{Rem}{Remark}}
+\theoremstyle{marginbreak} \newtheorem{Lem}[Cor]{Lemma}
+\theoremstyle{change}
+\theorembodyfont{\itshape} \newtheorem{Def}[Cor]{Definition}
+
+\theoremheaderfont{\scshape}
+
+\RecordChanges
+
+\begin{document}
+   \DocInput{theorem.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+% \section{Definition of the Macros}
+%
+% If the file has been loaded before, we abort immediately. If not the
+% package announces itself (this is actually done at the very top if
+% the file---the way it is done isn't good style so don't copy it).
+% \changes{v2.0e}{89/07/19}{Spaces removed from `typeout'.}
+% \changes{v2.2b}{95/11/19}{Announce moved to top of file}
+%    \begin{macrocode}
+%<*package>
+%\@ifundefined{theorem@style}{}{\endinput}
+%\def\FMithmInfo{1995/11/19 v2.2b Theorem extension package (FMi)}
+%\ProvidesPackage{theorem}[\FMithmInfo]
+%    \end{macrocode}
+%
+%
+% \subsection{Definition of theorem styles and fonts}
+%
+% All the definitions in this file are done globally to allow
+% inputting this file inside a group.
+%
+% \begin{macro}{\theoremstyle}
+%    Before a theorem style can be installed, the chosen style must be
+%    known. For that reason, we must test to see that
+%    |\th@|\meta{style} is known or, more precisely, that it is
+%    different from |\relax|. If the style is not known then
+%    |\th@plain| is used.
+%    \begin{macrocode}
+\gdef\theoremstyle#1{%
+   \@ifundefined{th@#1}{\@warning
+          {Unknown theoremstyle `#1'. Using `plain'}%
+          \theorem@style{plain}}%
+%    \end{macrocode}
+%    We save the theorem style to be used in the token register
+%    |\theorem@style|.
+%    \begin{macrocode}
+      {\theorem@style{#1}}%
+%    \end{macrocode}
+%    Now we ``evaluate'' the theorem style: this means, we call the
+%    macro |\th@|\meta{style} which will activate the relevant
+%    definitions which are contained in a separate file.  This is done
+%    in a group to suppress changes to the current font.  This could
+%    otherwise pose problems together with the new font selection
+%    scheme\footnote{When I printed the original article using the new
+%    font selection scheme I ended with a document with slanted
+%    typefaces (text headings and all) simply because one of the
+%    theorem styles used \texttt{\bslash sl} at toplevel.} if the
+%    |\th@|\meta{style} is evaluated a second time.
+% \changes{v2.1a}{90/02/15}{Group added around `th@..}
+% \changes{v2.1a}{90/02/15}{Reseting of `..@begintheorem removed.}
+%    \begin{macrocode}
+      \begingroup
+        \csname th@\the\theorem@style \endcsname
+      \endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@begintheorem}
+% \changes{v2.1a}{90/02/15}{Relaxed at toplevel.}
+% \begin{macro}{\@opargbegintheorem}
+% \changes{v2.1a}{90/02/15}{Relaxed at toplevel.}
+%    We reset |\@begintheorem| and |\@opargbegintheorem| to
+%    |\relax| since these commands are no longer necessary at
+%    toplevel. This will save a few tokens.
+%    \begin{macrocode}
+\global\let\@begintheorem\relax
+\global\let\@opargbegintheorem\relax
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\theorem@style}
+%    Obviously the \textsf{token} register used above has to be
+%    allocated. To assure the utmost compatibility with the
+%    original \LaTeX{} definition, we set the default theorem style to
+%    \texttt{plain}, which implements the usual \LaTeX{} convention.
+% \changes{v2.0f}{89/07/20}{Unnecessary `global' removed.}
+%    \begin{macrocode}
+\newtoks\theorem@style
+\global\theorem@style{plain}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\theorembodyfont}
+% \begin{macro}{\theorem@bodyfont}
+%    If the |\theorembodyfont| is set by the user then it should not
+%    interact with the default font set in the theorem style. When the
+%    new font selection is in force this may happen if, for example,
+%    the default is |\itshape| and the new |\theorembodyfont| is
+%    |\sffamily|. So we add a |\reset@font| command in front of the
+%    user definition.
+% \changes{v2.0f}{89/07/20}{Unnecessary `global' removed.}
+% \changes{v2.0g}{89/09/19}{`theoremfont to `theorembodyfont.}
+% \changes{v2.1c}{92/06/22}{`reset@font added and logic changed.}
+% \changes{v2.1d}{92/10/28}{Reset to empty if arg is empty}
+%    \begin{macrocode}
+\gdef\theorembodyfont#1{%
+%    \end{macrocode}
+%    We check if the argument supplied is empty and if so put nothing
+%    into the |\theorem@bodyfont| token register to allow for
+%    |\theorembodyfont{}| as a mean of using the default of the
+%    current |\theoremstyle|.
+%    \begin{macrocode}
+   \def\@tempa{#1}%
+   \ifx\@tempa\@empty
+    \theorem@bodyfont{}%
+   \else
+    \theorem@bodyfont{\reset@font#1}%
+   \fi
+   }
+\newtoks\theorem@bodyfont
+\global\theorem@bodyfont{}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\theoremheaderfont}
+% \changes{v2.0g}{89/09/19}{Macro added.}
+%    The font for the theorem headers is handled differently because
+%    this definition applies to all theorem styles.
+%    \begin{macrocode}
+\gdef\theoremheaderfont#1{\gdef\theorem@headerfont{#1}%
+%    \end{macrocode}
+%    After using the macro once it is redefined to produce an error
+%    message.
+%    \begin{macrocode}
+       \gdef\theoremheaderfont##1{%
+        \typeout{\string\theoremheaderfont\space should be used
+                 only once.}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\theorem@headerfont}
+% \changes{v2.0g}{89/09/19}{Macro added.}
+%    To set the |\theorem@headerfont| default we first test if
+%    the new fontselection scheme is in force.
+% \changes{v2.1a}{90/02/15}{Support for new font selection.}
+%    \begin{macrocode}
+\ifx\upshape\undefined
+%    \end{macrocode}
+%    If not we define it to expand into |\bfseries|. We don't use
+%    |\let| just in case a following style option redefines this
+%    macro.
+%    \begin{macrocode}
+\gdef\theorem@headerfont{\bfseries}
+%    \end{macrocode}
+%    Otherwise we reset the current shape before calling |\bfseries|.
+%    \begin{macrocode}
+\else \gdef\theorem@headerfont{\normalfont\bfseries}\fi
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\th@plain}
+% \begin{macro}{\th@break}
+% \begin{macro}{\th@marginbreak}
+% \begin{macro}{\th@changebreak}
+% \begin{macro}{\th@change}
+% \begin{macro}{\th@margin}
+%    The different styles are defined in macros such as
+%    |\th@plain|.  Since memory space is precious in
+%    ``non-Big-versions'', we have to avoid offering too many unused
+%    definitions.  Therefore we define these styles in separate files
+%    that can be loaded on demand.  Thus the commands themselves only
+%    load these files. We use |\@input@| a \LaTeXe{} internal command
+%    that ensures that the file will be listed with |\listfiles|
+% \changes{v2.2a}{94/02/02}{Use `@input@ to load theorem layout files}
+%    \begin{macrocode}
+\gdef\th@plain{\@input@{thp.sty}}
+\gdef\th@break{\@input@{thb.sty}}
+\gdef\th@marginbreak{\@input@{thmb.sty}}
+\gdef\th@changebreak{\@input@{thcb.sty}}
+\gdef\th@change{\@input@{thc.sty}}
+\gdef\th@margin{\@input@{thm.sty}}
+%    \end{macrocode}
+%    This list will be expanded when new styles become
+%    available.  For testing,  just append new theorem substyles
+%    as document options.
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \subsection{Definition of a new theorem set}
+%
+% As already pointed out, a new theorem environment can be defined in
+% three different ways:
+% \begin{verbatim}
+%    \newtheorem{Lem}{Lemma}
+%    \newtheorem{Lem}{Lemma}[section]
+%    \newtheorem{Lem}[Theorem]{Lemma}
+%\end{verbatim}
+% The function of the macro |\newtheorem| is to recognize these cases
+% and then to branch into one of the three macros |\@ynthm|, |\@xnthm|
+% or |\@othm|.  This mechanism is adopted unchanged from
+% \cite{latex:source}; the essential point here is that, for example,
+% in the second case, the arguments \texttt{Lem}, \texttt{Lemma} and
+% \texttt{section} are passed over to the macro |\@xnthm|.
+%
+% We inspect this case first because the others present fewer problems,
+% and thus are easily derived from this one.
+%
+% \begin{macro}{\@xnthm}
+%    For our example arguments, the macro |\@xnthm| must fulfill
+%    the following:
+%    \begin{itemize}
+%       \item
+%          Define a new \LaTeX-counter `Lem'
+%       \item
+%          reset this counter within a |\section|
+%       \item
+%          define the macro |\theLem|
+%       \item
+%          define the environment macros |\Lem| and
+%          |\endLem| using the current
+%          |\theoremstyle| and |\theorem@bodyfont|.
+%    \end{itemize}
+%    Obviously, all this should happen only if the first argument
+%    of |\@xnthm| (i.e.\ \texttt{Lem} in our example) is chosen so
+%    as not to conflict with any previously defined commands or
+%    environments.  This test is performed by the \LaTeX{} macro
+%    |\@ifdefinable|.
+%    \begin{macrocode}
+\gdef\@xnthm#1#2[#3]{\expandafter\@ifdefinable\csname #1\endcsname
+%    \end{macrocode}
+%    Therefore, the first argument of |\@ifdefinable| is the
+%    expansion (in the example, |\Lem|) of
+%    |\csname||#1\endcsname|.  The second argument is
+%    executed only if the test has been completed successfully.
+%    \begin{macrocode}
+   {%
+%    \end{macrocode}
+%    Now we define the new counter. The names of the \LaTeX{}
+%    macros employed should speak for themselves:
+% \changes{v2.2b}{1995/10/07}{Use \cs{@newctr}}
+% \changes{v2.2c}{1995/11/23}{Use \cs{@newctr} properly.}
+%    \begin{macrocode}
+    \@definecounter{#1}\@newctr{#1}[#3]%
+%    \end{macrocode}
+%    Using |\@newctr| will give a proper error message if the counter
+%    in |#3| is not defined.
+%    In defining `|\theLem|' we must generate the desired macro
+%    name by use of |\expandafter| and |\csname|.
+%    \begin{macrocode}
+    \expandafter\xdef\csname the#1\endcsname
+%    \end{macrocode}
+%    An |\xdef| is used in order to make the definition global,
+%    and to ensure that it contains the replacement texts of
+%    |\@thmcountersep| and |\@thmcounter|.\footnote{These
+%    two macros can be defined by the document style.  Their default
+%    values produce a `\texttt{.}' as separation and an arabic
+%    representation of the number.} However, not everything should be
+%    expanded. For example, it saves space to use |\thesection|
+%    instead of its---at times---lengthy expansion.
+%    \begin{macrocode}
+      {\expandafter \noexpand \csname the#3\endcsname
+       \@thmcountersep \@thmcounter{#1}}%
+%    \end{macrocode}
+%    Thus with the defaults of \LaTeX{}, |\theLem| would be
+%    replaced by the command sequence |\thesection.\arabic{Lem}|.
+%
+%    We will now look at the definition of the macro which is executed
+%    at the beginning of the actual environment (in our example this
+%    macro is |\Lem|). It should be noted that we use an
+%    ``|\expandafter| trick'' to expand only certain parts of the
+%    replacement text at the time of the definition.
+%    \begin{macrocode}
+    \def\@tempa{\global\@namedef{#1}}%
+    \expandafter \@tempa \expandafter{%
+%    \end{macrocode}
+%    First, the macro that contains the current definitions of
+%    |\@begintheorem| and |\@opargtheorem| should be called
+%    up.  The name of this macro---as is already known---has the form
+%    |\th@|\meta{theorem\ style}; therefore, it must be called by
+%    \begin{macrocode}
+      \csname th@\the \theorem@style
+%    \end{macrocode}
+%    In addition the default theorem font should be changeable, i.e.\
+%    we have to insert the contents of |\theorem@bodyfont|. For
+%    that reason, we expand even further, beyond |\endcsname|,
+%    and thus insert the contents of the \textsf{token} register
+%    |\theorem@bodyfont| in the replacement text.
+%    \begin{macrocode}
+            \expandafter \endcsname \the \theorem@bodyfont
+%    \end{macrocode}
+%    Now it is time to call the macro |\@thm| which takes over
+%    the further processing.  It has two arguments: the current
+%    counter name (in our example, \texttt{Lem}), and the text of the
+%    label (in our example, \texttt{Lemma}).
+%    \begin{macrocode}
+     \@thm{#1}{#2}}%
+%    \end{macrocode}
+%    With this, the `sub-definition' is complete.  The macro
+%    |\@endtheorem| ends a theorem environment and is, so far, nothing
+%    but an |\endtrivlist|.  (Hence it is defined globally, and not
+%    within the theorem styles.\footnote{This has to be changed as
+%    soon as theorem styles that change \texttt{\bslash @endtheorem}
+%    exist.  In such a case, all existing styles must be changed as
+%    well since they will have to reset the macro.}) Therefore, we can
+%    set it equivalent to the macro that ends the theorem set (in our
+%    example, |\endLem|).  However, if some day theorem styles exist
+%    that do change |\@endtheorem|, we would have to use the
+%    commented-out line instead.
+%    \begin{macrocode}
+    \global \expandafter \let \csname end#1\endcsname \@endtheorem
+%   \global\@namedef{end#1}{\@endtheorem}%
+%    \end{macrocode}
+%    With these commands all the required definitions are employed,
+%    unless the test |\@ifdefinable| has failed.  Therefore, we
+%    end the second argument of this macro and with it the definition
+%    of |\@xnthm|.
+%    \begin{macrocode}
+   }}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@ynthm}
+%    The definition of |\@ynthm| is completely analogous. In
+%    this case the new counter that is defined is not reset within
+%    another counter; thus the definition of |\the...|
+%    is simplified:
+%    \begin{macrocode}
+\gdef\@ynthm#1#2{\expandafter\@ifdefinable\csname #1\endcsname
+   {\@definecounter{#1}%
+    \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+%    \end{macrocode}
+%    The rest of the definition corresponds literally to that of
+%    |\@xnthm|:
+%    \begin{macrocode}
+    \def\@tempa{\global\@namedef{#1}}\expandafter \@tempa
+     \expandafter{\csname th@\the \theorem@style \expandafter
+     \endcsname \the\theorem@bodyfont \@thm{#1}{#2}}%
+    \global \expandafter \let \csname end#1\endcsname \@endtheorem}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@othm}
+%    The definition of |\@othm| does not contain anything new.
+%    \begin{macrocode}
+\gdef\@othm#1[#2]#3{%
+%    \end{macrocode}
+% \changes{v2.2b}{95/10/07}{Build in check for counter defined}
+%    We do not define a new counter but instead use one that has
+%    already been defined.  Thus the only definition we need is that
+%    of this pseudo-counter (i.e.\ |\the|\meta{env.\ name}).
+%    First we check if |#2| corresponds to a known counter name.
+%    \begin{macrocode}
+  \expandafter\ifx\csname c@#2\endcsname\relax
+   \@nocounterr{#2}%
+  \else
+   \expandafter\@ifdefinable\csname #1\endcsname
+   {\expandafter \xdef \csname the#1\endcsname
+     {\expandafter \noexpand \csname the#2\endcsname}%
+%    \end{macrocode}
+%    All other parts of the definition can be adopted from
+%    |\@xnthm|. We have to remember, though, that in this case
+%    the name of the current counter and the theorem label have moved
+%    to the second and third arguments.
+%    \begin{macrocode}
+    \def\@tempa{\global\@namedef{#1}}\expandafter \@tempa
+     \expandafter{\csname th@\the \theorem@style \expandafter
+     \endcsname \the\theorem@bodyfont \@thm{#2}{#3}}%
+    \global \expandafter \let \csname end#1\endcsname \@endtheorem}%
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Macros that are employed in a {\envfont theorem}
+%    environment}
+%
+% \begin{macro}{\@thm}
+%    The macro |\@thm| has to increase the current counter.  Then,
+%    depending on whether the environment has (or does not have) an
+%    optional argument, it has to branch into either |\@begintheorem|
+%    or |\@opargtheorem|.
+%    \begin{macrocode}
+\gdef\@thm#1#2{\refstepcounter{#1}%
+%    \end{macrocode}
+%    Now we start a {\envfont trivlist} environment, and give
+%    |\@topsep| and |\@topsepadd| the values of the \textsf{skip}
+%    registers |\theorempreskipamount| and |\theorempostskipamount|.
+%    The value in |\@topsep| is the vertical space that is inserted by
+%    the first (and only) |\item| in our |\trivlist| whilst
+%    |\@topsepadd| is inserted by |\@endparenv| at the end of that
+%    {\envfont trivlist} environment.  By using these registers, we
+%    obtain the desired space around a {\envfont theorem} environment.
+%    \begin{macrocode}
+   \trivlist
+   \@topsep \theorempreskipamount               % used by first \item
+   \@topsepadd \theorempostskipamount           % used by \@endparenv
+%    \end{macrocode}
+%    Now we have to test whether an optional argument has been given.
+% \changes{v2.0d}{89/07/18}{Forgotten percent added.}
+%    \begin{macrocode}
+   \@ifnextchar [%
+%    \end{macrocode}
+%    If there is an optional argument, we will call |\@ythm|, and
+%    move the arguments read back into the input stream.
+%    \begin{macrocode}
+   {\@ythm{#1}{#2}}%
+%    \end{macrocode}
+%    If not, we call |\@begintheorem|. Its first argument is the
+%    name of the theorem set (hence the second argument of
+%    |\@thm|). Its second argument is the macro that produces the
+%    current number.
+%    \begin{macrocode}
+   {\@begintheorem{#2}{\csname the#1\endcsname}\ignorespaces}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xthm}
+% \begin{macro}{\@ythm}
+%    Both these macros were originally called by |\@thm|.  We do
+%    not need |\@xthm| anymore, hence we reset it to
+%    |\relax|. The definition of |\@ythm| has not changed at
+%    all from its definition in \LaTeX. In order to make the macros
+%    easier to understand, we will
+%    nevertheless present it (commented out).
+%    \begin{macrocode}
+\global\let\@xthm\relax
+% \def\@ythm#1#2[#3]{\@opargbegintheorem{#2}{\csname
+%           the#1\endcsname}{#3}\ignorespaces}
+%</package>
+%    \end{macrocode}
+%    The primitive |\ignorespaces| in |\@ythm| and
+%    |\@thm| is needed to remove the spaces between the
+%    |\begin{...}| and the actual text.
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Definition of the theorem substyles}
+%
+% As already pointed out, the theorem substyles, defined below, are
+% only loaded when necessary.  Note that all these substyles, except
+% \texttt{plain}, have |\slshape| as the default body font.
+%
+% \subsubsection{The \texttt{plain} style}
+%
+% \label{dok:th@plain} As the following macros use |@|, we have
+% to locally set the |\catcode| of this symbol to ``letter''.
+% This happens within a group, so that we do not have to worry about
+% which |\catcode| that symbol had before.
+%    \begin{macrocode}
+%<*thp>
+\begingroup \makeatletter
+%    \end{macrocode}
+% Since we are now within a group, we must make all definitions
+% globally.  First we make sure that \texttt{theorem.sty} is loaded.
+% This will allow us to use this file as a document style option
+% without having to call \texttt{theorem} itself as an option.  At the
+% same time, we assure that at least version 2 is loaded, since
+% |\theorem@style| was not defined in earlier versions.
+%    \begin{macrocode}
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thp.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+%
+% \begin{macro}{\th@plain}
+% \begin{macro}{\@begintheorem}
+% \begin{macro}{\@opargbegintheorem}
+%    |\theoremstyle{plain}| corresponds to the original
+%    definition, except that the distances to the surrounding text are
+%    determined by the parameters |\theorempreskipamount| and
+%    |\theorempostskipamount|.
+%    First we set the default body font.
+%    \begin{macrocode}
+\gdef\th@plain{\normalfont\itshape
+%    \end{macrocode}
+%    Then we define |\@begintheorem| and
+%    |\@opargbegintheorem|. These two macros define how the
+%    header of a theorem is typeset.  |\@opargbegintheorem| will
+%    be called if a \textsf{theorem} environment with an optional
+%    argument is encountered; otherwise, the header is constructed by
+%    calling |\@begintheorem|.  If one of these macros is
+%    executed, we are within a \textsf{trivlist} environment started by
+%    |\@thm|.  So the theorem header is produced with an
+%    |\item| command.
+%
+%    Instead of specifying the header font directly, all standard
+%    theorem styles use the |\theorem@headerfont| macro to allow
+%    customization.  The extra space (|\labelsep|) is necessary
+%    because of problems in the \textsf{trivlist} environment.
+%    \begin{macrocode}
+  \def\@begintheorem##1##2{%
+        \item[\hskip\labelsep \theorem@headerfont ##1\ ##2]}%
+%    \end{macrocode}
+%    The definition of |\@opargbegintheorem| is completely
+%    analogous. The only difference is the fact that there exists a
+%    third argument (which is the optional parameter of the
+%    environment and contains additional information about the
+%    theorem).  Customarily we enclose it in parentheses.
+%    \begin{macrocode}
+\def\@opargbegintheorem##1##2##3{%
+   \item[\hskip\labelsep \theorem@headerfont ##1\ ##2\ (##3)]}}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \noindent
+% We conclude with an |\endgroup| to restore the
+% |\catcode| of |@|.
+%    \begin{macrocode}
+\endgroup
+%</thp>
+%    \end{macrocode}
+%
+%
+% \subsubsection{The \texttt{break} style}
+%
+% This style option is stored in the file |thb.sty|.
+% For the next two lines see the documentation for |\th@plain| on
+% page~\pageref{dok:th@plain}.
+%    \begin{macrocode}
+%<*thb>
+\begingroup \makeatletter
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thb.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+% \begin{macro}{\th@break}
+%    |\theoremstyle{break}| produces a line break after the name
+%    of the theorem.  The font is |\slshape|.  Hence, we define
+%    |\th@break| as follows:
+%    \begin{macrocode}
+\gdef\th@break{\normalfont\slshape
+  \def\@begintheorem##1##2{\item[%
+%    \end{macrocode}
+%    We run into the following problem: it is not possible to create
+%    the header with |\item[|\meta{title}|]| and then start
+%    a new line by, for example, |\mbox{}\\|. Such a definition
+%    will fail whenever a list environment follows immediately.  With
+%    the above construction, the |\mbox{}| causes the switch
+%    |@inlabel| (cf.\ definition of |\list| and
+%    |\trivlist| in \cite{latex:source}) to be set to \texttt{false}
+%    and so the following list will insert additional vertical
+%    space (|\topskip|). This is quite annoying. Therefore, we
+%    create the line break within the |\item|. In order to ensure
+%    that the text will begin at the proper position in the following
+%    line, we simply pretend that the label does not take any
+%    room.\footnote{This will lead to problems whenever very high
+%    symbols occurring in the line tower into the
+%    heading. So, something else has to be done here sometime.}
+%    \begin{macrocode}
+       \rlap{\vbox{\hbox{\hskip \labelsep\theorem@headerfont ##1\ ##2}%
+                   \hbox{\strut}}}]}%
+%    \end{macrocode}
+%    Again, the definition of |\@opargbegintheorem| is
+%    completely analogous.
+%    \begin{macrocode}
+\def\@opargbegintheorem##1##2##3{%
+  \item[\rlap{\vbox{\hbox{\hskip \labelsep \theorem@headerfont
+                     ##1\ ##2\ (##3)}%
+                    \hbox{\strut}}}]}}
+\endgroup
+%</thb>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsubsection{The \texttt{changebreak} style}
+%
+%    \begin{macrocode}
+% This style option is stored in the file |thcb.sty|.
+%    \begin{macrocode}
+%<*thcb>
+\begingroup \makeatletter
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thcb.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+% \begin{macro}{\th@changebreak}
+%    The \texttt{change-break} theorem style is like \texttt{break}
+%    but with interchange of theorem name and theorem number.  Thus we
+%    define |\th@changebreak| as follows:
+%    \begin{macrocode}
+\gdef\th@changebreak{\normalfont\slshape
+  \def\@begintheorem##1##2{\item
+       [\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont ##2\ ##1}%
+                    \hbox{\strut}}}]}%
+\def\@opargbegintheorem##1##2##3{%
+  \item[\rlap{\vbox{\hbox{\hskip\labelsep \theorem@headerfont
+                     ##2\ ##1\ (##3)}%
+                    \hbox{\strut}}}]}}
+\endgroup
+%</thcb>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsubsection{The \texttt{change} style}
+%
+% This style option is stored in the file |thc.sty|.
+%    \begin{macrocode}
+%<*thc>
+\begingroup \makeatletter
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thc.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+% \begin{macro}{\th@change}
+%    The \texttt{change} theorem style corresponds to the
+%    \texttt{change break} style without a linebreak after the header.
+%    To say it in another way, it's the same as the \texttt{plain}
+%    style but with number and name interchanged and |\slshape| as the
+%    default font.
+%    \begin{macrocode}
+\gdef\th@change{\normalfont\slshape
+  \def\@begintheorem##1##2{\item
+       [\hskip\labelsep \theorem@headerfont ##2\ ##1]}%
+\def\@opargbegintheorem##1##2##3{%
+  \item[\hskip\labelsep \theorem@headerfont ##2\ ##1\ (##3)]}}
+\endgroup
+%</thc>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsubsection{The \texttt{marginbreak} style}
+%
+% This style option is the one used most often at Mainz.  It is saved
+% in the file |thmb.sty|.
+%    \begin{macrocode}
+%<*thmb>
+\begingroup \makeatletter
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thmb.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+% \begin{macro}{\th@marginbreak}
+%    The \texttt{margin break} style is nearly the same as the
+%    \texttt{change break} style. The only difference is the placement
+%    of the theorem number.  We use |\llap| to place it in the left
+%    margin.
+%
+%    In this style |\labelsep| denotes the separation between the
+%    number and the text.
+%    \begin{macrocode}
+\gdef\th@marginbreak{\normalfont\slshape
+  \def\@begintheorem##1##2{\item
+       [\rlap{\vbox{\theorem@headerfont
+                    \hbox{\llap{##2}\hskip\labelsep ##1}%
+                    \hbox{\strut}}}]}%
+\def\@opargbegintheorem##1##2##3{%
+  \item[\rlap{\vbox{\theorem@headerfont
+                    \hbox{\llap{##2}\hskip\labelsep ##1\ (##3)}%
+                    \hbox{\strut}}}]}}
+\endgroup
+%</thmb>
+%    \end{macrocode}
+% \changes{v2.1c}{90/02/17}{`endgroup outside macrocode env.}
+% \end{macro}
+%
+%
+%
+% \subsubsection{The \texttt{margin} style}
+%
+% This style option is stored in the file |thm.sty|.
+%    \begin{macrocode}
+%<*thm>
+\begingroup \makeatletter
+\@ifundefined{theorem@style}{\input{theorem.sty}}{}
+\ProvidesFile{thm.sty}
+             [\FMithmInfo]
+%    \end{macrocode}
+%
+% \begin{macro}{\th@margin}
+%    Again this is only a variant of the theorem styles described
+%    above without any new ideas.
+%    \begin{macrocode}
+\gdef\th@margin{\normalfont\slshape
+  \def\@begintheorem##1##2{\item
+       [\theorem@headerfont \llap{##2}\hskip\labelsep ##1]}%
+\def\@opargbegintheorem##1##2##3{%
+  \item[\theorem@headerfont \llap{##2}\hskip\labelsep ##1\ (##3)]}}
+\endgroup
+%</thm>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+%
+% \subsection{Final Definitions}
+%
+% \begin{macro}{\theorempreskipamount}
+% \begin{macro}{\theorempostskipamount}
+%    The \textsf{skip} parameters that regulate the vertical empty space
+%    before and after the {\envfont theorem} environment have
+%    to be allocated as well.
+% \changes{v2.0f}{89/07/20}{Unnecessary `global' removed.}
+%    \begin{macrocode}
+%<*package>
+\newskip\theorempreskipamount
+\newskip\theorempostskipamount
+%    \end{macrocode}
+%    Since we have used the same values for all theorem sets, we now can
+%    assign them.
+%    \begin{macrocode}
+\global\setlength\theorempreskipamount{12pt plus 5pt minus 3pt}
+\global\setlength\theorempostskipamount{8pt plus 3pt minus 1.5pt}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\@endtheorem}
+%    The same holds for the macro |\@endtheorem|, which ends a
+%    {\envfont theorem} environment. Since it is the same for all
+%    theorem sets, it is removed from the macros |\th@|\meta{style}.
+%    It simply ends the {\envfont trivlist} environment, which was
+%    begun in |\@thm|.
+%    \begin{macrocode}
+\global\let\@endtheorem=\endtrivlist
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}{\@preamblecmds}
+%    All macros defined above are to be used only in the preamble.
+%    Therefore, we insert them in |\@preamblecmds| which will disable
+%    them at begin document. This is done by the internal \LaTeXe{}
+%    command |\@onlypreamble|.
+% \changes{v2.0g}{89/09/19}{`theoremheaderfont and `theorembodyfont
+%    added.}
+% \changes{v2.2a}{94/02/03}{Use \LaTeXe{} interface}
+%    \begin{macrocode}
+\@onlypreamble\@xnthm
+\@onlypreamble\@ynthm
+\@onlypreamble\@othm
+\@onlypreamble\newtheorem
+\@onlypreamble\theoremstyle
+\@onlypreamble\theorembodyfont
+\@onlypreamble\theoremheaderfont
+%    \end{macrocode}
+% \end{macro}
+%
+% Finally we declare the \texttt{plain} theorem style to be the default.
+% \changes{v2.1b}{90/06/04}{Fixed missing `item by declaring default
+%    style.}
+%    \begin{macrocode}
+\theoremstyle{plain}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+
+\endinput
diff --git a/macros/latex-dev/required/tools/theorem.pdf b/macros/latex-dev/required/tools/theorem.pdf
new file mode 100644
index 0000000000..0d14dda327
--- /dev/null
+++ b/macros/latex-dev/required/tools/theorem.pdf
diff --git a/macros/latex-dev/required/tools/tools-overview.pdf b/macros/latex-dev/required/tools/tools-overview.pdf
new file mode 100644
index 0000000000..9e651744df
--- /dev/null
+++ b/macros/latex-dev/required/tools/tools-overview.pdf
diff --git a/macros/latex-dev/required/tools/tools-overview.tex b/macros/latex-dev/required/tools/tools-overview.tex
new file mode 100644
index 0000000000..6a00580302
--- /dev/null
+++ b/macros/latex-dev/required/tools/tools-overview.tex
@@ -0,0 +1,217 @@
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesFile{tools-overview.tex}[2015/03/31 v1.0 Tools overview]
+
+% Copyright (C) 2006-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% Copyright (c) 2006-2014 Heiko Oberdiek
+%           (c) 2015-2019 The LaTeX3 Project
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% This file is derived from `tools.tex' and `tools-overview.cls'
+% from the `latex-tds' bundle maintained by Heiko Oberdiek.
+%
+\documentclass[a4paper,12pt]{article}
+
+% page layout
+\usepackage[
+  ignoreall,
+  hmargin=1in,
+  vmargin={.75in,1in},
+]{geometry}
+
+\pagestyle{empty}
+
+\usepackage{calc}[2005/08/06]
+
+\usepackage{hyperref}
+\hypersetup{
+  colorlinks,
+  filecolor=blue,
+  pdftitle={LaTeX's Tools Bundle},
+  pdfsubject={Overview},
+  pdfauthor={Heiko Oberdiek},
+  pdfcreator={Project `latex-tds'},
+}
+\title{Contents of \LaTeX's Tools Bundle}
+
+\makeatletter
+
+\let\TO@document\document
+\let\TO@enddocument\enddocument
+
+\def\document{%
+  \TO@document
+  \maketitle
+  \toks@={}%
+  \setlength{\maxlen}{0pt}%
+}
+\newlength{\maxlen}
+\def\enddocument{%
+  \begin{list}{}{%
+    \setlength{\leftmargin}{\maxlen + \labelsep}%
+    \setlength{\labelwidth}{\maxlen}%
+    \setlength{\partopsep}{0pt}%
+  }%
+    \the\toks@
+  \end{list}%
+  \TO@enddocument
+}
+\newcommand{\entry}[2]{%
+  \outline{#1}%
+  \toks@\expandafter{%
+    \the\toks@
+    \item[%
+      \href{file:#1.pdf}{\printpackage{#1}}%
+      \hfill
+    ]%
+    #2%
+  }%
+  \setlength{\maxlen}{%
+    \maxof{\maxlen}{\widthof{\printpackage{#1}}}%
+  }%
+  \global\maxlen\maxlen
+}
+\newcommand*{\printpackage}[1]{%
+  \textbf{\large #1:}%
+}
+\newcommand*{\outline}[1]{%
+  \pdfoutline
+    attr {/C[0 0 1]}
+    user {%
+      <<%
+        /S/GoToR%
+        /F(#1.pdf)%
+        /NewWindow true%
+        /D[0/XYZ null null null]%
+      >>%
+    }%
+  {[#1]}\relax
+}
+\renewcommand*{\maketitle}{%
+  \begingroup
+    \par
+    \centering
+    \bfseries
+    \LARGE
+    \@title
+    \par
+  \endgroup
+  \vspace{2em}%
+}
+
+\providecommand*{\cs}[1]{%
+  \texttt{\textbackslash#1}%
+}
+
+\makeatother
+
+\begin{document}
+\entry{afterpage}{%
+  Place text after the current page.
+}%
+\entry{array}{%
+  Extended versions of the environments array, tabular and tabular*.
+}%
+\entry{bm}{%
+  Access bold math symbols.
+}%
+\entry{calc}{%
+  Infix arithmetic expresions. Contributed to the distribution by
+  Kresten Krab Thorup and Frank Jensen.
+}%
+\entry{dcolumn}{%
+  Alignment on \emph{decimal points} in tabular entries. Requires array.
+}%
+\entry{delarray}{%
+  Adds \emph{large delimiters} around arrays. Requires array.
+}%
+\entry{enumerate}{%
+  Extended version of the enumerate environment.
+}%
+\entry{fileerr}{%
+  Suite of small files which may be used to control \TeX{}'s
+  missing file error loop.
+}%
+\entry{fontsmpl}{%
+  Package and test file for producing \emph{font samples}
+}%
+\entry{ftnright}{%
+  Place footnotes in the right hand column in two-column mode.
+}%
+\entry{hhline}{%
+  Finer control over horizontal rules in tables. Requires array.
+}%
+\entry{indentfirst}{%
+  Indent the first paragraph of sections etc.
+}%
+\entry{layout}{%
+  Produces an overview of the layout of the current document.
+}%
+\entry{longtable}{%
+  Multipage tables. (Does not require array, but uses the extended
+  features if both are loaded.)
+}%
+\entry{multicol}{%
+  Typeset text in columns, with the length of the final columns
+  \emph{balanced}.
+}%
+\entry{rawfonts}{%
+  Preload fonts under the old internal font names of \LaTeX{}2.09.
+  Not recomended for new packages, but may help when updating old
+  files.
+}%
+\entry{shellesc}{%
+ Unified interface to ``shell escape'' i.e., access to system commands
+ based on \texttt{\string\write18} or \texttt{os.execute} depending
+ on the system in use.
+}%
+\entry{showkeys}{%
+  Draft mode showing the \emph{keys} used by \cs{label}, \cs{ref}, \cs{cite} etc.
+}%
+\entry{somedefs}{%
+  Selective handling of package options. (Used in rawfonts.sty.)
+}%
+\entry{tabularx}{%
+  Defines tabularx environment (similar to tabular*) but modifies
+  column widths, not inter-column space, to achieve a desired
+  table width.
+}%
+\entry{theorem}{%
+  Flexible definition of \emph{theorem-like} environments.
+}%
+\entry{trace}{%
+  The package helps to suppress and to control the amount of tracing
+  output (\cs{tracingall}) by taming calc and making NFSS less noisy.
+}%
+\entry{varioref}{%
+  \emph{Smart} handling of page references.
+}%
+\entry{verbatim}{%
+  Flexible version of verbatim environment.
+}%
+\entry{xr}{%
+  eXternall References. Extend \cs{ref} to access \cs{label} commands in
+  other documents.
+}%
+\entry{xspace}{%
+  Smart space command that avoids the common mistake of missing
+  spaces after command names.
