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authorKarl Berry <karl@freefriends.org>2006-10-11 23:55:23 +0000
committerKarl Berry <karl@freefriends.org>2006-10-11 23:55:23 +0000
commite019e49dd7fa93bb7c60bea2d66ac668ebf1b72a (patch)
treed4a2c5532ed979ede28608aa1367b56ac425498b /Master/texmf-dist/doc/latex
parent82027e2f2b7bd2cb40d0d0f7d3d9b6f9f899c150 (diff)
amslatex now split into the original AMS names
git-svn-id: svn://tug.org/texlive/trunk@2309 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex')
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/00readme.txt143
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsart.template61
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsbook.template99
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsldoc.pdf5623
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsldoc.tex2620
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsproc.template61
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdfbin203601 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsrefs.faq15
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsrefs.pdfbin407399 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdfbin60826 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex374
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/changes.pdfbin111235 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/cite-xa.tex221
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/cite-xb.tex143
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/cite-xh.brf24
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/cite-xh.tex154
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/cite-xs.tex19
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt145
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/classes/install.txt106
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt41
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/diffs-c.txt319
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/diffs-m.txt552
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/exercise.thm8
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/gktest.ltb440
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/install.txt69
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/instr-l.pdfbin175195 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/instr-l.tex1233
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/manifest.txt56
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/math/00readme.txt123
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls517
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/math/install.txt108
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/math/manifest.txt38
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/mathscinet.pdfbin123073 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty82
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/subeqn.pdfbin36454 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/subeqn.tex202
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/technote.pdfbin58756 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/technote.tex233
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-rw-r--r--Master/texmf-dist/doc/latex/amslatex/testmath.tex2342
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-rw-r--r--Master/texmf-dist/doc/latex/amslatex/thmtest.pdfbin50063 -> 0 bytes
-rw-r--r--Master/texmf-dist/doc/latex/amslatex/thmtest.tex255
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diff --git a/Master/texmf-dist/doc/latex/amslatex/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/00readme.txt
deleted file mode 100644
index 0dec0fb6419..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/00readme.txt
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@@ -1,143 +0,0 @@
-00readme.txt for amsrefs 2.0 [2004-06-30]
-
-See also install.txt and manifest.txt. There is a history of changes at
-the end of this file.
-
-Please send bug reports and questions to tech-support@ams.org.
-
-========================================================================
-
-The amsrefs package deals with bibliographies and citations in LaTeX
-documents. The basic citation command remains more or less the same as
-in standard LaTeX (\cite), but a number of additional variations address
-certain known pitfalls or gaps in the standard LaTeX set of citation
-features.
-
-The command for bibliography items is different---\bib instead of
-\bibitem---for reasons that will be evident upon further reading in the
-documentation.
-
-A set of BibTeX style files are provided to allow people to extract
-data from .bib files and produce .bbl files in amsrefs format instead
-of conventional \bibitem format.
-
-User documentation is in amsrdoc.pdf.
-
-Technical documentation (including documentation for package writers)
-is in amsrefs.pdf.
-
-========================================================================
-I. FEATURES
-
----Preservation of structure.
-
-The internal structural information of the bibliography entries is not
-lost when they are imported from the database file into the LaTeX
-document. This takes on its greatest significance when archiving
-documents in LaTeX form or transmitting them to another user (such as a
-publisher).
-
----Deferred formatting.
-
-This means that the style of the bibliography can be changed on demand
-without reimporting everything from the original database(s).
-
----More natural data format for titles.
-
-Proper nouns do not need to have braces added to prevent capitalization
-problems.
-
----Less ambiguous format for author names.
-
-When author names are given in inverted order (last name first) it is
-possible for LaTeX to unambiguously identify the last name without any
-further markup, even in cases like Saunders Mac Lane (Mac Lane,
-Saunders) versus Stephen H. Lane (Lane, Stephen H.), or Cam Van Tran
-(Tran, Cam Van) versus Bert Van Keulen (Van Keulen, Bert). In
-BibTeX some of these would need to have extra braces added to ensure
-that the surname is accurately distinguished.
-
----Author-year citations.
-
-There is integrated support for citations in author-year form.
-
----Back-reference support.
-
-Works in conjunction with the hyperref package.
-
----Setup requires only LaTeX knowledge.
-
-All bibliography setup can be done in LaTeX; learning another
-programming language (such as, the one used in BibTeX bst files) is
-unnecessary.
-
----Self-printable database files.
-
-A LaTeX document that contains only a bibliography in amsrefs forms can
-be used as a database for exporting entries to other documents. And
-because it is a LaTeX document, the database can be printed directly at
-any time simply by running it through LaTeX in the usual way.
-
----Self-contained.
-
-In many cases it seems possible to do without BibTeX entirely. For
-example, if the entries are extracted from a single database file that
-is maintained in sorted order, the bibliography can be printed directly
-by LaTeX on the first pass and the citations resolved on the second
-pass.
-
-========================================================================
-II. GETTING STARTED
-
-1. Install the package, referring to install.txt as needed.
-
-2. There are four example files provided:
-
- cite-xa : Demonstrates an author-year citation scheme. The
- bibliography is embedded in the .tex file instead of
- residing in a separate .bbl file.
-
- cite-xb : Demonstrates usage with more-or-less standard BibTeX
- methods.
-
- cite-xs : Shows how the bbl file can be created by LaTeX itself from a
- suitably presorted ltb file.
-
- cite-xh : A working hyperref/backrefs example.
-
-3. Run LaTeX on cite-xa.tex. Take a look at the messages that have to do
-with citations and the bibliography section. Run LaTeX again to resolve
-the citations and check the output.
-
-4. Run LaTeX on cite-xb.tex. Run BibTeX. Look at the bbl file.
-Interesting, huh? Run LaTeX twice more to resolve the citations.
-
-5. Run LaTeX on cite-xs.tex and look at the output.
-
-6. Run pdflatex on cite-xh.tex (it is set up to use BibTeX also, like
-cite-xb).
-
-========================================================================
-III. REMARKS ON THIS RELEASE
-
-This is a thorough overhaul and rewrite of the the amsrefs package.
-Many (perhaps even most) of the internals have changed and a number of
-new features have been added. Backwards compatibility for documents
-created with previous versions of this package has been
-
-See changes.pdf for information on the user-visible changes.
-
-========================================================================
-IV. SETTING UP A CUSTOM BIBLIOGRAPHY STYLE
-
-More documentation is needed here, but the discussion in amsrefs.pdf
-should be enough to get you started. See especially sections 4, 6.10,
-6.26.15, and 6.27.
-
-========================================================================
-V. CHANGE LOG
-
-*amsrefs.dtx 2.0 2004-06-30 11:24:39 EDT
-
-Major rewrite of internals. See changes.pdf for information on the
-user-visible changes.
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsart.template b/Master/texmf-dist/doc/latex/amslatex/amsart.template
deleted file mode 100644
index 1923a23557c..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsart.template
+++ /dev/null
@@ -1,61 +0,0 @@
-%-----------------------------------------------------------------------
-% Beginning of amsart.template
-%-----------------------------------------------------------------------
-%
-% AMS-LaTeX v.2 template for use with amsart
-%
-% Remove any commented or uncommented macros you do not use.
-
-\documentclass{amsart}
-
-\newtheorem{theorem}{Theorem}[section]
-\newtheorem{lemma}[theorem]{Lemma}
-
-\theoremstyle{definition}
-\newtheorem{definition}[theorem]{Definition}
-\newtheorem{example}[theorem]{Example}
-\newtheorem{xca}[theorem]{Exercise}
-
-\theoremstyle{remark}
-\newtheorem{remark}[theorem]{Remark}
-
-\numberwithin{equation}{section}
-
-\begin{document}
-
-\title{}
-
-% Remove any unused author tags.
-
-% author one information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-% author two information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-\subjclass[2000]{Primary }
-
-\keywords{}
-
-\date{}
-
-\dedicatory{}
-
-\begin{abstract}
-\end{abstract}
-
-\maketitle
-
-\end{document}
-
-%-----------------------------------------------------------------------
-% End of amsart.template
-%-----------------------------------------------------------------------
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsbook.template b/Master/texmf-dist/doc/latex/amslatex/amsbook.template
deleted file mode 100644
index 4ac9c928dd9..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsbook.template
+++ /dev/null
@@ -1,99 +0,0 @@
-%-----------------------------------------------------------------------
-% Beginning of amsbook.template
-%-----------------------------------------------------------------------
-%
-% AMS-LaTeX v.2 driver file template for use with amsbook
-%
-% Remove any commented or uncommented macros you do not use.
-
-\documentclass{amsart}
-
-% For use when working on individual chapters
-%\includeonly{}
-
-% Include referenced packages here.