+}%
+
+\end{document}
diff --git a/macros/latex-dev/required/tools/tools.ins b/macros/latex-dev/required/tools/tools.ins
new file mode 100644
index 0000000000..12625e8166
--- /dev/null
+++ b/macros/latex-dev/required/tools/tools.ins
@@ -0,0 +1,217 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2005/12/01 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\def\SimplePackage#1{%
+  \generate{\file{#1.sty}{\from{#1.dtx}{package}}}}
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+% Array files
+%%%%%%%%%%%%%
+\generate{\file{array.sty}{\from{array.dtx}{package,ncols}}}
+
+\SimplePackage{delarray}
+
+\batchinput{tabularx.ins}
+
+\SimplePackage{dcolumn}
+
+\SimplePackage{hhline}
+
+\batchinput{longtable.ins}
+
+% Multicolumn
+%%%%%%%%%%%%%
+\batchinput{multicol.ins}
+
+% Bold Math Symbols
+%%%%%%%%%%%%%%%%%%%
+\batchinput{bm.ins}
+
+% Footnote Right
+%%%%%%%%%%%%%%%
+\SimplePackage{ftnright}
+
+% Theorem files
+%%%%%%%%%%%%%%%
+\generate{%
+  \file{theorem.sty}{\from{theorem.dtx}{package}}
+  \file{thb.sty}{\from{theorem.dtx}{thb}}
+  \file{thcb.sty}{\from{theorem.dtx}{thcb}}
+  \file{thc.sty}{\from{theorem.dtx}{thc}}
+  \file{thp.sty}{\from{theorem.dtx}{thp}}
+  \file{thmb.sty}{\from{theorem.dtx}{thmb}}
+  \file{thm.sty}{\from{theorem.dtx}{thm}}}
+
+% Verbatim
+%%%%%%%%%%
+\generate{%
+  \file{verbatim.sty}{\from{verbatim.dtx}{package}}
+  \file{verbtest.tex}{\from{verbatim.dtx}{testdriver}}}
+
+% Smart Page references
+%%%%%%%%%%%%%%%%%%%%%%%
+\batchinput{varioref.ins}
+
+% External references
+%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{xr}
+
+% Smart Space command
+%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{xspace}
+
+% Show \label \ref keys
+%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{showkeys}
+
+% Load fonts under old names
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{rawfonts}
+
+% Selective Option handling
+%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{somedefs}
+
+
+% Font sample
+%%%%%%%%%%%%%
+\generate{%
+  \file{fontsmpl.sty}{\from{fontsmpl.dtx}{package}}
+  \file{fontsmpl.tex}{\from{fontsmpl.dtx}{document}}}
+
+% After Page Package
+%%%%%%%%%%%%%%%%%%%%
+\batchinput{afterpage.ins}
+
+% Enumerate Package
+%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{enumerate}
+
+
+% Indent first paragraphs
+%%%%%%%%%%%%%%%%%%%
+\SimplePackage{indentfirst}
+
+
+% Show the layout of a document class
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{layout}
+
+
+% Infix Arithmetic 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{calc}
+
+% Debugging
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{trace}
+
+% Shell Escape
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\SimplePackage{shellesc}
+
+% File-Error files
+%%%%%%%%%%%%%%%%%%
+\generate{%
+  \file{h.tex}{\from{fileerr.dtx}{help}}
+  \file{s.tex}{\from{fileerr.dtx}{scroll}}
+  \file{e.tex}{\from{fileerr.dtx}{edit}}
+  \file{q.tex}{\from{fileerr.dtx}{batch}}
+  \file{r.tex}{\from{fileerr.dtx}{run}}
+  \file{x.tex}{\from{fileerr.dtx}{exit}}}
+
+
+\Msg{***********************************************************}
+\Msg{*}
+\Msg{* To finish the installation you have to move the following}
+\Msg{* files into a directory searched by TeX:}
+\Msg{*}
+\Msg{* All the files with extension `.sty' and `.tex'}
+\Msg{* Note there also may be a file .tex which is `invisible'}
+\Msg{* on some operating systems.}
+\Msg{*}
+\Msg{* To produce the documentation run the .dtx files through LaTeX.}
+\Msg{*}
+\Msg{* Happy TeXing}
+\Msg{***********************************************************}
+
+
+\Msg{}
+\Msg{* Finally trying to make a file `.tex'.}
+\Msg{* (Placed at the end of this run, as this}
+\Msg{*  may fail on some operating systems.)}
+
+\let\oldopenout\openout
+\def\openout{\batchmode\immediate\oldopenout}
+
+\generate{\file{.tex}{\from{fileerr.dtx}{return}}}
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/trace.dtx b/macros/latex-dev/required/tools/trace.dtx
new file mode 100644
index 0000000000..e808fdd431
--- /dev/null
+++ b/macros/latex-dev/required/tools/trace.dtx
@@ -0,0 +1,733 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%%
+%% (C) Copyright (C) 1999-2019 Frank Mittelbach
+%% All rights reserved.
+%%
+%<*dtx>
+          \ProvidesFile{trace.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{trace}
+%<driver>\ProvidesFile{trace.drv}
+% \fi
+%         \ProvidesFile{trace.dtx}
+          [2018/10/13 v1.1e trace LaTeX code]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{doc}
+\setcounter{StandardModuleDepth}{1}
+
+\usepackage{shortvrb}
+\MakeShortVerb\|
+
+\DeclareRobustCommand\eTeX{\ensuremath{\varepsilon}-\kern-.125em\TeX}
+
+\begin{document}
+\DocInput{trace.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+%
+% \GetFileInfo{trace.dtx}
+%
+% \title{The \textsf{trace} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}}
+% \author{Frank Mittelbach}
+% \date{\filedate}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+%
+% \section{Introduction}
+%
+% When writing new macros one often finds that they do not work as
+% expected (at least I do :-). If this happens and one can't
+% immediately figure out why there is a problem one has to start doing
+% some serious debugging. \TeX{} offers a lot of bells and whistles to
+% control what is being traced but often enough I find myself applying
+% the crude command |\tracingall| which essentially means ``give me
+% whatever tracing information is available''.
+%
+% In fact I normally use \eTeX{} in such a case, since that \TeX{}
+% extension offers me a number of additional tracing possibilities
+% which I find extremely helpful. The most important ones are
+% |\tracingassigns|, which will show you changes to register values
+% and changes to control sequences when they happen, and
+% |\tracinggroups|, which will tell you what groups are entered
+% or left (very useful if your grouping got out of sync).
+%
+% So what I really write is
+%\begin{verbatim}
+%  \tracingassigns=1\tracinggroups=1\tracingall
+%\end{verbatim}
+% That in itself is already a nuisance (since it is a mouthful) but
+% there is a worse catch: when using |\tracingall| you do get a awful
+% lot of information and some of it is really useless.
+%
+% For example, if \LaTeX{} has to load a new font it enters some
+% internal routines of NFSS which scan font definition tables etc.
+% And 99.9\% of the time you are not at all interested in that part of the
+% processing but in the two lines before and the five lines
+% after. However, you have to scan through a few hundred lines of
+% output to find the lines you need.
+%
+% Another example is the \texttt{calc} package. A simple statement
+% like |\setlength| |\linewidth| |{1cm}| inside your macro will result
+% in
+%
+% \renewcommand\MacroFont{\fontencoding\encodingdefault
+%                   \fontfamily\ttdefault
+%                   \fontseries\mddefault
+%                   \fontshape\updefault
+%                   \footnotesize}%
+%\begin{verbatim}
+%  \setlength ->\protect \setlength
+%  {\relax}
+%
+%  \setlength  ->\calc@assign@skip
+%
+%  \calc@assign@skip ->\calc@assign@generic \calc@Askip \calc@Bskip
+%
+%  \calc@assign@generic #1#2#3#4->\let \calc@A #1\let \calc@B #2\expandafter \calc
+%  @open \expandafter (#4!\global \calc@A \calc@B \endgroup #3\calc@B
+%  #1<-\calc@Askip
+%  #2<-\calc@Bskip
+%  #3<-\linewidth
+%  #4<-1cm
+%  {\let}
+%  {\let}
+%  {\expandafter}
+%  {\expandafter}
+%
+%  \calc@open (->\begingroup \aftergroup \calc@initB \begingroup \aftergroup \calc
+%  @initB \calc@pre@scan
+%  {\begingroup}
+%  {\aftergroup}
+%  {\begingroup}
+%  {\aftergroup}
+%
+%  \calc@pre@scan #1->\ifx (#1\expandafter \calc@open \else \ifx \widthof #1\expan
+%  dafter \expandafter \expandafter \calc@textsize \else \calc@numeric \fi \fi #1
+%  #1<-1
+%  {\ifx}
+%  {false}
+%  {\ifx}
+%  {false}
+%
+%  \calc@numeric ->\afterassignment \calc@post@scan \global \calc@A
+%  {\afterassignment}
+%  {\global}
+%  {\fi}
+%  {\fi}
+%
+%  \calc@post@scan #1->\ifx #1!\let \calc@next \endgroup \else \ifx #1+\let \calc@
+%  next \calc@add \else \ifx #1-\let \calc@next \calc@subtract \else \ifx #1*\let
+%  \calc@next \calc@multiplyx \else \ifx #1/\let \calc@next \calc@dividex \else \i
+%  fx #1)\let \calc@next \calc@close \else \calc@error #1\fi \fi \fi \fi \fi \fi \
+%  calc@next
+%  #1<-!
+%  {\ifx}
+%  {true}
+%  {\let}
+%  {\else}
+%  {\endgroup}
+%  {restoring \calc@next=undefined}
+%
+%  \calc@initB ->\calc@B \calc@A
+%  {\skip44}
+%  {\global}
+%  {\endgroup}
+%  {restoring \skip44=0.0pt}
+%
+%  \calc@initB ->\calc@B \calc@A
+%  {\skip44}
+%  {\dimen27}
+%\end{verbatim}
+%
+% \noindent Do you still remember what I was talking about?
+%
+% No? We're trying to find a problem in macro code without having to scan
+% too many uninteresting lines. To make this possible we have to
+% redefine a number of key commands to turn tracing off temporarily in
+% the hope that this will reduce the amount of noise during the
+% trace. For example, if we change one of the \texttt{calc} internals
+% slightly, the above tracing output can be reduced to:
+%
+%\begin{verbatim}
+%  \setlength ->\protect \setlength
+%  {\relax}
+%
+%  \setlength  ->\calc@assign@skip
+%
+%  \calc@assign@skip ->\calc@assign@generic \calc@Askip \calc@Bskip
+%
+%  \calc@assign@generic #1#2#3#4->\let \calc@A #1\let \calc@B #2\expandafter \calc
+%  @open \expandafter (#4!\global \calc@A \calc@B \endgroup #3\calc@B
+%  #1<-\calc@Askip
+%  #2<-\calc@Bskip
+%  #3<-\linewidth
+%  #4<-1cm
+%  {\let}
+%  {\let}
+%  {\expandafter}
+%  {\expandafter}
+%
+%  \calc@open (->\begingroup \conditionally@traceoff \aftergroup \calc@initB \begi
+%  ngroup \aftergroup \calc@initB \calc@pre@scan
+%  {\begingroup}
+%
+%  \conditionally@traceoff ->\tracingrestores \z@ \tracingcommands \z@ \tracingpag
+%  es \z@ \tracingmacros \z@ \tracingparagraphs \z@
+%  {\tracingrestores}
+%  {\tracingcommands}
+%  {restoring \tracingrestores=1}
+%
+%  \calc@initB ->\calc@B \calc@A
+%  {\skip44}
+%  {\dimen27}
+%\end{verbatim}
+%
+% \noindent\label{conttraceoffexample}
+% Still a lot of noise but definitely preferable to the
+% original case.
+%
+% I redefined those internals that I found most annoyingly
+% noisy. There are probably many others that could be treated in a
+% similar fashion, so if you think you found one worth adding please
+% drop me a short note.
+%
+% \[ * \quad * \quad * \]
+%
+% \DescribeMacro\traceon
+% \DescribeMacro\traceoff
+% The package defines the two macros |\traceon| and |\traceoff| to
+% unconditionally turn tracing on or off, respectively. |\traceon| is
+% like |\tracingall| but additionally adds |\tracingassigns| and
+% |\tracinggroups| if the \eTeX{} program (in extended mode) is
+% used. And |\traceoff| will turn tracing off again, a command which
+% is already badly missing in plain \TeX{}, since it is often not
+% desirable to restrict the tracing using extra groups in the
+% document.
+%
+% \DescribeMacro\conditionally@traceon
+% \DescribeMacro\conditionally@traceoff
+% There are also two internal macros that turn tracing on and off, but
+% only if the user requested tracing in the first place. These are the
+% ones that are used internally within the code below.
+%
+% Since the package overwrites some internals of other packages you
+% should load it as the last package in your preamble using
+% |\usepackage{trace}|.
+%
+% The package offers the option \texttt{logonly} that suppresses
+% terminal output during tracing (unless |\tracingall| is used). This
+% is useful if the \TeX{} implementation used gets rather slow when
+% writing a lot of information to the terminal.
+%
+% It also offers the option \texttt{full} in which case |\traceon|
+% will trace all parts of the code, i.e., essentially work like
+% |\tracingall|.
+%
+% \section{A sample file}
+%
+% The following small test file shows the benefits of the
+% \texttt{trace} package. If one uncomments the line loading the
+% package, the amount of tracing data will be drastically reduced.
+% Without the \texttt{trace} package we get 6594 lines in the log
+% file; adding the package will reduce this to 1618 lines.
+%
+%\begin{verbatim}
+%  \documentclass{article}
+%  \usepackage{calc}
+%  %\usepackage{trace} % uncomment to see difference
+%
+%  \begin{document}
+%  \ifx\traceon\undefined \tracingall \else \traceon \fi
+%
+%  \setlength\linewidth{1cm}
+%
+%  $foo=\bar a$
+%
+%  \small \texttt{\$}  \stop
+%\end{verbatim}
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \renewcommand\MacroFont{\fontencoding\encodingdefault
+%                   \fontfamily\ttdefault
+%                   \fontseries\mddefault
+%                   \fontshape\updefault
+%                   \small}
+%
+% This package is for use with \LaTeX{} (though something similar
+% could be produced for other formats).
+%    \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}[1998/12/01]
+%    \end{macrocode}
+%
+%    The package has a option that suppresses tracing on the
+%    terminal, i.e., if used will not set |\tracingonline| to
+%    one. This has been added in version 1.1a since some \TeX{}
+%    implementations get rather slow when outputting to a terminal.
+%    \begin{macrocode}
+\DeclareOption{logonly}
+   {\let\tracingonline@p\z@}
+%    \end{macrocode}
+%    The default is showing the tracing information on the terminal.
+%    \begin{macrocode}
+\let\tracingonline@p\@ne
+%    \end{macrocode}
+%
+%    If the option |full| is selected then all code should be traced,
+%    i.e., the commands |\conditionally@traceoff| and
+%    |\conditionally@traceon| should do nothing. We set them to
+%    |\@empty| not |\relax| since the latter might produce a math ord
+%    in certain circumstances.  We also have to make sure that
+%    |\traceon| (as defined further down) is not redefining
+%    |\conditionally@traceoff| again. To make this all work these
+%    redefinitions have to wait until the end of the package.
+%  \changes{v1.1c}{2003/04/30}{Option ``full'' added}
+%    \begin{macrocode}
+\DeclareOption{full}
+    {\AtEndOfPackage{\let\conditionally@traceoff\@empty
+                     \let\conditionally@traceon\@empty
+                     \let\traceon\tr@ce@n
+    }}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\ProcessOptions\relax
+%    \end{macrocode}
+%
+%
+%
+% \begin{macro}{\if@tracing}
+%    We need a switch to determine if we want any tracing at
+%    all. Otherwise, if we use |\traceoff|\ldots|\traceon|
+%    internally, we would unconditionally turn on tracing even when no
+%    tracing was asked for in the first place.
+%    \begin{macrocode}
+\newif\if@tracing
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\traceon}
+%    This macro ensures that |\conditionally@traceoff| is actually
+%    turning off switches (since |\tracinall| might have disabled it)
+%    and then calls |\tr@ce@n| to setup tracing.
+%    \begin{macrocode}
+\def\traceon{\let\conditionally@traceoff\unconditionally@traceoff
+             \tr@ce@n}
+%    \end{macrocode}
+% \end{macro}
+
+% \begin{macro}{\tr@ce@n}
+%  \changes{v1.1c}{2003/04/30}{Macro added}
+% \begin{macro}{\conditionally@traceoff}
+%    As stated in the introduction, the amount of tracing being done
+%    should depend on the formatter we use. Initially first test if we are
+%    running with \eTeX{} in extended mode. In the latter case the command
+%    |\tracinggroups| is defined.
+%    But for a number of years now \LaTeX{} only works with \eTeX{} so
+%    we drop that part of the code. For now I leave it in the file
+%    together with its documentation, but commented out.
+%    \begin{macrocode}
+%\ifx\tracinggroups\undefined
+%    \end{macrocode}
+%
+%    If we are using standard \TeX{} then |\tr@ce@n| is more or less
+%    another name for |\tracingall|. The only differences are that we
+%    set the above |@tracing| switch to true and reorder the
+%    assignments within it somewhat so that it will output no tracing
+%    information about itself. In contrast, |\tracingall| itself produces
+%
+%\begingroup
+%    \renewcommand\MacroFont{\fontencoding\encodingdefault
+%                   \fontfamily\ttdefault
+%                   \fontseries\mddefault
+%                   \fontshape\updefault
+%                   \footnotesize}%
+%\begin{verbatim}
+%  {vertical mode: \tracingstats}
+%  {\tracingpages}
+%  {\tracinglostchars}
+%  {\tracingmacros}
+%  {\tracingparagraphs}
+%  {\tracingrestores}
+%  {\errorcontextlines}
+%
+%  \showoutput ->\tracingoutput \@ne \showboxbreadth \maxdimen \showboxdepth \maxd
+%  imen \errorstopmode \showoverfull
+%  {\tracingoutput}
+%  {\showboxbreadth}
+%  {\showboxdepth}
+%  {\errorstopmode}
+%
+%  \showoverfull ->\tracingonline \@ne
+%  {\tracingonline}
+%\end{verbatim}
+%\endgroup
+%
+%    \noindent Which is quite a lot given that none of it is of any
+%    help to the task at hand. In contrast |\tr@ce@n| will produce
+%    nothing whatsoever since the noise generating switches are set at
+%    the very end.
+%    \begin{macrocode}
+%  \def\tr@ce@n{%
+%    \end{macrocode}
+%    We start by setting the |@tracing| switch to signal that tracing
+%    is asked for. This is then followed by setting the various
+%    tracing primitives of \TeX.
+%    \begin{macrocode}
+%    \@tracingtrue
+%    \tracingstats\tw@
+%    \tracingpages\@ne
+%    \tracinglostchars\@ne
+%    \tracingparagraphs\@ne
+%    \errorcontextlines\maxdimen
+%    \tracingoutput\@ne
+%    \showboxbreadth\maxdimen
+%    \showboxdepth\maxdimen
+%    \errorstopmode
+%    \tracingmacros\tw@
+%    \tracingrestores\@ne
+%    \tracingcommands\tw@
+%    \end{macrocode}
+%    The setting of |\tracingonline| depends on the option
+%    \texttt{logonly}:
+%    \begin{macrocode}
+%    \tracingonline\tracingonline@p
+%  }
+%    \end{macrocode}
+%
+%    Now what should |\conditionally@traceoff| do in this case? Should
+%    it revert all settings changed by |\tr@ce@n|? It should not, since
+%    our goal is to shorten the trace output, thus setting all of the
+%    uninteresting values back makes the output unnecessarily
+%    longer. Therefore we restrict ourselves to those |\tracing...|
+%    internals that really contribute to listings like the above.
+%
+%    And one additional point is worth mentioning. The order in which
+%    we turn the tracing internals off has effects on the output we
+%    see. So what needs to be turned off first? Either
+%    |\tracingrestores| or |\tracingcommands|; it makes no difference
+%    which, as long as they both come first. This is because those two
+%    are the only tracing switches that produce output while tracing
+%    the command |\conditionally@traceoff| itself (see example on
+%    page~\pageref{conttraceoffexample}).
+%
+%    In principle we would need to test the |@tracing| switch to see
+%    if there is anything to turn off; after all, this is the
+%    conditional trace off. However this would lead to
+%    extra output if we are currently tracing so we skip the test and
+%    instead accept that in case we are not doing any tracing we
+%    unnecessarily set the tracing primitives back to zero (i.e., the
+%    value they already have).
+%  \changes{v1.1c}{2003/04/30}{Turn off \cs{tracingoutput}}
+%    \begin{macrocode}
+%  \def\conditionally@traceoff{%
+%    \tracingrestores\z@
+%    \tracingcommands\z@
+%    \tracingpages\z@
+%    \tracingmacros\z@
+%    \tracingparagraphs\z@
+%    \tracingoutput\z@
+%    \showboxbreadth\m@ne
+%    \showboxdepth\m@ne
+%    \end{macrocode}
+%
+%    As remarked above there are more tracing switches set by
+%    |\tr@ce@n|, however there is no point in resetting
+%    |\tracinglostchars| so we leave it alone.
+%  \changes{v1.1c}{2003/04/30}{Reset \cs{tracingstats} to one}
+%    \begin{macrocode}
+%   \tracingstats\@ne
+%% \tracinglostchars\z@
+%    \end{macrocode}
+%    Since this is the command that only conditionally turns off
+%    tracing we do not touch the |@tracing| switch. This way a
+%    |\conditionally@traceon| will be able to turn the tracing on
+%    again.
+%    \begin{macrocode}
+%  }
+%    \end{macrocode}
+%
+%    That covers the case for the standard \TeX{} program. If
+%    |\tracingsgroups| was defined we assume that we are running with
+%    \eTeX{} in extended mode.
+%    \begin{macrocode}
+%\else
+%    \end{macrocode}
+%
+%    In that case |\tr@ce@n| does more than |\tracingall|: it also
+%    turns on tracing of assignments and tracing of
+%    grouping.\footnote{These are my personal preference settings;
+%    \eTeX{} does in fact offer some more tracing switches and perhaps
+%    one or or more of them should be added here as well.}
+%    To keep tracing at a minimum |\tracingassigns| should be turned
+%    on last (in fact like before we disassemble |\tracingall|
+%    and reorder it partially).
+%    \begin{macrocode}
+  \def\tr@ce@n{%
+    \@tracingtrue
+    \tracingstats\tw@
+    \tracingpages\@ne
+    \tracinglostchars\@ne
+    \tracingparagraphs\@ne
+    \errorcontextlines\maxdimen
+%    \end{macrocode}
+%    We only change |\tracingoutput| if it hasn't already been enabled by
+%    |\showoutput|. If that's not the case, we set it to 2 so that we
+%    can distingush the two cases.    
+%  \changes{v1.1e}{2018/10/13}{Only reset \cs{tracingoutput} if not
+%    set by \cs{showoutput} earlier}
+%    \begin{macrocode}
+    \ifnum\tracingoutput=\@ne
+    \else
+      \tracingoutput\tw@
+      \showboxbreadth\maxdimen
+      \showboxdepth\maxdimen
+    \fi
+%    \end{macrocode}
+%    
+%    \begin{macrocode}
+    \errorstopmode
+    \tracingmacros\tw@
+    \tracinggroups\@ne
+    \tracingrestores\@ne
+    \tracingcommands\tw@
+    \tracingassigns\@ne
+    \tracingonline\tracingonline@p
+  }
+%    \end{macrocode}
+%
+%    When turning tracing off again we now also have to turn off those
+%    additional tracing switches. But what to turn off in what order?
+%    Since |\tracingassigns| is quite noisy (two lines of output per
+%    assignment) and the whole command expansion consists of
+%    assignments, we had best start with this switch and follow it again
+%    by |\tracingrestores| and |\tracingcommands|. The rest can be in
+%    any order, it doesn't make a difference.
+%
+%    With the same reasoning as before we omit testing for the
+%    |@tracing| switch and always set the primitives back to zero.
+%  \changes{v1.1c}{2003/04/30}{Turn off \cs{tracingoutput}}
+%  \changes{v1.1c}{2003/04/30}{Reset \cs{tracingstats} to one}
+%    \begin{macrocode}
+  \def\conditionally@traceoff{%
+    \tracingassigns\z@
+    \tracingrestores\z@
+    \tracingcommands\z@
+    \tracingpages\z@
+    \tracingmacros\z@
+%    \end{macrocode}
+%    If |\tracingoutput| is 2 it was set above, if it is 1 it was set
+%    by |\showoutput| and we leave it alone and if it is 0 there is
+%    nothing to do as well.
+%  \changes{v1.1e}{2018/10/13}{Only reset \cs{tracingoutput} if not
+%    set by \cs{showoutput} earlier}
+%    \begin{macrocode}
+    \ifnum\tracingoutput=\tw@
+      \tracingoutput\z@
+      \showboxbreadth\m@ne
+      \showboxdepth\m@ne
+    \fi
+%    \end{macrocode}
+%    
+%    \begin{macrocode}
+    \tracingstats\@ne
+    \tracingparagraphs\z@
+    \tracinggroups\z@
+  }
+%    \end{macrocode}
+%
+%    This concludes the part that depends on the formatter being
+%    used.
+%    \begin{macrocode}
+%\fi
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\unconditionally@traceoff}
+%  \changes{v1.1c}{2003/04/30}{Macro added}
+%    A saved version of whatever |\conditionally@traceoff| was defined
+%    to be. We need this since the latter might get disabled by
+%    |\tracingall| or by the \texttt{full} option.
+%    \begin{macrocode}
+\let\unconditionally@traceoff\conditionally@traceoff
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tracingall}
+%  \changes{v1.1c}{2003/04/30}{Macro added}
+%    We redefine |\tracingall| to trace the same stuff than |\tr@ce@n| (i.e.,
+%    more when \eTeX{} is being used) and ensure that everything gets
+%    traced by disabling |\conditionally@traceoff|. And, of course,
+%    |\tracingall| should always report on the terminal.
+%    \begin{macrocode}
+\def\tracingall{\let\conditionally@traceoff\@empty
+  \let\tracingonline@p\@ne
+  \tr@ce@n
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\traceoff}
+% \begin{macro}{\conditionally@traceon}
+%    Above we have defined |\conditionally@traceoff| and |\traceon| so
+%    now we have to define their counterparts.
+%
+%    To stop tracing unconditionally we call
+%    |\unconditionally@traceoff| and then reset the |@tracing| switch
+%    to false.
+%    \begin{macrocode}
+\def\traceoff{\unconditionally@traceoff \@tracingfalse}
+%    \end{macrocode}
+%
+%    Now the |\conditionally@traceon| command will look at the
+%    |@tracing| switch and if it is true it will call |\traceon| to
+%    restart tracing (note that the latter command unnecessarily sets
+%    the switch to true as well). The reason for the |\expandafter| is
+%    to get rid of the |\fi| primitive which would otherwise show up in
+%    the tracing output (and perhaps puzzle somebody).
+%    \begin{macrocode}
+\def\conditionally@traceon{\if@tracing \expandafter \traceon \fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% The rest of the package now consists of redefinitions of certain
+% commands to make use of |\conditionally@traceoff|.
+%
+% \subsection{Taming \texttt{calc}}
+%
+% \begin{macro}{\calc@open}
+%    Near the start of parsing a calc expression the macro |\calc@open|
+%    is called. Since it already involves a group it is perfectly
+%    suitable for our task---we don't even have to restart the tracing as
+%    this is done automatically for us.
+%    \begin{macrocode}
+\def\calc@open({\begingroup
+   \conditionally@traceoff
+   \aftergroup\calc@initB
+   \begingroup\aftergroup\calc@initB
+   \calc@pre@scan}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Making NFSS less noisy}
+%
+% \begin{macro}{\define@newfont}
+%    Whenever NFSS determines that the font currently asked for is not
+%    already loaded, it will start looking through font definition
+%    files and then load the font. This results in a very large number
+%    of tracing lines which are  not normally of interest (unless there
+%    is a bug in that area---something we hope should have been found
+%    by now). Again the code already contains its own group so we only
+%    have to turn the tracing off.
+%    \begin{macrocode}
+\def\define@newfont{%
+  \begingroup
+    \conditionally@traceoff
+    \let\typeout\@font@info
+    \escapechar\m@ne
+    \expandafter\expandafter\expandafter
+       \split@name\expandafter\string\font@name\@nil
+      \try@load@fontshape % try always
+    \expandafter\ifx
+       \csname\curr@fontshape\endcsname \relax
+      \wrong@fontshape\else
+      \extract@font\fi
+  \endgroup}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\frozen@everymath}
+% \begin{macro}{\frozen@everydisplay}
+%    At the beginning of every math formula NFSS will check whether or
+%    not the math fonts are properly set up and if not will load
+%    whatever is needed. So we surround that part of the code
+%    with |\conditionally@traceoff| and |\conditionally@traceon|
+%    thereby avoiding all this uninteresting output.
+%    \begin{macrocode}
+\frozen@everymath =
+   {\conditionally@traceoff \check@mathfonts \conditionally@traceon
+    \the\everymath}
+\frozen@everydisplay =
+   {\conditionally@traceoff \check@mathfonts \conditionally@traceon
+    \the\everydisplay}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \section{Checking for italic corrections}
+%
+% \begin{macro}{\maybe@ic@}
+%    When executing |\textit| or its friends, \LaTeX{} looks ahead to
+%    determine whether or not to add an italic correction at the
+%    end. This involves looping through the |\nocorrlist| which
+%    outputs a lot of tracing lines we are normally not interested
+%    in. So we disable tracing for this part of the processing.
+%  \changes{v1.1d}{2014/04/21}{Use \cs{ifmaybe@ic} not
+%           \cs{if@tempswa} as the kernel does (pr/4200)}
+%    \begin{macrocode}
+\def \maybe@ic@ {%
+  \ifdim \fontdimen\@ne\font>\z@
+  \else
+    \conditionally@traceoff
+    \maybe@ictrue
+    \expandafter\@tfor\expandafter\reserved@a\expandafter:\expandafter=%
+        \nocorrlist
+    \do \t@st@ic
+    \ifmaybe@ic \sw@slant \fi
+    \conditionally@traceon
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+%
+% \Finale
+%
+% \endinput
diff --git a/macros/latex-dev/required/tools/trace.pdf b/macros/latex-dev/required/tools/trace.pdf
new file mode 100644
index 0000000000..5eb99c3e24
--- /dev/null
+++ b/macros/latex-dev/required/tools/trace.pdf
diff --git a/macros/latex-dev/required/tools/varioref-2016-02-16.sty b/macros/latex-dev/required/tools/varioref-2016-02-16.sty
new file mode 100644
index 0000000000..78aa06db6b
--- /dev/null
+++ b/macros/latex-dev/required/tools/varioref-2016-02-16.sty
@@ -0,0 +1,779 @@
+%%
+%% This is file `varioref.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% varioref.dtx  (with options: `package')
+%% 
+%% This is a generated file.
+%% 
+%% The source is maintained by the LaTeX Project team and bug
+%% reports for it can be opened at https://latex-project.org/bugs/
+%% (but please observe conditions on bug reports sent to that address!)
+%% 
+%% Copyright 1993-2017
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file.
+%% 
+%% This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+%% --------------------------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX
+%% version 2005/12/01 or later.
+%% 
+%% This file may only be distributed together with a copy of the LaTeX
+%% `Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+%% without such generated files.
+%% 
+%% The list of all files belonging to the LaTeX `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%% Package varioref to use with LaTeX2e
+%% Copyright (C) 1992-2016  Frank Mittelbach, all rights reserved.
+%%
+%% For additions or updates to the language options please contact
+%% the author at
+%%
+%%   frank.mittelbach@latex-project.org
+%%
+%% In case of bugs, please use "latexbug.tex" (category tools) to report them.
+%%
+\NeedsTeXFormat{LaTeX2e}[1995/05/16]
+\ProvidesPackage{varioref}
+    [2016/02/16 v1.5c package for extended references (FMi)]
+%%
+
+
+\def\vref@addto#1#2{%
+  #2%
+  \@temptokena{#2}%
+  \ifx#1\undefined
+     \edef#1{\the\@temptokena}%
+  \else
+     \toks@\expandafter{#1}%
+     \edef#1{\the\toks@\the\@temptokena}%
+  \fi
+  \@temptokena{}\toks@\@temptokena
+}
+\@onlypreamble\vref@addto
+\def\vref@excuse#1{%
+  \PackageWarningNoLine{varioref}{Sorry, language `#1'
+            not supported%
+            \MessageBreak
+            in this version.
+            English strings used by default.