-\usepackage{}
-
-\newtheorem{theorem}{Theorem}[chapter]
-\newtheorem{lemma}[theorem]{Lemma}
-
-\theoremstyle{definition}
-\newtheorem{definition}[theorem]{Definition}
-\newtheorem{example}[theorem]{Example}
-\newtheorem{xca}[theorem]{Exercise}
-
-\theoremstyle{remark}
-\newtheorem{remark}[theorem]{Remark}
-
-\numberwithin{section}{chapter}
-\numberwithin{equation}{chapter}
-
-% For a single index; for multiple indexes, see the manual
-% "Instructions for preparation of papers and monographs:
-% AMS-LaTeX" (instr-l.pdf in the AMS-LaTeX distribution).
-\makeindex
-
-\begin{document}
-
-\frontmatter
-
-\title{}
-
-% Remove any unused author tags.
-
-% author one information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-% author two information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-\subjclass[2000]{Primary }
-
-\keywords{}
-
-\date{}
-
-\begin{abstract}
-\end{abstract}
-
-\maketitle
-
-\setcounter{page}{4}
-
-% See the AMS Author FAQ, http://www.ams.org/authors/author-faq.html
-% regarding a dedication page.
-
-\tableofcontents
-
-% Include unnumbered chapters (preface, acknowledgments, etc.) here.
-\include{}
-
-\mainmatter
-% Include main chapters here.
-\include{}
-
-\appendix
-% Include appendix "chapters" here.
-\include{}
-
-\backmatter
-% Bibliography styles amsplain or harvard are also acceptable.
-\bibliographystyle{amsalpha}
-\bibliography{}
-% See note above about multiple indexes.
-\printindex
-\end{document}
-
-\end{document}
-
-%-----------------------------------------------------------------------
-% End of amsbook.template
-%-----------------------------------------------------------------------
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsldoc.pdf b/Master/texmf-dist/doc/latex/amslatex/amsldoc.pdf
deleted file mode 100644
index 24abc4d3f27..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsldoc.pdf
+++ /dev/null
@@ -1,5623 +0,0 @@
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diff --git a/Master/texmf-dist/doc/latex/amslatex/amsldoc.tex b/Master/texmf-dist/doc/latex/amslatex/amsldoc.tex
deleted file mode 100644
index abb532cccb8..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsldoc.tex
+++ /dev/null
@@ -1,2620 +0,0 @@
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "amsldoc.tex",
-%%% version = "2.09",
-%%% date = "2004/04/06",
-%%% time = "15:13:33 EDT",
-%%% checksum = "39446 2620 11111 93831",
-%%% author = "American Mathematical Society",
-%%% 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)",
-%%% 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.",
-%%% supported = "yes",
-%%% keywords = "latex, amsmath",
-%%% abstract = "This file is the source file for the user's
-%%% guide of the \LaTeX{} package amsmath .",
-%%% 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[leqno,titlepage,openany]{amsldoc}[1999/12/13]
-
-\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
-
-\title{User's Guide for the \pkg{amsmath} Package (Version~2.0)}
-\author{American Mathematical Society}
-\date{1999-12-13 (revised 2002-02-25)}
-
-% Use the amsmath package and amscd package in order to print
-% examples.
-\usepackage{amsmath}
-\usepackage{amscd}
-
-\makeindex % 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
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-
-% 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).
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-\renewcommand{\chaptername}[1]{}
-\newcommand{\chapnum}[1]{\mdash #1\mdash }
-\makeatletter
-\def\@makechapterhead#1{%
- \vspace{1.5\baselineskip}%
- {\parindent \z@ \raggedright \reset@font
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- \large\bfseries \chapnum{\thechapter}%
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- #1\par\nobreak
- \vskip\baselineskip
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-\makeatother
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-% 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}
-
-\DeclareMathOperator{\ix}{ix}
-\DeclareMathOperator{\nul}{nul}
-\DeclareMathOperator{\End}{End}
-\DeclareMathOperator{\xxx}{xxx}
-
-\begin{document}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\frontmatter
-
-\maketitle
-\pagestyle{headings}
-\tableofcontents
-\cleardoublepage % for better page number placement
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mainmatter
-\chapter{Introduction}
-
-The \pkg{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 \pkg{amsmath} package is normally
-provided along with it. Upgrading when a newer version of the
-\pkg{amsmath} package is released can be done via
-\url{http://www.ams.org/tex/amsmath.html} or
-\url{ftp://ftp.ams.org/pub/tex/}.
-
-This documentation describes the features of the \pkg{amsmath} package
-and discusses how they are intended to be used. It also covers some
-ancillary packages:
-\begin{ctab}{ll}
-\pkg{amsbsy}& \pkg{amstext}\\
-\pkg{amscd}& \pkg{amsxtra}\\
-\pkg{amsopn}
-\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{http://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{instr-l} and
-\url{http://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 \pkg{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 \pkg{amsmath} package is distributed together with some small
-auxiliary packages:
-\begin{description}
-\item[\pkg{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 \pkg{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.
-
-\chapter{Options for the \pkg{amsmath} package}\label{options}
-
-The \pkg{amsmath} package has the following options:
-\begin{description}
-
-\item[\opt{centertags}] (default) For a split equation, place equation
-numbers\index{equation numbers!vertical placement} vertically centered
-on the total height of the equation.
-
-\item[\opt{tbtags}] `Top-or-bottom tags': For a split equation, place
-equation numbers\index{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}
-
-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}".
-
-The \pkg{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{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}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Displayed equations}
-
-\section{Introduction}
-The \pkg{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* flalign flalign*
- multline multline* alignat alignat*
- split
-\end{verbatim}
-(Although the standard \env{eqnarray} environment remains available,
-it is better to use \env{align} or \env{equation}+\env{split} instead.)
-
-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 \cn{\\}; you can also
-override\index{equation numbers!overriding} it 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. 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 \pkg{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 \pkg{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.
-
-In the structures that do alignment (\env{split}, \env{align} and
-variants), relation symbols have an \verb'&' before them but not
-after\mdash unlike \env{eqnarray}. Putting the \verb'&' after the
-relation symbol will interfere with the normal spacing; it has to go
-before.
-
-\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}&
- a_{12}& =b_{12}\\
-a_{21}& =b_{21}&
- a_{22}& =b_{22}+c_{22}
-\end{flalign*}
-\end{verbatim}
-\producing
-\begin{flalign*}
-a_{11}& =b_{11}&
- a_{12}& =b_{12}\\
-a_{21}& =b_{21}&
- a_{22}& =b_{22}+c_{22}
-\end{flalign*}
-\end{eqxample}
-\end{table}
-
-\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}.}
-
-\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).
-
-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}.
-
-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 \pkg{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}: 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}
-
-\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
-\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 \verb'[t]' or \verb'[b]' argument to specify vertical
-positioning.
-
-\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 \pkg{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.
-
-\section{Adjusting tag placement}
-
-Placing equation numbers can be a rather complex problem in multiline
-displays. The environments of the \pkg{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. There is a
-\cn{raisetag} command 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}|. 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>|]| command to get extra vertical
-space between lines in all the \pkg{amsmath} displayed equation
-environments, as is usual in \latex/. When the \pkg{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 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 multi-line equation, then you might put
-\cn{allowdisplaybreaks}\texttt{[1]} in the preamble of your document. An
-optional argument 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: 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}
-
-\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 \pkg{amsmath} package provides a command\index{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{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).
-
-\subsection{Subordinate numbering sequences}
-
-The \pkg{amsmath} package provides also a \env{subequations}
-environment\index{equation numbers!subordinate numbering} to make it
-easy to number equations in a particular 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}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\chapter{Miscellaneous mathematical features}
-
-\section{Matrices}\label{ss:matrix}
-
-The \pkg{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 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 must resort to \env{array}.)
-
-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 must be provided; there are no |p|,|b|,|B|,|v|,|V|
-versions of \env{smallmatrix}. 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, 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 \pkg{amsmath} package slightly extends the set of math
-spacing\index{horizontal space!in math mode} 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{\,}&
- \cnbang& \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}
-
-\section{Nonbreaking dashes}
-
-A command \cn{nobreakdash} is provided to suppress the possibility
-of a linebreak after the following hyphen or dash. For example, if you
-write `pages 1\ndash 9' as |pages 1\nobreakdash--9| then a linebreak 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 linebreak 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 \pkg{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.
-
-\section{Roots}
-
-In ordinary \latex/ the placement of root indices is sometimes not so
-good: $\sqrt[\beta]{k}$ (|\sqrt||[\beta]{k}|). In the
-\pkg{amsmath} package \cn{leftroot} and \cn{uproot} allow you to adjust
-the position of the root:
-\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 \pkg{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 (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 \pkg{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
-\pkg{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 $\binom{n}{k}$
-\pkg{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 (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 \pkg{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}.
-
-\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 \pkg{amsmath} package \cn{smash} has optional
-arguments |t| and |b|, 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}
-
-\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.
-\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 \pkg{amsmath} package they are.
-
-\subsection{Vertical bar notations}
-
-The \pkg{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
-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
-double-bar command \ncn{\|}\index{"|@\verb"*+"\"|+}. This immediately
-rules out the use of \qc{|}
-and \ncn{\|}\index{"|@\verb"*+"\"|+} 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 $\lVert v\rVert$.
-
-\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
-\pkg{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
-space!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.
-
-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}.
-
-The following operator names are predefined:
-\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}
-\begin{ctab}{rlrl}
-\cn{varlimsup}& $\displaystyle\varlimsup$&
- \cn{varinjlim}& $\displaystyle\varinjlim$\\
-\cn{varliminf}& $\displaystyle\varliminf$&
- \cn{varprojlim}& $\displaystyle\varprojlim$
-\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 \pkg{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}
-
-\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 |..._{\text{word or phrase}}|, which is slightly
-easier than the \cn{mbox} equivalent: |..._{\mbox{\scriptsize| |word|
-|or| |phrase}}|. The other advantage is the more descriptive name.
-\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}
-
-\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!multi-line}\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 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}
-
-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
-\pkg{kuvio} or \xypic/, 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{tlc}. 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).
-
-\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}
-
-\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.
-
-The \pkg{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 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 \pkg{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). For the reader's convenience, the set of error
-messages discussed here overlaps somewhat with the set in that chapter,
-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|.
-
-There is also a section discussing some output errors, i.e., instances
-where the printed document has something wrong but there was no \latex/
-error during typesetting.
-
-\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}{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}
-
-\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}{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{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
-\fn{cmex10} for the \pkg{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}
-
-\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}
-
-\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 \pkg{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 linebreak 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}
-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}
-a+b\\
-{[f,g]}\\
-m+n
-\end{array}
-\end{verbatim}
-
-\end{error}
-
-\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 linebreak inside a
-\cn{left}-\cn{right} pair of delimiters in a \env{multline} or
-\env{split} environment:
-\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 of fixed size (\cn{bigl} \cn{bigr}
-\cn{biggl} \cn{biggr} \dots; see \secref{bigdel}); or (2)~use null
-delimiters to break up the \cn{left}-\cn{right} pair into parts for each
-line:
-\begin{verbatim}
-AAA\left(BBB\right.\\
- \left.CCC\right)
-\end{verbatim}
-The latter solution may result in mismatched delimiter sizes;
-ensuring that they match requires using \cn{vphantom} in the line
-that has the smaller delimiter (or possibly \cn{smash} in the line that
-has the larger delimiter). In the argument of \cn{vphantom} put a copy
-of the tallest element that occurs in the other line, e.g.,
-\begin{verbatim}
-xxx \left(\int_t yyy\right.\\
- \left.\vphantom{\int_t} zzz ... \right)
-\end{verbatim}
-\end{error}
-
-\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 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 \pkg{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 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}
-
-\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 \pkg{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}
-
-\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}
-
-\section{Warning messages}
-
-\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
-\pkg{amsmath} package is used because their syntax is foreign to \latex/
-and \pkg{amsmath} provides native \latex/ equivalents. See
-\fn{technote.tex} for further information.
-\end{error}
-
-\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}
-
-\section{Wrong output}
-
-\subsection{Section numbers 0.1, 5.1, 8.1 instead of 1, 2, 3}
-\label{numinverse}
-
-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}
-
-\subsection{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
-\secref{numinverse}.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\chapter{Additional information}
-
-\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 \pkg{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 \pkg{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 \pkg{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 \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}
-
-Questions or comments regarding \pkg{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}
-
-\section{Of possible interest}\label{a:possible-interest}
-Information about obtaining AMSFonts or other \tex/-related
-software from the AMS Internet archive \fn{e-math.ams.org}
-can be obtained by sending a request through electronic mail to:
-\mail{webmaster@ams.org}.
-
-Information about obtaining the \pkg{amsmath} distribution on diskette
-from the AMS is available from:
-\begin{infoaddress}
-American Mathematical Society\\
-Customer Services\\
-P. O. Box 6248\\
-Providence, RI 02940\\[3pt]
-Phone: 800-321-4AMS (321-4267) \quad or \quad 401-455-4000\\
-Internet: \mail{cust-serv@ams.org}
-\end{infoaddress}
-
-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 clearing-house of 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.
-
-There is a Usenet newsgroup called \fn{comp.text.tex} that is a fairly
-good source of information about \latex/ and \tex/ in general. If you
-don't know about reading newsgroups, check with your local system
-administrator to see if newsgroup service is available at your site.
-
-\begin{thebibliography}{9}
-\addcontentsline{toc}{chapter}{Bibliography}
-
-\bibitem{amsfonts}\booktitle{AMSFonts version \textup{2.2}\mdash user's guide},
-Amer. Math. Soc., Providence, RI, 1994; distributed
-with the AMSFonts package.
-
-\bibitem{instr-l}\booktitle{Instructions for preparation of
-papers and monographs\mdash \amslatex/},
-Amer. Math. Soc., Providence, RI, 1996, 1999.
-
-\bibitem{amsthdoc}\booktitle{Using the \pkg{amsthm} Package},
-Amer. Math. Soc., Providence, RI, 1999.
-
-\bibitem{tlc} 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
- \pkg{amsmath} package unless you refer to the errata for Chapter
- 8\mdash file \fn{compan.err}, distributed with \LaTeX{}.}]
-
-% 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{http://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{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.
-
-\end{thebibliography}
-
-\begin{theindex}
-
- \item {\normalfont \ttfamily \bslchar \qcbang }, 11
- \item \verb*+\,+, 11
- \item \verb*+\:+, 11
- \item \verb*+\;+, 11
- \item \verb*+\\+, 3, 5, 6, 8, 9, 24, 26
- \item \verb*+\\*+, 9
- \item \verb*+\|+, 16
-
- \indexspace
-
- \item \verb*+\above+, 14, 29
- \item \verb*+\abovewithdelims+, 14
- \item \verb*+\accentedsymbol+, 2
- \item \texttt{accents} package, 12
- \item \verb*+\addtocounter+, 10
- \item \verb*+\addtolength+, 5
- \item \texttt{align} environment, 3, 5--7, 28--30
- \item \texttt{alignat} environment, 7, 24, 26, 29
- \item \texttt{aligned} environment, 7, 9
- \item \texttt{alignedat} environment, 7, 9
- \item \verb*+\allowdisplaybreaks+, 8, 9
- \item \texttt{amsart} class, 1
- \item \texttt{amsbook} class, 1
- \item \texttt{amsbsy} package, 1, 2
- \item \texttt{amscd} package, 1, 2, 20
- \item \texttt{amsfonts} package, 21
- \item AMSFonts collection, 25
- \item \texttt{amsmath} package, i, 1--3, 5, 8--18, 22, 23, 25, 26,
- 28--32
- \item \texttt{amsopn} package, 1, 2
- \item \texttt{amssymb} package, 22
- \item \texttt{amstext} package, 1, 2
- \item \texttt{amsthm} package, 1, 32
- \item \texttt{amsxtra} package, 1, 2, 12
- \item \verb*+\arccos+, 18
- \item \verb*+\arcsin+, 18
- \item \verb*+\arctan+, 18
- \item \verb*+\arg+, 18
- \item \texttt{array} environment, 8, 10, 26
- \item arrows
- \subitem extensible, 13
- \subitem in commutative diagrams, 20
- \item \verb*+\atop+, 14, 29
- \item \verb*+\atopwithdelims+, 14
-
- \indexspace
-
- \item BaKoMa fonts, 25
- \item \cn{big}, \cn{Big}, \cn{bigg}, \dots\ delimiters, 16
- \item \verb*+\biggl+, 27
- \item \verb*+\biggr+, 27
- \item \verb*+\bigl+, 27
- \item \verb*+\bigr+, 27
- \item \verb*+\binom+, 14
- \item binomials, 14
- \item \texttt{bm} package, 2, 23