+            \MessageBreak
+            Please modify \protect\reftext... commands manually.%
+            \MessageBreak\MessageBreak
+            If you can suggest translations for
+            this language,%
+            \MessageBreak
+            please mail them
+            to the author of this package}}
+\@onlypreamble\vref@excuse
+\def\vref@stringwarning#1{%
+  \PackageWarningNoLine{varioref}{Sorry, there is no proper
+            translation for the string\MessageBreak
+            produced by \protect#1\on@line.\MessageBreak
+            English string used instead.\MessageBreak
+            \MessageBreak
+            If you can suggest translations for
+            the current\MessageBreak
+            language, please mail them
+            to the author of this\MessageBreak package}}
+\DeclareOption{afrikaans}
+  {\vref@addto\extrasafrikaans{%
+    \def\reftextfaceafter {op die \reftextvario{regterbladsy}%
+                                               {bladsy langsaan}}%
+    \def\reftextfacebefore{op die \reftextvario{linkerbladsy}%
+                                                {bladsy langsaan}}%
+    \def\reftextafter     {op die \reftextvario{volgende bladsy}%
+                                               {bladsy hierna}}%
+    \def\reftextbefore    {op die \reftextvario{vorige bladsy}%
+                                               {bladsy hiervoor}}%
+    \def\reftextcurrent   {op \reftextvario{hierdie}%
+                                           {die huidige} bladsy}%
+    \def\reftextfaraway#1{op bladsy~\pageref{#1}}%
+    \def\reftextpagerange#1#2{op bladsye~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} tot~\ref{#2}}%
+  }}
+\DeclareOption{american}
+  {\vref@addto\extrasamerican{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+\DeclareOption{austrian}
+  {\vref@addto\extrasaustrian{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+\DeclareOption{naustrian}
+  {\vref@addto\extrasnaustrian{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+\DeclareOption{basque}
+  {\vref@addto\extrasbasque{%
+    \def\reftextfaceafter {hurrengo orrialdean}%
+    \def\reftextfacebefore{aurreko orrialdean}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {uneko orrialdean}%
+    \def\reftextfaraway#1{~\pageref{#1}. orrialdean}%
+    \def\reftextpagerange#1#2{~\pageref{#1}--\pageref{#2} orrialdeetan}%
+    \def\reftextlabelrange#1#2{\ref{#1}.etik \ref{#2}.eraino}%
+  }}
+\DeclareOption{bahasam}
+  {\vref@addto\extrasbahasam{%
+    \def\reftextfaceafter {pada muka surat \reftextvario{bertentangan}{berikutnya}}%
+    \def\reftextfacebefore{pada muka surat \reftextvario{bertentangan}{sebelumnya} }%
+    \def\reftextafter     {pada muka surat berikutnya}%
+    \def\reftextbefore    {pada muka surat sebelumnya}%
+    \def\reftextcurrent   {pada muka surat ini}%
+    \def\reftextfaraway#1{pada muka surat~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pada muka surat~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+\DeclareOption{brazil}
+  {\vref@addto\extrasbrazil{%
+    \def\reftextfaceafter {na \reftextvario{p\'agina oposta}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextfacebefore{na p\'agina \reftextvario{oposta}{anterior}}%
+    \def\reftextafter     {na \reftextvario{p\'agina seguinte}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextbefore{na p\'agina \reftextvario{anterior}{precedente}}%
+    \def\reftextcurrent   {\reftextvario{nesta p\'agina}{na p\'agina
+                           corrente}}%
+    \def\reftextfaraway#1{na p\'agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{nas p\'aginas~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{breton}
+  {\vref@excuse{breton}%
+   \vref@addto\extrasbreton{%
+    \def\reftextfaceafter {war ar bajenn \reftextvario{a-dal}{da heul}}%
+    \def\reftextfacebefore{war ar bajenn \reftextvario{a-dal}{a-raok}}%
+    \def\reftextafter     {war ar bajenn da heul}%
+    \def\reftextbefore    {war ar bajenn a-raok}%
+    \def\reftextcurrent   {war ar \reftextvario{bajenn-ma\~n}%
+                                               {bajenn war-wel}}%
+    \def\reftextfaraway#1{war ar bajenn~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\vref@stringwarning\reftextpagerange
+                              on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\vref@stringwarning\reflabelpagerange
+                               \ref{#1} to~\ref{#2}}%
+  }}
+\DeclareOption{bulgarian}%
+ {\vref@addto\extrasbulgarian{%
+   \def\reftextfaceafter{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrery\cyrs\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextfacebefore{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrery\cyrs\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrp\cyrr\cyre\cyrd\cyrn\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextafter{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}%
+                      {\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextbefore{\cyrn\cyra\
+         \reftextvario{\cyrp\cyrr\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrp\cyrr\cyre\cyrd\cyri\cyrsh\cyrn\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextcurrent{\cyrn\cyra\
+         \reftextvario{\cyrt\cyra\cyrz\cyri}%
+                      {\cyrt\cyre\cyrk\cyru\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextfaraway#1{\cyrn\cyra\ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra
+                         ~\pageref{#1}}%
+   \def\reftextpagerange#1#2{\cyrn\cyra\
+                        \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyri
+                        ~\pageref{#1}--\pageref{#2}}%
+   \def\reftextlabelrange#1#2{\ref{#1} \cyrd\cyro~\ref{#2}}%
+ }}
+\DeclareOption{catalan}
+  {\vref@addto\extrascatalan{%
+    \def\reftextfaceafter {a la p\`agina seg\"uent}%
+    \def\reftextfacebefore{a la p\`agina anterior}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {en aquesta p\`agina}%
+    \def\reftextfaraway#1{a la p\`agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{a les
+                     p\`agines~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{croatian}
+   {\vref@addto\extrascroatian{%
+     \def\reftextfaceafter {na sljede\'coj stranici}%
+     \def\reftextfacebefore{na prethodnoj stranici}%
+     \let\reftextafter     \reftextfaceafter
+     \let\reftextbefore    \reftextfacebefore
+     \def\reftextcurrent   {na ovoj stranici}%
+     \def\reftextfaraway#1{na stranici~\pageref{#1}}%
+     \def\reftextpagerange#1#2{na stranicama~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} do~\ref{#2}}%
+   }}
+\DeclareOption{czech}
+  {%\vref@excuse{czech}%
+   \vref@addto\extrasczech{%
+    \def\reftextfaceafter {na n\'a\-sle\-du\-j\'\i c\'\i\ stran\v{e}}%
+    \def\reftextfacebefore{na p\v{r}ed\-choz\'\i\ stran\v{e}}%
+    \def\reftextafter     {na n\'a\-sle\-du\-j\'\i c\'\i\ stran\v{e}}%
+    \def\reftextbefore    {na p\v{r}ed\-choz\'\i\ stran\v{e}}%
+    \def\reftextcurrent   {na t\'eto stran\v{e}}%
+    \def\reftextfaraway#1{na stran\v{e}~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stran\'ach~\pageref{#1}\--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a\v{z}~\ref{#2}}%
+  }}
+\DeclareOption{danish}
+  {\vref@addto\extrasdanish{%
+    \def\reftextfaceafter {p\aa{} \reftextvario{modst\aa ende}%
+                                               {n\ae ste} side}%
+    \def\reftextfacebefore{p\aa{} \reftextvario{modst\aa ende}%
+                                               {forrige} side}%
+    \def\reftextafter     {p\aa{} \reftextvario{den f\o lgende}%
+                                               {n\ae ste} side}%
+    \def\reftextbefore    {p\aa{} \reftextvario{forrige side}
+                                               {foreg\aa ende side}}%
+    \def\reftextcurrent   {p\aa{} denne side}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+\DeclareOption{dutch}
+  {\vref@addto\extrasdutch{%
+    \def\refpagename{pagina}%
+    \def\reftextfaceafter {op de \reftextvario{rechter \refpagename}%
+                                          {\refpagename\ hiernaast}}%
+    \def\reftextfacebefore{op de \reftextvario{linker \refpagename}%
+                                         {\refpagename\ hiernaast}}%
+    \def\reftextafter     {op de \reftextvario{volgende \refpagename}%
+                                              {\refpagename\ hierna}}%
+    \def\reftextbefore    {op de \reftextvario{vorige \refpagename}%
+                                          {\refpagename\ hiervoor}}%
+    \def\reftextcurrent   {op deze \refpagename}%
+    \def\reftextfaraway#1{op \refpagename~\pageref{#1}}%
+    \def\reftextpagerange#1#2{op pagina's~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+\DeclareOption{english}
+  {\vref@addto\extrasenglish{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+\DeclareOption{esperanto}
+  {\vref@addto\extrasesperanto{%
+    \def\reftextfaceafter{en la
+        \reftextvario{flanka}{sekva} pa\^go}%
+    \def\reftextfacebefore{en la
+        \reftextvario{flanka}{anta\u ua} pa\^go}%
+    \def\reftextafter{en la sekva pa\^go}%
+    \def\reftextbefore{en la anta\u ua pa\^go}%
+    \def\reftextcurrent{\reftextvario{\^ci-pa\^ge}%
+        {en \^ci tiu pa\^go}}%
+    \def\reftextfaraway#1{en pa\^go~\pageref{#1}}%
+    \def\reftextpagerange#1#2{en pa\^goj~\pageref{#1} \^gis \pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} \^gis~\ref{#2}}%
+  }}
+\DeclareOption{finnish}
+  {\vref@addto\extrasfinnish{%
+    \def\reftextfaceafter {\reftextvario{viereisell\"a}%
+                                        {seuraavalla} sivulla}%
+    \def\reftextfacebefore{\reftextvario{viereisell\"a}%
+                                        {edellisell\"a} sivulla}%
+    \def\reftextafter     {seuraavalla sivulla}%
+    \def\reftextbefore    {edellisell\"a sivulla}%
+    \def\reftextcurrent   {t\"all\"a sivulla}%
+    \def\reftextfaraway#1{sivulla~\pageref{#1}}%
+     \def\reftextpagerange#1#2{sivuilla~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+\DeclareOption{french}
+  {\vref@addto\extrasfrench{%
+    \def\reftextfaceafter {page \reftextvario{ci-contre}{suivante}}%
+    \def\reftextfacebefore{page \reftextvario{ci-contre}%
+                          {pr\'ec\'edente}}%
+    \def\reftextafter     {page suivante}%
+    \def\reftextbefore    {page pr\'ec\'edente}%
+    \def\reftextcurrent   {de la pr\'esente page}%
+    \def\reftextfaraway#1{page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} \`a~\ref{#2}}%
+  }}
+\DeclareOption{galician}
+  {\vref@addto\extrasgalician{%
+    \def\reftextfaceafter {na p\'axina oposta}%
+    \def\reftextfacebefore\reftextfaceafter
+    \def\reftextafter     {na p\'axina seguinte}%
+    \def\reftextbefore    {na p\'axina anterior}%
+    \def\reftextcurrent   {nesta p\'axina}%
+    \def\reftextfaraway#1{na p\'axina~\pageref{#1}}%
+     \def\reftextpagerange#1#2{%
+                nas p\'axinas~\pageref{#1}-\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{german}
+  {\vref@addto\extrasgerman{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf den Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+\DeclareOption{ngerman}
+  {\vref@addto\extrasngerman{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf den Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+\DeclareOption{greek}
+  {\vref@addto\extrasgreek{%
+    \def\reftextfaceafter {sthn \reftextvario{paro'usa}%
+                           {ep'omenh} sel'ida}%
+    \def\reftextfacebefore{sthn \reftextvario{paro'usa}{prohgo'umenh}
+                           sel'ida}%
+    \def\reftextafter     {sthn ep'omenh sel'ida}%
+    \def\reftextbefore    {sthn prohgo'umenh sel'ida}%
+    \def\reftextcurrent   {s'' aut'h th sel'ida}%
+    \def\reftextfaraway#1{sth sel'ida\nobreakspace\pageref{#1}}%
+    \def\reftextpagerange#1#2{stis sel'ides\nobreakspace
+                          \pageref{#1}---\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} ws\nobreakspace\ref{#2}}%
+  }}
+\DeclareOption{icelandic}
+  {\vref@addto\extrasicelandic{%
+    \def\reftextfaceafter {\'{a} \reftextvario{n{\ae}stu}%
+                                              {n{\ae}stu} s\'{i}{\dh}u}%
+    \def\reftextfacebefore{\'{a} \reftextvario{fyrri}%
+                                              {fyrri} s\'{i}{\dh}u}%
+    \def\reftextafter     {\'{a} \reftextvario{n{\ae}stu}%
+                                              {n{\ae}stu} s\'{i}{\dh}u}%
+    \def\reftextbefore    {\'{a} \reftextvario{fyrri}{fyrri} s\'{i}{\dh}u}%
+    \def\reftextcurrent   {\'{a} \reftextvario{{\th}essari}%
+                                              {{\th}essari} s\'{i}{\dh}u}%
+    \def\reftextfaraway#1{\'{a} s\'{i}{\dh}u~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\'{a} s\'{i}{\dh}um~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+\DeclareOption{italian}
+  {\vref@addto\extrasitalian{%
+    \def\reftextfaceafter {\reftextvario{a fronte}%
+                           {nella pagina successiva}}%
+    \def\reftextfacebefore{\reftextvario{a fronte}%
+                           {nella pagina precedente}}%
+    \def\reftextafter     {nella pagina \reftextvario{seguente}%
+                           {successiva}}%
+    \def\reftextbefore    {nella pagina precedente}%
+    \def\reftextcurrent   {in questa pagina}%
+    \def\reftextfaraway#1{a pagina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{nelle pagine~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{da~\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{magyar}
+  {\vref@addto\extrasmagyar{%
+    \def\reftextafter {a k\"o\-vet\-kez\H{o} ol\-da\-lon}%
+    \def\reftextbefore{az el\H{o}\-z\H{o} ol\-da\-lon}%
+    \def\reftextfaceafter {\reftextvario{a t\'ul\-ol\-da\-lon}%
+                          {a k\"o\-vet\-kez\H{o} ol\-da\-lon}}%
+    \def\reftextfacebefore{\reftextvario{a t\'ul\-ol\-da\-lon}%
+                          {az el\H{o}\-z\H{o} ol\-da\-lon}}%
+    \def\reftextcurrent   {ezen az ol\-da\-lon}%
+    \def\reftextfaraway#1{\aza{\pageref{#1}} \pageref{#1}.~ol\-da\-lon}%
+    \def\reftextpagerange#1#2{\vref@stringwarning\reftextpagerange
+                              on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\vref@stringwarning\reflabelpagerange
+                               \ref{#1} to~\ref{#2}}%
+   }%
+   \AtBeginDocument{\providecommand\aza[1]{a/az%
+       \PackageError{varioref}{%
+         Proper definition for command \noexpand\aza missing}%
+        {You need to (re)define the command \noexpand\aza that
+         takes one argument (a number or a \noexpand\pageref command)
+         and produces the string `a' or `az' depending on the argument
+         value. It should also accept an optional argument (default `l')
+         to denote whether or not the string should be lowercase or
+         uppercase.}}}%
+  }
+\DeclareOption{norsk}
+  {\vref@addto\extrasnorsk{%
+    \def\reftextfaceafter {p\aa{} neste side}%
+    \def\reftextfacebefore{p\aa{} forrige side}%
+    \def\reftextafter     {p\aa{} neste side}%
+    \def\reftextbefore    {p\aa{} forrige side}%
+    \def\reftextcurrent   {p\aa{} denne siden}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+\DeclareOption{nynorsk}
+  {\vref@addto\extrasnynorsk{%
+    \def\reftextfaceafter {p\aa{} neste side}%
+    \def\reftextfacebefore{p\aa{} f\o{}rre side}%
+    \def\reftextafter     {p\aa{} neste side}%
+    \def\reftextbefore    {p\aa{} f\o{}rre side}%
+    \def\reftextcurrent   {p\aa{} denne sida}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+\DeclareOption{polish}
+  {\vref@addto\extraspolish{%
+    \def\reftextfaceafter {na \reftextvario{s\aob{}siedniej}%
+                                   {nast\eob{}pnej} stronie}%
+    \def\reftextfacebefore{na \reftextvario{s\aob{}siedniej}%
+                                   {poprzedniej} stronie}%
+    \def\reftextafter     {na nast\eob{}pnej stronie}%
+    \def\reftextbefore    {na poprzedniej stronie}%
+    \def\reftextcurrent   {na \reftextvario{tej
+                           samej}{bie\zkb{}\aob{}cej} stronie}%
+    \def\reftextfaraway#1{na stronie~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stronach~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{od~\ref{#1} do~\ref{#2}}%
+  }}
+\DeclareOption{portuges}
+  {\vref@addto\extrasportuges{%
+    \def\reftextfaceafter {na \reftextvario{p\'agina ao lado}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextfacebefore{na p\'agina \reftextvario{ao lado}{anterior}}%
+    \def\reftextafter     {na \reftextvario{p\'agina seguinte}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextbefore{na p\'agina \reftextvario{anterior}{precedente}}%
+    \def\reftextcurrent   {nesta p\'agina}%
+    \def\reftextfaraway#1{na p\'agina~\pageref{#1}}%
+     \def\reftextpagerange#1#2{nas p\'aginas~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{romanian}
+  {\vref@addto\extrasromanian{%
+    \def\reftextfaceafter {pe pagina \reftextvario{opus\u{a}}{urm\u{a}toarei}}%
+    \def\reftextfacebefore{pe pagina \reftextvario{opus\u{a}}{precedentei}}%
+    \def\reftextafter     {\reftextvario{pe pagina urm\u{a}toare}%
+                                        {pe urm\u{a}toarea pagin\u{a}}}%
+    \def\reftextbefore    {pe pagina \reftextvario{precedent\u{a}}%
+                                                  {precedentei}}%
+    \def\reftextcurrent   {pe aceast\u{a} pagin\u{a}}%
+    \def\reftextfaraway#1{pe pagina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pe paginile~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} la~\ref{#2}}%
+  }}
+\DeclareOption{russian}
+  {\vref@addto\extrasrussian{%
+    \def\reftextfaceafter{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+      \cyrt\cyri\cyrv\cyro\cyrp\cyro\cyrl\cyro\cyrzh\cyrn\cyro\cyrishrt}%
+      {\cyrs\cyrl\cyre\cyrd\cyru\cyryu\cyrshch\cyre\cyrishrt}\ \cyrs\cyrt
+      \cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextfacebefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+      \cyrt\cyri\cyrv\cyro\cyrp\cyro\cyrl\cyro\cyrzh\cyrn\cyro\cyrishrt}%
+      {\cyrp\cyrr\cyre\cyrd\cyrery\cyrd\cyru\cyrshch\cyre\cyrishrt}\
+      \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextafter{\cyrn\cyra\ \cyrs\cyrl\cyre\cyrd\cyru\cyryu\cyrshch
+      \cyre\cyrishrt\ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextbefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyre\cyrd
+      \cyrsh\cyre\cyrs\cyrt\cyrv\cyru\cyryu\cyrshch\cyre\cyrishrt}%
+      {\cyrp\cyrr\cyre\cyrd\cyrery\cyrd\cyru\cyrshch\cyre\cyrishrt}%
+      \ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextcurrent{\cyrn\cyra\ \reftextvario{\cyrerev\cyrt\cyro
+      \cyrishrt}{\cyrd\cyra\cyrn\cyrn\cyro\cyrishrt}\ \cyrs\cyrt\cyrr
+      \cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextfaraway#1{\cyrn\cyra\ \cyrs.~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\cyrn\cyra\ \cyrs\cyrt\cyrr\cyra\cyrn
+      \cyri\cyrc\cyra\cyrh~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\cyrs~\ref{#1}\ \cyrp\cyro~\ref{#2}}%
+  }}
+\DeclareOption{slovak}
+  {\vref@addto\extrasslovak{%
+    \def\reftextfaceafter {na \reftextvario{proti\v lahlej}%
+                          {nasleduj\'ucej} strane}%
+    \def\reftextfacebefore{na \reftextvario{proti\v lahlej}%
+                          {predch\'adzaj\'ucej} strane}%
+    \def\reftextafter     {na \reftextvario{nasleduj\'ucej}%
+                          {\v dal\v sej} strane}%
+    \def\reftextbefore    {na \reftextvario{predch\'adzaj\'ucej}%
+                          {predo\v slej} strane}%
+    \def\reftextcurrent   {na tejto strane}%
+    \def\reftextfaraway#1{na strane~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stran\'ach~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a\v z~\ref{#2}}%
+  }}
+\DeclareOption{slovene}
+  {\vref@addto\extrasslovene{%
+    \def\reftextfaceafter {na naslednji strani}%
+    \def\reftextfacebefore{na prej\v{s}nji strani}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {na \reftextvario{tej}{trenutni} strani}%
+    \def\reftextfaraway#1{na strani~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na straneh~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{od~\ref{#1} do~\ref{#2}}%
+  }}
+\DeclareOption{spanish}
+  {\vref@addto\extrasspanish{%
+    \def\reftextfaceafter {en la p\'agina siguiente}%
+    \def\reftextfacebefore{en la p\'agina anterior}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {en esta p\'agina}%
+    \def\reftextfaraway#1{en la p\'agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{en las p\'aginas~\pageref{#1}%
+                                             -\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+\DeclareOption{swedish}
+  {\vref@addto\extrasswedish{%
+     \def\reftextfaceafter {p\aa\ \reftextvario{motst\aa ende}%
+                                             {n\"{a}sta} sida}%
+     \def\reftextfacebefore{p\aa\ \reftextvario{motst\aa ende}%
+                                      {f\"{o}reg\aa ende} sida}%
+     \def\reftextafter     {p\aa\ \reftextvario{f\"{o}ljande}%
+                                            {n\"{a}sta} sida}%
+     \def\reftextbefore    {p\aa\ f\"{o}reg\aa ende sida}%
+     \def\reftextcurrent   {p\aa\ denna sida}%
+     \def\reftextfaraway#1{p\aa\ sidan~\pageref{#1}}%
+     \def\reftextpagerange#1#2{p\aa\
+                               sidorna~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} till~\ref{#2}}%
+  }}
+\DeclareOption{turkish}
+  {\vref@excuse{turkish}%
+   \vref@addto\extrasturkish{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+\DeclareOption{ukrainian}
+   {\vref@addto\extrasukrainian{%
+     \def\reftextfaceafter{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+       \cyrt\cyri\cyrl\cyre\cyrzh\cyrn\cyrii\cyrishrt}%
+       {\cyrn\cyra\cyrs\cyrt\cyru\cyrp\cyrn\cyrii\cyrishrt}\ \cyrs\cyrt
+       \cyro\cyrr\cyri\cyrn\cyrc\cyrii}%
+     \def\reftextfacebefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+       \cyrt\cyri\cyrl\cyre\cyrzh\cyrn\cyrii\cyrishrt}%
+       {\cyrp\cyro\cyrp\cyre\cyrr\cyre\cyrd\cyrn\cyrii\cyrishrt}\
+       \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextafter{\cyrn\cyra\ \cyrn\cyra\cyrs\cyrt\cyru\cyrp\cyrn
+       \cyrii\cyrishrt\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextbefore{\cyrn\cyra\ \cyrp\cyro\cyrp\cyre\cyrr\cyre\cyrd
+       \cyrn\cyrii\cyrishrt\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextcurrent{\cyrn\cyra\ \reftextvario{\cyrc\cyrii\cyrishrt}%
+       {\cyrd\cyra\cyrn\cyrii\cyrishrt}\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn
+       \cyrc\cyrii}%
+     \def\reftextfaraway#1{\cyrn\cyra\ \cyrs.~\pageref{#1}}%
+     \def\reftextpagerange#1#2{\cyrn\cyra\ \cyrs\cyrt\cyro\cyrr\cyrii
+       \cyrn\cyrk\cyra\cyrh~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\cyrz~\ref{#1}\ \cyrd\cyro~\ref{#2}}%
+   }}
+\DeclareOption{francais}{%
+   \typeout{Please use `french' instead of `francais'}%
+   \ExecuteOptions{french}}
+\DeclareOption{germanb}{%
+   \typeout{Please use `german' instead of `germanb'}%
+   \ExecuteOptions{german}}
+\DeclareOption{draft}{\AtEndOfPackage\vrefwarning}
+\DeclareOption{final}{\AtEndOfPackage\vrefshowerrors} % the default
+\ExecuteOptions{english,final}
+\ProcessOptions*
+\newcounter{vrcnt}
+\DeclareRobustCommand\vpageref{\@ifstar
+     {\let\vref@space\relax\vp@geref}%
+     {\let\vref@space\space\vp@geref}}
+\def\vp@geref{\@ifnextchar[%
+  \@vpageref{\@vpageref[\reftextcurrent]}%
+}
+\let\vref@space\space
+\def\@vpageref[#1]{\@ifnextchar[%
+  {\@@vpageref{#1}}{\@@vpageref{#1}[\unskip\vref@space]}}
+\def\@@vpageref#1[#2]#3{%
+  \leavevmode\unskip
+  \global\advance\c@vrcnt\@ne
+  \vref@pagenum\@tempa{\the\c@vrcnt @vr}%
+  \vref@pagenum\@tempb{\the\c@vrcnt @xvr}%
+  \vref@label{\the\c@vrcnt @xvr}%
+  \ifx\@tempa\@tempb
+    \let\vref@may@loop\relax
+  \else
+    \edef\vref@may@loop{%
+      \noexpand\vref@err{\noexpand\vref or \noexpand\vpageref
+              at page boundary
+              \@tempb-\@tempa\space (may loop)%
+              }%
+      }%
+   \fi
+  \vrefpagenum\thevpagerefnum{#3}%
+  \vref@space
+  \ifx\@tempa\thevpagerefnum
+    \def\@tempc{#1}%
+    \ifx\@tempc\@empty
+       \unskip
+    \else
+       #1%
+    \fi
+  \else
+    #2%
+    \is@pos@number\thevpagerefnum
+       {%
+        \is@pos@number\@tempa
+         {\@tempcnta\@tempa
+          \advance\@tempcnta\@ne
+         }%
+         {\@tempcnta\maxdimen}%
+        \ifnum \thevpagerefnum =\@tempcnta
+         \ifodd\@tempcnta
+           \if@twoside
+             \reftextfaceafter
+           \else
+             \reftextafter
+           \fi
+         \else
+           \reftextafter
+         \fi
+        \else
+          \advance\@tempcnta-2
+          \ifnum \thevpagerefnum =\@tempcnta
+            \ifodd\@tempcnta
+              \reftextbefore
+            \else
+              \if@twoside
+                \reftextfacebefore
+              \else
+                \reftextbefore
+              \fi
+            \fi
+          \else
+          \let\vref@may@loop\relax % added
+          \reftextfaraway{#3}%
+          \fi
+        \fi
+       }%
+       {%
+         \let\vref@may@loop\relax %added
+         \reftextfaraway{#3}}%
+  \fi
+   \vref@label{\the\c@vrcnt @vr}%
+   \vref@may@loop
+}
+\def\vref@label#1{\@bsphack
+  \protected@write\@auxout{}%
+         {\string\newlabel{#1}{{}{\thepage}}}%
+  \@esphack}
+\let\thevpagerefnum\@empty
+\def\vrefwarning{\def\vref@err{\PackageWarning{varioref}}}
+\def\vrefshowerrors{\def\vref@err##1{\PackageError{varioref}{##1}%
+    {Please check the pages in question. You might need to replace
+     the \string\vref\MessageBreak
+     or \noexpand\vpageref by a normal \noexpand\(page)ref to
+     stop LaTeX running forever.}}}
+\DeclareRobustCommand\vref{\@ifstar
+   {\let\vref@space\relax\vr@f}%
+   {\let\vref@space\nobreakspace\vr@f}}
+\def\vr@f#1{%
+  \leavevmode\unskip\vref@space
+  \ref{#1}%
+  \vpageref[\unskip]{#1}}
+\def\is@pos@number#1{\is@pos@num0#1\space\@nil}
+\def\is@pos@num{\afterassignment\is@pos@num@ \count@}
+\def\is@pos@num@#1\@nil{%
+  \ifx\@nil#1\@nil
+    \expandafter\@firstoftwo \else
+    \expandafter\@secondoftwo  \fi}
+\def\reftextvario#1#2{\ifodd\c@vrcnt #1\else#2\fi}
+\def\fullref#1{\ref{#1} \reftextfaraway{#1}}
+\def\vref@pagenum#1#2{%
+  \@ifundefined{r@#2}{\@namedef{r@#2}{{??}{??}}}{}%
+  \expandafter\expandafter\expandafter\vref@@pagenum
+  \csname r@#2\endcsname{}{}\@nil#1%
+}
+\def\vref@@pagenum#1#2#3\@nil#4{%
+  \def#4{#2}%
+}
+\def\vrefpagenum#1#2{%
+  \@ifundefined{r@#2}%
+    {\G@refundefinedtrue
+     \@latex@warning{Reference `#2' on page \thepage \space
+             undefined}}{}%
+  \vref@pagenum{#1}{#2}}
+\newcommand\@svpagerefrange[3][\reftextcurrent]{%
+  \vrefpagenum\@tempa{#2}%
+  \vrefpagenum\@tempb{#3}%
+  \ifx\@tempa\@tempb
+    \vpageref*[{#1}]{#2}%
+  \else
+    \reftextpagerange{#2}{#3}%
+  \fi
+}
+\newcommand\@vpagerefrange[3][\reftextcurrent]{%
+  \vrefpagenum\@tempa{#2}%
+  \vrefpagenum\@tempb{#3}%
+  \ifx\@tempa\@tempb
+    \vpageref[{#1}]{#2}%
+  \else
+    \reftextpagerange{#2}{#3}%
+  \fi
+}
+\newcommand\vpagerefrange{\@ifstar\@svpagerefrange\@vpagerefrange}
+\newcommand\vrefrange[3][\reftextcurrent]
+  {\reftextlabelrange{#2}{#3} \vpagerefrange[{#1}]{#2}{#3}}
+\def\refstepcounter#1{\stepcounter{#1}%
+    \protected@edef\@currentlabel
+       {\csname p@#1\expandafter\endcsname\csname the#1\endcsname}%
+}
+\def\labelformat#1{\expandafter\def\csname p@#1\endcsname##1}
+\DeclareRobustCommand\Ref[1]{\protected@edef\@tempa{\ref{#1}}%
+   \expandafter\MakeUppercase\@tempa}
+\DeclareRobustCommand\Vref{\@ifstar
+   {\let\vref@space\relax\Vr@f}%
+   {\let\vref@space\nobreakspace\Vr@f}}
+\def\Vr@f#1{%
+  \leavevmode\unskip\vref@space
+  \Ref{#1}%
+  \vpageref[\unskip]{#1}}
+\endinput
+%%
+%% End of file `varioref.sty'.
diff --git a/macros/latex-dev/required/tools/varioref.dtx b/macros/latex-dev/required/tools/varioref.dtx
new file mode 100644
index 0000000000..049bd0d55e
--- /dev/null
+++ b/macros/latex-dev/required/tools/varioref.dtx
@@ -0,0 +1,2447 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2008 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% Package varioref to use with LaTeX2e
+%% Copyright (C) 1992-2019  Frank Mittelbach, all rights reserved.
+%%
+%% For additions or updates to the language options please contact
+%% the author at
+%%
+%%   frank.mittelbach@latex-project.org
+%%
+%% or open an issue at https://github.com/latex3/latex2e.
+%%
+%
+%<package>\NeedsTeXFormat{LaTeX2e}[1995/05/16]
+%<package>\providecommand\DeclareRelease[3]{}
+%<package>\providecommand\DeclareCurrentRelease[2]{}
+%<package>
+%<package>\DeclareRelease{}{2016-02-16}{varioref-2016-02-16.sty}
+%<package>\DeclareCurrentRelease{}{2019-10-01}
+%<package>
+%<package>\ProvidesPackage{varioref}
+%<package>    [2019/09/08 v1.6b package for extended references (FMi)]
+% \fi
+%
+%%
+%
+%
+% \changes{v1.0a}{1993/12/06}{Upgrade to LaTeX2e}
+% \changes{v1.0g}{1994/05/27}{Use \cmd\DeclareRobustCommand}
+% \changes{v1.5c}{2016/02/09}{Revamped some of the documentation to better
+%	explain how varioref could be used in a multi-lingual context}
+% \changes{v1.6a}{2019/08/25}{\cs{labelformat} and \cs{Ref} now available in the kernel
+%       so removed from this package but only in new kernel}
+%
+%
+% \newcommand\NewIn[1]{\marginpar{\fbox{\fbox{\sffamily\tabular{l}New
+%    in\\#1\endtabular}}}}
+% \newcommand\ChangedIn[1]{\marginpar{\fbox{\fbox{\sffamily\tabular{l}Changed
+%    in\\#1\endtabular}}}}
+%
+% \providecommand\pkg[1]{\texttt{#1}}
+% \providecommand\option[1]{\texttt{#1}}
+% \providecommand\meta[1]{$\langle§\textit{#1}$\rangle$}
+%
+%
+% \makeatletter
+% \def\allowtofu{^^A
+%\def\UTFviii@undefined@err##1{^^A
+%  \PackageWarning{inputenc}{Unicode character \expandafter
+%                          \UTFviii@splitcsname\string##1\relax
+%                          \MessageBreak
+%                          not set up for use with LaTeX}^^A
+%  \raisebox{.8pt}{\fboxsep1pt\kern.1pt\fbox{$\cdot$}\kern.1pt}^^A
+%   }}
+% \makeatother
+%
+% \title{The \pkg{varioref} package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{Frank Mittelbach}
+% \date{\filedate}
+%
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+%
+% \begin{abstract}
+%   This package defines the commands |\vref|, |\vpageref|,
+%   |\vrefrange|, and |\vpagerefrange| for
+%   \LaTeXe. |\vref| is similar to |\ref| but adds an additional
+%   page reference, like `on the facing page' or `on page 27' whenever
+%   the corresponding |\label| is not on the same page. The command
+%   |\vpageref| is a variation to |\pageref| with a similar
+%   functionality.  The |\v...range| commands take two labels as arguments
+%   and produce strings which depend on whether or not these labels
+%    fall onto a single page or on different pages.
+%   Generated strings are customizable so that these
+%   commands are usable with various languages.
+% \end{abstract}
+%
+%
+% \columnsep=2\columnsep
+% \begin{multicols}{2}
+%   \tableofcontents
+% \end{multicols}
+%
+% \section{Introduction}
+%
+% In many cases it is helpful when referring to a figure or table to
+% put both a |\ref| and a |\pageref| command into the document
+% especially when there are one or more pages between the reference
+% and the object.  Therefore some people use a command like
+% \begin{verbatim}
+%  \newcommand{\fullref}[1]{\ref{#1} on page~\pageref{#1}}
+%\end{verbatim}
+% which reduces the number of key strokes, necessary to make such a
+% complete reference.  But since one never knows where the referenced
+% object finally falls, using such a device may result in a page
+% reference to the current page which is disturbing and therefore
+% should be avoided.
+%
+%
+%
+% \section{Loading the package}
+%
+%
+% The suggested way of loading the package these days is by
+% \emph{always} using
+% the package option \option{nospace},
+% \NewIn{2019}
+% i.e.,
+% \begin{verbatim}
+%  \usepackage[nospace]{varioref}
+%\end{verbatim}
+% See below for an explanation of why this is needed. There are some
+% other options that you may want to use additionally; they are
+% explained \vpageref{options}.
+%
+%
+%
+% \section{The user interface}
+%
+%\DescribeMacro\vref The implementation of |\vref| below produces only
+% a |\ref| when reference and |\label| are on the same page. It will
+% additionally produce one of the strings `on the facing page', `on
+% the preceding page', or `on the following page', if label and
+% reference differ by one and it will produce both |\ref| and
+% |\pageref| when the difference is larger.  The word `facing' is used
+% when label and reference both fall onto a double spread.  However,
+% if a special page numbering scheme is used instead of the usual
+% arabic numbering (e.g., |\pagenumbering{roman}|) then there will be
+% no distinction between one or many pages off.
+%
+%\DescribeMacro\vpageref Sometimes one wants to refer only to page
+% number and again such a reference should normally be suppressed if
+% we are referring to the current page. For this purpose the package
+% defines the |\vpageref| command. It will produce the same strings as
+% |\vref| except that it doesn't start with the |\ref|. A further
+%    difference is that
+% it will produce the string that is saved in |\reftextcurrent| if
+% label and reference fall onto the same page (and no optional
+%    argument is used). By defining
+% |\reftextcurrent| to produce ``on this page'' or something similar,
+% we can avoid that
+% \begin{verbatim}
+%   ... see the example \vpageref{ex:foo} which shows ...
+%\end{verbatim}
+% comes out as ``\ldots~see the example which shows~\ldots'', which
+% could be misleading.
+%
+% A space in front of |\vpageref| it will be ignored if
+% the command doesn't produce any text at all.
+%
+% But in fact |\vpageref| allows even more control. If has two
+% optional arguments. With the first one, one can specify the text
+% that should be used if label and reference fall on the same page.
+% This is very helpful if both are near to each other, so that they
+% may or may not be separated by a page break. In such a case we
+% usually know (!) whether the reference is before or after the label
+% so that we can say something like
+% \begin{verbatim}
+%   ... see the example \vpageref[above]{ex:foo} which shows ...
+%\end{verbatim}
+% which will then come out as ``\ldots~see the example above which
+% shows~\ldots'' if we are still on the same page, but as ``\ldots~see
+% the example on the page before which shows~\ldots'' (or something
+% similar depending on the settings of the |\reftext..before|
+% commands) when there was a page break in the meantime. One warning
+% however, if you use |\vpageref| with the optional argument to refer
+% to a figure or table, keep in mind that depending on the float
+% placement parameters the float may show up on top of the current
+% page and therefore before the reference even if it came after it in
+% the source file.
+%
+% But maybe you prefer to say ``\ldots~see the above example'' if
+% example and reference fall onto the same page, i.e., reverse the
+% word order.  In fact, in some languages the word order automatically
+% changes in that case.  To allow for this variation the second
+% optional argument can be used. It specifies the text preceding the
+% generated reference if object and reference do not fall onto the
+% same page. Thus one would write
+% \begin{verbatim}
+%   ... see the \vpageref[above example][example]{ex:foo}
+%       which shows ...
+%\end{verbatim}
+% to achieve the desired effect.
+%
+%
+% \DescribeMacro\vrefrange 
+% This command is similar to |\vref| but it
+% takes two mandatory arguments denoting a range to refer to (e.g., a
+% sequences of figures or a sequence of equations, etc.). So if
+% |fig:a| is your first figure in the sequence and |fig:c| your last
+% you can write
+%\begin{verbatim}
+%   ... see figures \vrefrange{fig:a}{fig:c} ...
+%\end{verbatim}
+% which would then be formatted as
+% \begin{quote}
+% \ldots\ see figures 3.4 to 3.6 on pages 23--24 \ldots
+% \end{quote}
+% or, if they happen to all fall onto the next page, as
+% \begin{quote}
+% \ldots\ see figures 3.4 to 3.6 on the following page \ldots
+% \end{quote}
+% i.e., the command is deciding what to say depending on where the two
+% labels are placed in relation to each other; it is essentially
+% implemented using |\vpagerefrange| described below.
+% The optional argument the command may take is the text to use in case
+% both labels are placed on the current page.
+%
+%
+% \DescribeMacro\vpagerefrange This command is similar to |\vpageref|
+% but takes two mandatory arguments which are two labels denoting a
+% range. If both labels fall onto the same page, the command acts
+% exactly like |\vpageref| (with a single label), otherwise it produces
+% something like ``on pages~15--18'' (see customization possibilities
+% below). The optional argument it may take is the text to use in case
+% both labels are placed on the current page.
+
+% \DescribeMacro\vrefpagenum This macro is provided to allow the user
+% to write their own small commands which implement functions similar
+% to those provided by the two previous commands. It takes two
+% arguments: the second is a label (i.e., as used in |\label| or
+% |\ref|) and the first is an arbitrary command name (make sure you
+% use our own) that receives the page number related to this label.
+% So if you have two (or more) labels you could retrieve their page
+% numbers, compare them and then decide what to print.  For example,
+% the following not very serious definition (also using the
+% \pkg{ifthen} package)
+%\begin{verbatim}
+% \newcommand\amusingversion[2]{the definition%
+%   \vrefpagenum\firstnum{#1}%
+%   \vrefpagenum\secondnum{#2}%
+%   \ifthenelse{\equal\firstnum\secondnum}%
+%     {s of \ref{#1} and \ref{#2} \vpageref{#1}}%
+%     { of \ref{#1} \vpageref{#1} and of \ref{#2} \vpageref{#2}}%
+% }
+%
+% ...\amusingversion{foo}{bar}
+%\end{verbatim}
+% will print something like
+% \begin{quote}
+%  \ldots the definitions of 3 and 4 on the previous page
+% \end{quote}
+% in the case both labels are on the same page but something like
+% \begin{quote}
+%  \ldots the definition of 3 on the next page and of 4 on page~13
+% \end{quote}
+% in case they are on different pages.
+%
+% \DescribeMacro\vpagerefcompare
+% \NewIn{2019}
+% For this kind of application the package also provides
+% |\vpagerefcompare| as a command that takes four argument: two labels for
+% comparison and a \meta{true} and \meta{false} argument. One of them
+% is executed depending on whether the two labels are on the same page
+% or on different pages. With its help the above definition could be
+% shortened to
+%\begin{verbatim}
+% \newcommand\amusingversion[2]{the definition%
+%   \vpagerefcompare{#1}{#2}%
+%     {s of \ref{#1} and \ref{#2} \vpageref{#1}}%
+%     { of \ref{#1} \vpageref{#1} and of \ref{#2} \vpageref{#2}}%
+% }
+%\end{verbatim}
+% and you don't have to load the \pkg{ifthen} package any longer to
+% make it work.
+%
+% \DescribeMacro\vpagerefnearby
+% \NewIn{2019}
+% Another command for conditional processing is |\vpagerefnearby|. It
+% takes three arguments: a label and a \meta{true} and \meta{false}
+% argument. It compares the page reference to the label with the
+% current page number and if both are arabic number and only differ by
+% $\pm1$ the \meta{true} argument is executed otherwise the
+% \meta{false} argument. In other words it tells you if a |\vpageref|
+% to the label would result in a textual reference to the previous,
+% current or next page.\footnote{There is also a
+% \cs{vpagerefcomparenearby} but this is only meant for package
+% writers, so it is only documented in the implementation section.}
+
+%
+%
+% If you don't use the \texttt{nospace} option the user commands
+% |\vref|, |\vpageref|, and |\vpagerefrange| all work by first
+% removing any space on their left and then inserting some space of
+% their own (|\vref|, for example, a nonbreakable space). That seemed
+% like a good idea back then, but it has the disadvantage that you
+% can't use these macros in situations where you definitely do not
+% want any space before the generated text. E.g., in situations like
+% |(\vref{foo} ...)| you end up with a space after the open
+% parenthesis.
+%
+% \DescribeMacro{\vref*}
+% \DescribeMacro{\vpageref*}
+% \DescribeMacro{\vpagerefrange*}
+% Since it was too late to change the default in 2001 I  added star
+% versions of the macros which do not add any space before the
+% generated text (they do nevertheless remove space at the left).
+%
+% However, that too has problems (one is that \pkg{hyperref}
+% \ChangedIn{2019}
+% introduced the star forms as a means to generating references
+% without hyperlinks (which is clearly the more important
+% application).
+% So these days I recommend to always call the package with the option
+% \option{nospace} which prevents \pkg{varioref} from messing with the
+% space in front. Of course you are then responsible to always add it
+% when necessary, but that does make the source more readable so it is
+% a good thing. This also has the advantage that the star forms are
+% now unnecessary again and can be used in the way implemeented by
+% \pkg{hyperref} if both packages are used together.
+%
+% In fact it would be much nicer to make that the
+% default but the package has been used by many people for so many
+% years that changing the default would break way to many older documents.
+%
+%
+% \DescribeMacro\labelformat
+% A reference via |\ref| produces by default the data associated with
+% the corresponding |\label| command (typically a number); any
+% additional formatting has to be provided by the user. With
+% |\labelformat| it is possible to declare scuch formatting for each
+% ``reference'' counter, e.g.,
+%\begin{verbatim}
+%  \labelformat{section}{section~#1}
+%  \labelformat{equation}{equation~(#1)}}
+%\end{verbatim}
+%
+%
+% \DescribeMacro\Vref
+% \DescribeMacro\Ref
+% A side effect of using |\labelformat| is that, depending on the
+% defined formatting, it becomes impossible to use |\ref| at the
+% beginning of a sentence (if its replacement text starts with a
+% lowercase letter).
+% \ChangedIn{2019}
+% For that reason \pkg{varioref} provided the commands |\Ref| and
+% |\Vref|.  They behave like |\ref| and |\vref| except that they
+% uppercase the first token of the generated string. These days
+% |\labelformat| and |\Ref| are already provided by the \LaTeX{}
+% kernel; only |\Vref| is still defined within the \pkg{varioref}
+% package.
+%
+% To make |\Ref| or |\Vref| work properly the very first token in the
+% second argument of |\labelformat| has to be a simple \textsc{ascii}
+% or UTF-8 letter, otherwise the capitalization will fail or worse,
+% you will end up with some error messages. If you actually need
+% something more complicated in this place (e.g., an accented letter
+% not written as a UTF-8 character) you have to explicitly surround it
+% with braces, to identify the part that needs to be capitalized. For
+% example, for figure references in the Hungarian language you might
+% want to write |\labelformat{figure}{{\'a}bra~\thefigure}| or use
+% |\labelformat{figure}{ábra~\thefigure}| which avoids the brace
+% problem.