- \item \texttt{Bmatrix} environment, 10
- \item \texttt{bmatrix} environment, 10
- \item \verb*+\bmod+, 18
- \item \verb*+\boldsymbol+, 22, 23
- \item \verb*+\boxed+, 13
-
- \indexspace
-
- \item \verb*+\C+, 22
- \item \texttt{cases} environment, 8
- \item \verb*+\cases+, 28
- \item \texttt{CD} environment, 2, 21
- \item \verb*+\cdots+, 12
- \item \texttt{centertags} option, 2
- \item \verb*+\cfrac+, 15
- \item \texttt{cmbsy5}, 25
- \item \texttt{cmex}, 25
- \item \texttt{cmex10}, 25
- \item \texttt{cmex7}, 25
- \item \texttt{cmmib5}, 25
- \item \texttt{comp.text.tex}, 31
- \item \texttt{compan.err}, 32
- \item continued fractions, 15
- \item \verb*+\cos+, 18
- \item \verb*+\cosh+, 18
- \item \verb*+\cot+, 18
- \item \verb*+\coth+, 18
- \item \verb*+\csc+, 18
-
- \indexspace
-
- \item \verb*+\dbinom+, 14
- \item \verb*+\ddddot+, 12
- \item \verb*+\dddot+, 12
- \item \verb*+\ddot+, 12
- \item \verb*+\DeclareMathOperator+, 2, 17, 18
- \item \verb*+\deg+, 18
- \item \verb*+\det+, 18
- \item \verb*+\dfrac+, 14
- \item \texttt{diffs-m.txt}, 30
- \item \verb*+\dim+, 18
- \item \verb*+\displaybreak+, 8, 9
- \item displayed equations, 3
- \item displayed equations
- \subitem centering, 3
- \item \verb*+\displaylimits+, 20
- \item \texttt{displaymath} environment, 3
- \item \verb*+\displaystyle+, 14
- \item \verb*+\documentclass+, 2
- \item \verb*+\dot+, 12
- \item dots, \see{ellipsis dots}{11}
- \item \verb*+\dotsb+, 12
- \item \verb*+\dotsc+, 12
- \item \verb*+\dotsi+, 12
- \item \verb*+\dotsm+, 12
- \item \verb*+\dotso+, 12
-
- \indexspace
-
- \item \texttt{e-math.ams.org}, 31
- \item ellipsis dots
- \subitem in matrices, 11
- \item \texttt{eqnarray} environment, 1, 3, 26, 30
- \item \verb*+\eqref+, 10
- \item \texttt{equation} environment, 1, 3, 5, 7, 24, 30
- \item equation numbers
- \subitem cross-references, 10
- \subitem hierarchy, 9
- \subitem left or right placement, 3
- \subitem overriding, 3
- \subitem subordinate numbering, 10
- \subitem vertical placement, 2
- \item \texttt{equation*} environment, 3
- \item equations, \see{displayed equations}{3}
- \item \texttt{euscript} package, 21
- \item \verb*+\exp+, 18
-
- \indexspace
-
- \item \verb*+\fbox+, 13
- \item \texttt{fleqn} option, 3, 5
- \item \texttt{fntguide.tex}, 21
- \item \verb*+\frac+, 14, 15
- \item fractions, 14
- \item \verb*+\fracwithdelims+, 2
- \item function names, \see{operator names}{17}
-
- \indexspace
-
- \item \texttt{gather} environment, 5--7, 24, 28--30
- \item \texttt{gathered} environment, 7, 9
- \item \verb*+\gcd+, 18
- \item \verb*+\genfrac+, 14
-
- \indexspace
-
- \item \verb*+\hat+, 12
- \item \verb*+\hdotsfor+, 11
- \item \verb*+\hom+, 18
- \item horizontal space
- \subitem around operator names, 17
- \subitem in math mode, 11
-
- \indexspace
-
- \item \verb*+\idotsint+, 20
- \item \verb*+\iiiint+, 20
- \item \verb*+\iiint+, 20
- \item \verb*+\iint+, 20
- \item \verb*+\inf+, 18
- \item \verb*+\injlim+, 18
- \item integrals
- \subitem multiple, 20
- \subitem placement of limits, 2
- \item \verb*+\intertext+, 9
- \item \texttt{intlimits} option, 2, 20
-
- \indexspace
-
- \item \verb*+\ker+, 18
- \item \texttt{kuvio} package, 20
-
- \indexspace
-
- \item \verb*+\label+, 6, 10
- \item \verb*+\langle+, 16
- \item \verb*+\ldots+, 12
- \item \verb*+\left+, 15, 16, 27
- \item \verb*+\leftroot+, 13
- \item \texttt{leqno} option, 3, 5
- \item \verb*+\lg+, 18
- \item \verb*+\lim+, 1, 2, 17, 18
- \item \verb*+\liminf+, 18
- \item limits, \see{subscripts and superscripts}{2}
- \item \verb*+\limits+, 20
- \item \verb*+\limsup+, 18
- \item \verb*+\ln+, 18
- \item \verb*+\log+, 17, 18
- \item \verb*+\lVert+, 16
- \item \verb*+\lvert+, 16
-
- \indexspace
-
- \item math fonts, 21
- \item math symbols, \see{math fonts}{21}
- \item \verb*+\mathbb+, 21, 22
- \item \verb*+\mathbf+, 21, 22
- \item \verb*+\mathcal+, 21
- \item \verb*+\mathfrak+, 21
- \item \verb*+\mathit+, 21
- \item \verb*+\mathrm+, 21
- \item \verb*+\mathscr+, 21
- \item \verb*+\mathsf+, 21
- \item \verb*+\mathtt+, 21
- \item matrices, 10
- \subitem ellipsis dots, 11
- \item \texttt{matrix} environment, 10
- \item \verb*+\matrix+, 28
- \item \verb*+\max+, 18
- \item \verb*+\mbox+, 18
- \item \verb*+\medspace+, 11
- \item Metafont source files, 25
- \item \verb*+\min+, 18
- \item \verb*+\mod+, 18
- \item \verb*+\mspace+, 11
- \item \texttt{multline} environment, 3, 5, 27, 30
- \item \verb*+\multlinegap+, 5
-
- \indexspace
-
- \item \texttt{namelimits} option, 2
- \item \verb*+\negmedspace+, 11
- \item \verb*+\negthickspace+, 11
- \item \verb*+\negthinspace+, 11
- \item \verb*+\newcommand+, 21
- \item \verb*+\nobreakdash+, 12
- \item \texttt{nointlimits} option, 2
- \item \verb*+\nolimits+, 19, 20
- \item \texttt{nonamelimits} option, 2
- \item \texttt{nosumlimits} option, 2
- \item \verb*+\notag+, 3, 5
- \item \verb*+\numberwithin+, 9, 29, 30
-
- \indexspace
-
- \item operator names, 17
- \item \verb*+\operatorname+, 18
- \item \verb*+\operatorname*+, 18
- \item \verb*+\over+, 14, 29
- \item \verb*+\overleftarrow+, 13
- \item \verb*+\overleftrightarrow+, 13
- \item \verb*+\overrightarrow+, 13
- \item \verb*+\overset+, 13
- \item \verb*+\overwithdelims+, 14
-
- \indexspace
-
- \item page breaks, 8
- \item \verb*+\pagebreak+, 8
- \item \texttt{pmatrix} environment, 10
- \item \verb*+\pmatrix+, 28
- \item \verb*+\pmb+, 22
- \item \verb*+\pmod+, 18
- \item \verb*+\pod+, 18
- \item PostScript fonts, 25
- \item \verb*+\Pr+, 18
- \item \verb*+\projlim+, 18
-
- \indexspace
-
- \item \verb*+\qquad+, 11
- \item \verb*+\quad+, 11
-
- \indexspace
-
- \item \verb*+\R+, 22
- \item \verb*+\raisetag+, 8
- \item \verb*+\rangle+, 16
- \item \verb*+\ref+, 10
- \item \texttt{reqno} option, 3, 5
- \item \verb*+\right+, 15, 16, 27
- \item \verb*+\rVert+, 16
- \item \verb*+\rvert+, 16
-
- \indexspace
-
- \item \verb*+\scriptscriptstyle+, 14
- \item \verb*+\scriptstyle+, 14
- \item \verb*+\sec+, 18
- \item \verb*+\setcounter+, 9, 10
- \item \verb*+\setlength+, 5
- \item \verb*+\shoveleft+, 5
- \item \verb*+\shoveright+, 5
- \item \verb*+\sideset+, 13, 19
- \item \verb*+\sin+, 1, 2, 17, 18
- \item \verb*+\sinh+, 18
- \item \texttt{smallmatrix} environment, 11
- \item \verb*+\smash+, 15, 27
- \item \verb*+\sphat+, 12
- \item \texttt{split} environment, 3, 5, 6, 9, 24, 27--30
- \item \verb*+\sptilde+, 12
- \item \verb*+\stackrel+, 13
- \item \texttt{subarray} environment, 19
- \item \texttt{subeqn.tex}, 3
- \item \texttt{subequations} environment, 10
- \item subscripts and superscripts, 13
- \subitem multi-line, 19
- \subitem on sums, 19
- \subitem placement, 2
- \item \verb*+\substack+, 19
- \item \verb*+\sum+, 20, 22
- \item \texttt{sumlimits} option, 2
- \item \verb*+\sup+, 18
- \item superscripts, \see{subscripts and superscripts}{19}
-
- \indexspace
-
- \item \texttt{tabular} environment, 26
- \item \verb*+\tag+, 3
- \item \verb*+\tag*+, 3
- \item \verb*+\tan+, 18
- \item \verb*+\tanh+, 18
- \item \verb*+\tbinom+, 14
- \item \texttt{tbtags} option, 2
- \item \texttt{technote.tex}, 14, 28--30
- \item \texttt{testmath.tex}, 3
- \item \tex/ Users Group, 31
- \item \verb*+\text+, 2, 7--9, 18
- \item text fragments inside math, 9, 18
- \item \verb*+\textstyle+, 14
- \item \verb*+\tfrac+, 14
- \item \verb*+\theequation+, 9, 10
- \item \verb*+\thickspace+, 11
- \item \verb*+\thinspace+, 11
- \item \journalname{TUGboat}, 31
-
- \indexspace
-
- \item \verb*+\underleftarrow+, 13
- \item \verb*+\underleftrightarrow+, 13
- \item \verb*+\underrightarrow+, 13
- \item \verb*+\underset+, 13
- \item \verb*+\uproot+, 13
- \item \verb*+\usepackage+, 2, 25
-
- \indexspace
-
- \item \verb*+\value+, 10
- \item \verb*+\varDelta+, 23
- \item \verb*+\varGamma+, 23
- \item \verb*+\varinjlim+, 18
- \item \verb*+\varLambda+, 23
- \item \verb*+\varliminf+, 18
- \item \verb*+\varlimsup+, 18
- \item \verb*+\varOmega+, 23
- \item \verb*+\varPhi+, 23
- \item \verb*+\varPi+, 23
- \item \verb*+\varprojlim+, 18
- \item \verb*+\varPsi+, 23
- \item \verb*+\varSigma+, 23
- \item \verb*+\varTheta+, 23
- \item \verb*+\varUpsilon+, 23
- \item \verb*+\varXi+, 23
- \item \texttt{Vmatrix} environment, 10
- \item \texttt{vmatrix} environment, 10
- \item \verb*+\vphantom+, 27
-
- \indexspace
-
- \item \verb*+\xleftarrow+, 13
- \item \verb*+\xrightarrow+, 13
-
-\end{theindex}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsproc.template b/Master/texmf-dist/doc/latex/amslatex/amsproc.template
deleted file mode 100644
index 2409fc62991..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsproc.template
+++ /dev/null
@@ -1,61 +0,0 @@
-%-----------------------------------------------------------------------
-% Beginning of amsproc.template
-%-----------------------------------------------------------------------
-%
-% AMS-LaTeX v.2 template for use with amsproc
-%
-% Remove any commented or uncommented macros you do not use.