+%
+% \DescribeMacro\thevpagerefnum
+% If you like to have |\vref| suppress the page number on pages where
+% label and reference fall onto the same page, but prefer reference to
+% page numbers otherwise then |\thevpagerefnum| can be used. This macro
+% hold the current page ``number'' when |\vpageref| and friends are
+% executed. Thus, by defining, for example
+%\begin{verbatim}
+%\renewcommand\reftextfaceafter {on page~\thevpagerefnum}
+%\renewcommand\reftextfacebefore{on page~\thevpagerefnum}
+%\renewcommand\reftextafter     {on page~\thevpagerefnum}
+%\renewcommand\reftextbefore    {on page~\thevpagerefnum}
+%\end{verbatim}
+% textual references can be suppressed.
+%
+% \section{Multi-lingual usage}
+%
+% The package works well together with the babel system if it is
+% loaded \textit{after} the babel package, e.g., a document in English
+% (default), French and German text could load the packages as
+% follows:
+%\begin{verbatim}
+%   \usepackage[ngerman,french,english]{babel,varioref}
+%\end{verbatim}
+% (or in two separate lines if you prefer one |\usepackage| line per
+% package). Depending on the current babel language |\vref| and
+% friends would then generate strings in different languages. If the
+% language options are given as global options to the document class
+% then it is enough to use
+%\begin{verbatim}
+%   \usepackage{babel,varioref}
+%\end{verbatim}
+% to achieve the same effect.
+%
+% If more than one language is specified with \pkg{varioref} then
+% it will start using the last language selected. Switching of
+% languages is managed through Babel; nevertheless all languages of
+% interest need to be specified when \pkg{varioref} is loaded so
+% that it can integrate their strings into the Babel system.
+%
+%
+% \section{Customization}
+%
+% The package supports all options defined by the babel package to
+% translate the fixed strings into other languages than English.
+% (Some languages need updating, however---help is appreciated.)  It
+% also supports languages currently not in babel (those can only be
+% used standalone, obviously); check the section on options later~on.
+%
+%
+% \pagebreak[3]
+%
+% You can also modify some or all of the strings by redefining the
+% following commands after the package has been loaded.
+%\DescribeMacro\reftextbefore
+%\DescribeMacro\reftextfacebefore
+%\DescribeMacro\reftextafter
+%\DescribeMacro\reftextfaceafter Backward references use
+% |\reftextbefore| if the label is on the preceding page but invisible
+% and |\reftextfacebefore| if it is one the facing page (i.e., if the
+% current page number is odd).  Similarly |\reftextafter| is used
+% when the label comes on the next page but one has to turn the page
+% and |\reftextfaceafter| if it is on the following but facing page.
+%
+% In fact, |\reftextface...| is used only if the user or the document
+% class specified two-sided printing.
+%
+%\DescribeMacro\reftextfaraway Finally we have |\reftextfaraway| which
+% is used whenever label and reference differ by more than one or when
+% they aren't numeric. This macro is a bit different because it takes
+% one argument, the symbolic reference string so that one cane make
+% use of |\pageref| in its replacement text.
+%
+%
+%\DescribeMacro\reftextvario To allow a bit random variation in the
+% generated strings one can use the command |\reftextvario| inside the
+% string macros. It takes two arguments and selects one or the other
+% for printing depending on the number of already seens |\vref| or
+% |\vpageref| commands.  As an example see the definitions of
+% |\reftextbefore| etc.\ \vpageref[below]{reftextbefore}.
+%
+% The commands |\vrefrange| and |\vpagerefrange| produce their text
+% \NewIn{1998}
+% using two macros described below. By redefining them one can modify
+% the results to accommodate special requirements.
+%
+%
+% They both take two mandatory arguments denoting the first and the
+% last label of the range.
+%
+%
+% \DescribeMacro\reftextpagerange This macro produces text that
+% describes the page range of the two labels, e.g., the default
+% for English is ``|on pages~\pageref{#1}--\pageref{#2}}|''.
+%
+%
+% \DescribeMacro\reftextlabelrange This macro produces text that
+% describes the range of figures, tables, or whatever the labels refer
+% to, the default for English is ``|\ref{#1} to~\ref{#2}|''.
+%
+% \subsection{\ldots\ if Babel is used}
+%
+% \begin{itshape} If babel is being used then the above commands need to be
+% changed using the Babel mechanism, e.g.,
+%\begin{verbatim}
+%  \addto\extrasngerman{%
+%     \renewcommand\reftextfaceafter {auf der n\"achsten Seite}%
+%      ... }
+%\end{verbatim}
+% Otherwise babel will reintroduce its own defaults whenever the language is
+% changed (which happens in particular during |\begin{document}| where the
+%    main language is selected).
+% \end{itshape}
+%
+%
+%
+%
+% \section{Options} \label{options}
+%
+% As mentioned above the package supports all standard options offered
+% by the Babel system to customize the strings produced, it may also
+% have a few not supported by babel, for a full list look
+% in section\vref{sec:impoptions}. In addition it offers the option
+% \texttt{draft} to turn error messages into warnings during
+% development. The default \texttt{final} produces error message when
+% a generated string falls onto a page boundary (see next section).
+%
+% Newly introduced in 2019 are the options \option{space} (default)
+% and \option{nospace}. While the former is the default to allow
+% \NewIn{2019}
+% documents written in the last twenty years to continue to work
+% correctly, I nowadays, suggest that you always use the package with
+% the option \option{nospace}. This will stop \pkg{varioref} from
+% meddling with the spaces preceding commands and thus make the star
+% forms |\vref*| and |\vpageref*| unnecessary.
+%
+% This means that the star forms can then be used as defined by
+% \pkg{hyperref} for suppressing a hyperlink when both packages are
+% used together (which is a rather typical scenario these days).
+%
+%
+% \section{A few warnings}
+%
+% Defining commands like the ones described above poses some
+% interesting problems. Suppose, for example, that a generated text
+% like `on the next page' gets broken across pages. If this happens it
+% is very difficult to find an acceptable solution and in fact can
+% even result in a document that will always change from one state to
+% another (i.e., inserting one string, finding that this is wrong,
+% inserting another string on the next run which makes the first
+% string correct again, inserting \ldots).  The current implementation
+% of \pkg{varioref} therefore issues an error message whenever the
+% generated text is broken across page boundaries, e.g.,
+% \begin{quote}
+%   table 5 on the current \meta{page break} page
+% \end{quote}
+% would would result in an error, which needs to be resolved by the
+% user by replacing the |\vref| command with an ordinary |\ref| just
+% before the final run.  This is not
+% completely satisfactory but in such case no solution really is.
+% \DescribeMacro\vrefwarning
+% During document preparation, while one is still changing the text,
+% such error messages can be turned into warnings by placing a
+% |\vrefwarning| command in the preamble. This is equivalent to
+% specifying ``draft'' as an option to the package.
+% \DescribeMacro\vrefshowerrors
+% |\vrefshowerrors| ensures that varioref stops when detecting a
+% possible loop. This is the default and equivalent to specifying
+% ``final'' as an option.
+%
+% At the end final a warning: every use of |\vref| will internally
+% generate two macro names to keep track of the string positions
+% within the document. As a result you may run out of name space or
+% main memory\footnote{Not really that likely these days, but one
+% never knows \ldots.  In any case \TeX{} will process your document a
+% tiny bit faster.} if you make heavy use of this macro on a small
+% \TeX{} installation.
+%\DescribeMacro\fullref For this reason the primitive command
+% |\fullref| is also provided. This command can be used whenever you
+% know for sure that label and reference can't fall onto nearby pages.
+%
+% \StopEventually{\PrintIndex\PrintChanges}
+%
+%
+% \section{The documentation driver file}
+%
+% The next bit of code contains the documentation driver file for
+% \TeX{}, i.e., the file that will produce the documentation you are
+% currently reading. It will be extracted from this file by the
+% \pkg{docstrip} program.
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{multicol,varioref}
+\GetFileInfo{varioref.sty}
+\setlength\hfuzz{1pt}    % ignore slight overfulls
+\EnableCrossrefs
+%\DisableCrossrefs   % Say \DisableCrossrefs if index is ready
+
+\RecordChanges       % Gather update information
+%\OnlyDescription    % comment out for implementation details
+\begin{document}
+   \DocInput{varioref.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+%
+% \section{The implementation}
+%
+% The main implementation idea is to generate an internal label
+% command for every |\vpageref| and compare the page reference of this
+% label with the page reference of the user-requested label.  Since
+% this means one additional macro name for each use of |\vpageref| or
+% |vref| (which is implemented in terms of |\vpageref|) the memory
+% requirements of this package may be high in terms of main and macro
+% name memory.  Since the information held in the internal labels is
+% used only once one could envision a different scheme if suitable
+% primitives for this kind of ``one place information'' would be
+% provided by \LaTeX.  This type of data structure is planned for
+% \LaTeX3 but for the moment we have to live with the memory
+% restrictions.
+%
+% We start by checking if this file was already loaded. If not we
+% identify the current version. This is actually done at the top
+% of the file, so we comment it out here
+% \changes{v0.1h}{1993/08/15}{Small documentation changes}
+%    \begin{macrocode}
+%<*package>
+%\NeedsTeXFormat{LaTeX2e}[1994/06/01]
+%\ProvidesPackage{varioref}[\filedate\space\fileversion\space
+%                     LaTeX2e package for extended references (FMi)]
+%    \end{macrocode}
+%
+%
+%  \begin{macro}{\vref@addto}
+% \changes{v1.0b}{1994/01/31}{Avoid using babel `addto}
+% \changes{v1.0b}{1994/01/31}{The babel commands are starting
+%                             with extras}
+%    To support the use of babel we want to add the additional strings
+%    to the |\extras|\meta{language} commands. Since |\addto| in the
+%    current implementation of babel has a bug that does not allow to
+%    use arguments containing hashmarks we do this by hand.
+%    \begin{macrocode}
+\def\vref@addto#1#2{%
+  #2%
+  \@temptokena{#2}%
+  \ifx#1\undefined
+     \edef#1{\the\@temptokena}%
+  \else
+     \toks@\expandafter{#1}%
+     \edef#1{\the\toks@\the\@temptokena}%
+  \fi
+  \@temptokena{}\toks@\@temptokena
+}
+\@onlypreamble\vref@addto
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \subsection{Options}\label{sec:impoptions}
+%
+%  \begin{macro}{\vref@excuse}
+%    Excuse that we don't know the strings for a certain language.
+% \changes{v1.0q}{1995/04/06}{Use `PackageWarning}
+%    \begin{macrocode}
+\def\vref@excuse#1{%
+  \PackageWarningNoLine{varioref}{Sorry, language `#1'
+            not supported%
+            \MessageBreak
+            in this version.
+            English strings used by default.
+            \MessageBreak
+            Please modify \protect\reftext... commands manually.%
+            \MessageBreak\MessageBreak
+            If you can suggest translations for
+            this language,%
+            \MessageBreak
+            please mail them
+            to the author of this package}}
+\@onlypreamble\vref@excuse
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\vref@stringwarning}
+%    And we sometimes just don't know some strings~\ldots
+% \changes{v1.2a}{1998/08/01}{Macro added}
+%    \begin{macrocode}
+\def\vref@stringwarning#1{%
+  \PackageWarningNoLine{varioref}{Sorry, there is no proper
+            translation for the string\MessageBreak
+            produced by \protect#1\on@line.\MessageBreak
+            English string used instead.\MessageBreak
+            \MessageBreak
+            If you can suggest translations for
+            the current\MessageBreak
+            language, please mail them
+            to the author of this\MessageBreak package}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\reftextfaceafter}
+%  \begin{macro}{\reftextfacebefore}
+%  \begin{macro}{\reftextafter}
+%  \begin{macro}{\reftextbefore}
+%  \begin{macro}{\reftextcurrent}
+% \label{reftextbefore} The options do set the macros that
+%    generate the textual strings. Note, that they do not start with a
+%    space, the space is already added in the main macro below.
+% \changes{v1.2a}{1998/08/22}{Added american defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+% \changes{v1.4d}{2002/11/11}{Changed default for \cs{reftextbefore}}
+%
+%    Afrikaans option contributed by Danie Els
+%    (\texttt{dnjels@sun.ac.za}).
+% \changes{v1.4g}{2003/03/29}{Added afrikaans option}
+%    \begin{macrocode}
+\DeclareOption{afrikaans}
+  {\vref@addto\extrasafrikaans{%
+    \def\reftextfaceafter {op die \reftextvario{regterbladsy}%
+                                               {bladsy langsaan}}%
+    \def\reftextfacebefore{op die \reftextvario{linkerbladsy}%
+                                                {bladsy langsaan}}%
+    \def\reftextafter     {op die \reftextvario{volgende bladsy}%
+                                               {bladsy hierna}}%
+    \def\reftextbefore    {op die \reftextvario{vorige bladsy}%
+                                               {bladsy hiervoor}}%
+    \def\reftextcurrent   {op \reftextvario{hierdie}%
+                                           {die huidige} bladsy}%
+    \def\reftextfaraway#1{op bladsy~\pageref{#1}}%
+    \def\reftextpagerange#1#2{op bladsye~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} tot~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\DeclareOption{american}
+  {\vref@addto\extrasamerican{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Arabic option text was contributed by Ihab Samir Mattar
+%    (\texttt{dr\_kremlin@hotmail.com}). As our standard documentation
+%    workflow uses pdf\TeX{} the Arabic letters can't be displayed
+%    easily, so you will see missing glyphs below. To see the real
+%    letters you have to look at the source or package file.
+% \changes{v1.6b}{2019/09/8}{Option arabic added}
+% \begin{allowtofu}  
+%    \begin{macrocode}
+\DeclareOption{arabic}
+  {\vref@addto\extrasarabic{%
+    \def\reftextfaceafter {بالص�حة \reftextvario{المقابلة}{اللاحقة}}%
+    \def\reftextfacebefore{بالص�حة \reftextvario{المقابلة}{الم�نْصَر�مَةٌ}}%
+    \def\reftextafter     {بالص�حة \reftextvario{اللاحقة}{التالية}}%
+    \def\reftextbefore    {بالص�حة \reftextvario{السابقة}{الم�نْصَر�مَةٌ}}%
+    \def\reftextcurrent   {ب\reftextvario{الص�حة الحالية}{هذه الص�حة}}%
+    \def\reftextfaraway#1{بالص�حة رقم~\pageref{#1}}%
+    \def\reftextpagerange#1#2{بالص�حات~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} حتى~\ref{#2}}%
+  }}
+%    \end{macrocode}
+% \end{allowtofu}  
+% \changes{v1.2a}{1998/11/27}{Added austrian defaults (identical to german)}
+%    The austrian defaults are the same as the german ones.
+%    \begin{macrocode}
+\DeclareOption{austrian}
+  {\vref@addto\extrasaustrian{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+%    \end{macrocode}
+% \changes{v1.2d}{2000/01/11}{Added naustrian defaults (identical to german)}
+%    The naustrian defaults are the same but needed for ``Neue Rechtschreibung''.
+%    \begin{macrocode}
+\DeclareOption{naustrian}
+  {\vref@addto\extrasnaustrian{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for basque defaults was contributed by
+%    I\~naki Larra\~naga Murgoitio (aka dooteo)
+%    (|<dooteo@euskalgnu.org>|).
+% \changes{v1.4k}{2005/04/09}{Basque defaults added.}
+%    \begin{macrocode}
+\DeclareOption{basque}
+  {\vref@addto\extrasbasque{%
+    \def\reftextfaceafter {hurrengo orrialdean}%
+    \def\reftextfacebefore{aurreko orrialdean}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {uneko orrialdean}%
+    \def\reftextfaraway#1{~\pageref{#1}. orrialdean}%
+    \def\reftextpagerange#1#2{~\pageref{#1}--\pageref{#2} orrialdeetan}%
+    \def\reftextlabelrange#1#2{\ref{#1}.etik \ref{#2}.eraino}%
+  }}
+%    \end{macrocode}
+%    Text for the Bahasa Malaysia defaults was contributed by
+%    Bob Margolis 2005-12-02.
+%
+%    Notes: pada muka surat translates as ``on the page'' though BM has no
+%    definite (or indefinite) article; adjectives and other modifiers follow
+%    the noun (clause); bertentangan is ``opposite'' in the sense of
+%    ``facing''; berikutnya is ``next'' (in this context - actually
+%    next-to-this, literally); berikutnya also translates as ``following
+%    this'' sebelumnya is ``preceding''; also ``previous'' ``ini'' translates,
+%    literally, as ``this'' but is also used in the sense of current page.
+% \changes{v1.4o}{2005/12/02}{Bahasa Malaysia defaults added.}
+%    \begin{macrocode}
+\DeclareOption{bahasam}
+  {\vref@addto\extrasbahasam{%
+    \def\reftextfaceafter {pada muka surat \reftextvario{bertentangan}{berikutnya}}%
+    \def\reftextfacebefore{pada muka surat \reftextvario{bertentangan}{sebelumnya} }%
+    \def\reftextafter     {pada muka surat berikutnya}%
+    \def\reftextbefore    {pada muka surat sebelumnya}%
+    \def\reftextcurrent   {pada muka surat ini}%
+    \def\reftextfaraway#1{pada muka surat~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pada muka surat~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for brazil defaults was contributed by
+%    Alcino Dall Igna Junior\\
+%    (|adij@di.ufpe.br|).
+% \changes{v1.0g}{1994/05/18}{Brazil defaults added.}
+% \changes{v1.4o}{2005/11/07}{Added a few more brazil strings}
+% \changes{v1.4r}{2007/05/26}{Misspelling of \cs{extrasbrazil}}
+%    \begin{macrocode}
+\DeclareOption{brazil}
+  {\vref@addto\extrasbrazil{%
+    \def\reftextfaceafter {na \reftextvario{p\'agina oposta}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextfacebefore{na p\'agina \reftextvario{oposta}{anterior}}%
+    \def\reftextafter     {na \reftextvario{p\'agina seguinte}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextbefore{na p\'agina \reftextvario{anterior}{precedente}}%
+    \def\reftextcurrent   {\reftextvario{nesta p\'agina}{na p\'agina
+                           corrente}}%
+    \def\reftextfaraway#1{na p\'agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{nas p\'aginas~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for Breton defaults was contributed by
+%    Christian ROLLAND\\
+%    (|Christian.Rolland@univ-brest.fr|).
+% \changes{v1.0o}{1994/09/27}{Added defaults for breton}
+%    \begin{macrocode}
+\DeclareOption{breton}
+  {\vref@excuse{breton}%
+   \vref@addto\extrasbreton{%
+    \def\reftextfaceafter {war ar bajenn \reftextvario{a-dal}{da heul}}%
+    \def\reftextfacebefore{war ar bajenn \reftextvario{a-dal}{a-raok}}%
+    \def\reftextafter     {war ar bajenn da heul}%
+    \def\reftextbefore    {war ar bajenn a-raok}%
+    \def\reftextcurrent   {war ar \reftextvario{bajenn-ma\~n}%
+                                               {bajenn war-wel}}%
+    \def\reftextfaraway#1{war ar bajenn~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\vref@stringwarning\reftextpagerange
+                              on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\vref@stringwarning\reflabelpagerange
+                               \ref{#1} to~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for Bulgarian defaults was contributed by
+%    Georgi Boshnakov\\  (|georgi.boshnakov@gmail.com|).
+% \changes{v1.4q}{2006/05/23}{Added defaults for bulgarian}
+%    \begin{macrocode}
+\DeclareOption{bulgarian}%
+ {\vref@addto\extrasbulgarian{%
+   \def\reftextfaceafter{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrery\cyrs\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextfacebefore{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrery\cyrs\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrp\cyrr\cyre\cyrd\cyrn\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextafter{\cyrn\cyra\
+         \reftextvario{\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}%
+                      {\cyrs\cyrl\cyre\cyrd\cyrv\cyra\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextbefore{\cyrn\cyra\
+         \reftextvario{\cyrp\cyrr\cyre\cyrd\cyrn\cyra\cyrt\cyra}%
+                      {\cyrp\cyrr\cyre\cyrd\cyri\cyrsh\cyrn\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextcurrent{\cyrn\cyra\
+         \reftextvario{\cyrt\cyra\cyrz\cyri}%
+                      {\cyrt\cyre\cyrk\cyru\cyrshch\cyra\cyrt\cyra}
+         \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra}%
+   \def\reftextfaraway#1{\cyrn\cyra\ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyra
+                         ~\pageref{#1}}%
+   \def\reftextpagerange#1#2{\cyrn\cyra\
+                        \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyri
+                        ~\pageref{#1}--\pageref{#2}}%
+   \def\reftextlabelrange#1#2{\ref{#1} \cyrd\cyro~\ref{#2}}%
+ }}
+%    \end{macrocode}
+%    Text for catalan defaults was contributed by Robert Fuster\\
+%    (\verb=rfuster@mat.upv.es=).
+% \changes{v1.1c}{1997/06/12}{Added defaults for catalan}
+% \changes{v1.2g}{2000/08/22}{Updated defaults for catalan}
+%    \begin{macrocode}
+\DeclareOption{catalan}
+  {\vref@addto\extrascatalan{%
+    \def\reftextfaceafter {a la p\`agina seg\"uent}%
+    \def\reftextfacebefore{a la p\`agina anterior}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {en aquesta p\`agina}%
+    \def\reftextfaraway#1{a la p\`agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{a les
+                     p\`agines~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for croatian defaults was contributed by \v{S}ime Ungar
+%    (\verb=ungar@math.hr=).
+% \changes{v1.4p}{2006/05/13}{Added defaults for croatian}
+%    \begin{macrocode}
+\DeclareOption{croatian}
+   {\vref@addto\extrascroatian{%
+     \def\reftextfaceafter {na sljede\'coj stranici}%
+     \def\reftextfacebefore{na prethodnoj stranici}%
+     \let\reftextafter     \reftextfaceafter
+     \let\reftextbefore    \reftextfacebefore
+     \def\reftextcurrent   {na ovoj stranici}%
+     \def\reftextfaraway#1{na stranici~\pageref{#1}}%
+     \def\reftextpagerange#1#2{na stranicama~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} do~\ref{#2}}%
+   }}
+%    \end{macrocode}
+%    Defaults for the Czech option provided by Milan Vancura
+%    \verb=<milan@suse.cz>=.
+% \changes{v1.2e}{2000/04/04}{Added czech defaults}
+%    \begin{macrocode}
+\DeclareOption{czech}
+  {%\vref@excuse{czech}%
+   \vref@addto\extrasczech{%
+    \def\reftextfaceafter {na n\'a\-sle\-du\-j\'\i c\'\i\ stran\v{e}}%
+    \def\reftextfacebefore{na p\v{r}ed\-choz\'\i\ stran\v{e}}%
+    \def\reftextafter     {na n\'a\-sle\-du\-j\'\i c\'\i\ stran\v{e}}%
+    \def\reftextbefore    {na p\v{r}ed\-choz\'\i\ stran\v{e}}%
+    \def\reftextcurrent   {na t\'eto stran\v{e}}%
+    \def\reftextfaraway#1{na stran\v{e}~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stran\'ach~\pageref{#1}\--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a\v{z}~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Defaults for Danish provided by Torsten Martinsen
+%    (\verb=tmar91@kom.auc.dk=). Further defaults by Ole Laursen
+%    (\verb=olau@hardworking.dk=).
+% \changes{v1.0n}{1994/09/25}{Added Danish defaults}
+% \changes{v1.2h}{2000/12/30}{Updates to Danish defaults}
+%    \begin{macrocode}
+\DeclareOption{danish}
+  {\vref@addto\extrasdanish{%
+    \def\reftextfaceafter {p\aa{} \reftextvario{modst\aa ende}%
+                                               {n\ae ste} side}%
+    \def\reftextfacebefore{p\aa{} \reftextvario{modst\aa ende}%
+                                               {forrige} side}%
+    \def\reftextafter     {p\aa{} \reftextvario{den f\o lgende}%
+                                               {n\ae ste} side}%
+    \def\reftextbefore    {p\aa{} \reftextvario{forrige side}
+                                               {foreg\aa ende side}}%
+    \def\reftextcurrent   {p\aa{} denne side}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Default string for dutch have been contributed by Frank Poppe
+%    (\verb=POPPE@SWOV.NL=).
+%    This option currently supports one additional string macro
+%    |\refpagename| so that you can easily change to |bladzijde|
+%    instead of |pagina| if you prefer this word for ``page''.
+%    However, I will not guarantee that this will survive future
+%    versions of this package, so use it on your own risk (you can
+%    always update the full strings to be on the safe side).
+% \changes{v1.0l}{1994/07/07}{Added dutch defaults}
+% \changes{v1.2a}{1998/08/22}{Added dutch defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+%    \begin{macrocode}
+\DeclareOption{dutch}
+  {\vref@addto\extrasdutch{%
+    \def\refpagename{pagina}%
+    \def\reftextfaceafter {op de \reftextvario{rechter \refpagename}%
+                                          {\refpagename\ hiernaast}}%
+    \def\reftextfacebefore{op de \reftextvario{linker \refpagename}%
+                                         {\refpagename\ hiernaast}}%
+    \def\reftextafter     {op de \reftextvario{volgende \refpagename}%
+                                              {\refpagename\ hierna}}%
+    \def\reftextbefore    {op de \reftextvario{vorige \refpagename}%
+                                          {\refpagename\ hiervoor}}%
+    \def\reftextcurrent   {op deze \refpagename}%
+    \def\reftextfaraway#1{op \refpagename~\pageref{#1}}%
+%    \end{macrocode}
+%    Concerning the next defaults I received the following comment by
+%    Frederik Fouvry \texttt{<fouvry@coli.uni-sb.de>}:
+%    ``In the Dutch options (where I can exert a proper language
+%    judgement ;-), `t/m' is not used in formal (scientific) texts.  I
+%    would either use `--' or `tot en met' (the abbreviation written
+%    out). ''
+% \changes{v1.4d}{2002/11/11}{Changed default for \cs{reftextlabelrange}}
+% \changes{v1.4m}{2005/06/09}{Fixed \cs{reftextlabelrange} (pr/3791)}
+%    \begin{macrocode}
+    \def\reftextpagerange#1#2{op pagina's~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+%    \end{macrocode}
+% \changes{v1.2a}{1998/08/22}{Added english defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+% \changes{v1.4d}{2002/11/11}{Changed default for \cs{reftextbefore}}
+%    \begin{macrocode}
+\DeclareOption{english}
+  {\vref@addto\extrasenglish{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%
+%    The esperanto strings were suggested by Albert Reiner
+%    (\verb=areiner@tph.tuwien.ac.at=).
+%  \changes{v1.4x}{2010/08/04}{Defaults for esperanto added}
+%    \begin{macrocode}
+\DeclareOption{esperanto}
+  {\vref@addto\extrasesperanto{%
+    \def\reftextfaceafter{en la
+        \reftextvario{flanka}{sekva} pa\^go}%
+    \def\reftextfacebefore{en la
+        \reftextvario{flanka}{anta\u ua} pa\^go}%
+    \def\reftextafter{en la sekva pa\^go}%
+    \def\reftextbefore{en la anta\u ua pa\^go}%
+    \def\reftextcurrent{\reftextvario{\^ci-pa\^ge}%
+        {en \^ci tiu pa\^go}}%
+    \def\reftextfaraway#1{en pa\^go~\pageref{#1}}%
+    \def\reftextpagerange#1#2{en pa\^goj~\pageref{#1} \^gis \pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} \^gis~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The finnish strings were suggested by Matti Rintala
+%    (\verb=bitti@cs.tut.fi=) and Hillevi Gavel
+%    \verb=Hillevi.Gavel@mdh.se=.
+% \changes{v1.0m}{1994/09/23}{Added finnish strings}
+% \changes{v1.4o}{2005/11/07}{Added a few more finnish strings}
+%    \begin{macrocode}
+\DeclareOption{finnish}
+  {\vref@addto\extrasfinnish{%
+    \def\reftextfaceafter {\reftextvario{viereisell\"a}%
+                                        {seuraavalla} sivulla}%
+    \def\reftextfacebefore{\reftextvario{viereisell\"a}%
+                                        {edellisell\"a} sivulla}%
+    \def\reftextafter     {seuraavalla sivulla}%
+    \def\reftextbefore    {edellisell\"a sivulla}%
+    \def\reftextcurrent   {t\"all\"a sivulla}%
+    \def\reftextfaraway#1{sivulla~\pageref{#1}}%
+     \def\reftextpagerange#1#2{sivuilla~\pageref{#1}--\pageref{#2}}%
+%    \end{macrocode}
+%    Can't combine numbers with the necessary suffix well.
+%    \begin{macrocode}
+     \def\reftextlabelrange#1#2{\ref{#1}--\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    French defaults are provided by Daniel Flippo
+%    (\verb=Daniel.Flipo@univ-lille1.fr=).
+% \changes{v1.0j}{1994/06/21}{Added french defaults}
+% \changes{v1.2a}{1998/08/22}{Added french defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+%    \begin{macrocode}
+\DeclareOption{french}
+  {\vref@addto\extrasfrench{%
+    \def\reftextfaceafter {page \reftextvario{ci-contre}{suivante}}%
+    \def\reftextfacebefore{page \reftextvario{ci-contre}%
+                          {pr\'ec\'edente}}%
+    \def\reftextafter     {page suivante}%
+    \def\reftextbefore    {page pr\'ec\'edente}%
+    \def\reftextcurrent   {de la pr\'esente page}%
+    \def\reftextfaraway#1{page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} \`a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Galician defaults are provided by Matthias Moebius\\
+%    (\texttt{Matthias.Moebius@uni-konstanz.de}).
+% \changes{v1.1f}{1998/04/25}{Added galician defaults}
+% \changes{v1.4o}{2005/11/10}{Added further galician defaults}
+% \changes{v1.4o}{2005/11/26}{Some further corrections}
+% \changes{v1.5b}{2015/09/22}{Fixed blunder from 2005 -
+%                             galician option clearly never used}
+%    \begin{macrocode}
+\DeclareOption{galician}
+  {\vref@addto\extrasgalician{%
+    \def\reftextfaceafter {na p\'axina oposta}%
+    \def\reftextfacebefore\reftextfaceafter
+    \def\reftextafter     {na p\'axina seguinte}%
+    \def\reftextbefore    {na p\'axina anterior}%
+    \def\reftextcurrent   {nesta p\'axina}%
+    \def\reftextfaraway#1{na p\'axina~\pageref{#1}}%
+     \def\reftextpagerange#1#2{%
+                nas p\'axinas~\pageref{#1}-\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    There are no good variants for German (I think and still think but
+%    this is a matter of taste :-).
+% \changes{v1.0b}{1994/01/31}{Replace in incorrect `def by `let}
+%    The following definitions were recently suggested to me but since
+%    the original are in for a long time i don't want to change them
+%    now since that could make a lot of documents change their formatting.
+%    If you fancy them, add a redefinition of the corresponding macro(s)
+%    to the preamble of your document.
+%\begin{verbatim}
+%    \def\reftextfaceafter {auf der \reftextvario
+%          {gegen\"uberliegenden}{anderen} Seite}%
+%    \def\reftextfacebefore {auf der \reftextvario
+%          {gegen\"uberliegenden}{anderen} Seite}%
+%    \def\reftextafter     {auf der \reftextvario
+%          {n\"achsten}{folgenden} Seite}%
+%    \def\reftextbefore    {auf der \reftextvario
+%          {vorigen}{vorhergehenden} Seite}%
+%    \def\reftextcurrent   {\reftextvario
+%          {auf dieser}{diese} Seite}%
+%\end{verbatim}
+% \changes{v1.4n}{2005/07/24}{Small change}
+%    \begin{macrocode}
+\DeclareOption{german}
+  {\vref@addto\extrasgerman{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf den Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+%    \end{macrocode}
+% \changes{v1.2d}{2000/01/11}{Added ngerman defaults (identical to german)}
+% \changes{v1.4n}{2005/07/24}{Small change}
+%    The ngerman defaults are the same but needed for ``Neue Rechtschreibung''
+%    (i.e., a different set of hyphenation patterns).
+%    \begin{macrocode}
+\DeclareOption{ngerman}
+  {\vref@addto\extrasngerman{%
+    \def\reftextfaceafter {auf der n\"achsten Seite}%
+    \def\reftextfacebefore{auf der vorherigen Seite}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {auf dieser Seite}%
+    \def\reftextfaraway#1{auf Seite~\pageref{#1}}%
+    \def\reftextpagerange#1#2{auf den Seiten~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} bis~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Defaults for greek suggested by Apostolos Syropoulos\\
+%    (\verb=apostolo@obelix.ee.duth.gr=).
+% \changes{v1.2a}{1998/08/22}{Added defaults for greek}
+%    \begin{macrocode}
+\DeclareOption{greek}
+  {\vref@addto\extrasgreek{%
+    \def\reftextfaceafter {sthn \reftextvario{paro'usa}%
+                           {ep'omenh} sel'ida}%
+    \def\reftextfacebefore{sthn \reftextvario{paro'usa}{prohgo'umenh}
+                           sel'ida}%
+    \def\reftextafter     {sthn ep'omenh sel'ida}%
+    \def\reftextbefore    {sthn prohgo'umenh sel'ida}%
+    \def\reftextcurrent   {s'' aut'h th sel'ida}%
+    \def\reftextfaraway#1{sth sel'ida\nobreakspace\pageref{#1}}%
+    \def\reftextpagerange#1#2{stis sel'ides\nobreakspace
+                          \pageref{#1}---\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} ws\nobreakspace\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Icelandic defaults suggested by Thorhallur Sverrisson
+%    (\verb=thorhs@basis.is=).
+% \changes{v1.4t}{2007/09/07}{Added defaults for icelandic}
+%    \begin{macrocode}
+\DeclareOption{icelandic}
+  {\vref@addto\extrasicelandic{%
+    \def\reftextfaceafter {\'{a} \reftextvario{n{\ae}stu}%
+                                              {n{\ae}stu} s\'{i}{\dh}u}%
+    \def\reftextfacebefore{\'{a} \reftextvario{fyrri}%
+                                              {fyrri} s\'{i}{\dh}u}%
+    \def\reftextafter     {\'{a} \reftextvario{n{\ae}stu}%
+                                              {n{\ae}stu} s\'{i}{\dh}u}%
+    \def\reftextbefore    {\'{a} \reftextvario{fyrri}{fyrri} s\'{i}{\dh}u}%
+    \def\reftextcurrent   {\'{a} \reftextvario{{\th}essari}%
+                                              {{\th}essari} s\'{i}{\dh}u}%
+    \def\reftextfaraway#1{\'{a} s\'{i}{\dh}u~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\'{a} s\'{i}{\dh}um~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Defaults for Italian suggested by Giovanni Pensa
+%    (\verb=pensa@dsi.unimi.it=) with i{\TeX}nici.
+% \changes{v1.1b}{1995/10/19}{Added defaults for Italian}
+% \changes{v1.2a}{1998/08/22}{Removed incorrect warning}
+% \changes{v1.4k}{2004/10/30}{Added missing defaults supplied by Lapo Mori}
+% \changes{v1.4n}{2005/07/24}{Small change}
+% \changes{v1.4u}{2009/03/21}{Correction for \cs{reftextfaraway} suggested
+%                             by Lorenzo Pantieri}
+%    \begin{macrocode}
+\DeclareOption{italian}
+  {\vref@addto\extrasitalian{%
+    \def\reftextfaceafter {\reftextvario{a fronte}%
+                           {nella pagina successiva}}%
+    \def\reftextfacebefore{\reftextvario{a fronte}%
+                           {nella pagina precedente}}%
+    \def\reftextafter     {nella pagina \reftextvario{seguente}%
+                           {successiva}}%
+    \def\reftextbefore    {nella pagina precedente}%
+    \def\reftextcurrent   {in questa pagina}%
+    \def\reftextfaraway#1{a pagina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{nelle pagine~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{da~\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%   Defaults for Hungarian by Jeff Goldberg
+%   (\verb=jeffrey@goldmark.org=).
+%   There is a problem with the use of the definite article
+%   \textit{a} or \textit{az} in Hungarian before expansions
+%   of |\vref| or |\ref|.  The problem is that the word
+%   should be \textit{az} if the number following would begin with
+%   a vowel if spelled out, and \textit{a} if the number would begin
+%   with a consonant.
+%
+%   The option assumes that there is a command |\aza| defined which
+%   helps resolving this problem.\footnote{This information is actually quite
+%   old but unfortunately never made it into varioref. In case any work
+%   has been undertaken to resolve this please inform the author about it.}
+% \changes{v1.2a}{1998/08/22}{Added defaults for magyar}
+% \changes{v1.4j}{2005/01/22}{Defined \cs{reftextfaceafter} and
+%       \cs{reftextfacebefore} instead of \cs{reftextafter} and \cs{reftextbefore}}
+%    \begin{macrocode}
+\DeclareOption{magyar}
+  {\vref@addto\extrasmagyar{%
+    \def\reftextafter {a k\"o\-vet\-kez\H{o} ol\-da\-lon}%
+    \def\reftextbefore{az el\H{o}\-z\H{o} ol\-da\-lon}%
+    \def\reftextfaceafter {\reftextvario{a t\'ul\-ol\-da\-lon}%
+                          {a k\"o\-vet\-kez\H{o} ol\-da\-lon}}%
+    \def\reftextfacebefore{\reftextvario{a t\'ul\-ol\-da\-lon}%
+                          {az el\H{o}\-z\H{o} ol\-da\-lon}}%
+    \def\reftextcurrent   {ezen az ol\-da\-lon}%
+%    \end{macrocode}
+%    The following suggested patch has not been added yet (pending changes
+%    in babel system).
+%\begin{verbatim}
+%    \def\reftextfaraway#1{a~\csname @@magyar@az@lowxu\endcsname
+%                                                {\pageref{#1}}.~ol\-da\-lon}%
+%    \def\reftextpagerange#1#2{a~\csname @@magyar@az@lowxu\endcsname
+%                                                        {\pageref{#1}}%
+%      --\pageref{#2}.~ol\-da\-la\-kon}%
+%    \def\reftextlabelrange#1#2{{}\csname @@magyar@told\endcsname\ref{#1}+tol
+%      \ref{#2}-ig}% Dat: `{}' is here for anti-\capitalize
+%\end{verbatim}
+%    \begin{macrocode}
+    \def\reftextfaraway#1{\aza{\pageref{#1}} \pageref{#1}.~ol\-da\-lon}%
+    \def\reftextpagerange#1#2{\vref@stringwarning\reftextpagerange
+                              on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\vref@stringwarning\reflabelpagerange
+                               \ref{#1} to~\ref{#2}}%
+   }%
+%    \end{macrocode}
+%    The |\AtBeginDocument| needs to be executed when the option is
+%    processed and not inside the babel interface.
+% \changes{v1.4i}{2004/02/27}{Moved \cs{AtBeginDocument}}
+%    \begin{macrocode}
+   \AtBeginDocument{\providecommand\aza[1]{a/az%
+       \PackageError{varioref}{%
+         Proper definition for command \noexpand\aza missing}%
+        {You need to (re)define the command \noexpand\aza that
+         takes one argument (a number or a \noexpand\pageref command)
+         and produces the string `a' or `az' depending on the argument
+         value. It should also accept an optional argument (default `l')
+         to denote whether or not the string should be lowercase or
+         uppercase.}}}%
+  }
+%    \end{macrocode}
+%    The Norwegian and `nynorsk' translations have been provided by
+%    Dag F Langmyhr \verb=<dag@ifi.uio.no>= and Karl Ove Hufthammer
+%    \verb=<huftis@bigfoot.com>=.
+% \changes{v1.0q}{1995/04/06}{Added defaults for norsk}
+% \changes{v1.0q}{1995/04/06}{Added defaults for nynorsk}
+% \changes{v1.2a}{1998/08/22}{Updated defaults for norsk}
+% \changes{v1.2a}{1998/08/22}{Updated defaults for nynorsk}
+% \changes{v1.2a}{1998/08/22}{Added norsk defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+% \changes{v1.2a}{1998/08/22}{Added nynorsk defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+% \changes{v1.2i}{2001/01/12}{Updated nynorsk defaults}
+%    \begin{macrocode}
+\DeclareOption{norsk}
+  {\vref@addto\extrasnorsk{%
+    \def\reftextfaceafter {p\aa{} neste side}%
+    \def\reftextfacebefore{p\aa{} forrige side}%
+    \def\reftextafter     {p\aa{} neste side}%
+    \def\reftextbefore    {p\aa{} forrige side}%
+    \def\reftextcurrent   {p\aa{} denne siden}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+\DeclareOption{nynorsk}
+  {\vref@addto\extrasnynorsk{%
+    \def\reftextfaceafter {p\aa{} neste side}%
+    \def\reftextfacebefore{p\aa{} f\o{}rre side}%
+    \def\reftextafter     {p\aa{} neste side}%
+    \def\reftextbefore    {p\aa{} f\o{}rre side}%
+    \def\reftextcurrent   {p\aa{} denne sida}%
+    \def\reftextfaraway#1{p\aa{} side~\pageref{#1}}%
+    \def\reftextpagerange#1#2{p\aa{} side~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} til~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The polish translations have been provided by
+%    Tomasz Michniewski \\
+%    \verb=<tomekm@ias.wat.waw.pl>=.
+%    The use of the command \verb=\eob= and \verb=aob= etc.\
+%    requires appropriate definitions as provided, for example, by
+%    the babel system. This should probably be handled differently
+%    but it would require modifications in babel's language support.
+% \changes{v1.1d}{1997/12/06}{Added defaults for polish}
+% \changes{v1.2a}{1998/08/22}{Added polish defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+% \changes{v1.4n}{2005/09/14}{Changed default for \cs{reftextfaraway}}
+%    \begin{macrocode}
+\DeclareOption{polish}
+  {\vref@addto\extraspolish{%
+    \def\reftextfaceafter {na \reftextvario{s\aob{}siedniej}%
+                                   {nast\eob{}pnej} stronie}%
+    \def\reftextfacebefore{na \reftextvario{s\aob{}siedniej}%
+                                   {poprzedniej} stronie}%
+    \def\reftextafter     {na nast\eob{}pnej stronie}%
+    \def\reftextbefore    {na poprzedniej stronie}%
+    \def\reftextcurrent   {na \reftextvario{tej
+                           samej}{bie\zkb{}\aob{}cej} stronie}%
+    \def\reftextfaraway#1{na stronie~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stronach~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{od~\ref{#1} do~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The portuguese default text has been provided by
+%    Jos\'e Carlos Oliveira Santos \verb=jcsantos@fc.up.pt=.
+% \changes{v1.2b}{1999/11/25}{Added portuguese defaults}
+% \changes{v1.2c}{1999/12/02}{Added more portuguese defaults}
+% \changes{v1.4r}{2007/05/26}{Misspelling of \cs{extrasportuges}}
+%    \begin{macrocode}
+\DeclareOption{portuges}
+  {\vref@addto\extrasportuges{%
+    \def\reftextfaceafter {na \reftextvario{p\'agina ao lado}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextfacebefore{na p\'agina \reftextvario{ao lado}{anterior}}%
+    \def\reftextafter     {na \reftextvario{p\'agina seguinte}{pr\'oxima
+                           p\'agina}}%
+    \def\reftextbefore{na p\'agina \reftextvario{anterior}{precedente}}%
+    \def\reftextcurrent   {nesta p\'agina}%
+    \def\reftextfaraway#1{na p\'agina~\pageref{#1}}%
+     \def\reftextpagerange#1#2{nas p\'aginas~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+% Updates to the default text for Romanian have been suggested by Florin Oprina
+%  (\verb=<florin.oprina@gmail.com>=).
+% \changes{v1.4v}{2009/06/13}{Incorrect text in \cs{reftextafter} (pr/4070)}
+% \changes{v1.5a}{2014/07/03}{Correct text in \cs{reftextbefore}}
+%    \begin{macrocode}
+\DeclareOption{romanian}
+  {\vref@addto\extrasromanian{%
+    \def\reftextfaceafter {pe pagina \reftextvario{opus\u{a}}{urm\u{a}toarei}}%
+    \def\reftextfacebefore{pe pagina \reftextvario{opus\u{a}}{precedentei}}%
+    \def\reftextafter     {\reftextvario{pe pagina urm\u{a}toare}%
+                                        {pe urm\u{a}toarea pagin\u{a}}}%
+    \def\reftextbefore    {pe pagina \reftextvario{precedent\u{a}}%
+                                                  {precedentei}}%
+    \def\reftextcurrent   {pe aceast\u{a} pagin\u{a}}%
+    \def\reftextfaraway#1{pe pagina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{pe paginile~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} la~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The text for russian was taken from the book in Russian by
+%    I.~A.~Kotelnikov and P.~Z.~Chebotaev, and adapted
+%    to the encoding-independent form by Vladimir Volovich
+%    (\verb=vvv@vsu.ru=).
+% \changes{v1.2a}{1998/11/23}{Added russian strings}
+% \changes{v1.2a}{1998/11/24}{Added defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+%    \begin{macrocode}
+\DeclareOption{russian}
+  {\vref@addto\extrasrussian{%
+    \def\reftextfaceafter{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+      \cyrt\cyri\cyrv\cyro\cyrp\cyro\cyrl\cyro\cyrzh\cyrn\cyro\cyrishrt}%
+      {\cyrs\cyrl\cyre\cyrd\cyru\cyryu\cyrshch\cyre\cyrishrt}\ \cyrs\cyrt
+      \cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextfacebefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+      \cyrt\cyri\cyrv\cyro\cyrp\cyro\cyrl\cyro\cyrzh\cyrn\cyro\cyrishrt}%
+      {\cyrp\cyrr\cyre\cyrd\cyrery\cyrd\cyru\cyrshch\cyre\cyrishrt}\
+      \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextafter{\cyrn\cyra\ \cyrs\cyrl\cyre\cyrd\cyru\cyryu\cyrshch
+      \cyre\cyrishrt\ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextbefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyre\cyrd
+      \cyrsh\cyre\cyrs\cyrt\cyrv\cyru\cyryu\cyrshch\cyre\cyrishrt}%
+      {\cyrp\cyrr\cyre\cyrd\cyrery\cyrd\cyru\cyrshch\cyre\cyrishrt}%
+      \ \cyrs\cyrt\cyrr\cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextcurrent{\cyrn\cyra\ \reftextvario{\cyrerev\cyrt\cyro
+      \cyrishrt}{\cyrd\cyra\cyrn\cyrn\cyro\cyrishrt}\ \cyrs\cyrt\cyrr
+      \cyra\cyrn\cyri\cyrc\cyre}%
+    \def\reftextfaraway#1{\cyrn\cyra\ \cyrs.~\pageref{#1}}%
+    \def\reftextpagerange#1#2{\cyrn\cyra\ \cyrs\cyrt\cyrr\cyra\cyrn
+      \cyri\cyrc\cyra\cyrh~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\cyrs~\ref{#1}\ \cyrp\cyro~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The text for slovak defaults was contributed by Miroslav Sedivy\\
+%    (\verb=<miro@slovensko.com>=).
+% \changes{v1.4b}{2002/03/11}{Contributed defaults added}
+%    \begin{macrocode}
+\DeclareOption{slovak}
+  {\vref@addto\extrasslovak{%
+    \def\reftextfaceafter {na \reftextvario{proti\v lahlej}%
+                          {nasleduj\'ucej} strane}%
+    \def\reftextfacebefore{na \reftextvario{proti\v lahlej}%
+                          {predch\'adzaj\'ucej} strane}%
+    \def\reftextafter     {na \reftextvario{nasleduj\'ucej}%
+                          {\v dal\v sej} strane}%
+    \def\reftextbefore    {na \reftextvario{predch\'adzaj\'ucej}%
+                          {predo\v slej} strane}%
+    \def\reftextcurrent   {na tejto strane}%
+    \def\reftextfaraway#1{na strane~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na stran\'ach~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a\v z~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The text for slovene defaults was contributed by Roman Maurer\\
+%    (\verb=<roman.maurer@amis.net>=).
+% \changes{v1.4a}{2002/03/05}{Contributed defaults added}
+%    \begin{macrocode}
+\DeclareOption{slovene}
+  {\vref@addto\extrasslovene{%
+    \def\reftextfaceafter {na naslednji strani}%
+    \def\reftextfacebefore{na prej\v{s}nji strani}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {na \reftextvario{tej}{trenutni} strani}%
+    \def\reftextfaraway#1{na strani~\pageref{#1}}%
+    \def\reftextpagerange#1#2{na straneh~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{od~\ref{#1} do~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    Text for spanish defaults was contributed by Julio Sanchez
+%    (\verb=jsanchez@gmv.es=) and Fernando Dobladez (\verb=<ferd@fuego.com>=).
+% \changes{v1.0f}{1994/03/16}{Inserted missing hash mark}
+% \changes{v1.0k}{1994/06/05}{Corrected misspelled cmd `extrasspanish}
+% \changes{v1.4a}{2002/03/05}{Missing defaults added}
+% \changes{v1.4o}{2005/11/26}{Single hyphen in range}
+%    \begin{macrocode}
+\DeclareOption{spanish}
+  {\vref@addto\extrasspanish{%
+    \def\reftextfaceafter {en la p\'agina siguiente}%
+    \def\reftextfacebefore{en la p\'agina anterior}%
+    \let\reftextafter     \reftextfaceafter
+    \let\reftextbefore    \reftextfacebefore
+    \def\reftextcurrent   {en esta p\'agina}%
+    \def\reftextfaraway#1{en la p\'agina~\pageref{#1}}%
+    \def\reftextpagerange#1#2{en las p\'aginas~\pageref{#1}%
+                                             -\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} a~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The text for swedish was contributed by Mats Dahlgren
+%    (\verb=matsd@sssk.se=).
+% \changes{v1.0p}{1995/01/10}{Added swedish strings}
+% \changes{v1.2a}{1998/08/22}{Added swedish defaults for
+%      \cs{reftextpagerange} and \cs{reftextlabelrange}}
+%    \begin{macrocode}
+\DeclareOption{swedish}
+  {\vref@addto\extrasswedish{%
+     \def\reftextfaceafter {p\aa\ \reftextvario{motst\aa ende}%
+                                             {n\"{a}sta} sida}%
+     \def\reftextfacebefore{p\aa\ \reftextvario{motst\aa ende}%
+                                      {f\"{o}reg\aa ende} sida}%
+     \def\reftextafter     {p\aa\ \reftextvario{f\"{o}ljande}%
+                                            {n\"{a}sta} sida}%
+     \def\reftextbefore    {p\aa\ f\"{o}reg\aa ende sida}%
+     \def\reftextcurrent   {p\aa\ denna sida}%
+     \def\reftextfaraway#1{p\aa\ sidan~\pageref{#1}}%
+     \def\reftextpagerange#1#2{p\aa\
+                               sidorna~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\ref{#1} till~\ref{#2}}%
+  }}
+\DeclareOption{turkish}
+  {\vref@excuse{turkish}%
+   \vref@addto\extrasturkish{%
+    \def\reftextfaceafter {on the \reftextvario{facing}{next} page}%
+    \def\reftextfacebefore{on the \reftextvario{facing}{preceding}
+                           page}%
+    \def\reftextafter     {on the \reftextvario{following}{next} page}%
+    \def\reftextbefore    {on the \reftextvario{preceding}{previous} page}%
+    \def\reftextcurrent   {on \reftextvario{this}{the current} page}%
+    \def\reftextfaraway#1{on page~\pageref{#1}}%
+    \def\reftextpagerange#1#2{on pages~\pageref{#1}--\pageref{#2}}%
+    \def\reftextlabelrange#1#2{\ref{#1} to~\ref{#2}}%
+  }}
+%    \end{macrocode}
+%    The text for Ukrainian defaults was contributed by Mykola Lyakhovych\\
+%    (\verb=<lyakhovych@mail.ru>=).
+% \changes{v1.4l}{2005/04/24}{Contributed defaults added}
+%    \begin{macrocode}
+\DeclareOption{ukrainian}
+   {\vref@addto\extrasukrainian{%
+     \def\reftextfaceafter{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+       \cyrt\cyri\cyrl\cyre\cyrzh\cyrn\cyrii\cyrishrt}%
+       {\cyrn\cyra\cyrs\cyrt\cyru\cyrp\cyrn\cyrii\cyrishrt}\ \cyrs\cyrt
+       \cyro\cyrr\cyri\cyrn\cyrc\cyrii}%
+     \def\reftextfacebefore{\cyrn\cyra\ \reftextvario{\cyrp\cyrr\cyro
+       \cyrt\cyri\cyrl\cyre\cyrzh\cyrn\cyrii\cyrishrt}%
+       {\cyrp\cyro\cyrp\cyre\cyrr\cyre\cyrd\cyrn\cyrii\cyrishrt}\
+       \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextafter{\cyrn\cyra\ \cyrn\cyra\cyrs\cyrt\cyru\cyrp\cyrn
+       \cyrii\cyrishrt\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextbefore{\cyrn\cyra\ \cyrp\cyro\cyrp\cyre\cyrr\cyre\cyrd
+       \cyrn\cyrii\cyrishrt\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn\cyrc\cyrii}%
+     \def\reftextcurrent{\cyrn\cyra\ \reftextvario{\cyrc\cyrii\cyrishrt}%
+       {\cyrd\cyra\cyrn\cyrii\cyrishrt}\ \cyrs\cyrt\cyro\cyrr\cyrii\cyrn
+       \cyrc\cyrii}%
+     \def\reftextfaraway#1{\cyrn\cyra\ \cyrs.~\pageref{#1}}%
+     \def\reftextpagerange#1#2{\cyrn\cyra\ \cyrs\cyrt\cyro\cyrr\cyrii
+       \cyrn\cyrk\cyra\cyrh~\pageref{#1}--\pageref{#2}}%
+     \def\reftextlabelrange#1#2{\cyrz~\ref{#1}\ \cyrd\cyro~\ref{#2}}%
+   }}
+%    \end{macrocode}
+%    We support francais as an alternative to french since people
+%    might be used to it, but we discurrage it.
+%    \begin{macrocode}
+\DeclareOption{francais}{%
+   \typeout{Please use `french' instead of `francais'}%
+   \ExecuteOptions{french}}
+\DeclareOption{germanb}{%
+   \typeout{Please use `german' instead of `germanb'}%
+   \ExecuteOptions{german}}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%    During document preparation errors due to |\vref| are usually of
+%    not much interest. For this reason the draft option turns them into
+%    warnings by issuing a |\vrefwarning| command. The final option
+%    (default) stops with an error message when varioref detects a possible
+%    loop.
+% \changes{v1.1h}{1998/08/01}{Added draft and final options}
+%    \begin{macrocode}
+\DeclareOption{draft}{\AtEndOfPackage\vrefwarning}
+\DeclareOption{final}{\AtEndOfPackage\vrefshowerrors} % the default
+%    \end{macrocode}
+%
+%
+%    Whether or not \pkg{varioref} uses its own white space and
+%    removes the one in the source document is handeled by the
+%    following two options. For historical reasons the default is to
+%    handle the space, but the recommendation these days is to use
+%    \texttt{nospace}.
+% \changes{v1.6a}{2019/08/25}{Provide options \texttt{space} and \texttt{nospace}}
+%    \begin{macrocode}
+\newif\if@vrefhandlespace
+\DeclareOption{space}  {\@vrefhandlespacetrue}
+\DeclareOption{nospace}{\@vrefhandlespacefalse}
+%    \end{macrocode}
+%
+%
+%
+%
+%    After all options are declared we execute the default option
+%    \texttt{english} to set up the defaults and then call
+%    |\ProcessOptions*| to handle any option passed to the package.
+%    The star form is used since we want to execute the options in the
+%    order they are given (in case this isn't used together with the
+%    \pkg{babel} package).
+%    \begin{macrocode}
+\ExecuteOptions{english,final,space}
+\ProcessOptions*
+%    \end{macrocode}
+%
+%
+% \subsection{Defining the main macros}
+%
+% \begin{macro}{\vr@cnt}
+%    To generate new labels we use a counter and construct the
+%    internal label names by prefixing the current counter value with
+%    the string |vr@|. We need a \LaTeX{} counter to get |\include|s
+%    handled correctly.
+% \changes{v0.1e}{1992/11/15}{use LaTeX counter}
+%    \begin{macrocode}
+\newcounter{vrcnt}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\vpageref}
+% \changes{v1.3a}{2001/04/12}{Scan for star form}
+% \begin{macro}{\vp@geref}
+%    The command |\vpageref| generates the appropriate string by first
+%    parsing the optional arguments (if any) and then compares the
+%    internal and the user label.  This command should be robust since
+%    the user might put it anywhere.
+%
+%    We now start by scanning for a star and then call either
+%    |\vp@gerefstar| or |\vp@geref|.
+%    The space handling logic is a bit twisted these days: if the
+%    option \texttt{space} is
+%    in force then preceding spaces in the document are removed and
+%    the star means that the command should not add its own
+%    space. However, with option \texttt{nospace} any space already in the
+%    source will be left alone and the command doesn't add its own
+%    space either. Thus in this case the star form doesn't
+%    have any effect and below |\vp@gerefstar| is let to
+%    |\vp@geref|. This allows a package like \pkg{hyperef} to redefine
+%    it and useit for its own tasks (like denoting that no link should
+%    be produced).
+%    \begin{macrocode}
+\DeclareRobustCommand\vpageref{\@ifstar
+     {\let\vref@maybe@space\@empty\vp@gerefstar}%
+     {\let\vref@maybe@space\space \vp@geref}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\def\vp@geref{\@ifnextchar[%
+%    \end{macrocode}
+%    The default for the first optional argument is the string hidden
+%    in the macro |\reftextcurrent|.
+%    \begin{macrocode}
+  \@vpageref{\@vpageref[\reftextcurrent]}%
+}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\vref@space}
+% \changes{v1.4a}{2002/03/06}{Default added}
+%    A default for |\vref@space|. This isn't really needed except in
+%    the case that somebody has hooked into the \pkg{varioref}
+%    interfaces at a lower level (which isn't really supported,
+%    but\ldots). So giving a default will prevent an error message in
+%    that case (and should hopefully produce the same behavior as before).
+%    \begin{macrocode}
+\let\vref@space\space
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@vpageref}
+%    More parsing\ldots
+%    \begin{macrocode}
+\def\@vpageref[#1]{\@ifnextchar[%
+%    \end{macrocode}
+%    By default the second optional argument is empty.
+% \changes{v1.0h}{1994/06/11}{Pass first argument in both cases}
+% \changes{v1.0i}{1994/06/20}{Do it correctly}
+% \changes{v1.6a}{2019/08/25}{Default for optional argumet changed}
+%    \begin{macrocode}
+  {\@@vpageref{#1}}{\@@vpageref{#1}[]}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@vpageref}
+%     The |\@@vpageref| macro finally generates the references by
+%    comparing the value of an internal label with the value of the
+%    user label.
+% \changes{v1.0h}{1994/06/11}{Change internal interface}
+%    \begin{macrocode}
+\def\@@vpageref#1[#2]#3{%
+%    \end{macrocode}
+%    First it switches to horizontal mode if necessary. If there was a
+%    preceding space we remember its size in |\@tempskipa| and then remove it for
+%    reinsertion later.
+% \changes{v1.6a}{2019/08/25}{Don't drop a preceding space completely
+%     but reinsert it later after setting a label}
+%    \begin{macrocode}
+  \leavevmode
+  \@tempskipa\lastskip \unskip
+%    \end{macrocode}
+%    Then it advances the counter |\c@vrcnt| by one which is used to
+%    generate internal label names.
+%    \begin{macrocode}
+  \global\advance\c@vrcnt\@ne
+%    \end{macrocode}
+%    Then it checks if for the current value of |\c@vrcnt| a label
+%    command was issued in the last run. If not it pretends that there
+%    was one with the value |{??}{??}|.  Thereafter it stores the
+%    pageref value for this label in the macro |\@tempa|.
+%    \begin{macrocode}
+  \vref@pagenum\@tempa{\the\c@vrcnt @vr}%
+%    \end{macrocode}
+%    Here we check that the generated text is not going across a page
+%    boundary.
+% \changes{v0.1f}{1993/01/01}{Add another label to catch cross-overs}
+%    \begin{macrocode}
+  \vref@pagenum\@tempb{\the\c@vrcnt @xvr}%
+%    \end{macrocode}
+% \changes{v1.0l}{1994/07/07}{Explicitly expand `label argument for
+%                            babel}
+%    In version 1.0l the label string has been turned around so that
+%    the number comes first. This was done to allow easy explicit
+%    expansion of the number before it is passed to the |\label|
+%    command. In the babel system the argument of |label| was not
+%    expanded with the result that wrong label strings have been
+%    generated. This is a general problem that might need a completely
+%    different solution in babel but for now the change below (and in
+%    some other places in the code) should solve the problem for this
+%    special combination of packages.
+%
+%    These days we actually use |\vref@label| instead of |\label| as
+%    this avoids problems with Babel or \pkg{amsmath} redefining
+%    the latter command.
+% \changes{v1.4e}{2003/01/08}{Use \cs{vref@label} instead of
+%    \cs{label} (pr/3489)}
+%    \begin{macrocode}
+  \vref@label{\the\c@vrcnt @xvr}%
+%    \end{macrocode}
+%    Since we have removed
+%    any leading space above we now insert a space here after the
+%    label. It is done here so that it is still visible from following
+%    code---the space before the label would be hidden.
+%    What kind of space depends on the options to the
+%    package. If \texttt{space} was specified, we insert our own
+%    space, namely |\vref@maybe@space|. This will typeset a space
+%    unless the star form of the current command was used.
+%    \begin{macrocode}
+  \if@vrefhandlespace
+    \vref@maybe@space
+  \else
+%    \end{macrocode}
+%    But if \texttt{nospace} is in force we simply use the same space
+%    value that was used in the source document (unless that was zero
+%    or non-existent.
+%    \begin{macrocode}
+    \ifdim\@tempskipa=\z@ \else
+      \hskip\@tempskipa
+    \fi
+  \fi
+%    \end{macrocode}
+% \changes{v1.1g}{1998/05/10}{Test if inside AMS display (pr2175)}
+%    Inside displays of the \pkg{amsmath} package the |\label| command
+%    is redefined which makes the test for loops incorrect if a |\vref|
+%    is used in, say, |\intertext|. So we test this condition first and
+%    only do the test if |\label| doesn't have a special meaning.
+%    [This is no longer necessary as |\label| isn't used any more]
+%    \begin{macrocode}
+%  \ifx\label\label@in@display\else
+  \ifx\@tempa\@tempb
+    \let\vref@may@loop\relax
+  \else
+%    \end{macrocode}
+%    If both points do not fall onto the same page with either issue
+%    an error or a warning message.
+%    However, we do no longer issue that warning now but wait until we
+%    are sure that both labels aren't ``far away'' because in that
+%    case it doesn't matter. So we just save that info in a macro now.
+% \changes{v1.0g}{1994/05/27}{Looping pages shown in wrong order}
+% \changes{v1.5c}{2016/02/16}{Delay generating the looping warning
+%                until we know more}
+%    \begin{macrocode}
+    \edef\vref@may@loop{%
+      \noexpand\vref@err{\noexpand\vref or \noexpand\vpageref
+              at page boundary
+              \@tempb-\@tempa\space (may loop)%
+              }%
+      }%
+   \fi
+%  \fi
+%    \end{macrocode}
+%    Same game for the user requested label; this time the page
+%    reference is saved in |\thevpagerefnum|.
+% \changes{v1.4c}{2002/06/14}{Use \cs{thevpagerefnum} instead of \cs{@tempb}}
+%    \begin{macrocode}
+  \vrefpagenum\thevpagerefnum{#3}%
+%    \end{macrocode}
+%    Now after the internal label has served its purpose if would be
+%    nice to free the memory it occupies by using something like
+%    \begin{verbatim}
+% \global\expandafter\let
+%        \csname r@\the\c@vrcnt @vr\endcsname\@empty
+%\end{verbatim}
+%    But this is not possible because it would result in getting
+%    `Labels may have changed\ldots' warnings for every run.  Now we
+%    are ready to produce the textual strings.
+%    \begin{macrocode}
+  \ifx\@tempa\thevpagerefnum
+%    \end{macrocode}
+%    If they are the same we insert the first argument into the input
+%    stream.  Otherwise we insert the second argument.  Recall that
+%    those are the two optional arguments of |...|. However, if the
+%    user explicitly requested an empty text string using the optional
+%    argument we cancel any preceding space since in this case we are
+%    otherwise likely to end up with spaces one before and one after
+%    |\vpageref|. 
+% \changes{v1.2f}{2000/07/07}{Don't output space if optional argument
+%    empty (pr/3230)}
+%    \begin{macrocode}
+    \def\@tempc{#1}%
+    \ifx\@tempc\@empty
+       \unskip
+    \else
+       #1%
+    \fi
+  \else
+%    \end{macrocode}
+%    If |#2| is empty we do nothing otherwise we insert it followed by
+%    a space.
+%    \begin{macrocode}
+    \def\@tempc{#2}%
+    \ifx\@tempc\@empty \else 
+      #2\vref@space
+    \fi
+%    \end{macrocode}
+%    Now we check if the page number of the referenced object (stored
+%    in |\thevpagerefnum| is a single positive number.
+%    \begin{macrocode}
+    \is@pos@number\thevpagerefnum
+       {%
+%    \end{macrocode}
+%    If so, we check if the current position (stored in |\@tempa|) is
+%    a positive number. If this is the case we assign this number to
+%    the counter register |\@tempcnta| and add one to it.
+%    \begin{macrocode}
+        \is@pos@number\@tempa
+         {\@tempcnta\@tempa
+          \advance\@tempcnta\@ne
+         }%
+%    \end{macrocode}
+%    If it is not a positive number we assign the largest possible
+%    number to |\@tempcnta| and thereby pretending that label and
+%    reference are miles away from each other.
+%    \begin{macrocode}
+         {\@tempcnta\maxdimen}%
+%    \end{macrocode}
+%    Now we are ready to check if reference and object are on nearby
+%    pages. |\thevpagerefnum| will expand to the page number of the object
+%    (and we know that this is a number) and |\@tempcnta| is either
+%    one higher than the reference page or completely out of bounds.
+%    So if both represent the same value then the object lies one page
+%    after its reference.
+%    \begin{macrocode}
+        \ifnum \thevpagerefnum =\@tempcnta
+%    \end{macrocode}
+%    Thus if the object falls onto an odd page then the reference is
+%    on the facing even page (and so we insert |\reftextfaceafter|),
+%    otherwise the object can not be seen from the reference (and we
+%    in insert |\reftextafter|).  Don't be surprised if we are not
+%    using |\thevpagerefnum| in the check. Since |\@tempcnta| has the same
+%    value it is faster to use the register instead of parsing the
+%    macro contents anew.
+%    \begin{macrocode}
+         \ifodd\@tempcnta
+%    \end{macrocode}
+%    In fact we are going to use |\reftextfaceafter| only if we are
+%    doing two-sided printing, otherwise |\reftextafter| is always
+%    used.
+%    Since the value of |\if@twoside| is evaluated before reading in
+%    packages we could do better (saving some tokens) by defining
+%    the current macro in dependence of this boolean.
+%    \begin{macrocode}
+           \if@twoside
+             \reftextfaceafter
+           \else
+             \reftextafter
+           \fi
+         \else
+           \reftextafter
+         \fi
+%    \end{macrocode}
+%    If the object is not on the page following the reference we check
+%    if it is on the page before the reference. In \LaTeX{} this
+%    situation is not too common, for example with floats it normally
+%    does not occur, but of course it isn't impossible if you more
+%    than one reference to the same object, or if you have back
+%    references to sections, theorems, etc.  To test this we now
+%    subtract two from the current value of |\@tempcnta| (which was
+%    set to one higher as the reference page number). Note, that
+%    subtraction is also possible if the value was |\maxdimen| --- we
+%    still get something that is much larger than any sensible page
+%    number.
+%    \begin{macrocode}
+        \else
+          \advance\@tempcnta-2
+%    \end{macrocode}
+%    If now |\thevpagerefnum| and |\@tempcnta| have the same value then the
+%    object lies one page before the reference.
+%    \begin{macrocode}
+          \ifnum \thevpagerefnum =\@tempcnta
+%    \end{macrocode}
+%    Again we have to check for odd or even pages to distinguish
+%    between the facing and the non-facing situation.
+%    \begin{macrocode}
+            \ifodd\@tempcnta
+              \reftextbefore
+            \else
+%    \end{macrocode}
+%    Again the |\reftextfacebefore| only if |@twoside| evaluates to
+%    true.
+%    \begin{macrocode}
+              \if@twoside
+                \reftextfacebefore
+              \else
+                \reftextbefore
+              \fi
+            \fi
+%    \end{macrocode}
+%    If the above test also returns false then we have object and
+%    references on pages which are far away or don't contain simple
+%    page numbers. Therefore we generate the |\reftextfaraway| string
+%    and drop any possible ``looping warning'' in |\vref@may@loop|.
+%    Recall that this is a macro which has the user label as an
+%    argument.
+%    \begin{macrocode}
+          \else
+          \let\vref@may@loop\relax % added
+          \reftextfaraway{#3}%
+          \fi
+        \fi
+       }%
+%    \end{macrocode}
+%    We do the same if our first test (that the page with the object
+%    has a positive page number) turns out to be false.
+%    \begin{macrocode}
+       {%
+         \let\vref@may@loop\relax %added
+         \reftextfaraway{#3}}%
+  \fi
+%    \end{macrocode}
+%    Finally we generate the internal label so that it can be check on
+%    the next run. This means that we compare the position after the
+%    string with the position of the referenced object. There is one
+%    thing to note: to conserve space we locally make |\@currentlabel|
+%    empty since we are only interested in the page number value of
+%    this internal label.
+% \changes{v1.0l}{1994/07/07}{Explicitly expand \cs{label} argument for babel}
+%
+%    These days we actually use |\vref@label| instead of |\label| as
+%    this avoids problems with Babel or \pkg{amsmath} redefining
+%    the latter command.
+% \changes{v1.4e}{2003/01/08}{Use \cs{vref@label} instead of
+%    \cs{label}  (pr/3489)}
+% \changes{v1.5c}{2016/02/16}{}
+%    \begin{macrocode}
+   \vref@label{\the\c@vrcnt @vr}%
+%    \end{macrocode}
+%    Finally we run |\vref@may@loop| which is either |\relax| or generates
+%    a ``may loop'' warning or error as appropriate.
+%    \begin{macrocode}
+   \vref@may@loop
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%  \begin{macro}{\vp@gerefstar}
+%    The default code for the star form is identical to the previous
+%    macro |\vp@geref|. It only produces a different result because
+%    before calling it we set |\vref@maybe@space| to do nothing.
+%
+%    The \pkg{hyperref} package can then change the meaning of this
+%    command to suppress a hyperlink.
+%
+%    It is is also a good way to check if we are running with a new
+%    \pkg{varioref} by testing
+%\begin{verbatim}
+%  \ifdefined\vp@gerefstar
+%     ... code fore noew varioref
+%  \else
+%    ... code for old varioref
+%  \fi
+%\end{verbatim}
+%
+% \changes{v1.6a}{2019/08/25}{Command added to support hyperref better}
+%    \begin{macrocode}
+\let\vp@gerefstar\vp@geref
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+
+%  \begin{macro}{\vref@label}
+% \changes{v1.4e}{2003/01/08}{Macro added (pr/3489)}
+%    This macro is like |\label| in the kernel but without passing on
+%    |\@currentlabel|, ie useful if all we are interested in is the
+%    page number. It also has the effect that it is unaffected by
+%    \pkg{amsmath} or Babel redefining the |\label| command.
+%    \begin{macrocode}
+\def\vref@label#1{\@bsphack
+  \protected@write\@auxout{}%
+         {\string\newlabel{#1}{{}{\thepage}}}%
+  \@esphack}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%  \begin{macro}{\vpagerefnum}
+% \changes{v1.4c}{2002/06/14}{Macro added}
+%    This macro allows to define |\reftextafter| and friends to refer
+%    to the page number rather than producing a textual reference.
+%    \begin{macrocode}
+\let\thevpagerefnum\@empty
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%  \begin{macro}{\vrefwarning}
+% \changes{v0.1g}{1993/02/14}{Macro added}
+%  \begin{macro}{\vrefshowerrors}
+% \changes{v1.1h}{1998/08/01}{Macro added}
+%  \begin{macro}{\vref@err}
+% \changes{v0.1g}{1993/02/14}{Macro added}
+%    When the |\vref| command detects a possible crossing over a page
+%    boundary it will call |\vref@err| to generate an error message.
+%    During document preparation one can turn such errors into
+%    warnings by issuing a |\vrefwarning| declaration.
+% \changes{v1.0g}{1993/02/14}{Macro added}
+%    \begin{macrocode}
+\def\vrefwarning{\def\vref@err{\PackageWarning{varioref}}}
+%    \end{macrocode}
+%    \begin{macrocode}
+\def\vrefshowerrors{\def\vref@err##1{\PackageError{varioref}{##1}%
+    {Please check the pages in question. You might need to replace
+     the \string\vref\MessageBreak
+     or \noexpand\vpageref by a normal \noexpand\(page)ref to
+     stop LaTeX running forever.}}}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+% \begin{macro}{\vref}
+%    We start by scanning for a star form and then continue in a
+%    different macro depending on the result.
+% \changes{v1.3a}{2001/04/12}{Scan for star form}
+% \changes{v1.6a}{2019/08/25}{Adjusted for new spacing regime}
+%    \begin{macrocode}
+\DeclareRobustCommand\vref{\@ifstar
+   {\vref@star}{\vr@f}}
+%    \end{macrocode}
+%  \end{macro}
+
+
+
+%  \begin{macro}{\vref@star}
+%
+%    The star form is easy (and just a convenient shortcut), just call
+%    |\ref| followed by |\vpageref| and pass the optional argument to
+%    the latter. We don't support the second optional argument of
+%    |\vpageref|, it that is needed one has to call both commands
+%    explicitly
+% \changes{v1.6a}{2019/08/25}{Command added to support hyperref better}
+%    \begin{macrocode}
+\newcommand\vref@star[2][]{%
+  \ref{#2}
+  \vpageref[#1]{#2}}
+%    \end{macrocode}
+%  \end{macro}
+
+% \begin{macro}{\vr@f}
+%    The normal case is a little bit more elaborated \ldots
+% \changes{v1.3c}{2001/09/04}{Correct typo in name}
+% \changes{v1.6a}{2019/08/25}{Adjusted for new spacing regime}
+%    \begin{macrocode}
+\def\vr@f{%
+  \leavevmode
+%    \end{macrocode}
+%    If option \texttt{space} is used then we remove a preceding space
+%    and add our own unbreakable space instead. Otherwise we don't do
+%    any space-handling.  
+%    \begin{macrocode}
+  \if@vrefhandlespace
+    \unskip \nobreakspace
+  \fi
+%    \end{macrocode}
+%    The use of|\nobreakspace| or |~| after the |\unskip| means that
+%    this command will always produce a normal space while
+%    something like |\nobreak\space| will
+%    react to settings of |\nonfrenchspacing|.
+%    Unfortunately the latter will also act in cases where one really
+%    wants a normal space, e.g., in |Fig.~\vref{..}|, resulting in
+%    a large extra space after the dot. For this reason the first solution
+%    is used.
+% \changes{v1.1e}{1998/03/09}{Don't use \cs{nobreakspace} (pr/1866)}
+% \changes{v1.2a}{1998/11/27}{Use \cs{nobreakspace} (pr/2909)}
+% \changes{v1.2a}{1998/11/27}{Add \cs{leavevmode}}
+%
+%    After having handled (or not  handled) the spacing we call
+%    |\vref@star| to scan the optional arguments and do the rest.
+%    If that command has been altered by \pkg{hyperref} then the
+%    current one needs altering too and does the argument scanning explicitly.  
+%    \begin{macrocode}
+  \vref@star                    % in hyperref this needs to be explicit
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%  \begin{macro}{\is@pos@number}
+%    The utility macro |\is@pos@number| takes three arguments: a
+%    string that is tested for being a valid non-negative integer and the
+%    actions to be taken in case the test comes out true or false.
+%
+%    We start by passing the string to the macro |\is@pos@num| after
+%    prefixing it with a \texttt{0} and adding a space after it. To have
+%    a well-defined ending point we also add |\@nil| at the end.