-
-\documentclass{amsproc}
-
-\newtheorem{theorem}{Theorem}[section]
-\newtheorem{lemma}[theorem]{Lemma}
-
-\theoremstyle{definition}
-\newtheorem{definition}[theorem]{Definition}
-\newtheorem{example}[theorem]{Example}
-\newtheorem{xca}[theorem]{Exercise}
-
-\theoremstyle{remark}
-\newtheorem{remark}[theorem]{Remark}
-
-\numberwithin{equation}{section}
-
-\begin{document}
-
-\title{}
-
-% Remove any unused author tags.
-
-% author one information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-% author two information
-\author{}
-\address{}
-\curraddr{}
-\email{}
-\thanks{}
-
-\subjclass[2000]{Primary }
-
-\keywords{}
-
-\date{}
-
-\dedicatory{}
-
-\begin{abstract}
-\end{abstract}
-
-\maketitle
-
-\end{document}
-
-%-----------------------------------------------------------------------
-% End of amsproc.template
-%-----------------------------------------------------------------------
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf b/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf
deleted file mode 100644
index ab9fe5ab91d..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsrdoc.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq b/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq
deleted file mode 100644
index 3484e5d13d8..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsrefs.faq
+++ /dev/null
@@ -1,15 +0,0 @@
-amsrefs.faq [2004/06/30] American Mathematical Society
-
-Frequently asked questions about the amsrefs package and its companion
-packages.
-
-Suggestions? Please send mail to tech-support@ams.org.
-
-------------------------------------------------------------------------
-(1) Question: Where should I look for documentation?
-
-Answer: User documentation is found in the file amsrdoc.pdf (or
-amsrdoc.dvi).
-
-Some example files (cite-xa.tex cite-xb.tex cite-xh.tex cite-xs.tex
-gktest.ltb) are also provided.
diff --git a/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf b/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf
deleted file mode 100644
index 79061f69b83..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsrefs.pdf
+++ /dev/null
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diff --git a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf
deleted file mode 100644
index 5a0a59efa2f..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.pdf
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diff --git a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex b/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex
deleted file mode 100644
index 21e824f5ba0..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/amsthdoc.tex
+++ /dev/null
@@ -1,374 +0,0 @@
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "amsthdoc.tex",
-%%% version = "2.20",
-%%% date = "2004/08/03",
-%%% time = "15:02:46 EDT",
-%%% checksum = "15807 374 1763 14655",
-%%% author = "American Mathematical Society",
-%%% copyright = "Copyright 1999, 2004 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,
-%%% Publications Technical Group,
-%%% 201 Charles Street,
-%%% Providence, RI 02904,
-%%% 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",
-%%% supported = "yes",
-%%% keywords = "latex, theorem, proof, amsthm",
-%%% abstract = "This file is the User's Guide for the amsthm
-%%% 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.",
-%%% }
-%%% ====================================================================
-\documentclass[twoside]{article}
-\pagestyle{myheadings}
-
-% Use the same version numbers as for the amslatex instructions.
-\def\instrversion{2.20}
-\def\instrdate{August 2004}
-
-\title{Using the \pkg{amsthm} Package}
-\author{Version \instrversion, \instrdate\\American Mathematical Society}
-\date{}
-
-\providecommand{\qq}[1]{\textquotedblleft#1\textquotedblright}
-\providecommand{\mdash}{\textemdash\penalty\hyphenpenalty}
-
-% Embedded \index commands are a legacy from the time when this
-% documentation was part of amsldoc. Since they don't hurt anything,
-% let's leave them in. Maybe they will become useful again in the
-% future. [mjd,2000/06/06]
-
-\chardef\bslchar=`\\ % p. 424, TeXbook
-\newcommand{\ntt}{%
- \fontfamily\ttdefault \fontseries\mddefault \fontshape\updefault
- \selectfont
-}
-\DeclareRobustCommand{\cn}[1]{{\ntt\bslchar#1}}
-\DeclareRobustCommand{\cls}[1]{{\ntt#1}}
-\DeclareRobustCommand{\pkg}[1]{{\ntt#1}}
-\DeclareRobustCommand{\opt}[1]{{\ntt#1}}
-\DeclareRobustCommand{\env}[1]{{\ntt#1}}
-\DeclareRobustCommand{\fn}[1]{{\ntt#1}}
-
-\providecommand{\qedsymbol}{\leavevmode
- \hbox to.77778em{%
- \hfil\vrule
- \vbox to.675em{\hrule width.6em\vfil\hrule}%
- \vrule\hfil}}
-
-%% Provide a meta-command facility; provide an alternate escape
-%% character so it can be used within the verbatim environment.
-
-\catcode`\|=0
-\begingroup \catcode`\>=13 % in LaTeX2e verbatim env makes > active
-\gdef\?#1>{{\normalfont$\langle$\textup{#1}$\rangle$}}
-\gdef\0{\relax}
-\endgroup
-\def\<#1>{{\normalfont$\langle$\textup{#1}$\rangle$}}
-\def\ntnote#1{{\normalfont$^{#1}$}}
-
-\hfuzz4pt \vbadness9999 \hbadness5000
-\def\latex/{{\protect\LaTeX}}
-
-\setlength{\textwidth}{210mm}\addtolength{\textwidth}{-2in}
-\setlength{\oddsidemargin}{39pt}
-\setlength{\evensidemargin}{39pt}
-\addtolength{\textwidth}{-2\oddsidemargin}
-
-\begin{document}
-\maketitle
-\markboth{USING THE \pkg{amsthm} PACKAGE}{USING THE \pkg{amsthm} PACKAGE}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\section{Introduction}
-
-\begin{sloppypar}
-The \pkg{amsthm} package provides an enhanced version of \latex/'s
-\cn{newtheorem} command for defining theorem-like environments. The
-enhanced \cn{newtheorem} recognizes a
-\cn{theoremstyle} specification (as in Mittelbach's \pkg{theorem}
-package) and has a \verb'*' form for defining unnumbered environments. The
-\pkg{amsthm} package also defines a \env{proof} environment that
-automatically adds a QED symbol at the end. AMS document classes
-incorporate the \pkg{amsthm} package, so everything described here
-applies to them as well.
-\end{sloppypar}
-
-If the \pkg{amsthm} package is used with a non-AMS document class and
-with the \pkg{amsmath} package, \pkg{amsthm} must be loaded
-\emph{after} \pkg{amsmath}, not before.
-
-Examples are given in the file \fn{thmtest.tex}. For best understanding,
-examine the output side-by-side with the input.
-
-
-\section{The \cn{newtheorem} command}
-
-In mathematical research articles and books, theorems\index{theorems}
-and proofs\index{proofs} are among the most common elements, but authors
-also use many others that fall in the same general class: lemmas,
-propositions, axioms, corollaries, conjectures, definitions, remarks,
-cases, steps, and so forth. It is natural to handle these elements as
-\latex/ environments, but document classes do not
-provide predefined environments for theorem-like elements because
-(a)~that would make it difficult for authors to exercise the necessary
-control over the automatic numbering, and (b)~the variety of such
-elements is so wide that it's not possible for a document class to
-provide every one that will ever be needed. Instead there is a command
-\cn{newtheorem}, similar in effect to \cn{newenvironment}, that makes it
-easy for authors to set up the elements required for a particular
-document.
-
-The \cn{newtheorem} command has two mandatory arguments; the first one
-is the environment name that the author would like to use for this
-element; the second one is the heading text. For example,
-\begin{verbatim}
-\newtheorem{lem}{Lemma}
-\end{verbatim}
-means that instances in the document of
-\begin{verbatim}
-\begin{lem} Text text ... \end{lem}
-\end{verbatim}
-will produce
-\[\makebox[.8\columnwidth]{%
- \textbf{Lemma 1.} \textit{Text text \dots}\hfill}\]
-where the heading consists of the specified text \qq{Lemma} and an
-automatically generated number and punctuation.
-
-If \cn{newtheorem*} is used instead of \cn{newtheorem} in this
-example, numbers will not be generated automatically for
-any of the lemmas in the document. This form of the command can be
-useful if you have only one lemma and don't want it to be
-numbered; more often, though, it is used to produce a special named
-variant of one of the common theorem types. For example, if you have a
-lemma that should be labeled \qq{Klein's Lemma}, then the statement
-\begin{verbatim}
-\newtheorem*{KL}{Klein's Lemma}
-\end{verbatim}
-would allow you to write
-\begin{verbatim}
-\begin{KL} Text text ... \end{KL}
-\end{verbatim}
-and get the desired output.
-
-Sometimes additional information is desired in the heading of a
-theorem or lemma, often because it is cited from another source.
-An optional argument is used to provide this information:
-\begin{verbatim}
-\begin{lem}[Alinhac-Lerner \cite{a-l}]
-\end{verbatim}
-yielding the output
-\[\makebox[.8\columnwidth]{%
- \textbf{Lemma 2.} (Alinhac-Lerner [1]). \textit{Text text \dots}\hfill}\]
-
-
-\section{Numbering modifications}
-
-In addition to the two mandatory arguments, \cn{newtheorem} has two
-mutually exclusive optional arguments. These affect the
-sequencing\index{theorems!numbering} and hierarchy of the numbering.
-
-By default each kind of theorem-like environment is numbered
-independently. Thus if you have three lemmas and two theorems
-interspersed, they will be numbered something like this: Lemma 1, Lemma
-2, Theorem 1, Lemma 3, Theorem 2. If you want lemmas and theorems to
-share the same numbering sequence\mdash Lemma 1, Lemma 2, Theorem 3, Lemma
-4, Theorem 5\mdash then you should indicate the desired relationship as
-follows:
-\begin{verbatim}
-\newtheorem{thm}{Theorem}
-\newtheorem{lem}[thm]{Lemma}
-\end{verbatim}
-The optional argument \verb'[thm]' in the second statement means that
-the \texttt{lem} environment should share the \texttt{thm} numbering
-sequence instead of having its own independent sequence.
-
-To have a theorem environment numbered subordinately within a
-sectional unit\mdash e.g., to get propositions numbered Proposition 2.1,
-Proposition 2.2, and so on in Section~2\mdash put the name of the parent
-unit in square brackets in final position:
-\begin{verbatim}
-\newtheorem{prop}{Proposition}[section]
-\end{verbatim}
-With the optional argument \verb'[section]', the \verb'prop' counter
-will be reset to 0 whenever the parent counter \verb'section' is
-incremented, and the proposition label will have the section number
-prepended.
-
-Note that theorem numbering is not accomplished by the same method
-as the \cn{numberwithin} facility of \pkg{amsmath}, so an attempt to
-use that to relate theorem numbers to equation numbers will not work
-in the expected way. A method for accomplishing that, as well as
-some other variations, is given in the AMS Author FAQ \cite{AF},
-in the section on \qq{Theorems in AMS-\LaTeX}.
-
-
-\section{Changing styles for theorem-like environments}
-
-\subsection{The \cn{theoremstyle} command}
-
-The \pkg{amsthm} package supports the notion of a current theorem style,
-which determines what will be produced by a given \cn{newtheorem}
-command. The three theorem styles provided\mdash
-\verb'plain',\index{plain theo@\texttt{plain} theorem style}\relax
-\index{definition theo@\texttt{definition} theorem style}\relax
-\index{remark theo@\texttt{remark} theorem style} \verb'definition',
-and \verb'remark'\mdash specify different degrees of
-visual emphasis corresponding to their relative importance. The
-details of this typographical treatment may vary depending on the
-document class, but typically the \verb'plain' style produces italic
-body text, while the other two styles produce roman body text.
-
-If no \cn{theoremstyle} command is given, the style used will be
-\texttt{plain}. To specify different styles,
-divide your \cn{new\-theorem} commands into groups and preface each
-group with the appropriate \cn{theo\-rem\-style}. Some examples:
-\begin{verbatim}
-\theoremstyle{plain}% default
-\newtheorem{thm}{Theorem}[section]
-\newtheorem{lem}[thm]{Lemma}
-\newtheorem{prop}[thm]{Proposition}
-\newtheorem*{cor}{Corollary}
-\newtheorem*{KL}{Klein's Lemma}
-
-\theoremstyle{definition}
-\newtheorem{defn}{Definition}[section]
-\newtheorem{conj}{Conjecture}[section]
-\newtheorem{exmp}{Example}[section]
-
-\theoremstyle{remark}
-\newtheorem*{rem}{Remark}
-\newtheorem*{note}{Note}
-\newtheorem{case}{Case}
-\end{verbatim}
-
-The following list summarizes the types of structures which are
-normally associated with each theorem style.
-
-\smallskip
-\begin{tabular}{ll}
- \relax\env{plain} & Theorem, Lemma, Corollary, Proposition, Conjecture, \\
- & Criterion, Algorithm \\
- \relax\env{definition} \quad & Definition, Condition, Problem, Example \\
- \relax\env{remark} & Remark, Note, Notation, Claim, Summary, \\
- & Acknowledgment, Case, Conclusion
-\end{tabular}
-
-\subsection{Number swapping}
-
-A common style variation is to have the theorem number at the beginning
-of the heading instead of at the end, for example \qq{1.4 Theorem}
-instead of \qq{Theorem 1.4}. As this variation is usually applied
-to all \cn{theoremstyle}s, it is done by
-placing a \cn{swapnumbers} command at the beginning of the list of
-\cn{newtheorem} statements that should be affected. For example:
-\begin{verbatim}
-\swapnumbers
-\theoremstyle{plain}
-\newtheorem{thm}{Theorem}
-\theoremstyle{remark}
-\newtheorem{rem}{Remark}
-\end{verbatim}
-
-In AMS document classes, when numbers are swapped, the style of the
-numbers matches that of section headings; this may not be the same
-style as the rest of the theorem heading.
-
-\subsection{New theorem styles}
-
-The \pkg{amsthm} package provides a \cn{newtheoremstyle} command
-to aid in the creation of custom styles, should the three predefined
-styles prove insufficient. The following example illustrates the use
-of the \cn{newtheoremstyle} command.
-\begin{verbatim}
-\newtheoremstyle{note}% |?name>
- {3pt}% |?Space above>
- {3pt}% |?Space below>
- {}% |?Body font>
- {}% |?Indent amount>|ntnote1
- {\itshape}% |?Theorem head font>
- {:}% |?Punctuation after theorem head>
- {.5em}% |?Space after theorem head>|ntnote2
- {}% |?Theorem head spec (can be left empty, meaning `normal')>
-\end{verbatim}
-\noindent
-\ntnote1 Indent amount: empty = no indent, \cn{parindent} = normal
- paragraph indent
-
-\noindent
-\ntnote2 Space after theorem head: \verb+{ }+ = normal interword space;
- \cn{newline} = linebreak
-
-\smallskip
-Apply the new theorem style in the same manner as the predefined ones.
-For examples, see the file \fn{thmtest.tex}.
-
-
-\section{Proofs}
-
-A predefined \env{proof} environment provided by the \pkg{amsthm}
-package produces the heading \qq{Proof} with appropriate spacing and
-punctuation. The proof environment is primarily intended for short
-proofs, no more than a page or two in length; longer proofs are
-usually better done as a separate \cn{section} or \cn{subsection} in
-your document.
-
-An optional argument of the proof environment allows you to substitute
-a different name for the standard \qq{Proof\/}. If you want
-the proof heading to be, say, \qq{Proof of the Main Theorem}, then write
-\begin{verbatim}
-\begin{proof}[Proof of the Main Theorem]
-\end{verbatim}
-
-A QED symbol, \qedsymbol, is automatically appended at the end of
-a \env{proof} environment. To substitute a different end-of-proof
-symbol, use \cn{renewcommand} to redefine the command \cn{qedsymbol}.
-For a long proof done as a subsection or section instead of with the
-\env{proof} environment, you can obtain the symbol and the usual
-amount of preceding space by using \cn{qed}.