+%\label{isposnumber}
+%    \begin{macrocode}
+\def\is@pos@number#1{\is@pos@num0#1\space\@nil}
+%    \end{macrocode}
+%    Now we parse the enlarged string into a counter register.  To get
+%    control back after everything that is regarded by \TeX{} as a
+%    number is put into that register we assign |\is@pos@num@| to the
+%    |\afterassignment| token.  Since the string started with 0, we
+%    can be sure that the register assignment will be carried out
+%    without an error message.  In case of counter assignments leading
+%    zeros are discarded.
+%    \begin{macrocode}
+\def\is@pos@num{\afterassignment\is@pos@num@ \count@}
+%    \end{macrocode}
+%    Now we have to check whether or not the whole string was parsed
+%    into that register or some remainder was left over. Since we have
+%    added a |\@nil| token at the very end we can use that to delimit
+%    the argument of |\is@pos@num@|. Note, that the added space in
+%    |\is@pos@number| \vpageref[above]{isposnumber} gets parsed away
+%    by the counter assignment. If it would be missing, and the full
+%    string would consist of a number, \TeX{}would try to replace
+%    |\@nil| by its definition to see if it would contain additional
+%    digits and thus we would be in trouble at this point.
+%    \begin{macrocode}
+\def\is@pos@num@#1\@nil{%
+%    \end{macrocode}
+%    Now we have to check if the argument is empty. We can do this
+%    with an |\ifx| (i.e., in an expandable way) since we know for
+%    sure that it can not start with |\@nil|.
+% \changes{v1.4j}{2004/05/08}{Use \cs{@nil} for testing}
+%    \begin{macrocode}
+  \ifx\@nil#1\@nil
+%    \end{macrocode}
+%    Depending on the result we execute the second or third argument
+%    of the command |\is@pos@number| using a technique that removes
+%    the |\else| or |\fi| from the input stream first, so that in
+%    principle input stream parsing could be done from within the
+%    arguments.
+%    \begin{macrocode}
+    \expandafter\@firstoftwo \else
+    \expandafter\@secondoftwo  \fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\reftextvario}
+%    This macro gives a little bit of random variation in the text
+%    because the outcome depends on the number of |\vref| commands
+%    seen before.
+%    \begin{macrocode}
+\def\reftextvario#1#2{\ifodd\c@vrcnt #1\else#2\fi}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\fullref}
+%    And here is the primitive command that always produces a |\ref|
+%    and a |\pageref|.
+%    \begin{macrocode}
+\def\fullref#1{\ref{#1} \reftextfaraway{#1}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+% \subsubsection{Supporting ranges}
+%
+%  \begin{macro}{\vref@pagenum}
+% \changes{v1.2a}{1998/08/01}{Macro added}
+%    This command takes a label as |#1| extracts the page number
+%    associated with it and saves the result in a csname which is
+%    passed as |#1|. If the label isn't associated with a page number
+%    it essentially associates it with |??| for both the label number
+%    and the page, thus defining the label this way.  This means that
+%    no label warning is generated for this label in case it is
+%    undefined.
+%    \begin{macrocode}
+\def\vref@pagenum#1#2{%
+  \@ifundefined{r@#2}{\@namedef{r@#2}{{??}{??}}}{}%
+%    \end{macrocode}
+%    Extracting and saving the page number turned out to be a source of subtle
+%    bugs. Initially it was done through an |\edef| with a bunch of
+%    |\expandafter| commands inside. This posed a problem if the page number
+%    itself contained code which needed protection (e.g., pr/4080) so this got
+%    changed to use |\protected@edef|. However, that in turn failed with Babel
+%    (pr/4093)
+%    if the label contained active characters, e.g., a ``:'' in French. So now
+%    we use even more |\expandafter| commands to avoid any expansion other
+%    than what is absolutely  required---I'm sure there is now a simpler way
+%    to code this, but \ldots\ in fact we didn't use enough initially resulting in another
+%    bug (pr/4159):
+% \changes{v1.4w}{2009/09/13}{Use \cs{protected@edef} to avoid problems
+%              in complicated setups, e.g., microtype (pr/4080)}
+% \changes{v1.4y}{2010/11/12}{Avoid even \cs{protected@edef} to pacify french
+%    babel (pr/4093)}
+% \changes{v1.4z}{2011/10/02}{Previous fix need one more expansion
+%                            (pr/4159,pr/4171)}
+%    \begin{macrocode}
+  \expandafter\expandafter\expandafter\vref@@pagenum
+  \csname r@#2\endcsname{}{}\@nil#1%
+}
+\def\vref@@pagenum#1#2#3\@nil#4{%
+  \def#4{#2}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\vrefpagenum}
+% \changes{v1.2a}{1998/08/01}{Macro added}
+%    Same as the above but this time we generate a warning for
+%    undefined labels.
+%    \begin{macrocode}
+\def\vrefpagenum#1#2{%
+  \@ifundefined{r@#2}%
+    {\G@refundefinedtrue
+     \@latex@warning{Reference `#2' on page \thepage \space
+             undefined}}{}%
+  \vref@pagenum{#1}{#2}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \begin{macro}{\vpagerefrange}
+%  \begin{macro}{\@vpagerefrange}
+%  \begin{macro}{\@svpagerefrange}
+% \changes{v1.2a}{1998/08/01}{Macro added}
+% \changes{v1.3b}{2001/04/14}{Scan for star form}
+% \changes{v1.4s}{2007/08/07}
+%         {Prevent loss of brackets}
+%    If both labels refer to the same page then we produce a
+%    |\vpageref|. Otherwise we produce the result of
+%    |\reftextpagerange|.
+%
+%    One could think of making this command even more clever by
+%    producing a special string if the difference between the two page
+%    number is one (but this is not done).
+%
+%    We need two versions to implement a star form:
+%    \begin{macrocode}
+\newcommand\@svpagerefrange[3][\reftextcurrent]{%
+  \vrefpagenum\@tempa{#2}%
+  \vrefpagenum\@tempb{#3}%
+  \ifx\@tempa\@tempb
+    \vpageref*[{#1}]{#2}%
+  \else
+    \reftextpagerange{#2}{#3}%
+  \fi
+}
+%    \end{macrocode}
+%    And the same but using |\vpageref|:
+%    \begin{macrocode}
+\newcommand\@vpagerefrange[3][\reftextcurrent]{%
+  \vrefpagenum\@tempa{#2}%
+  \vrefpagenum\@tempb{#3}%
+  \ifx\@tempa\@tempb
+    \vpageref[{#1}]{#2}%
+  \else
+    \reftextpagerange{#2}{#3}%
+  \fi
+}
+%    \end{macrocode}
+%    And here we put things together.
+%    \begin{macrocode}
+\newcommand\vpagerefrange{\@ifstar\@svpagerefrange\@vpagerefrange}
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%
+%  \begin{macro}{\vrefrange}
+% \changes{v1.2a}{1998/08/01}{Macro added}
+% \changes{v1.4s}{2006/08/07}
+%         {Prevent loss of brackets}
+%    \begin{macrocode}
+\newcommand\vrefrange[3][\reftextcurrent]
+  {\reftextlabelrange{#2}{#3} \vpagerefrange[{#1}]{#2}{#3}}
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%
+%  \begin{macro}{\Vref}
+%  \changes{v1.4a}{2002/02/24}{Macro added}
+%    |\Vref| is the counterpart to |\vref| with |\ref| replaced by
+%    |\Ref| in its definition.
+% \changes{v1.6a}{2019/08/25}{Adjusted for new spacing regime}
+%    \begin{macrocode}
+\DeclareRobustCommand\Vref{\@ifstar
+   {\Vref@star}%
+   {\Vr@f}}
+%    \end{macrocode}
+%  \end{macro}
+%    
+%  \begin{macro}{\Vref@star}
+% \changes{v1.6a}{2019/08/25}{Command added to support hyperref better}
+%    \begin{macrocode}
+\newcommand\Vref@star[2][]{%
+  \Ref{#2}
+  \vpageref[#1]{#2}}
+%    \end{macrocode}
+%  \end{macro}
+%    
+%  \begin{macro}{\Vr@f}
+%  \changes{v1.4a}{2002/02/24}{Macro added}
+%  \changes{v1.4x}{2010/08/04}{Correct spacing -- same mistake as in \cs{vref}
+%                              (pr/4123)}
+% \changes{v1.6a}{2019/08/25}{Adjusted for new spacing regime}
+%    \begin{macrocode}
+\def\Vr@f{%
+  \if@vrefhandlespace
+    \unskip \vref@space
+  \fi
+  \Vref@star                  % in hyperref this needs to be explicit
+}
+%    \end{macrocode}
+%  \end{macro}
+
+
+%  \begin{macro}{\vpagerefcompare}
+%    
+% \changes{v1.6a}{2019/08/25}{Macro added}
+%    \begin{macrocode}
+\DeclareRobustCommand\vpagerefcompare[2]{%  label1, label2, TRUE, FALSE
+  \vrefpagenum\@tempa{#1}%
+  \vrefpagenum\@tempb{#2}%
+  \ifx\@tempa\@tempb
+    \expandafter\@firstoftwo
+  \else
+    \expandafter\@secondoftwo
+  \fi
+}  
+%    \end{macrocode}
+%  \end{macro}
+%
+%
+%
+%  \begin{macro}{\vpagerefnearby}
+% \changes{v1.6a}{2019/08/25}{Macro added}
+%    Test if |\vpageref| is going to be at most $\pm1$ off from
+%    current page.
+%    \begin{macrocode}
+\DeclareRobustCommand\vpagerefnearby[1]{%  label, TRUE, FALSE
+  \leavevmode
+  \@tempskipa\lastskip \unskip
+  \global\advance\c@vrcnt\tw@    % keep oddness to not disturb \vrefvario
+  \vref@label{\the\c@vrcnt @vn}%
+  \ifdim\@tempskipa=\z@ \else
+    \hskip\@tempskipa
+  \fi
+  \vref@pagenum\@tempa{\the\c@vrcnt @vn}%
+  \is@pos@number\@tempa
+      {%
+        \vrefpagenum\@tempb{#1}%
+        \is@pos@number\@tempb
+            {%
+              \ifcase\numexpr \@tempa -\@tempb+1\relax
+              \or \or \else \expandafter \@thirdofthree \fi
+              \@firstoftwo
+            }%
+            {\@secondoftwo}%
+      }%
+      {\@secondoftwo}%
+}
+%    \end{macrocode}
+%  \end{macro}
+%
+
+%  \begin{macro}{\vpagerefcomparenearby}
+% \changes{v1.6a}{2019/08/25}{Macro added}
+%    True if the two pages have arabic page numbers are at most off by
+%    one so that |\vpageref| would produce a special string.
+%
+%    This is n some sense a general version of |\vpagerefnearby| for
+%    use in more complex situations. I.e., if you try to determine if
+%    a larger set of references would be close to the current page and
+%    you use each time |\vpagerefnearby| then you generate a lot of
+%    internal labels for the current point. Thus by setting the label
+%    yourself you can save processing time and space. On the other
+%    hand you have to be careful to place the label into the right
+%    place which can be a bit complicated if you look at the
+%    definition of |\vpagerefnearby| that does all this automatically
+%    for you. This is why the current macro is not discussed in the
+%    user interface section as it is really just for package
+%    developers.
+%    \begin{macrocode}
+\DeclareRobustCommand\vpagerefcomparenearby[2]{%  label1, label2, TRUE, FALSE
+  \vrefpagenum\@tempa{#1}%
+  \is@pos@number\@tempa
+      {%
+        \vrefpagenum\@tempb{#2}%
+        \is@pos@number\@tempb
+            {%
+              \ifcase\numexpr \@tempa -\@tempb+1\relax
+              \or \or \else \expandafter \@thirdofthree \fi
+              \@firstoftwo
+            }%
+            {\@secondoftwo}%
+      }%
+      {\@secondoftwo}%
+}
+%    \end{macrocode}
+%  \end{macro}
+
+%
+%
+%  \subsubsection{Compatibility with older \LaTeX{} formats}
+%
+%
+%  \begin{macro}{\labelformat}
+%  \begin{macro}{\Ref}
+%  \begin{macro}{\refstepcounter}
+%    We don't need to define \cs{labelformat} and \cs{Ref} or change the
+%    definition of \cs{refstepcounter} any longer because this is now
+%    done in the \LaTeX{} kernel. However, if this package is used
+%    together with an older kernel, this is not true, so for this
+%    special case we keep the definitions.
+%    \begin{macrocode}
+\ifx\labelformat\@undefined  % assume we are in an older kernel
+  \def\labelformat#1{\expandafter\def\csname p@#1\endcsname##1}
+  \DeclareRobustCommand\Ref[1]{\protected@edef\@tempa{\ref{#1}}%
+     \expandafter\MakeUppercase\@tempa}
+  \def\refstepcounter#1{\stepcounter{#1}%
+      \protected@edef\@currentlabel
+         {\csname p@#1\expandafter\endcsname\csname the#1\endcsname}}
+\fi
+%    \end{macrocode}
+%  \end{macro}
+%  \end{macro}
+%  \end{macro}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+% \Finale
+%
+\endinput
+
diff --git a/macros/latex-dev/required/tools/varioref.ins b/macros/latex-dev/required/tools/varioref.ins
new file mode 100644
index 0000000000..e436202e4d
--- /dev/null
+++ b/macros/latex-dev/required/tools/varioref.ins
@@ -0,0 +1,76 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright (C) 1993-2019
+%% The LaTeX3 Project and any individual authors listed elsewhere
+%% in this file. 
+%% 
+%% This file is part of the Standard LaTeX `Tools Bundle'.
+%% -------------------------------------------------------
+%% 
+%% It may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3c
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in
+%%    https://www.latex-project.org/lppl.txt
+%% and version 1.3c or later is part of all distributions of LaTeX 
+%% version 2008 or later.
+%% 
+%% As this file contains legal notices, it is NOT PERMITTED to modify
+%% this file in any way that the legal information placed into
+%% generated files is changed (i.e., the files generated when the
+%% original file is executed). This restriction does not apply if
+%% (parts of) the content is reused in a different WORK producing its
+%% own generated files.
+%% 
+%% The list of all files belonging to the `Tools Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\input docstrip
+
+\keepsilent
+
+\usedir{tex/latex/tools}
+
+\preamble
+
+This is a generated file.
+
+The source is maintained by the LaTeX Project team and bug
+reports for it can be opened at https://latex-project.org/bugs/
+(but please observe conditions on bug reports sent to that address!)
+
+Copyright (C) 1993-2019
+The LaTeX3 Project and any individual authors listed elsewhere
+in this file. 
+
+This file was generated from file(s) of the Standard LaTeX `Tools Bundle'.
+--------------------------------------------------------------------------
+
+It may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3c
+of this license or (at your option) any later version.
+The latest version of this license is in
+   https://www.latex-project.org/lppl.txt
+and version 1.3c or later is part of all distributions of LaTeX 
+version 2005/12/01 or later.
+
+This file may only be distributed together with a copy of the LaTeX
+`Tools Bundle'. You may however distribute the LaTeX `Tools Bundle'
+without such generated files.
+
+The list of all files belonging to the LaTeX `Tools Bundle' is
+given in the file `manifest.txt'.
+
+\endpreamble
+
+
+\generateFile{varioref.sty}{t}{\from{varioref.dtx}{package}}
+
+
+\endbatchfile
diff --git a/macros/latex-dev/required/tools/varioref.pdf b/macros/latex-dev/required/tools/varioref.pdf
new file mode 100644
index 0000000000..2346645c1b
--- /dev/null
+++ b/macros/latex-dev/required/tools/varioref.pdf
diff --git a/macros/latex-dev/required/tools/verbatim.dtx b/macros/latex-dev/required/tools/verbatim.dtx
new file mode 100644
index 0000000000..1dc8682f79
--- /dev/null
+++ b/macros/latex-dev/required/tools/verbatim.dtx
@@ -0,0 +1,1858 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+%
+%\iffalse   % this is a METACOMMENT !
+%
+%
+%% Package `verbatim' to use with LaTeX2e
+%% Copyright (C) 1989--2003 by Rainer Sch\"opf. All rights reserved.
+%
+% Copying of this file is authorized only if either
+% (1) you make absolutely no changes to your copy, including name, or
+% (2) if you do make changes, you name it something other than
+%     verbatim.dtx.
+% This restriction helps ensure that all styles developed here
+% remain identical.
+%
+%
+%
+% \section{Producing the documentation}
+%
+% We provide a short driver file that can be extracted by the
+% \textsf{DocStrip} program using the conditional `\textsf{driver}'.
+%
+%    \begin{macrocode}
+%<*driver>
+\documentclass{ltxdoc}
+
+\pagestyle{myheadings}
+
+\title{A New Implementation of \LaTeX{}'s \\ \texttt{verbatim}
+       and \texttt{verbatim*} Environments.}
+\author{Rainer Sch\"opf\\
+        \and
+        Bernd Raichle\\
+        \and
+        Chris Rowley}
+
+\date{2001/03/12}
+\begin{document}
+\markboth{Verbatim style option}{Verbatim style option}
+\MaintainedByLaTeXTeam{tools}
+\maketitle
+  \DocInput{verbatim.dtx}
+\end{document}
+%</driver>
+%    \end{macrocode}
+%
+%
+%\fi
+%
+%
+% \changes{v1.5q}{2003/08/22}{Reintroduced \cs{@noligs}, by popular
+%                             request.}
+% \changes{v1.5i}{1996/06/04}{Move setting of verbatim font and
+%                             \cs{@noligs}.}
+% \changes{v1.5g}{1995/04/26}{Removed \cs{fileversion} and
+%                             \cs{filedate} from running head in
+%                             driver file, as these are no longer
+%                             defined.}
+% \changes{v1.5f}{1994/10/25}{Removed extra \cs{typeout} commands.}
+% \changes{v1.5e}{1994/06/10}{Added missing closing verbtest guard.}
+% \changes{v1.5d}{1994/05/30}{\cs{NeedsTeXFormat} and
+%                             \cs{ProvidesPackage} added.}
+% \changes{v1.5d}{1994/05/30}{\cs{addto@hook} removed, now in kernel.}
+% \changes{v1.5a}{1993/10/12}{Included \cs{newverbtext} command, as
+%          written by Chris Rowley.}
+% \changes{v1.5}{1993/10/11}{Included vrbinput style option by Bernd
+%          Raichle.}
+%
+% \changes{v1.4j}{1992/06/30}{Used \cs{lowercase}\{\cs{endgroup}
+%    \ldots\} trick proposed by Bernd Raichle; changed all \cs{gdef}
+%    to \cs{def} since no longer necessary.}
+% \changes{v1.4g}{1991/11/21}{Several improvements in the
+%                           documentation.}
+% \changes{v1.4f}{1991/08/05}{Corrected bug in documentation.
+%                           Found by Bernd Raichle.}
+% \changes{v1.4e}{1991/07/24}{Avoid reading this file twice.}
+% \changes{v1.4d}{1991/04/24}{\cs{penalty}\cs{interlinepenalty} added to
+%                           definition of \cs{par} in \cs{@verbatim}.
+%                           Necessary to avoid page breaks in
+%                           the scope of a \cs{samepage} declaration.}
+% \changes{v1.4c}{1990/10/18}{Added \cs{leavevmode} to definition of
+%       backquote macro.}
+% \changes{v1.4b}{1990/07/14}{Converted nearly all \cs{verb}'s to
+%       \texttt{\protect\string!|\ldots\protect\string!|}.}
+% \changes{v1.4a}{1990/04/04}{Added a number of percent characters
+%       to suppress blank space at the end of some code lines.}
+% \changes{v1.4}{1990/03/07}{\cs{verb} rewritten.}
+%
+% \changes{v1.3a}{1990/02/04}{Removed \texttt{verbatimwrite} environment
+%       from the code. Now only shown as an example.}
+%
+% \changes{v1.2g}{1990/02/01}{Revised documentation.}
+% \changes{v1.2e}{1990/01/15}{Added \cs{every@verbatim} hook.}
+% \changes{v1.2d}{1989/11/29}{Use token register \cs{@temptokena}
+%                           instead of macro \cs{@tempb}.}
+% \changes{v1.2d}{1989/11/29}{Use token register \cs{verbatim@line}
+%                           instead of macro \cs{@tempd}.}
+% \changes{v1.2b}{1989/10/25}{\cs{verbatimfile} renamed to
+%           \cs{verbatiminput}. Suggested by Reinhard Wonneberger.}
+%
+% \changes{v1.1a}{1989/10/16}{\cs{verb} added.}
+% \changes{v1.1}{1989/10/09}{Made the code more modular (as suggested by
+%                          Chris Rowley):  introduced
+%                          \cs{verbatim@addtoline}, etc.  Added
+%                          \cs{verbatimwrite} environment.}
+%
+% \changes{v1.0e}{1989/07/17}{Fixed bug in \cs{verbatimfile} (*-form
+%         handling, discovered by Dirk Kreimer).}
+% \changes{v1.0d}{1989/05/16}{Revised documentation, fixed silly bug
+%         in \cs{verbatim@@@}.}
+% \changes{v1.0c}{1989/05/12}{Added redefinition of \cs{@sverb}, change
+%         in end-of-line handling.}
+% \changes{v1.0b}{1989/05/09}{Change in \cs{verbatim@rescan}.}
+% \changes{v1.0a}{1989/05/07}{Change in \cs{verbatim@@testend}.}
+%
+%
+% \DoNotIndex{\ ,\!,\C,\[,\\,\],\^,\`,\{,\},\~}
+% \DoNotIndex{\@M,\@empty,\@flushglue,\@gobble,\@ifstar,\@ifundefined}
+% \DoNotIndex{\@namedef,\@spaces,\@tempa,\@tempb,\@tempc,\@tempd}
+% \DoNotIndex{\@temptokena,\@totalleftmargin,\@warning,\active}
+% \DoNotIndex{\aftergroup,\arabic,\begingroup,\catcode,\char,\closein}
+% \DoNotIndex{\csname,\def,\do,\docdate,\dospecials,\edef,\else}
+% \DoNotIndex{\endcsname,\endgraf,\endgroup,\endinput,\endlinechar}
+% \DoNotIndex{\endtrivlist,\expandafter,\fi,\filedate,\fileversion}
+% \DoNotIndex{\frenchspacing,\futurelet,\if,\ifcat,\ifeof,\ifnum}
+% \DoNotIndex{\ifx,\immediate,\item,\kern,\lccode,\leftskip,\let}
+% \DoNotIndex{\lowercase,\m@ne,\makeatletter,\makeatother,\newread}
+% \DoNotIndex{\newread,\next,\noexpand,\noindent,\openin,\parfillskip}
+% \DoNotIndex{\parindent,\parskip,\penalty,\read,\relax,\rightskip}
+% \DoNotIndex{\sloppy,\space,\string,\the,\toks@,\trivlist,\tt,\typeout}
+% \DoNotIndex{\vskip,\write,\z@}
+%
+% \begin{abstract}
+%   This package reimplements the \LaTeX{} \texttt{verbatim} and
+%   \texttt{verbatim*} environments.
+%   In addition it provides a \texttt{comment} environment
+%   that skips any commands or text between
+%   |\begin{comment}|
+%   and the next |\end{comment}|.
+%   It also defines the command \texttt{verbatiminput} to input a whole
+%   file verbatim.
+% \end{abstract}
+%
+% \section{Usage notes}
+%
+% \let\docDescribeMacro\DescribeMacro
+% \let\docDescribeEnv\DescribeEnv
+% \def\DescribeMacro#1{}
+% \def\DescribeEnv#1{}
+% \LaTeX's \texttt{verbatim} and \texttt{verbatim*} environments
+% have a few features that may give rise to problems. These are:
+% \begin{itemize}
+%   \item
+%     Due to the method used to detect the closing |\end{verbatim}|
+%     (i.e.\ macro parameter delimiting) you cannot leave spaces
+%     between the |\end| token and |{verbatim}|.
+%   \item
+%     Since \TeX{} has to read all the text between the
+%     |\begin{verbatim}| and the |\end{verbatim}| before it can output
+%     anything, long verbatim listings may overflow \TeX's memory.
+% \end{itemize}
+% Whereas the first     of these points can be considered
+% only a minor nuisance the other one is a real limitation.
+%
+%
+% \DescribeEnv{verbatim}
+% \DescribeEnv{verbatim*}
+% This package file contains a reimplementation of the \texttt{verbatim}
+% and \texttt{verbatim*} environments which overcomes these
+% restrictions.
+% There is, however, one incompatibility between the old and the
+% new implementations of these environments: the old version
+% would treat text on the same line as the |\end{verbatim}|
+% command as if it were on a line by itself.
+% \begin{center}
+%   \bf This new version will simply ignore it.
+% \end{center}
+% (This is the price one has to pay for the removal of the old
+% \texttt{verbatim} environment's size limitations.)
+% It will, however, issue a warning message of the form
+% \begin{verbatim}
+%LaTeX warning: Characters dropped after \end{verbatim*}!
+%\end{verbatim}
+% This is not a real problem since this text can easily be put
+% on the next line without affecting the output.
+%
+% This new implementation also solves the second problem mentioned
+% above: it is possible to leave spaces (but \emph{not} begin a new
+% line) between the |\end| and the |{verbatim}| or |{verbatim*}|:
+% \begin{verbatim}
+%\begin {verbatim*}
+%   test
+%   test
+%\end {verbatim*}
+%\end{verbatim}
+%
+% \DescribeEnv{comment}
+% Additionally we introduce a \texttt{comment} environment, with the
+% effect that the text between |\begin{comment}| and |\end{comment}|
+% is simply ignored, regardless of what it looks like.
+% At first sight this seems to be quite different from the purpose
+% of verbatim listing, but actually the implementation of these two
+% concepts turns out to be very similar.
+% Both rely on the fact that the text between |\begin{...}| and
+% |\end{...}| is read by \TeX{} without interpreting any commands or
+% special characters.
+% The remaining difference between \texttt{verbatim} and
+% \texttt{comment} is only that the text is to be typeset in the
+% first case and to be thrown away in the latter. Note that these
+% environments cannot be nested.
+%
+% \DescribeMacro{\verbatiminput}
+% |\verbatiminput| is a command with one argument that inputs a file
+% verbatim, i.e.\ the command |verbatiminput{xx.yy}|
+% has the same effect as\\[2pt]
+%   \hspace*{\MacroIndent}|\begin{verbatim}|\\
+%   \hspace*{\MacroIndent}\meta{Contents of the file \texttt{xx.yy}}\\
+%   \hspace*{\MacroIndent}|\end{verbatim}|\\[2pt]
+% This command has also a |*|-variant that prints spaces as \verb*+ +.
+%
+%
+% \StopEventually{}
+%
+%
+% \section{Interfaces for package writers}
+%
+% The \texttt{verbatim} environment of \LaTeXe{} does not
+% offer a good interface to programmers.
+% In contrast, this package provides a simple mechanism to
+% implement similar features, the \texttt{comment} environment
+% implemented here being an example of what can be done and how.
+%
+%
+% \subsection{Simple examples}
+%
+% It is now possible to use the \texttt{verbatim} environment to define
+% environments of your own.
+% E.g.,
+%\begin{verbatim}
+% \newenvironment{myverbatim}%
+%   {\endgraf\noindent MYVERBATIM:%
+%    \endgraf\verbatim}%
+%   {\endverbatim}
+%\end{verbatim}
+% can be used afterwards like the \texttt{verbatim} environment, i.e.
+% \begin{verbatim}
+%\begin {myverbatim}
+%  test
+%  test
+%\end {myverbatim}
+%\end{verbatim}
+% Another way to use it is to write
+% \begin{verbatim}
+%\let\foo=\comment
+%\let\endfoo=\endcomment
+%\end{verbatim}
+% and from that point on environment \texttt{foo} is the same as the
+% comment environment, i.e.\ everything inside its body is ignored.
+%
+% You may also add special commands after the |\verbatim| macro is
+% invoked, e.g.
+%\begin{verbatim}
+%\newenvironment{myverbatim}%
+%  {\verbatim\myspecialverbatimsetup}%
+%  {\endverbatim}
+%\end{verbatim}
+% though you may want to learn about the hook |\every@verbatim| at
+% this point.
+% \changes{v1.5h}{1995/09/21}{Clarified documentation on use of other
+%               environments to define new verbatim-type ones.}
+% However, there are still a number of restrictions:
+% \begin{enumerate}
+%   \item
+%     You must not use the |\begin| or the |\end| command inside a
+%     definition, e.g.~the following two examples will \emph{not} work:
+%\begin{verbatim*}
+%\newenvironment{myverbatim}%
+%{\endgraf\noindent MYVERBATIM:%
+% \endgraf\begin{verbatim}}%
+%{\end{verbatim}}
+%\newenvironment{fred}
+%{\begin{minipage}{30mm}\verbatim}
+%{\endverbatim\end{minipage}}
+%\end{verbatim*}
+%     If you try these examples, \TeX{} will report a
+%     ``runaway argument'' error.
+%     More generally, it is not possible to use
+%     |\begin|\ldots\allowbreak|\end|
+%     or the related environments in the definition of the new
+%     environment. Instead, the correct way to define this environment
+%     would be
+%    \begin{verbatim*}
+%\newenvironment{fred}
+%{\minipage{30mm}\verbatim}
+%{\endverbatim\endminipage}
+%\end{verbatim*}
+%   \item
+%     You can\emph{not} use the \texttt{verbatim} environment inside
+%     user defined \emph{commands}; e.g.,
+% \changes{v1.4g}{1991/11/21}{Corrected wrong position of optional
+%        argument to \cs{newcommand}. Discovered by Piet van Oostrum.}
+%     \begin{verbatim*}
+%\newcommand{\verbatimfile}[1]%
+%           {\begin{verbatim}\input{#1}\end{verbatim}}
+%\end{verbatim*}
+%     does \emph{not} work; nor does
+%     \begin{verbatim}
+%\newcommand{\verbatimfile}[1]{\verbatim\input{#1}\endverbatim}
+%\end{verbatim}
+%   \item The name of the newly defined environment must not contain
+%     characters with category code other than $11$ (letter) or
+%     $12$ (other), or this will not work.
+% \end{enumerate}
+%
+%
+% \subsection{The interfaces}
+%
+% \DescribeMacro{\verbatim@font}
+% Let us start with the simple things.
+% Sometimes it may be necessary to use a special typeface for your
+% verbatim text, or perhaps the usual computer modern typewriter shape
+% in a reduced size.
+%
+% You may select this by redefining the macro |\verbatim@font|.
+% This macro is executed at the beginning of every verbatim text to
+% select the font shape.
+% Do not use it for other purposes; if you find yourself abusing this
+% you may want to read about the |\every@verbatim| hook below.
+%
+% By default, |\verbatim@font| switches to the typewriter font and
+% disables the ligatures contained therein.
+%
+%
+% \DescribeMacro{\every@verbatim}
+% \DescribeMacro{\addto@hook}
+% There is a hook (i.e.\ a token register) called |\every@verbatim|
+% whose contents are inserted into \TeX's mouth just before every
+% verbatim text.
+% Please use the |\addto@hook| macro to add something to this hook.
+% It is used as follows:\\[2pt]
+% \hspace*{\MacroIndent}|\addto@hook|\meta{name of the hook}^^A
+%  |{|\meta{commands to be added}|}|
+% \vspace*{2pt}
+%
+%
+%
+% \DescribeMacro{\verbatim@start}
+% After all specific setup, like switching of category codes, has been
+% done, the |\verbatim@start| macro is called.
+% This starts the main loop of the scanning mechanism implemented here.
+% Any other environment that wants to make use of this feature should
+% execute this macro as its last action.
+%
+%
+% \DescribeMacro{\verbatim@startline}
+% \DescribeMacro{\verbatim@addtoline}
+% \DescribeMacro{\verbatim@processline}
+% \DescribeMacro{\verbatim@finish}
+% These are the things that concern the start of a verbatim
+% environment.
+% Once this (and other) setup has been done, the code in this package
+% reads and processes characters from the input stream in the
+% following way:
+% \begin{enumerate}
+%   \item Before the first character of an input line is read, it
+%     executes the macro |\verbatim@startline|.
+%   \item After some characters have been read, the macro
+%     |\verbatim@addtoline| is called with these characters as its only
+%     argument.
+%     This may happen several times per line (when an |\end| command is
+%     present on the line in question).
+%   \item When the end of the line is reached, the macro
+%     |\verbatim@processline| is called to process the characters that
+%     |\verbatim@addtoline| has accumulated.
+%   \item Finally, there is the macro |\verbatim@finish| that is called
+%     just before the environment is ended by a call to the |\end|
+%      macro.
+% \end{enumerate}
+%
+%
+% To make this clear let us consider the standard \texttt{verbatim}
+% environment.
+% In this case the three macros above are defined as follows:
+% \begin{enumerate}
+%   \item |\verbatim@startline| clears the character buffer
+%     (a token register).
+%   \item |\verbatim@addtoline| adds its argument to the character
+%     buffer.
+%   \item |\verbatim@processline| typesets the characters accumulated
+%     in the buffer.
+% \end{enumerate}
+% With this it is very simple to implement the \texttt{comment}
+% environment:
+% in this case |\verbatim@startline| and |\verbatim@processline| are
+% defined to be
+% no-ops whereas |\verbatim@addtoline| discards its argument.
+%
+%
+% Let's use this to define a variant of the |verbatim|
+% environment that prints line numbers in the left margin.
+% Assume that this would be done by a counter called |VerbatimLineNo|.
+% Assuming that this counter was initialized properly by the
+% environment, |\verbatim@processline| would be defined in this case as
+% \begin{verbatim}
+%\def\verbatim@processline{%
+%  \addtocounter{VerbatimLineNo}{1}%
+%  \leavevmode
+%  \llap{\theVerbatimLineNo\ \hskip\@totalleftmargin}%
+%  \the\verbatim@line\par}
+%\end{verbatim}
+%
+% A further possibility is to define a variant of the |verbatim|
+% environment that boxes and centers the whole verbatim text.
+% Note that the boxed text should be less than a page otherwise you
+% have to change this example.
+%
+%\begin{verbatim}
+%\def\verbatimboxed#1{\begingroup
+%  \def\verbatim@processline{%
+%    {\setbox0=\hbox{\the\verbatim@line}%
+%     \hsize=\wd0
+%     \the\verbatim@line\par}}%
+%  \setbox0=\vbox{\parskip=0pt\topsep=0pt\partopsep=0pt
+%                 \verbatiminput{#1}}%
+%  \begin{center}\fbox{\box0}\end{center}%
+% \endgroup}
+%\end{verbatim}
+%
+% As a final nontrivial example we describe the definition of an
+% environment called \texttt{verbatimwrite}.
+% It writes all text in its body to a file whose name is
+% given as an argument.
+% We assume that a stream number called |\verbatim@out| has already
+% been reserved by means of the |\newwrite| macro.
+%
+% Let's begin with the definition of the macro |\verbatimwrite|.
+% \begin{verbatim}
+%\def\verbatimwrite#1{%
+%\end{verbatim}
+% First we call |\@bsphack| so that this environment does not influence
+% the spacing.
+% Then we open the file and set the category codes of all special
+% characters:
+% \begin{verbatim}
+%  \@bsphack
+%  \immediate\openout \verbatim@out #1
+%  \let\do\@makeother\dospecials
+%  \catcode`\^^M\active
+%\end{verbatim}
+% The default definitions of the macros
+% \begin{verbatim}
+%  \verbatim@startline
+%  \verbatim@addtoline
+%  \verbatim@finish
+%\end{verbatim}
+% are also used in this environment.
+% Only the macro |\verbatim@processline| has to be changed before
+% |\verbatim@start| is called:
+% \begin{verbatim}
+%  \def\verbatim@processline{%
+%    \immediate\write\verbatim@out{\the\verbatim@line}}%
+%  \verbatim@start}
+%\end{verbatim}
+% The definition of |\endverbatimwrite| is very simple:
+% we close the stream and call |\@esphack| to get the spacing right.
+% \begin{verbatim}
+%\def\endverbatimwrite{\immediate\closeout\verbatim@out\@esphack}
+%\end{verbatim}
+%
+% \section{The implementation}
+%
+% \let\DescribeMacro\docDescribeMacro
+% \let\DescribeEnv\docDescribeEnv
+%
+% \changes{v1.4e}{1991/07/24}{Avoid reading this file twice.}
+% The very first thing we do is to ensure that this file is not read
+% in twice. To this end we check whether the macro |\verbatim@@@| is
+% defined. If so, we just stop reading this file. The `package'
+% guard here allows most of the code to be excluded when extracting
+% the driver file for testing this package.
+%    \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{verbatim}
+     [2014/10/28 v1.5q LaTeX2e package for verbatim enhancements]
+\@ifundefined{verbatim@@@}{}{\endinput}
+%    \end{macrocode}
+%
+% We use a mechanism similar to the one implemented for the
+% |\comment|\ldots\allowbreak|\endcomment| macro in \AmSTeX:
+% We input one line at a time and check if it contains the |\end{...}|
+% tokens.
+% Then we can decide whether we have reached the end of the verbatim
+% text, or must continue.
+%
+%
+% \subsection{Preliminaries}
+%
+% \begin{macro}{\every@verbatim}
+%    The hook (i.e.\ token register) |\every@verbatim|
+%    is initialized to \meta{empty}.
+%    \begin{macrocode}
+\newtoks\every@verbatim
+\every@verbatim={}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@makeother}
+% \changes{v1.1a}{1989/10/16}{\cs{@makeother} added.}
+%    |\@makeother| takes as argument a character and changes
+%    its category code to $12$ (other).
+%    \begin{macrocode}
+\def\@makeother#1{\catcode`#112\relax}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@vobeyspaces}
+% \changes{v1.5}{1993/10/11}{Changed definition to not use \cs{gdef}.}
+% \changes{v1.1a}{1989/10/16}{\cs{@vobeyspaces} added.}
+%    The macro |\@vobeyspaces| causes spaces in the input
+%    to be printed as spaces in the output.
+%    \begin{macrocode}
+\begingroup
+ \catcode`\ =\active%
+ \def\x{\def\@vobeyspaces{\catcode`\ \active\let \@xobeysp}}
+ \expandafter\endgroup\x
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@xobeysp}
+% \changes{v1.1a}{1989/10/16}{\cs{@xobeysp} added.}
+%    The macro |\@xobeysp| produces exactly one space in
+%    the output, protected against breaking just before it.
+%    (|\@M| is an abbreviation for the number $10000$.)
+%    \begin{macrocode}
+\def\@xobeysp{\leavevmode\penalty\@M\ }
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\verbatim@line}
+% \changes{v1.2d}{1989/11/29}{Introduced token register
+%                \cs{verbatim@line}.}
+%    We use a newly defined token register called |\verbatim@line|
+%    that will be used as the character buffer.
+%    \begin{macrocode}
+\newtoks\verbatim@line
+%    \end{macrocode}
+% \end{macro}
+%
+% The following four macros are defined globally in a way suitable for
+% the \texttt{verbatim} and \texttt{verbatim*} environments.
+% \begin{macro}{\verbatim@startline}
+% \begin{macro}{\verbatim@addtoline}
+% \begin{macro}{\verbatim@processline}
+%    |\verbatim@startline| initializes processing of a line
+%    by emptying the character buffer (|\verbatim@line|).
+%    \begin{macrocode}
+\def\verbatim@startline{\verbatim@line{}}
+%    \end{macrocode}
+%    |\verbatim@addtoline| adds the tokens in its argument
+%    to our buffer register |\verbatim@line| without expanding
+%    them.
+%    \begin{macrocode}
+\def\verbatim@addtoline#1{%
+  \verbatim@line\expandafter{\the\verbatim@line#1}}
+%    \end{macrocode}
+%    Processing a line inside a \texttt{verbatim} or \texttt{verbatim*}
+%    environment means printing it.
+% \changes{v1.2c}{1989/10/31}{Changed \cs{@@par} to \cs{par} in
+%    \cs{verbatim@processline}.  Removed \cs{leavevmode} and \cs{null}
+%    (i.e.\ the empty \cs{hbox}).}
+%    Ending the line means that we have to begin a new paragraph.
+%    We use |\par| for this purpose.  Note that |\par|
+%    is redefined in |\@verbatim| to force \TeX{} into horizontal
+%    mode and to insert an empty box so that empty lines in the input
+%    do appear in the output.
+% \changes{v1.2f}{1990/01/31}{\cs{verbatim@startline} removed.}
+%    \begin{macrocode}
+\def\verbatim@processline{\the\verbatim@line\par}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@finish}
+%    As a default, |\verbatim@finish| processes the remaining
+%    characters.
+%    When this macro is called we are facing the following problem:
+%    when the |\end{verbatim}|
+%    command is encountered |\verbatim@processline| is called
+%    to process the characters preceding the command on the same
+%    line.  If there are none, an empty line would be output if we
+%    did not check for this case.
+%
+%    If the line is empty |\the\verbatim@line| expands to
+%    nothing.  To test this we use a trick similar to that on p.\ 376
+%    of the \TeX{}book, but with |$|\ldots|$| instead of
+%    the |!| tokens.  These |$| tokens can never have the same
+%    category code as a |$| token that might possibly appear in the
+%    token register |\verbatim@line|, as such a token will always have
+%    been read with category code $12$ (other).
+%    Note that |\ifcat| expands the following tokens so that
+%    |\the\verbatim@line| is replaced by the accumulated
+%    characters
+% \changes{v1.2d}{1989/11/29}{Changed \cs{ifx} to \cs{ifcat} test.}
+% \changes{v1.1b}{1989/10/18}{Corrected bug in if test (found by CRo).}
+%    \begin{macrocode}
+\def\verbatim@finish{\ifcat$\the\verbatim@line$\else
+  \verbatim@processline\fi}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{The \texttt{verbatim} and \texttt{verbatim*} environments}
+%
+% \begin{macro}{\verbatim@font}
+% \changes{v1.2f}{1990/01/31}{\cs{@lquote} macro removed.}
+% \changes{v1.1b}{1989/10/18}{\cs{@noligs} removed.  Code inserted
+%                           directly into \cs{verbatim@font}.}
+% \changes{v1.1a}{1989/10/16}{\cs{verbatim@font} added.}
+% \changes{v1.1a}{1989/10/16}{\cs{@noligs} added.}
+% \changes{v1.1a}{1989/10/16}{\cs{@lquote} added.}
+%    We start by defining the macro |\verbatim@font| that is
+%    to select the font and to set font-dependent parameters.
+%    Then we expand |\@noligs| (defined in the \LaTeXe{} kernel). Among
+%    possibly other things, it will go through |\verbatim@nolig@list|
+%    to avoid certain ligatures.
+%    |\verbatim@nolig@list| is a macro defined in the \LaTeXe{} kernel
+%    to expand to
+%    \begin{verbatim}
+%    \do\`\do\<\do\>\do\,\do\'\do\-
+%\end{verbatim}
+%    All the characters in this list can be part of a ligature in some
+%    font or other.
+% \changes{v1.2f}{1990/01/31}{\cs{@lquote} macro removed.}
+% \changes{v1.4c}{1990/10/18}{Added \cs{leavevmode}.}
+% \changes{v1.4k}{1992/07/13}{Replaced Blank after $96$ by \cs{relax}.
+%                           (Proposed by Dan Dill.)}
+% \changes{v1.5}{1993/10/11}{Definition changed according to new code
+%          in latex.tex and to avoid global definition.}
+% \changes{v1.5c}{1994/02/07}{Changed to use new font switching
+%                           commands.}
+% \changes{v1.5m}{2000/01/07}{Disable hyphenation even if the font
+%    allows it.}
+% \changes{v1.5q}{2003/08/22}{Use \cs{@noligs}, as it is by now properly
+%    defined in the \LaTeXe{} kernel.}
+%    \begin{macrocode}
+\def\verbatim@font{\normalfont\ttfamily
+                   \hyphenchar\font\m@ne
+                   \@noligs}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\@verbatim}
+% \changes{v1.1a}{1989/10/16}{\cs{@verbatim} added.}
+%    The macro |\@verbatim| sets up things properly.
+%    First of all, the tokens of the |\every@verbatim| hook
+%    are inserted.
+%    Then a \texttt{trivlist} environment is started and its first
+%    |\item| command inserted.
+%    Each line of the \texttt{verbatim} or \texttt{verbatim*}
+%    environment will be treated as a separate paragraph.
+% \changes{v1.2e}{1990/01/15}{Added \cs{every@verbatim} hook.}
+% \changes{v1.5b}{1994/01/24}{Removed optional argument of \cs{item}.}
+%    \begin{macrocode}
+\def\@verbatim{\the\every@verbatim
+  \trivlist \item \relax
+%    \end{macrocode}
+% \changes{v1.5b}{1994/01/24}{Set \texttt{@inlabel} switch to false.}
+% \changes{v1.5f}{1994/10/25}{Removed setting of \texttt{@inlabel}
+%                             switch again.}
+% \changes{v1.3c}{1990/02/26}{Removed extra vertical space.
+%           Suggested by Frank Mittelbach.}
+% \changes{v1.5h}{1995/09/21}{Added the space again, since it is
+%           necessary for correct vertical spacing if \texttt{verbatim}
+%           is nested inside \texttt{quote}.}
+%    The following extra vertical space is for compatibility with the
+%    \LaTeX kernel: otherwise, using the |verbatim| package changes
+%    the vertical spacing of a |verbatim| environment nested within a
+%    |quote| environment.
+%    \begin{macrocode}
+  \if@minipage\else\vskip\parskip\fi
+%    \end{macrocode}
+% \changes{v1.4k}{1992/07/13}{Added setting for
+%        \cs{@beginparpenalty}. Suggested by Frank Mittelbach.}
+%    The paragraph parameters are set appropriately:
+%    the penalty at the beginning of the environment,
+%    left and right margins, paragraph indentation, the glue to
+%    fill the last line, and the vertical space between paragraphs.
+%    The latter space has to be zero since we do not want to add
+%    extra space between lines.
+%    \begin{macrocode}
+  \@beginparpenalty \predisplaypenalty
+  \leftskip\@totalleftmargin\rightskip\z@
+  \parindent\z@\parfillskip\@flushglue\parskip\z@
+%    \end{macrocode}
+% \changes{v1.1b}{1989/10/18}{Added resetting of \cs{parshape}
+%                           if at beginning of a list.
+%                           (Problem pointed out by Chris Rowley.)}
+%    There's one point to make here:
+%    the \texttt{list} environment uses \TeX's |\parshape|
+%    primitive to get a special indentation for the first line
+%    of the  list.
+%    If the list begins with a \texttt{verbatim} environment
+%    this |\parshape| is still in effect.
+%    Therefore we have to reset this internal parameter explicitly.
+%    We could do this by assigning $0$ to |\parshape|.
+%    However, there is a simpler way to achieve this:
+%    we simply tell \TeX{} to start a new paragraph.
+%    As is explained on p.~103 of the \TeX{}book, this resets
+%    |\parshape| to zero.
+% \changes{v1.1c}{1989/10/19}{Replaced explicit resetting of
+%                           \cs{parshape} by \cs{@@par}.}
+%    \begin{macrocode}
+  \@@par
+%    \end{macrocode}
+%    We now ensure that |\par| has the correct definition,
+%    namely to force \TeX{} into horizontal mode
+%    and to include an empty box.
+%    This is to ensure that empty lines do appear in the output.
+%    Afterwards, we insert the |\interlinepenalty| since \TeX{}
+%    does not add a penalty between paragraphs (here: lines)
+%    by its own initiative. Otherwise a |verbatim| environment
+%    could be broken across pages even if a |\samepage|
+%    declaration were present.
+%
+%    However, in a top-aligned minipage, this will result in an extra
+%    empty line added at the top. Therefore, a slightly more
+%    complicated construct is necessary.
+%    One of the important things here is the inclusion of
+%    |\leavevmode| as the first macro in the first line, for example,
+%    a blank verbatim line is the first thing in a list item.
+% \changes{v1.2c}{1989/10/31}{Definition of \cs{par} added.
+%                           Ensures identical behaviour for
+%                           verbatim and \cs{verbatiminput}.
+%                           Problem pointed out by Chris.}
+% \changes{v1.4d}{1991/04/24}{\cs{penalty}\cs{interlinepenalty} added.
+%                           Necessary to avoid page breaks in
+%                           the scope of a \cs{samepage} declaration.}
+% \changes{v1.5b}{1994/01/24}{Improved definition of \cs{par} to work
+%                           under all circumstances.}
+% \changes{v1.5f}{1994/10/25}{\cs{leavevmode} added for first line.}
+%    \begin{macrocode}
+  \def\par{%
+    \if@tempswa
+      \leavevmode\null\@@par\penalty\interlinepenalty
+    \else
+      \@tempswatrue
+      \ifhmode\@@par\penalty\interlinepenalty\fi
+    \fi}%
+%    \end{macrocode}
+%    But to avoid an error message when the environment
+%    doesn't contain any text, we redefine |\@noitemerr|
+%    which will in this case be called by |\endtrivlist|.
+% \changes{v1.4j}{1992/06/30}{Introduced warning instead of error
+%        for empty body of verbatim text.
+%        Suggested by Nelson Beebe.}
+%    \begin{macrocode}
+  \def\@noitemerr{\@warning{No verbatim text}}%
+%    \end{macrocode}
+%    Now we call |\obeylines| to make the end of line character
+%    active,
+%    \begin{macrocode}
+  \obeylines
+%    \end{macrocode}
+%    change the category code of all special characters,
+%    to $12$ (other).
+%    \changes{v1.5i}{1996/06/04}{Moved \cs{verbatim@font} after
+%           \cs{dospecials}.}
+%    \begin{macrocode}
+  \let\do\@makeother \dospecials
+%    \end{macrocode}
+%    and switch to the font to be used.
+%    \begin{macrocode}
+  \verbatim@font
+%    \end{macrocode}
+%    To avoid a breakpoint after the labels box, we remove the penalty
+%    put there by the list macros: another use of |\unpenalty|!
+% \changes{v1.5f}{1994/10/25}{Change to \cs{everypar} added.}
+%    \begin{macrocode}
+  \everypar \expandafter{\the\everypar \unpenalty}}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\verbatim}
+% \begin{macro}{\verbatim*}
+%    Now we define the toplevel macros.
+%    |\verbatim| is slightly changed:
+%    after setting up things properly it calls
+%    |\verbatim@start|.
+% \changes{v1.5l}{1999/12/14}{Added \cs{begingroup} for cases where
+%    \cs{verbatim} is used directly, rather than in \cs{begin}: see
+%    pr/3115.}
+%    This is done inside a group, so that |\verbatim| can be used
+%    directly, without |\begin|.
+%    \begin{macrocode}
+\def\verbatim{\begingroup\@verbatim \frenchspacing\@vobeyspaces
+              \verbatim@start}
+%    \end{macrocode}
+%    |\verbatim*| is defined accordingly.
+%    \begin{macrocode}
+\@namedef{verbatim*}{\begingroup\@verbatim\verbatim@start}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\endverbatim}
+% \begin{macro}{\endverbatim*}
+%    To end the \texttt{verbatim} and \texttt{verbatim*}
+%    environments it is only necessary to finish the
+%    \texttt{trivlist} environment started in |\@verbatim| and
+%    close the corresponding group.
+% \changes{v1.5l}{1999/12/14}{Added \cs{endgroup} for cases where
+%    \cs{endverbatim} is used directly, rather than in \cs{end}: see
+%    pr/3115.}
+% \changes{v1.5n}{2000/08/03}{Added \cs{@endpetrue}: needed when
+%    faking such a \cs{end} (pr/3234).}
+% \changes{v1.5o}{2000/08/23}{Changed \cs{@endpetrue} to \cs{@doendpe}:
+%    see (pr/3234).}
+%    \begin{macrocode}
+\def\endverbatim{\endtrivlist\endgroup\@doendpe}
+\expandafter\let\csname endverbatim*\endcsname =\endverbatim
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{The \texttt{comment} environment}
+%
+% \begin{macro}{\comment}
+% \begin{macro}{\endcomment}
+% \changes{v1.1c}{1989/10/19}{Added \cs{@bsphack}/\cs{@esphack} to the
+%            \texttt{comment} environment.  Suggested by Chris Rowley.}
+%    The |\comment| macro is similar to |\verbatim*|.
+%    However, we do not need to switch fonts or set special
+%    formatting parameters such as |\parindent| or |\parskip|.
+%    We need only set the category code of all special characters
+%    to $12$ (other) and that of |^^M| (the end of line character)
+%    to $13$ (active).
+%    The latter is needed for macro parameter delimiter matching in
+%    the internal macros defined below.
+%    In contrast to the default definitions used by the
+%    |\verbatim| and |\verbatim*| macros,
+%    we define |\verbatim@addtoline| to throw away its argument
+%    and |\verbatim@processline|, |\verbatim@startline|,
+%    and |\verbatim@finish| to act as no-ops.
+%    Then we call |\verbatim@|.
+%    But the first thing we do is to call |\@bsphack| so that
+%    this environment has no influence whatsoever upon the spacing.
+% \changes{v1.1c}{1989/10/19}{Changed \cs{verbatim@start} to
+%                           \cs{verbatim@}.  Suggested by Chris Rowley.}
+% \changes{v1.1c}{1989/10/19}{\cs{verbatim@startline} and
+%                           \cs{verbatim@finish} are now
+%                           also redefined to do nothing.}
+%    \begin{macrocode}
+\def\comment{\@bsphack
+             \let\do\@makeother\dospecials\catcode`\^^M\active
+             \let\verbatim@startline\relax
+             \let\verbatim@addtoline\@gobble
+             \let\verbatim@processline\relax
+             \let\verbatim@finish\relax
+             \verbatim@}
+%    \end{macrocode}
+%    |\endcomment| is very simple: it only calls
+%    |\@esphack| to take care of the spacing.
+%    The |\end| macro closes the group and therefore takes care
+%    of restoring everything we changed.
+%    \begin{macrocode}
+\let\endcomment=\@esphack
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+%
+% \subsection{The main loop}
+%
+% Here comes the tricky part:
+% During the definition of the macros we need to use the special
+% characters |\|, |{|, and |}| not only with their
+% normal category codes,
+% but also with category code $12$ (other).
+% We achieve this by the following trick:
+% first we tell \TeX{} that |\|, |{|, and |}|
+% are the lowercase versions of |!|, |[|, and |]|.
+% Then we replace every occurrence of |\|, |{|, and |}|
+% that should be read with category code $12$ by |!|, |[|,
+% and |]|, respectively,
+% and give the whole list of tokens to |\lowercase|,
+% knowing that category codes are not altered by this primitive!
+%
+% But first we have ensure that
+% |!|, |[|, and |]| themselves have
+% the correct category code!
+% \changes{v1.3b}{1990/02/07}{Introduced \cs{vrb@catcodes} instead
+%                  of explicit setting of category codes.}
+% To allow special settings of these codes we hide their setting in
+% the macro |\vrb@catcodes|.  If it is already defined our new
+% definition is skipped.
+%    \begin{macrocode}
+\@ifundefined{vrb@catcodes}%
+  {\def\vrb@catcodes{%
+     \catcode`\!12\catcode`\[12\catcode`\]12}}{}
+%    \end{macrocode}
+% This trick allows us to use this code for applications where other
+% category codes are in effect.
+%
+% We start a group to keep the category code changes local.
+%    \begin{macrocode}
+\begingroup
+ \vrb@catcodes
+ \lccode`\!=`\\ \lccode`\[=`\{ \lccode`\]=`\}
+%    \end{macrocode}
+% \changes{v1.2f}{1990/01/31}{Code for TABs removed.}
+%    We also need the end-of-line character |^^M|,
+%    as an active character.
+%    If we were to simply write |\catcode`\^^M=\active|
+%    then we would get an unwanted active end of line character
+%    at the end of every line of the following macro definitions.
+%    Therefore we use the same trick as above:
+%    we write a tilde |~| instead of |^^M| and
+%    pretend that the
+%    latter is the lowercase variant of the former.
+%    Thus we have to ensure now that the tilde character has
+%    category code $13$ (active).
+%    \begin{macrocode}
+ \catcode`\~=\active \lccode`\~=`\^^M
+%    \end{macrocode}
+%    The use of the |\lowercase| primitive leads to one problem:
+%    the uppercase character `|C|' needs to be used in the
+%    code below and its case must be preserved.
+%    So we add the command:
+%    \begin{macrocode}
+ \lccode`\C=`\C
+%    \end{macrocode}
+%    Now we start the token list passed to |\lowercase|.
+%    We use the following little trick (proposed by Bernd Raichle):
+%    The very first token in the token list we give to |\lowercase| is
+%    the |\endgroup| primitive. This means that it is processed by
+%    \TeX{} immediately after |\lowercase| has finished its operation,
+%    thus ending the group started by |\begingroup| above. This avoids
+%    the global definition of all macros.
+%    \begin{macrocode}
+ \lowercase{\endgroup
+%    \end{macrocode}
+% \begin{macro}{\verbatim@start}
+%    The purpose of |\verbatim@start| is to check whether there
+%    are any characters on the same line as the |\begin{verbatim}|
+%    and to pretend that they were on a line by themselves.
+%    On the other hand, if there are no characters remaining
+%    on the current line we shall just find an end of line character.
+%    |\verbatim@start| performs its task by first grabbing the
+%    following character (its argument).
+%    This argument is then compared to an active |^^M|,
+%    the end of line character.
+%    \begin{macrocode}
+    \def\verbatim@start#1{%
+      \verbatim@startline
+      \if\noexpand#1\noexpand~%
+%    \end{macrocode}
+%    If this is true we transfer control to |\verbatim@|
+%    to process the next line.  We use
+%    |\next| as the macro which will continue the work.
+%    \begin{macrocode}
+        \let\next\verbatim@
+%    \end{macrocode}
+%    Otherwise, we define |\next| to expand to a call
+%    to |\verbatim@| followed by the character just
+%    read so that it is reinserted into the text.
+%    This means that those characters remaining on this line
+%    are handled as if they formed a line by themselves.
+%    \begin{macrocode}
+      \else \def\next{\verbatim@#1}\fi
+%    \end{macrocode}
+%    Finally we call |\next|.
+%    \begin{macrocode}
+      \next}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@}
+%    The three macros |\verbatim@|, |\verbatim@@|,
+%    and |\verbatim@@@| form the ``main loop'' of the
+%    \texttt{verbatim} environment.
+%    The purpose of |\verbatim@| is to read exactly one line
+%    of input.
+%    |\verbatim@@| and |\verbatim@@@| work together to
+%    find out whether the four characters
+%    |\end| (all with category code $12$ (other)) occur in that
+%    line.
+%    If so, |\verbatim@@@| will call
+%    |\verbatim@test| to check whether this |\end| is
+%    part of |\end{verbatim}| and will terminate the environment
+%    if this is the case.
+%    Otherwise we continue as if nothing had happened.
+%    So let's have a look at the definition of |\verbatim@|:
+% \changes{v1.1a}{1989/10/16}{Replaced \cs{verbatim@@@} by \cs{@nil}.}
+%    \begin{macrocode}
+    \def\verbatim@#1~{\verbatim@@#1!end\@nil}%
+%    \end{macrocode}
+%    Note that the |!| character will have been replaced by a
+%    |\| with category code $12$ (other) by the |\lowercase|
+%    primitive governing this code before the definition of this
+%    macro actually takes place.
+%    That means that
+%    it takes the line, puts |\end| (four character tokens)
+%    and |\@nil| (one control sequence token) as a
+%    delimiter behind it, and
+%    then calls |\verbatim@@|.
+% \end{macro}
+%
+% \begin{macro}{\verbatim@@}
+%    |\verbatim@@| takes everything up to the next occurrence of
+%    the four characters |\end| as its argument.
+%    \begin{macrocode}
+    \def\verbatim@@#1!end{%
+%    \end{macrocode}
+%    That means: if they do not occur in the original line, then
+%    argument |#1| is the
+%    whole input line, and |\@nil| is the next token
+%    to be processed.
+%    However, if the four characters |\end| are part of the
+%    original line, then
+%    |#1| consists of the characters in front of |\end|,
+%    and the next token is the following character (always remember
+%    that the line was lengthened by five tokens).
+%    Whatever |#1| may be, it is verbatim text,
+%    so |#1| is added to the line currently built.
+%    \begin{macrocode}
+       \verbatim@addtoline{#1}%
+%    \end{macrocode}
+%    The next token in the input stream
+%    is of special interest to us.
+%    Therefore |\futurelet| defines |\next| to be equal
+%    to it before calling |\verbatim@@@|.
+%    \begin{macrocode}
+       \futurelet\next\verbatim@@@}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@@@}
+% \changes{v1.1a}{1989/10/16}{Replaced \cs{verbatim@@@} by
+%                           \cs{@nil} where used as delimiter.}
+%    |\verbatim@@@| will now read the rest of the tokens on
+%    the current line,
+%    up to the final |\@nil| token.
+%    \begin{macrocode}
+    \def\verbatim@@@#1\@nil{%
+%    \end{macrocode}
+%    If the first of the above two cases occurred, i.e.\ no
+%    |\end| characters were on that line, |#1| is empty
+%    and |\next| is equal to |\@nil|.
+%    This is easily checked.
+%    \begin{macrocode}
+       \ifx\next\@nil
+%    \end{macrocode}
+%    If so, this was a simple line.
+%    We finish it by processing the line we accumulated so far.
+%    Then we prepare to read the next line.
+% \changes{v1.2f}{1990/01/31}{Added \cs{verbatim@startline}.}
+%    \begin{macrocode}
+         \verbatim@processline
+         \verbatim@startline
+         \let\next\verbatim@
+%    \end{macrocode}
+%    Otherwise we have to check what follows these |\end|
+%    tokens.
+%    \begin{macrocode}
+       \else
+%    \end{macrocode}
+%    Before we continue, it's a good idea to stop for a moment
+%    and remember where we are:
+%    We have just read the four character tokens |\end|
+%    and must now check whether the name of the environment (surrounded
+%    by braces) follows.
+%    To this end we define a macro called |\@tempa|
+%    that reads exactly one character and decides what to do next.
+%    This macro should do the following: skip spaces until
+%    it encounters either a left brace or the end of the line.
+%    But it is important to remember which characters are skipped.
+%    The |\end|\meta{optional spaces}|{| characters
+%    may be part of the verbatim text, i.e.\ these characters
+%    must be printed.
+%
+%    Assume for example that the current line contains
+%    \begin{verbatim*}
+%      \end {AVeryLongEnvironmentName}
+%\end{verbatim*}
+%    As we shall soon see, the scanning mechanism implemented here
+%    will not find out that this is text to be printed until
+%    it has read the right brace.
+%    Therefore we need a way to accumulate the characters read
+%    so that we can reinsert them if necessary.
+%    The token register |\@temptokena| is used for this purpose.
+%
+%    Before we do this we have to get rid of the superfluous
+%    |\end| tokens at the end of the line.
+% \changes{v1.4j}{1992/06/30}{Removed use of \cs{toks@}. Suggested by
+%           Bernd Raichle.}
+%    To this end we define a temporary macro whose argument
+%    is delimited by |\end\@nil| (four character tokens
+%    and one control sequence token) to be used below
+%    on the rest of the line, after appending a |\@nil| token to it.
+%    (Note that this token can never appear in |#1|.)
+%    We use the following definition of
+%    |\@tempa| to get the rest of the line (after the first
+%    |\end|).
+%    \begin{macrocode}
+         \def\@tempa##1!end\@nil{##1}%
+%    \end{macrocode}
+%    We mentioned already that we use token register
+%    |\@temptokena|
+%    to remember the characters we skip, in case we need them again.
+%    We initialize this with the |\end| we have thrown away
+%    in the call to |\@tempa|.
+%    \begin{macrocode}
+         \@temptokena{!end}%
+%    \end{macrocode}
+%    We shall now call |\verbatim@test|
+%    to process the characters
+%    remaining on the current line.
+%    But wait a moment: we cannot simply call this macro
+%    since we have already read the whole line.
+%    Therefore we have to first expand the macro |\@tempa| to insert
+%    them again after the |\verbatim@test| token.
+%    A |^^M| character is appended to denote the end of the line.
+%    (Remember that this character comes disguised as a tilde.)
+% \changes{v1.2}{1989/10/20}{Taken local definition of \cs{@tempa} out
+%                          of \cs{verbatim@@@} and introduced
+%                          \cs{verbatim@test} instead.}
+%    \begin{macrocode}
+         \def\next{\expandafter\verbatim@test\@tempa#1\@nil~}%
+%    \end{macrocode}
+%    That's almost all, but we still have to
+%    now call |\next| to do the work.
+%    \begin{macrocode}
+       \fi \next}%
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\verbatim@test}
+% \changes{v1.2}{1989/10/20}{Introduced \cs{verbatim@test}.}
+%    We define |\verbatim@test| to investigate every token
+%    in turn.
+%    \begin{macrocode}
+    \def\verbatim@test#1{%
+%    \end{macrocode}
+%    First of all we set |\next| equal to |\verbatim@test|
+%    in case this macro must call itself recursively in order to
+%    skip spaces.
+%    \begin{macrocode}
+           \let\next\verbatim@test
+%    \end{macrocode}
+%    We have to distinguish four cases:
+%    \begin{enumerate}
+%      \item The next token is a |^^M|, i.e.\ we reached
+%            the end of the line.  That means that nothing
+%            special was found.
+%            Note that we use |\if| for the following
+%            comparisons so that the category code of the
+%            characters is irrelevant.
+%    \begin{macrocode}
+           \if\noexpand#1\noexpand~%
+%    \end{macrocode}
+%            We add the characters accumulated in token register
+%            |\@temptokena| to the current line.  Since
+%            |\verbatim@addtoline| does not expand its argument,
+%            we have to do the expansion at this point.  Then we
+%            |\let| |\next| equal to |\verbatim@|
+%            to prepare to read the next line.
+% \changes{v1.2f}{1990/01/31}{Added \cs{verbatim@startline}.}
+%    \begin{macrocode}
+             \expandafter\verbatim@addtoline
+               \expandafter{\the\@temptokena}%
+             \verbatim@processline
+             \verbatim@startline
+             \let\next\verbatim@
+%    \end{macrocode}
+%      \item A space character follows.
+%            This is allowed, so we add it to |\@temptokena|
+%            and continue.
+%    \begin{macrocode}
+           \else \if\noexpand#1
+             \@temptokena\expandafter{\the\@temptokena#1}%
+%    \end{macrocode}
+% \changes{v1.2f}{1990/01/31}{Code for TABs removed.}
+%      \item An open brace follows.
+%            This is the most interesting case.
+%            We must now collect characters until we read the closing
+%            brace and check whether they form the environment name.
+%            This will be done by |\verbatim@testend|, so here
+%            we let |\next| equal this macro.
+%            Again we will process the rest of the line, character
+%            by character.
+% \changes{v1.2}{1989/10/20}{Moved the initialization of
+%                          \cs{@tempc} from \cs{verbatim@testend} into
+%                          \cs{verbatim@test}.}
+%            The characters forming the name of the environment will
+%            be accumulated in |\@tempc|.
+%            We initialize this macro to expand to nothing.
+% \changes{v1.3b}{1990/02/07}{\cs{noexpand} added.}
+%    \begin{macrocode}
+           \else \if\noexpand#1\noexpand[%
+             \let\@tempc\@empty
+             \let\next\verbatim@testend
+%    \end{macrocode}
+%            Note that the |[| character will be a |{| when
+%            this macro is defined.
+%      \item Any other character means that the |\end| was part
+%            of the verbatim text.
+%            Add the characters to the current line and prepare to call
+%            |\verbatim@| to process the rest of the line.
+%  \changes{v1.0f}{1989/10/09}{Fixed \cs{end} \cs{end} bug
+%                            found by Chris Rowley}
+%    \begin{macrocode}
+           \else
+             \expandafter\verbatim@addtoline
+               \expandafter{\the\@temptokena}%
+             \def\next{\verbatim@#1}%
+           \fi\fi\fi
+%    \end{macrocode}
+%    \end{enumerate}
+%    The last thing this macro does is to call |\next|
+%    to continue processing.
+%    \begin{macrocode}
+           \next}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@testend}
+%    |\verbatim@testend| is called when
+%    |\end|\meta{optional spaces}|{| was seen.
+%    Its task is to scan everything up to the next |}|
+%    and to call |\verbatim@@testend|.
+%    If no |}| is found it must reinsert the characters it read
+%    and return to |\verbatim@|.
+%    The following definition is similar to that of
+%    |\verbatim@test|:
+%    it takes the next character and decides what to do.
+% \changes{v1.2}{1989/10/20}{Removed local definition of \cs{@tempa}
+%                          from \cs{verbatim@testend} which now
+%                          does the work itself.}
+%    \begin{macrocode}
+    \def\verbatim@testend#1{%
+%    \end{macrocode}
+%    Again, we have four cases:
+%    \begin{enumerate}
+%      \item |^^M|: As no |}| is found in the current line,
+%            add the characters to the buffer.  To avoid a
+%            complicated construction for expanding
+%            |\@temptokena|
+%            and |\@tempc| we do it in two steps.  Then we
+%            continue with |\verbatim@| to process the
+%            next line.
+% \changes{v1.2f}{1990/01/31}{Added \cs{verbatim@startline}.}
+%    \begin{macrocode}
+         \if\noexpand#1\noexpand~%
+           \expandafter\verbatim@addtoline
+             \expandafter{\the\@temptokena[}%
+           \expandafter\verbatim@addtoline
+             \expandafter{\@tempc}%
+           \verbatim@processline
+           \verbatim@startline
+           \let\next\verbatim@
+%    \end{macrocode}
+%      \item |}|: Call |\verbatim@@testend| to check
+%            if this is the right environment name.
+% \changes{v1.3b}{1990/02/07}{\cs{noexpand} added.}
+%    \begin{macrocode}
+         \else\if\noexpand#1\noexpand]%
+           \let\next\verbatim@@testend
+%    \end{macrocode}
+%  \changes{v1.0f}{1989/10/09}{Introduced check for
+%              {\tt\string\verb!\string|!\string\!\string|} to fix
+%              single brace bug found by Chris Rowley}
+%      \item |\|: This character must not occur in the name of
+%            an environment.  Thus we stop collecting characters.
+%            In principle, the same argument would apply to other
+%            characters as well, e.g., |{|.
+%            However, |\| is a special case, since it may be
+%            the first character of |\end|.  This means that
+%            we have to look again for
+%            |\end{|\meta{environment name}|}|.
+%            Note that we prefixed the |!| by a |\noexpand|
+%            primitive, to protect ourselves against it being an
+%            active character.
+% \changes{v1.3b}{1990/02/07}{\cs{noexpand} added.}
+%    \begin{macrocode}
+         \else\if\noexpand#1\noexpand!%
+           \expandafter\verbatim@addtoline
+             \expandafter{\the\@temptokena[}%
+           \expandafter\verbatim@addtoline
+             \expandafter{\@tempc}%
+           \def\next{\verbatim@!}%
+%    \end{macrocode}
+%      \item Any other character: collect it and continue.
+%            We cannot use |\edef| to define |\@tempc|
+%            since its replacement text might contain active
+%            character tokens.
+%    \begin{macrocode}
+         \else \expandafter\def\expandafter\@tempc\expandafter
+           {\@tempc#1}\fi\fi\fi
+%    \end{macrocode}
+%    \end{enumerate}
+%    As before, the macro ends by calling itself, to
+%    process the next character if appropriate.
+%    \begin{macrocode}
+         \next}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@@testend}
+%    Unlike the previous macros |\verbatim@@testend| is simple:
+%    it has only to check if the |\end{|\ldots|}|
+%    matches the corresponding |\begin{|\ldots|}|.
+%    \begin{macrocode}
+    \def\verbatim@@testend{%
+%    \end{macrocode}
+%    We use |\next| again to define the things that are
+%    to be done.
+%    Remember that the name of the current environment is
+%    held in |\@currenvir|, the characters accumulated
+%    by |\verbatim@testend| are in |\@tempc|.
+%    So we simply compare these and prepare to execute
+%    |\end{|\meta{current environment}|}|
+%    macro if they match.
+%    Before we do this we call |\verbatim@finish| to process
+%    the last line.
+%    We define |\next| via |\edef| so that
+%    |\@currenvir| is replaced by its expansion.
+%    Therefore we need |\noexpand| to inhibit the expansion
+%    of |\end| at this point.
+%    \begin{macrocode}
+       \ifx\@tempc\@currenvir
+         \verbatim@finish
+         \edef\next{\noexpand\end{\@currenvir}%
+%    \end{macrocode}
+%    Without this trick the |\end| command would not be able
+%    to correctly check whether its argument matches the name of
+%    the current environment and you'd get an
+%    interesting \LaTeX{} error message such as:
+%    \begin{verbatim}
+%! \begin{verbatim*} ended by \end{verbatim*}.
+%\end{verbatim}
+%    But what do we do with the rest of the characters, those
+%    that remain on that line?
+%    We call |\verbatim@rescan| to take care of that.
+%    Its first argument is the name of the environment just
+%    ended, in case we need it again.
+%    |\verbatim@rescan| takes the list of characters to be
+%    reprocessed as its second argument.
+%    (This token list was inserted after the current macro
+%    by |\verbatim@@@|.)
+%    Since we are still in an |\edef| we protect it
+%    by means of|\noexpand|.
+%    \begin{macrocode}
+                    \noexpand\verbatim@rescan{\@currenvir}}%
+%    \end{macrocode}
+%    If the names do not match, we reinsert everything read up
+%    to now and prepare to call |\verbatim@| to process
+%    the rest of the line.
+%    \begin{macrocode}
+       \else
+         \expandafter\verbatim@addtoline
+           \expandafter{\the\@temptokena[}%
+           \expandafter\verbatim@addtoline
+             \expandafter{\@tempc]}%
+         \let\next\verbatim@
+       \fi
+%    \end{macrocode}
+%    Finally we call |\next|.
+%    \begin{macrocode}
+       \next}%
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@rescan}
+%    In principle |\verbatim@rescan| could be used to
+%    analyse the characters remaining after the |\end{...}|
+%    command and pretend that these were read
+%    ``properly'', assuming ``standard'' category codes are in
+%    force.\footnote{Remember that they were all read with
+%          category codes $11$ (letter) and $12$ (other) so
+%          that control sequences are not recognized as such.}
+%    But this is not always possible (when there are unmatched
+%    curly braces in the rest of the line).
+%    Besides, we think that this is not worth the effort:
+%    After a \texttt{verbatim} or \texttt{verbatim*} environment
+%    a new line in the output is begun anyway,
+%    and an |\end{comment}| can easily be put on a line by itself.
+%    So there is no reason why there should be any text here.
+%    For the benefit of the user who did put something there
+%    (a comment, perhaps)
+%    we simply issue a warning and drop them.
+%    The method of testing is explained in Appendix~D, p.\ 376 of
+%    the \TeX{}book. We use |^^M| instead of the |!|
+%    character used there
+%    since this is a character that cannot appear in |#1|.
+%    The two |\noexpand| primitives are necessary to avoid
+%    expansion of active characters and macros.
+%
+%    One extra subtlety should be noted here: remember that
+%    the token list we are currently building will first be
+%    processed by the |\lowercase| primitive before \TeX{}
+%    carries out the definitions.
+%    This means that the `|C|' character in the
+%    argument to the |\@warning| macro must be protected against
+%    being changed to `|c|'.  That's the reason why we added the
+%    |\lccode`\C=`\C| assignment above.
+%    We can now finish the argument to |\lowercase| as well as the
+%    group in which the category codes were changed.
+%    \begin{macrocode}
+    \def\verbatim@rescan#1#2~{\if\noexpand~\noexpand#2~\else
+        \@warning{Characters dropped after `\string\end{#1}'}\fi}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{The \cs{verbatiminput} command}
+%
+% \begin{macro}{\verbatim@in@stream}
+%    We begin by allocating an input stream (out of the 16 available
+%    input streams).
+%\iffalse
+%  Vorstellbar ist auch der Aufruf von |`verbatiminput| innerhalb eines
+%  |`verbatiminput| (z.B: wenn man |`input|-Anweisungen im zu lesenden
+%  File hat und auch diese Files automatisch lesen will).  Dies kann
+%  man jedoch nur ermoeglichen, wenn man einen besseren Mechanismus
+%  verwendet als es das simple, statische |`newread| darstellt.