-
-Placement of the QED symbol can be problematic if the last part of
-a \env{proof} environment is a displayed equation or list environment
-or something of that nature. In that case put a \cn{qedhere} command at
-the place where the QED symbol should appear, for example,
-\begin{verbatim}
-\begin{proof}
-...
-\begin{equation}
-G(t)=L\gamma!\,t^{-\gamma}+t^{-\delta}\eta(t) \qedhere
-\end{equation}
-\end{proof}
-\end{verbatim}
-When used with the \pkg{amsmath} package, version 2 or later, \cn{qedhere}
-will position the QED symbol flush right; with earlier versions, the
-symbol will be spaced a quad away from the end of the text or display.
-
-If \cn{qedhere} produces an error message in an equation, try using
-\verb'\mbox{\qedhere}' instead.
-
-\begin{thebibliography}{[AF]}
-
-\bibitem[AF]{AF} AMS Author FAQ,
-\texttt{http://www.ams.org/authors/author-faq.html}
-
-\end{thebibliography}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/changes.pdf b/Master/texmf-dist/doc/latex/amslatex/changes.pdf
deleted file mode 100644
index c74e7bc063f..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/changes.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex
deleted file mode 100644
index d6930f7cbf1..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/cite-xa.tex
+++ /dev/null
@@ -1,221 +0,0 @@
-\documentclass{article}
-\usepackage[author-year]{amsrefs}
-
-\newcommand{\latin}{\emph}
-
-\begin{document}
-
-\title{Evolutionary walks through a land plant morphospace}
-\author{Karl J. Niklas}
-\def\jinfo{Journal of Experimental Botany, Vol. 50, No. 330, pp. 39-52,
- January 1999, \copyright\ Oxford University Press 1999}
-
-\maketitle
-\section{Introduction}
-
-Wright's protocol has been successfully recast in terms of spatial
-domains containing all (or at least many) of the conceivable
-morphological variants (`morphospaces' \latin{sensu}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%Thomas and Reif, 1993).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\ocite{TR93}).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-In this paper, I review the construction of a morphospace for early land
-plants
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%(Niklas and Kerchner, 1984; Niklas, 1997a, b)
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\cites{NK84,N97-adaptive-walks,N97-effects}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-and show how it can be used \ldots.
-
-\ldots\ horizontally cantilevered branches impose the largest bending
-moments on subtending branches
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%(Niklas, 1992, 1994a).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\cites{N92,N94-allometry}.
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\ldots\ This definition removes the sharp dichotomy said to exist
-between `object' and `process' complexity (i.e. the number of different
-parts in an organic system versus the number of different interactions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%among them; McShea, 1996).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-among them \cite{M96}).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\ldots\ fossil record for Devonian and Carboniferous vascular land
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%plants (Niklas et al., 1980, 1983; Gensel and Andrews, 1984).
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-plants \cites{NTK80,NTK83,GA84}.
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\begin{bibsection}
-\begin{biblist}
-
-\bib*{HSW80}{collection}{
- editor={Hecht, M.},
- editor={Steere, W.},
- editor={Wallace, B.},
- date={1980},
- title={Evolutionary biology},
- publisher={Plenum Publishing},
- address={New York},
-}
-
-\bib{fn95}{article}{
- author={Farnsworth, K. D.},
- author={Niklas, K. J.},
- date={1995},
- title={Theories of optimization, form and function in branching
- architectures in plants},
- journal={Functional Ecology},
- volume={9},
- pages={355\ndash 363},
-}
-
-\typeout{}
-\typeout{ [Testing some of the amsrefs warning messages ...]}
-
-\bib{GMW81}{book}{
- author={Gill, P. E.},
- author={Murray, W.}
- author={Wright, M. H.},
- date={1981},
- title={Practical optimization},
- publisher={Academic Press},
- address={London},
-}
-
-\bib{GA84}{book}{
- author={Gensel, P. G.},
- author={Andrews, H. N.},
- date={1984},
- title={Plant life in the Devonian},
- publisher={Praeger Press},
- address={New York},
-}
-
-\bib{M96}{article}{
- author={McShea, D. W.},
- date={1996},
- title={Metazoan complexity and evolution: is there a trend},
- journal={Evolution},
- volume={50},
- pages={477\ndash 492},
-}
-
-\bib{MWWW73}{book}{
- author={Meredith, D. D.},
- author={Wong, K. W.},
- author={Woodhead, R. W.},
- author={Wortman, R. H.},
- date={1973},
- title={Design and planning of engineering systems},
- publisher={Prentice-Hall},
- address={Englewood Cliffs, New Jersey},
-}
-
-\bib{N92}{book}{
- author={Niklas, K. J.},
- date={1992},
- title={Plant biomechanics: an engineering approach to plant form and
- function},
- publisher={University of Chicago Press},
- address={Illinois},
-}
-
-\bib{N94-allometry}{book}{
- author={Niklas, K. J.},
- date={1994},
- title={Plant allometry: the scaling of form and process},
- publisher={University of Chicago Press},
- address={Illinois},
-}
-
-\bib{N94-simulation}{article}{
- author={Niklas, K. J.},
- date={1994},
- title={Simulation of organic shape: the roles of phenomenology and
- mechanism},
- journal={Journal of Morphology},
- volume={219},
- pages={243\ndash 246},
-}
-
-\bib{N97-adaptive-walks}{article}{
- author={Niklas, K. J.},
- date={1997},
- title={Adaptive walks through fitness landscapes for early vascular
- land plants},
- journal={American Journal of Botany},
- volume={84},
- pages={16\ndash 25},
-}
-
-\bib{N97-effects}{article}{
- author={Niklas, K. J.},
- date={1997},
- title={Effects of hypothetical developmental barriers and abrupt
- environmental changes on adaptive walks in a computer-generated
- domain for early vascular land plants},
- journal={Paleobiology},
- volume={23},
- pages={63\ndash 76},
-}
-
-\bib{NK84}{article}{
- author={Niklas, K. J.},
- author={Kerchner, V.},
- date={1984},
- title={Mechanical and photosynthetic constraints on the evolution of
- plant shape},
- journal={Paleobiology},
- volume={10},
- pages={79\ndash 101},
-}
-
-\bib{NTK80}{article}{
- author={Niklas, K. J.},
- author={Tiffney, B. H.},
- author={Knoll, A. H.},
- date={1980},
- title={Apparent changes in the diversity of fossil plants: a
- preliminary assessment},
- xref={HSW80},
- volume={12},
- pages={1\ndash 89},
-}
-
-\bib{NTK83}{article}{
- author={Niklas, K. J.},
- author={Tiffney, B. H.},
- author={Knoll, A. H.},
- date={1983},
- title={Patterns in vascular land plant diversification},
- journal={Nature},
- volume={303},
- pages={614\ndash 616},
-}
-
-\bib{TR93}{article}{
- author={Thomas, R. D. K.},
- author={Reif, W.-E.},
- % This is just to show what the warning looks like for an empty field:
- author={},
- date={1993},
- title={The skeleton space: a finite set of organic designs},
- journal={Evolution},
- volume={47},
- pages={341\ndash 360},
-}
-
-\end{biblist}
-\end{bibsection}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex
deleted file mode 100644
index ab6265a6cec..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/cite-xb.tex
+++ /dev/null
@@ -1,143 +0,0 @@
-\documentclass{amsart}
-\usepackage{amsrefs}
-
-%\usepackage{dual} % not released yet, needs more work
-%\setlength{\dualindent}{-2em}
-
-\newenvironment{dual}{%
- \par\medskip
- \trivlist\item[]%
-}{%
- \endtrivlist
-}
-
-\newcommand{\backup}{%
- \vspace*{-\baselineskip}\vspace*{-\medskipamount}\nopagebreak
-}
-
-\newtheorem{thm}{Theorem}[section]
-
-\begin{document}
-\title{Citation tests}
-\author{Michael Downes}
-
- The following examples are derived from
- \emph{Homology manifold bordism} by Heather Johnston and Andrew
- Ranicki (Trans.\ Amer.\ Math.\ Soc.\ \textbf{352} no 11 (2000), PII: S
- 0002-9947(00)02630-1).
-
-\bigskip \noindent \rule{\columnwidth}{0.5pt}\par
-
-\setcounter{section}{3}
-\begin{dual}
-The results of Johnston \cite{Jo} on homology
-manifolds are extended here. It is not
-possible to investigate transversality by
-geometric methods---as in \cite{Jo} we employ
-bordism and surgery instead.
-\end{dual}
-
-%Kirby and Siebenmann \cite{KS} (III,\S 1),
-\begin{dual}
-The proof of transversality is indirect,
-relying heavily on surgery theory\mdash see
-Kirby and Siebenmann \cite{KS}*{III, \S 1},
-Marin \cite{M} and Quinn \cite{Q3}. We shall
-use the formulation in terms of topological
-block bundles of Rourke and Sanderson
-\cite{RS}.