+%  Vorstellbar fuer eine neuere \LaTeX-Version ist eine (lokale)
+%  Allokation des Streams durch ein |`open| und eine Freigabe des
+%  Streams durch |`close| oder Verlassen der Gruppe.
+%\fi
+%    \begin{macrocode}
+\newread\verbatim@in@stream
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@readfile}
+%    The macro |\verbatim@readfile| encloses the main loop by calls to
+%    the macros |\verbatim@startline| and |\verbatim@finish|,
+%    respectively.  This makes sure
+%    that the user can initialize and finish the command when the file
+%    is empty or doesn't exist.  The \texttt{verbatim} environment has a
+%    similar behaviour when called with an empty text.
+%    \begin{macrocode}
+\def\verbatim@readfile#1{%
+  \verbatim@startline
+%    \end{macrocode}
+%    When the file is not found we issue a warning.
+%    \begin{macrocode}
+  \openin\verbatim@in@stream #1\relax
+  \ifeof\verbatim@in@stream
+    \typeout{No file #1.}%
+  \else
+%    \end{macrocode}
+%    At this point we pass the name of the file to |\@addtofilelist|
+%    so that its appears appears in the output of a |\listfiles|
+%    command.
+% \changes{v1.5j}{1996/09/25}{Add \cs{@addtofilelist} and
+%    \cs{ProvidesFile} so that the name of the file
+%    read in appears in the \cs{listfiles} output (Omission pointed
+%    out by Patrick W.~Daly).}
+%    In addition, we use |\ProvidesFile| to make a log entry in the
+%    transcript file and to distinguish files read in via
+%    |\verbatiminput| from others.
+%    \begin{macrocode}
+    \@addtofilelist{#1}%
+    \ProvidesFile{#1}[(verbatim)]%
+%    \end{macrocode}
+%    While reading from the file it is useful to switch off the
+%    recognition of the end-of-line character.  This saves us stripping
+%    off spaces from the contents of the line.
+%    \begin{macrocode}
+    \expandafter\endlinechar\expandafter\m@ne
+    \expandafter\verbatim@read@file
+    \expandafter\endlinechar\the\endlinechar\relax
+    \closein\verbatim@in@stream
+  \fi
+  \verbatim@finish
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@read@file}
+%    All the work is done in |\verbatim@read@file|.  It reads the input
+%    file line by line and recursively calls itself until the end of
+%    the file.
+%    \begin{macrocode}
+\def\verbatim@read@file{%
+  \read\verbatim@in@stream to\next
+  \ifeof\verbatim@in@stream
+  \else
+%    \end{macrocode}
+%    For each line we call |\verbatim@addtoline| with the contents of
+%    the line. \hskip0pt plus 3cm\penalty0\hskip0pt plus -3cm
+%    |\verbatim@processline| is called next.
+%    \begin{macrocode}
+    \expandafter\verbatim@addtoline\expandafter{\next}%
+    \verbatim@processline
+%    \end{macrocode}
+%    After processing the line we call |\verbatim@startline| to
+%    initialize all before we read the next line.
+%    \begin{macrocode}
+    \verbatim@startline
+%    \end{macrocode}
+%    Without |\expandafter| each call of |\verbatim@read@file| uses
+%    space in \TeX's input stack.\footnote{A standard \TeX\ would
+%    report an overflow error if you try to read a file with more than
+%    ca.\ 200~lines.  The same error occurs if the first line of code
+%    in \S 390 of \textsl{``TeX: The Program''\/} is missing.}
+%    \begin{macrocode}
+    \expandafter\verbatim@read@file
+  \fi
+}
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}{\verbatiminput}
+%    |\verbatiminput| first starts a group to keep font and category
+%    changes local.
+%    Then it calls the macro |\verbatim@input| with additional
+%    arguments, depending on whether an asterisk follows.
+%    \begin{macrocode}
+\def\verbatiminput{\begingroup
+  \@ifstar{\verbatim@input\relax}%
+          {\verbatim@input{\frenchspacing\@vobeyspaces}}}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\verbatim@input}
+% \changes{1.5k}{1997/04/30}{Have \cs{verbatim@input} check for
+%    existence of file.}
+%    |\verbatim@input| first checks whether the file exists, using
+%    the standard macro |\IfFileExists| which leaves the name of the
+%    file found in |\@filef@und|.
+%    Then everything is set up as in the |\verbatim| macro.
+%    \begin{macrocode}
+\def\verbatim@input#1#2{%
+   \IfFileExists {#2}{\@verbatim #1\relax
+%    \end{macrocode}
+%    Then it reads in the file, finishes off the \texttt{trivlist}
+%    environment started by |\@verbatim| and closes the group.
+%    This restores everything to its normal settings.
+%    \begin{macrocode}
+    \verbatim@readfile{\@filef@und}\endtrivlist\endgroup\@doendpe}%
+%    \end{macrocode}
+%   If the file is not found a more or less helpful message is
+%    printed. The final |\endgroup| is  needed to close the group
+%    started in |\verbatiminput| above.
+%    \begin{macrocode}
+   {\typeout {No file #2.}\endgroup}}
+%</package>
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Getting verbatim text into arguments.}
+%
+% One way of achieving this is to define a macro (command) whose
+% expansion is the required verbatim text.  This command can then be
+% used anywhere that the verbatim text is required.  It can be used in
+% arguments, even moving ones, but it is fragile (at least, the
+% version here is).
+%
+% Here is some code which claims to provide this.  It is a much revised
+% version of something I (Chris) did about 2 years ago.  Maybe it needs
+% further revision.
+%
+% It is only intended as an extension to |\verb|, not to the
+% \texttt{verbatim} environment.  It should therefore, perhaps, treat
+% line-ends similarly to whatever is best for |\verb|.
+%
+% \begin{macro}{\newverbtext}
+% This is the command to produce a new macro whose expansion is
+% verbatim text.  This command itself cannot be used in arguments,
+% of course! It is used as follows:
+%
+% \begin{verbatim}
+%    \newverbtext{\myverb}"^%{ &~_\}}@ #"
+% \end{verbatim}
+%
+% The rules for delimiting the verbatim text are the same as those for
+% |\verb|.
+%
+%    \begin{macrocode}
+%<*verbtext>
+\def \newverbtext {%
+  \@ifstar {\@tempswatrue \@verbtext }{\@tempswafalse \@verbtext *}%
+}
+%    \end{macrocode}
+% \end{macro}
+%    I think that a temporary switch is safe here: if not, then
+%    suitable |\let|s can be used.
+%    \changes{v1.5i}{1996/06/04}{Moved processing of
+%              \cs{verbatim@nolig@list} after \cs{dospecials}.}
+%    \changes{v1.5p}{2001/03/12}{Added missing right brace in
+%               definition of \cs{@verbtext} (PR 3314).}
+%    \begin{macrocode}
+\def \@verbtext *#1#2{%
+   \begingroup
+     \let\do\@makeother \dospecials
+     \let\do\do@noligs \verbatim@nolig@list
+     \@vobeyspaces
+     \catcode`#2\active
+     \catcode`~\active
+     \lccode`\~`#2%
+     \lowercase
+%    \end{macrocode}
+%    We use a temporary macro here and a trick so that the definition of
+%    the command itself can be done inside the group and be a local
+%    definition (there may be better ways to achieve this).
+%    \begin{macrocode}
+     {\def \@tempa ##1~%
+           {\whitespaces
+%    \end{macrocode}
+%    If these |\noexpand|s were |\noexpand\protect\noexpand|, would
+%    this make these things robust?
+%    \begin{macrocode}
+            \edef #1{\noexpand \@verbtextmcheck
+                     \bgroup
+                     \if@tempswa
+                       \noexpand \visiblespaces
+                     \fi
+                     \noexpand \@verbtextsetup
+                     ##1%
+                     \egroup}%
+            }%
+      \expandafter\endgroup\@tempa
+     }
+}
+%    \end{macrocode}
+%    This sets up the correct type of group for the mode: it must not
+%    be expanded at define time!
+%    \begin{macrocode}
+\def \@verbtextmcheck {%
+   \relax\ifmmode
+           \hbox
+         \else
+           \leavevmode
+           \null
+         \fi
+}
+%    \end{macrocode}
+%    This contains other things which should not be expanded during the
+%    definition.
+%    \begin{macrocode}
+\def \@verbtextsetup {%
+   \frenchspacing
+   \verbatim@font
+   \verbtextstyle
+}
+%    \end{macrocode}
+%    The command |\verbtextstyle| is a document-level hook which can be
+%    used to override the predefined typographic treatment of commands
+%    defined with |\newverbtext| commands.
+%
+%    |\visiblespaces| and |\whitespaces| are examples of possible values
+%    of this hook.
+%    \begin{macrocode}
+\let \verbtextstyle \relax
+\def \visiblespaces {\chardef \  32\relax}
+\def \whitespaces {\let \ \@@space}
+\let \@@space \ %
+%</verbtext>
+%    \end{macrocode}
+%
+%
+% \section{Testing the implementation}
+%
+% For testing the implementation and for demonstration we provide
+% an extra file. It can be extracted by using the conditional
+% `\textsf{testdriver}'. It uses a small input file called
+% `\texttt{verbtest.tst}' that is distributed separately.
+% Again, we use individual `+' guards.
+%    \begin{macrocode}
+%<*testdriver>
+\documentclass{article}
+
+\usepackage{verbatim}
+
+\newenvironment{myverbatim}%
+   {\endgraf\noindent MYVERBATIM:\endgraf\verbatim}%
+   {\endverbatim}
+
+\makeatletter
+
+\newenvironment{verbatimlisting}[1]%
+ {\def\verbatim@startline{\input{#1}%
+    \def\verbatim@startline{\verbatim@line{}}%
+    \verbatim@startline}%
+  \verbatim}{\endverbatim}
+
+\newwrite\verbatim@out
+
+\newenvironment{verbatimwrite}[1]%
+ {\@bsphack
+  \immediate\openout \verbatim@out #1
+  \let\do\@makeother\dospecials\catcode`\^^M\active
+  \def\verbatim@processline{%
+    \immediate\write\verbatim@out{\the\verbatim@line}}%
+  \verbatim@start}%
+ {\immediate\closeout\verbatim@out\@esphack}
+
+\makeatother
+
+\addtolength{\textwidth}{30pt}
+
+\begin{document}
+
+\typeout{}
+\typeout{===> Expect ``characters dropped''
+         warning messages in this test! <====}
+\typeout{}
+
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin{verbatim}
+    test
+    \end{verbatim*}
+    test
+    \end{verbatim
+    test of ligatures: <`!`?`>
+    \endverbatim
+    test
+    \end  verbatim
+    test
+    test of end of line:
+    \end
+    {verbatim}
+  \end{verbatim} Further text to be typeset: $\alpha$.
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin{verbatim*}
+    test
+    test
+  \end {verbatim*}
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin{verbatim*}  bla bla
+    test
+    test
+  \end {verbatim*}
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+
+First of Chris Rowley's fiendish tests:
+\begin{verbatim}
+the double end test<text>
+\end\end{verbatim}  or even \end \end{verbatim}
+%
+%not \end\ended??
+%\end{verbatim}
+
+Another of Chris' devils:
+\begin{verbatim}
+the single brace test<text>
+\end{not the end\end{verbatim}
+%
+%not \end}ed??
+%\end{verbatim}
+Back to my own tests:
+  \begin{myverbatim}
+    test
+    test
+  \end {myverbatim} rest of line
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+
+Test of empty verbatim:
+\begin{verbatim}
+\end{verbatim}
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin {verbatimlisting}{verbtest.tex}
+    Additional verbatim text
+      ...
+  \end{verbatimlisting}
+And here for listing a file:
+  \verbatiminput{verbtest.tex}
+And again, with explicit spaces:
+  \verbatiminput*{verbtest.tex}
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin{comment}
+    test
+    \end{verbatim*}
+    test
+    \end {comment
+    test
+    \endverbatim
+    test
+    \end  verbatim
+    test
+  \end {comment} Further text to be typeset: $\alpha$.
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+  \begin{comment}  bla bla
+    test
+    test
+  \end {comment}
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+Text Text Text Text Text Text Text Text Text Text Text
+
+\begin{verbatimwrite}{verbtest.txt}
+asfa<fa<df
+sdfsdfasd
+asdfa<fsa
+\end{verbatimwrite}
+
+\end{document}
+%</testdriver>
+%    \end{macrocode}
+%
+%
+% \Finale
+%
+\endinput
+%%
diff --git a/macros/latex-dev/required/tools/verbatim.pdf b/macros/latex-dev/required/tools/verbatim.pdf
new file mode 100644
index 0000000000..14ed89c8ec
--- /dev/null
+++ b/macros/latex-dev/required/tools/verbatim.pdf
diff --git a/macros/latex-dev/required/tools/xr.dtx b/macros/latex-dev/required/tools/xr.dtx
new file mode 100644
index 0000000000..417a98c1c1
--- /dev/null
+++ b/macros/latex-dev/required/tools/xr.dtx
@@ -0,0 +1,186 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: xr.dtx Copyright (C) 1993-2019 David Carlisle
+%
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{xr}
+%<package>         [2019/07/22 v5.05 eXternal References (DPC)]
+%
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{xr}
+\GetFileInfo{xr.sty}
+\begin{document}
+\title{The \textsf{xr} package\thanks{This file
+        has version number \fileversion, last
+        revised \filedate.}}
+\author{David Carlisle\thanks{%
+  The Author of Versions 1--4 was Jean-Pierre Drucbert}}
+\date{\filedate}
+\MaintainedByLaTeXTeam{tools}
+\maketitle
+\DocInput{xr.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+% \changes{v5.00}{1993/07/07}
+%         {First DPC version (by agreement with J-PD).  New mechanism
+%         (\cmd{\read} instead of \cmd\input).}
+%
+% \changes{v5.01}{1993/07/20}{Fix bug added by DPC, v5.00 did not import
+%           aux files of \cmd\include'ed files. (Reported by J-PD)}
+%
+% \changes{v5.02}{1994/05/28}{Update for LaTeX2e}
+% \changes{v5.03}{2018/10/01}{Fix for conditionals in aux file}
+% \changes{v5.05}{2019/07/20}{include xcite}
+%
+%
+% This package implements a system for eXternal References.
+%
+% If one document needs to refer to sections of another, say |aaa.tex|,
+% then this package may be loaded in the main file, and the command\\
+% |\externaldocument{aaa}|\\
+%  given in the preamble.
+%
+% Then you may use |\ref| and |\pageref| to refer to anything which has
+% been given a |\label| in either |aaa.tex| or the main document.
+% You may declare any number of such external documents.
+%
+% If any of the external documents, or the main document, use the same
+% |\label| then an error will occur as the label will be multiply
+% defined. To overcome this problem |\externaldocument| has an optional
+% argument. If you declare |\externaldocument[A-]{aaa}| Then all
+% references from |aaa| are prefixed by |A-|. So for instance, if a
+% section of |aaa| had |\label{intro}|, then this could be referenced
+% with |\ref{A-intro}|. The prefix need not be |A-|, it can be any
+% string chosen to ensure that all the labels imported from external
+% files are unique. Note however that if your style declares certain
+% active characters (|:| in French, |"| in German) then these
+% characters can not usually be used in |\label|, and similarly may not
+% be used in the optional argument to |\externaldocument|.
+%
+% As first suggested in Enrico Gregorio's |xcite| package, the current version
+% also allows |\cite| to reference |\bibitem| in the external document.
+% For fcompatibility with |xcite|, |\externalcitedocument| is made available 
+% as an alias for |\externaldocument|
+%
+% \StopEventually{}
+%
+% \section{The macros}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% Check for the optional argument.
+%    \begin{macrocode}
+\def\externaldocument{\@ifnextchar[\XR@{\XR@[]}}
+\let\externalcitedocument\externaldocument
+%    \end{macrocode}
+%
+% Save the optional prefix. Start processing the first |aux| file.
+%    \begin{macrocode}
+\def\XR@[#1]#2{{%
+  \makeatletter
+  \def\XR@prefix{#1}%
+  \XR@next#2.aux\relax\\}}
+%    \end{macrocode}
+%
+% Process the next |aux| file in the list and remove it from the head of
+% the list of files to process.
+%    \begin{macrocode}
+\def\XR@next#1\relax#2\\{%
+  \edef\XR@list{#2}%
+  \XR@loop{#1}}
+%    \end{macrocode}
+%
+% Check whether the list of |aux| files is empty.
+%    \begin{macrocode}
+\def\XR@aux{%
+  \ifx\XR@list\@empty\else\expandafter\XR@explist\fi}
+%    \end{macrocode}
+%
+
+% Expand the list of aux files, and call |\XR@next| to process the first
+% one.
+%    \begin{macrocode}
+\def\XR@explist{\expandafter\XR@next\XR@list\\}
+%    \end{macrocode}
+%
+% If the |aux| file exists, loop through line by line, looking for
+% |\newlabel| and |\@input|. Otherwise process the next file in the
+% list.
+%    \begin{macrocode}
+\def\XR@loop#1{\openin\@inputcheck#1\relax
+  \ifeof\@inputcheck
+    \PackageWarning{xr}{^^JNo file #1^^JLABELS NOT IMPORTED.^^J}%
+    \expandafter\XR@aux
+  \else
+    \PackageInfo{xr}{IMPORTING LABELS FROM #1}%
+    \expandafter\XR@read\fi}
+%    \end{macrocode}
+%
+% Read the next line of the aux file.
+%    \begin{macrocode}
+\def\XR@read{%
+  \read\@inputcheck to\XR@line
+%    \end{macrocode}
+% The |...| make sure that |\XR@test| always has sufficient arguments.
+%    \begin{macrocode}
+  \expandafter\XR@test\XR@line...\XR@}
+%    \end{macrocode}
+%
+% Look at the first token of the line.
+% If it is |\newlabel|, do the |\newlabel|. If it is |\@input|, add the
+% filename to the list of files to process. Otherwise ignore.
+% Go around the loop if not at end of file. Finally process the next
+% file in the list.
+%
+% 2018 update: make sure the arguments are handled outside the |\ifx| test,
+%    \begin{macrocode}
+\long\def\XR@test#1#2#3#4\XR@{%
+  \let\XR@tempa\@gobbletwo
+  \ifx#1\newlabel
+    \let\XR@tempa\@firstoftwo
+  \else\ifx#1\bibcite
+    \let\XR@tempa\@firstoftwo
+  \else\ifx#1\@input
+     \let\XR@tempa\@secondoftwo
+  \fi\fi\fi
+   \XR@tempa{#1{\XR@prefix#2}{#3}}{\edef\XR@list{\XR@list#2\relax}}%
+  \ifeof\@inputcheck\expandafter\XR@aux
+  \else\expandafter\XR@read\fi}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
+%
+
diff --git a/macros/latex-dev/required/tools/xr.pdf b/macros/latex-dev/required/tools/xr.pdf
new file mode 100644
index 0000000000..c051173362
--- /dev/null
+++ b/macros/latex-dev/required/tools/xr.pdf
diff --git a/macros/latex-dev/required/tools/xspace.dtx b/macros/latex-dev/required/tools/xspace.dtx
new file mode 100644
index 0000000000..0745caf507
--- /dev/null
+++ b/macros/latex-dev/required/tools/xspace.dtx
@@ -0,0 +1,507 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 1993-2019
+%
+% The LaTeX3 Project and any individual authors listed elsewhere
+% in this file.
+%
+% This file is part of the Standard LaTeX `Tools Bundle'.
+% -------------------------------------------------------
+%
+% It may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%    https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% The list of all files belonging to the LaTeX `Tools Bundle' is
+% given in the file `manifest.txt'.
+%
+% \fi
+% \iffalse
+%% File: xspace.dtx Copyright (C) 1991-1997 David Carlisle
+%% File: xspace.dtx Copyright (C) 2004-2006 David Carlisle,
+%%                                          Morten H\o gholm
+%
+%<*dtx>
+          \ProvidesFile{xspace.dtx}
+%</dtx>
+%<package>\NeedsTeXFormat{LaTeX2e}
+%<package>\ProvidesPackage{xspace}
+%<driver>\ProvidesFile{xspace.drv}
+% \fi
+%         \ProvidesFile{xspace.dtx}
+          [2014/10/28 v1.13 Space after command names (DPC,MH)]
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\makeatletter
+\providecommand*\eTeX{{%
+  \if b\expandafter\@car\f@series\@nil\boldmath\fi$\m@th
+  \varepsilon$-\TeX}}
+\makeatother
+\usepackage{xspace}[2006/05/08]
+\begin{document}
+\DocInput{xspace.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \GetFileInfo{xspace.dtx}
+% \title{The \textsf{xspace} package\thanks{This file
+%        has version number \fileversion, last
+%        revised \filedate.}}
+% \author{David Carlisle \and Morten H\o gholm}
+% \date{\filedate}
+% \MaintainedByLaTeXTeam{tools}
+% \maketitle
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%
+% \changes{v1.00}{1991/08/30}{Initial version}
+% \changes{v1.01}{1992/06/26}{Re-issue for the new doc and docstrip}
+% \changes{v1.02}{1994/01/31}{Re-issue for LaTeX2e (no change to
+%   code)}
+% \changes{v1.07}{2004/12/07}{Make extensible. tools/3712}
+% \changes{v1.07}{2004/12/07}{Fix active characters. tools/3747}
+% \changes{v1.07}{2004/12/07}{Update documentation}
+% \changes{v1.08}{2005/05/07}{Better fix for active characters}
+% \changes{v1.09}{2005/07/26}{Improve test by exiting if
+%   \cs{@let@token} is a letter}
+% \changes{v1.10}{2005/10/04}{Use higher level functions for
+% conditional processing}
+% \changes{v1.10}{2005/10/04}{Improve expansion method}
+%
+% \begin{abstract}
+% |\xspace| should be used at the end of a macro designed to
+% be used mainly in text. It adds a space unless the macro is
+% followed by certain punctuation characters.
+% \end{abstract}
+%
+% \section{Introduction}
+% \newcommand{\gb}{Great Britain\xspace}\DescribeMacro{\xspace}
+% After defining |\newcommand{\gb}{Great Britain\xspace}|,
+% the command |\gb| will determine when to insert a space
+% after itself and when not. Thus the input
+% \begin{quote}
+% |\gb is a very nice place to live.\\| \\
+% |\gb, a small island off the coast of France.\\|\\
+% |\gb\footnote{The small island off the coast of France.}|\\
+% |is a very nice place to live.|
+% \end{quote}
+% results in the output
+% \begin{quote}
+% \gb is a very nice place to live. \\
+% \gb, a small island off the coast of France.\\
+% \gb\footnote{The small island off the coast of France.}
+% is a very nice place to live.
+% \end{quote}
+% |\xspace| saves the user from having to type \verb*+\ + or
+% |{}| after most occurrences of a macro name in text.
+% However if either of these constructions follows |\xspace|,
+% a space is not added by |\xspace|. This means that it is
+% safe to add |\xspace| to the end of an existing macro
+% without making too many changes in your document. In particular,
+% |\xspace| will always insert a space if the thing following it is
+% a normal letter which is the usual case.
+%
+% Sometimes |\xspace| may make the wrong decision, and add a
+% space when it is not required. There may be different
+% reasons for this behavior but it can always be handled by
+% following the macro with |{}|, as this has the effect of
+% suppressing the space.
+%
+%
+% \subsection{Adding new exceptions}
+%
+% One of the most common reasons for |\xspace| to add an
+% unwanted space is when it is followed by a macro not on its
+% list of exceptions.
+% \DescribeMacro{\xspaceaddexceptions}%
+% With |\xspaceaddexceptions| you can add new commands or
+% characters to be recognized by |\xspace|'s scanning
+% mechanism. Users of advanced footnote packages like
+% \textsf{manyfoot} will often define new footnote macros
+% that should not cause a command ``enhanced'' with |\xspace|
+% to insert a space. If you define the additional footnote
+% macros |\footnoteA| and |\footnoteB|, simply add the
+% following line to your preamble:
+% \begin{quote}
+% |\xspaceaddexceptions{\footnoteA \footnoteB}|
+% \end{quote}
+%
+%
+% \subsection{Support for active characters}
+%
+%
+% The other common instance of |\xspace| not working quite right
+% happens with active characters. Generally this package must be
+% loaded \emph{after} any language (or other) packages that make
+% punctuation characters `active'. This makes it difficult for
+% \textsf{xspace} to work flawlessly with the popular \textsf{babel}
+% package especially since the punctuation characters can switch
+% between being `active' and `other'. Starting at \textsf{xspace}
+% version~1.08 there are two different ways to handle this depending
+% on which engine your \LaTeX-format uses:
+% \begin{description}
+%   \item[\TeX] The punctuation characters are added to the
+%   exception list in both their normal and active states thus
+%   ensuring that they are always recognized.
+%   \item[\eTeX] The characters are re-read when going through
+%   the exception list which means the internal comparison will test
+%   against the current state of the character. This works for
+%   whatever category code tricks some packages may use.
+% \end{description}
+%
+% At the time of writing all major \TeX\ distributions are using
+% \eTeX\ as engine for \LaTeX\ so usually everything should work out
+% of the box. If you find that you're running normal \TeX\ and
+% |\xspace| seems to be making the wrong choice then either use |{}|
+% as described above to fix it or add the character to the list but
+% with the desired category code. See the implementation for an example
+% of how to do that.
+%
+% \subsection{Still not satisfied?}
+%
+% Some people don't like the default list of exceptions so they can
+% remove one item at a time with the command
+% \DescribeMacro{\xspaceremoveexception}^^A
+% \cs{xspaceremoveexception}\marg{token}.  Furthermore the command
+% \DescribeMacro{\@xspace@hook}\cs{@xspace@hook} can be redefined to
+% scan forward in the input stream in case you want to check more
+% tokens. It is called after \cs{xspace} has determined if it needed
+% to insert a space or if an exception was found (the default
+% definition is for \cs{@xspace@hook} to be empty). Hence you can use
+% \cs{unskip} to remove the space inserted if \cs{@let@token} matches
+% something special. Below is an example of how one can make sure an
+% endash gets a space inserted before it but a single dash not.
+% \begin{verbatim}
+% \xspaceremoveexception{-}
+% \makeatletter
+% \renewcommand*\@xspace@hook{%
+%   \ifx\@let@token-%
+%     \expandafter\@xspace@dash@i
+%   \fi
+% }
+% \def\@xspace@dash@i-{\futurelet\@let@token\@xspace@dash@ii}
+% \def\@xspace@dash@ii{%
+%   \ifx\@let@token-%
+%   \else
+%     \unskip
+%   \fi
+%   -%
+% }
+% \makeatother
+% \end{verbatim}
+%
+%
+% \StopEventually{}
+%
+% \section{The Macros}
+%
+% |\xspace| peeks ahead for the next token. If the token is in our
+% exception list we break the loop and do nothing; else we try to
+% expand the token once and start over again. If this leads us to an
+% unexpandable token without finding one of the exceptions we insert a
+% space.
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+%
+% \begin{macro}{\xspace}
+% |\xspace| just looks ahead, and then calls |\@xspace|.
+% \changes{v1.03}{1994/11/15}{Make robust}
+%    \begin{macrocode}
+\DeclareRobustCommand\xspace{\@xspace@firsttrue
+  \futurelet\@let@token\@xspace}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\if@xspace@first}
+% \changes{v1.11}{2006/02/12}{Added macro}
+% \begin{macro}{\@xspace@simple}
+% \changes{v1.11}{2006/02/12}{Added macro}
+% Some helpers to avoid multiple calls of |\@xspace@eTeX@setup|.
+%    \begin{macrocode}
+\newif\if@xspace@first
+\def\@xspace@simple{\futurelet\@let@token\@xspace}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@xspace@exceptions@tlp}
+% \changes{v1.07}{2004/12/07}{Added macro}
+% The exception list. If the scanning mechanism finds one of
+% these, it won't insert a space after the command. The
+% \texttt{tlp} in the name means `token list pointer.'
+%    \begin{macrocode}
+\def\@xspace@exceptions@tlp{%
+  ,.'/?;:!~-)\ \/\bgroup\egroup\@sptoken\space\@xobeysp
+  \footnote\footnotemark
+  \xspace@check@icr
+}
+%    \end{macrocode}
+% And here we get the non-empty definition of \cs{check@icr}.
+% \changes{v1.13}{2009/10/20}{fix for "tools/3895": `text font commands fool xspace'}
+%    \begin{macrocode}
+\begingroup
+  \text@command\relax
+  \global\let\xspace@check@icr\check@icr
+\endgroup
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\xspaceaddexceptions}
+% \changes{v1.07}{2004/12/07}{Added macro}
+% The user command, which just adds tokens to the list.
+%    \begin{macrocode}
+\newcommand*\xspaceaddexceptions{%
+  \g@addto@macro\@xspace@exceptions@tlp
+}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\xspaceremoveexception}
+% \changes{v1.10}{2005/10/04}{Use higher level functions for
+% conditional processing}
+% This command removes an exception globally.
+%    \begin{macrocode}
+\newcommand*\xspaceremoveexception[1]{%
+%    \end{macrocode}
+% First check that it is in the list at all.
+%    \begin{macrocode}
+  \def\reserved@a##1#1##2##3\@@{%
+    \@xspace@if@q@nil@NF##2{%
+%    \end{macrocode}
+% It's in the list, remove it.
+%    \begin{macrocode}
+      \def\reserved@a####1#1####2\@@{%
+        \gdef\@xspace@exceptions@tlp{####1####2}}%
+      \expandafter\reserved@a\@xspace@exceptions@tlp\@@
+    }%
+  }%
+  \expandafter\reserved@a\@xspace@exceptions@tlp#1\@xspace@q@nil\@@
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xspace@break@loop}
+% \changes{v1.08}{2005/04/28}{Added macro}
+% \changes{v1.10}{2005/10/04}{Use quark instead}
+% To stop the loop.
+%    \begin{macrocode}
+\def\@xspace@break@loop#1\@nil{}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xspace@hook}
+% \changes{v1.09}{2005/07/26}{Added macro}
+% A hook for users with special needs.
+%    \begin{macrocode}
+\providecommand*\@xspace@hook{}
+%    \end{macrocode}
+% \end{macro}
+%
+% Now we check if we're running \eTeX. We can't use \cs{@ifundefined}
+% as that will lock catcodes and we need to change some of those.
+% As there is a small risk that someone already set \cs{eTeXversion}
+% to \cs{relax} by accident we make sure we check for that case but
+% without setting it to \cs{relax} if it wasn't already.
+%    \begin{macrocode}
+\begingroup\expandafter\expandafter\expandafter\endgroup
+  \expandafter\ifx\csname eTeXversion\endcsname\relax
+%    \end{macrocode}
+% If we are running normal \TeX\ we add the most common cases of active
+% punctuation characters. First we make them active.
+%    \begin{macrocode}
+  \begingroup
+    \catcode`\;=\active  \catcode`\:=\active
+    \catcode`\?=\active  \catcode`\!=\active
+%    \end{macrocode}
+%  The \texttt{alltt} environment also makes |,|, |'|, and |-| active
+%  so we add them as well.
+%    \begin{macrocode}
+    \catcode`\,=\active  \catcode`\'=\active  \catcode`\-=\active
+    \xspaceaddexceptions{;:?!,'-}
+  \endgroup
+  \let\@xspace@eTeX@setup\relax
+%    \end{macrocode}
+% \begin{macro}{\@xspace@eTeX@setup}
+% \changes{v1.10}{2005/10/04}{Added macro}
+% \changes{v1.12}{2006/05/08}{Bug fix for verbatim in output routine}
+% When we're running \eTeX, we have the advantage of \cs{scantokens}
+% which will rescan tokens with current catcodes. This little
+% expansion trick makes sure that the exception list is redefined to
+% itself but with the contents of it exposed to the current catcode
+% regime. That is why we must make sure the catcode of space is 10,
+% since we have a \verb*|\ | inside the list.
+%    \begin{macrocode}
+\else
+  \def\@xspace@eTeX@setup{%
+    \begingroup
+      \everyeof{}%
+      \endlinechar=-1\relax
+      \catcode`\ =10\relax
+      \makeatletter
+%    \end{macrocode}
+% We may also be so unfortunate that the re-reading of the list takes
+% place when the catcodes of |\|, |{| and |}| are ``other,'' e.g., if
+% it takes place in a header and the output routine was called in the
+% middle of a \texttt{verbatim} environment.
+%    \begin{macrocode}
+      \catcode`\\\z@
+      \catcode`\{\@ne
+      \catcode`\}\tw@
+      \scantokens\expandafter{\expandafter\gdef
+        \expandafter\@xspace@exceptions@tlp
+        \expandafter{\@xspace@exceptions@tlp}}%
+    \endgroup
+  }
+\fi
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@xspace}
+% \changes{v1.03}{1994/11/15}{Add exclamation mark}
+% \changes{v1.04}{1996/05/17}{Add slash}
+% \changes{v1.05}{1996/12/06}{Add space for alltt etc. tools/2322}
+% \changes{v1.06}{1997/10/13}{Add normal space. tools/2632}
+% \changes{v1.07}{2004/12/07}{Now runs through a list of exceptions}
+% \changes{v1.07}{2004/12/07}{Added \cs{footnote} and
+% \cs{footnotemark}}
+% \changes{v1.08}{2005/05/07}{Use recursive loop instead of \cs{@tfor}}
+% \changes{v1.09}{2005/07/26}{Only check non-letters and add hook}
+% \changes{v1.10}{2005/10/04}{Use higher level functions for
+% conditional processing}
+% \changes{v1.10}{2005/10/04}{Improve expansion method}
+% If the next token is one of a specified list of characters,
+% do nothing, otherwise add a space. With version~1.07 the
+% approach was altered dramatically to run through the
+% exception list |\@xspace@exceptions@tlp| and check each
+% token one at a time.
+%    \begin{macrocode}
+\def\@xspace{%
+%    \end{macrocode}
+% Before we start checking the exception list it makes sense to
+% perform a quick check on the token in question. Most of the time
+% \cs{xspace} is used in regular text so \cs{@let@token} is set equal
+% to a letter. In that case there is no point in checking the list
+% because it will definitely not contain any tokens with catcode~11.
+%
+% You may wonder why there are special functions here instead of
+% simpler \cs{ifx} conditionals. The reason is that a)~this way we
+% don't have to add many, many \cs{expandafter}s to get the nesting
+% right and b)~we don't get into trouble when \cs{@let@token} has been
+% let equal to \cs{if} etc.
+%    \begin{macrocode}
+  \@xspace@lettoken@if@letter@TF \space{%
+%    \end{macrocode}
+% Otherwise we start testing after setting up a few things. If running
+% \eTeX{} we rescan the catcodes but only the first time around.
+%    \begin{macrocode}
+    \if@xspace@first
+      \@xspace@firstfalse
+      \let\@xspace@maybespace\space
+      \@xspace@eTeX@setup
+    \fi
+    \expandafter\@xspace@check@token
+      \@xspace@exceptions@tlp\@xspace@q@nil\@nil
+%    \end{macrocode}
+% If an exception was found \cs{@xspace@maybespace} is let to
+% \cs{relax} and we do nothing.
+%    \begin{macrocode}
+    \@xspace@token@if@equal@NNT \space \@xspace@maybespace
+%    \end{macrocode}
+% Otherwise we check to see if we found something expandable and try
+% again with that token one level expanded. If no expandable token is
+% found we insert a space and then execute the hook.
+%    \begin{macrocode}
+    {%
+      \@xspace@lettoken@if@expandable@TF
+      {\expandafter\@xspace@simple}%
+      {\@xspace@maybespace\@xspace@hook}%
+    }%
+  }%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@xspace@check@token}
+% \changes{v1.07}{2004/12/07}{Added macro}
+% \changes{v1.08}{2005/05/07}{Made function recursive}
+% \changes{v1.10}{2005/10/04}{Use higher level functions for
+% conditional processing}
+% \changes{v1.11}{2006/02/12}{Modified so the \cs{@let@token} can be
+%   \cs{outer}}
+% This macro just checks the current item in the exception list
+% against the \cs{@let@token}. If they are equal we make sure that no
+% space is inserted and break the loop.
+%    \begin{macrocode}
+\def\@xspace@check@token #1{%
+  \ifx\@xspace@q@nil#1%
+    \expandafter\@xspace@break@loop
+  \fi
+  \expandafter\ifx\csname @let@token\endcsname#1%
+    \let\@xspace@maybespace\relax
+    \expandafter\@xspace@break@loop
+  \fi
+  \@xspace@check@token
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% That's all, folks! That is, if we were running \LaTeX3. In that case
+% we would have had nice functions for all the conditionals but here
+% we must define them ourselves. We also optimize them here as
+% \cs{@let@token} will always be the argument in some cases.
+%
+% \begin{macro}{\@xspace@if@lettoken@letter@TF}
+% \begin{macro}{\@xspace@if@lettoken@expandable@TF}
+% \begin{macro}{\@xspace@cs@if@equal@NNF}
+% First a few comparisons.
+%    \begin{macrocode}
+\def\@xspace@lettoken@if@letter@TF{%
+  \ifcat\noexpand\@let@token @% letter
+    \expandafter\@firstoftwo
+  \else
+    \expandafter\@secondoftwo
+  \fi}
+\def\@xspace@lettoken@if@expandable@TF{%
+  \expandafter\ifx\noexpand\@let@token\@let@token%
+    \expandafter\@secondoftwo
+  \else
+    \expandafter\@firstoftwo
+  \fi
+}
+\def\@xspace@token@if@equal@NNT#1#2{%
+  \ifx#1#2%
+    \expandafter\@firstofone
+  \else
+    \expandafter\@gobble
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\@xspace@q@nil}
+% \begin{macro}{\@xspace@if@q@nil@NF}
+% Some macros dealing with quarks.
+%    \begin{macrocode}
+\def\@xspace@q@nil{\@xspace@q@nil}
+\def\@xspace@if@q@nil@NF#1{%
+  \ifx\@xspace@q@nil#1%
+    \expandafter\@gobble
+  \else
+    \expandafter\@firstofone
+  \fi}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%    \begin{macrocode}
+%</package>
+%    \end{macrocode}
+%
+% \Finale
diff --git a/macros/latex-dev/required/tools/xspace.pdf b/macros/latex-dev/required/tools/xspace.pdf
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+++ b/macros/latex-dev/required/tools/xspace.pdf