-\end{dual}
-
-\begin{dual}
-$Q$ is a codimension $q$ subspace by Theorem
-4.9 of Rourke and Sanderson \cite{RS}.
-(Hughes, Taylor and Williams \cite{HTW}
-obtained a topological regular neighborhood
-theorem for arbitrary submanifolds \dots.)
-\end{dual}
-
-%Wall \cite{Wa} (Chapter 11) obtained a
-\begin{dual}
-Wall \cite{Wa}*{Chapter 11} obtained a
-codimension $q$ splitting obstruction \dots.
-\end{dual}
-
-\begin{dual}
-\dots\ following the work of Cohen \cite{Co}
-on $PL$ manifold transversality.
-\end{dual}
-
-\begin{dual}
-In this case each inverse image is
-automatically a $PL$ submanifold of
-codimension $\sigma$ (Cohen \cite{Co}), so
-there is no need to use $s$-cobordisms.
-\end{dual}
-
-%Quinn (\cite{Q2}, 1.1) proved that \dots
-\begin{dual}
-Quinn \cite{Q2}*{1.1} proved that \dots
-\end{dual}
-
-\begin{dual}\backup
-\begin{thm}[The additive structure of
- homology manifold bordism, Johnston
- \cite{Jo}]
-\dots
-\end{thm}
-\end{dual}
-
-\begin{dual}
-For $m\geq 5$ the Novikov-Wall surgery theory
-for topological manifolds gives an exact
-sequence (Wall \cite{Wa}*{Chapter 10}.
-\end{dual}
-
-\begin{dual}
-The surgery theory of topological manifolds
-was extended to homology manifolds in Quinn
-\cites{Q1,Q2} and Bryant, Ferry, Mio
-and Weinberger \cite{BFMW}.
-\end{dual}
-
-\begin{dual}
-The 4-periodic obstruction is equivalent to
-an $m$-dimensional homology manifold, by
-\cite{BFMW}.
-\end{dual}
-
-\begin{dual}
-Thus, the surgery exact sequence of
-\cite{BFMW} does not follow Wall \cite{Wa} in
-relating homology manifold structures and
-normal invariants.
-\end{dual}
-
-\begin{dual}
-\dots\ the canonical $TOP$ reduction
-(\cite{FP}) of the Spivak normal fibration of
-$M$ \dots
-\end{dual}
-
-\begin{dual}\backup
-\begin{thm}[Johnston \cite{Jo}]
-\dots
-\end{thm}
-\end{dual}
-
-\begin{dual}
-Actually \cite{Jo}*{(5.2)} is for $m\geq 7$,
-but we can improve to $m\geq 6$ by a slight
-variation of the proof as described below.
-\end{dual}
-
-\begin{dual}
-(This type of surgery on a Poincar\'e space
-is in the tradition of Lowell Jones
-\cite{Jn}.)
-\end{dual}
-
-\bibliographystyle{amsxport}
-\bibliography{jr}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf b/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf
deleted file mode 100644
index 217558e24ab..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/cite-xh.brf
+++ /dev/null
@@ -1,24 +0,0 @@
-\backcite {Jo}{{1}{4}{section.1}}
-\backcite {Jo}{{1}{4}{section.1}}
-\backcite {KS}{{1}{4}{section.1}}
-\backcite {M}{{1}{4}{section.1}}
-\backcite {Q3}{{1}{4}{section.1}}
-\backcite {RS}{{1}{4}{section.1}}
-\backcite {RS}{{1}{4}{section.1}}
-\backcite {HTW}{{1}{4}{section.1}}
-\backcite {Wa}{{1}{4}{section.1}}
-\backcite {Co}{{1}{4}{section.1}}
-\backcite {Co}{{1}{4}{section.1}}
-\backcite {Q2}{{1}{4}{section.1}}
-\backcite {Jo}{{2}{4.1}{thm.2}}
-\backcite {Wa}{{2}{4}{thm.2}}
-\backcite {Q1}{{2}{4}{thm.2}}
-\backcite {Q2}{{2}{4}{thm.2}}
-\backcite {BFMW}{{2}{4}{thm.2}}
-\backcite {BFMW}{{2}{4}{thm.2}}
-\backcite {BFMW}{{2}{4}{thm.2}}
-\backcite {Wa}{{2}{4}{thm.2}}
-\backcite {FP}{{2}{4}{thm.2}}
-\backcite {Jo}{{2}{4.2}{thm.3}}
-\backcite {Jo}{{2}{4}{thm.3}}
-\backcite {Jn}{{2}{4}{thm.3}}
diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex
deleted file mode 100644
index e6bc80cc6aa..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/cite-xh.tex
+++ /dev/null
@@ -1,154 +0,0 @@
-%&pdfelatex
-%% This is intended to be a working example of using the amsrefs
-%% backrefs option in conjunction with hyperref. It works for me using
-%% pdflatex [mjd,2002-01-03]. Cf testbib.tex in the hyperref distrib.
-%%
-%% This is pdfTeX, Version 3.14159-14h-released-20010417 (Web2C 7.3.3.1)
-%% (format=pdflatex 2001.12.21)
-%% Package: hyperref 2000/01/22 v6.69c Hypertext links for LaTeX
-
-\documentclass{article}
-\usepackage{times}
-\usepackage[colorlinks,citecolor=red,pagebackref,hypertexnames=false]{hyperref}
-\usepackage[backrefs]{amsrefs}
-
-\newenvironment{dual}{%
- \par\medskip
- \trivlist\item[]%
-}{%
- \endtrivlist
-}
-
-\newcommand{\backup}{%
- \vspace*{-\baselineskip}\vspace*{-\medskipamount}\nopagebreak
-}
-
-\newtheorem{thm}{Theorem}[section]
-
-\providecommand{\MR}{}
-
-\begin{document}
-\title{Testing amsrefs with the hyperref package}
-\author{MJD}
-\maketitle
-
- The following examples are derived from
- \emph{Homology manifold bordism} by Heather Johnston and Andrew
- Ranicki (Trans.\ Amer.\ Math.\ Soc.\ \textbf{352} no 11 (2000), PII: S
- 0002-9947(00)02630-1).
-
-\setcounter{section}{3}
-\section{Homology manifold bordism}
-
-\begin{dual}
-The results of Johnston \cite{Jo} on homology
-manifolds are extended here. It is not
-possible to investigate transversality by
-geometric methods---as in \cite{Jo} we employ
-bordism and surgery instead.
-\end{dual}
-
-%Kirby and Siebenmann \cite{KS} (III,\S 1),
-\begin{dual}
-The proof of transversality is indirect,
-relying heavily on surgery theory\mdash see
-Kirby and Siebenmann \cite{KS}*{III, \S 1},
-Marin \cite{M} and Quinn \cite{Q3}. We shall
-use the formulation in terms of topological
-block bundles of Rourke and Sanderson
-\cite{RS}.
-\end{dual}
-
-\begin{dual}
-$Q$ is a codimension $q$ subspace by Theorem
-4.9 of Rourke and Sanderson \cite{RS}.
-(Hughes, Taylor and Williams \cite{HTW}
-obtained a topological regular neighborhood
-theorem for arbitrary submanifolds \dots.)
-\end{dual}
-
-%Wall \cite{Wa} (Chapter 11) obtained a
-\begin{dual}
-Wall \cite{Wa}*{Chapter 11} obtained a
-codimension $q$ splitting obstruction \dots.
-\end{dual}
-
-\begin{dual}
-\dots\ following the work of Cohen \cite{Co}
-on $PL$ manifold transversality.
-\end{dual}
-
-\begin{dual}
-In this case each inverse image is
-automatically a $PL$ submanifold of
-codimension $\sigma$ (Cohen \cite{Co}), so
-there is no need to use $s$-cobordisms.
-\end{dual}
-
-%Quinn (\cite{Q2}, 1.1) proved that \dots
-\begin{dual}
-Quinn \cite{Q2}*{1.1} proved that \dots
-\end{dual}
-
-\begin{dual}\backup
-\begin{thm}[The additive structure of
- homology manifold bordism, Johnston
- \cite{Jo}]
-\dots
-\end{thm}
-\end{dual}
-
-\begin{dual}
-For $m\geq 5$ the Novikov-Wall surgery theory
-for topological manifolds gives an exact
-sequence (Wall \cite{Wa}*{Chapter 10}.
-\end{dual}
-
-\begin{dual}
-The surgery theory of topological manifolds
-was extended to homology manifolds in Quinn
-\cites{Q1,Q2} and Bryant, Ferry, Mio
-and Weinberger \cite{BFMW}.
-\end{dual}
-
-\begin{dual}
-The 4-periodic obstruction is equivalent to
-an $m$-dimensional homology manifold, by
-\cite{BFMW}.
-\end{dual}
-
-\begin{dual}
-Thus, the surgery exact sequence of
-\cite{BFMW} does not follow Wall \cite{Wa} in
-relating homology manifold structures and
-normal invariants.
-\end{dual}
-
-\begin{dual}
-\dots\ the canonical $TOP$ reduction
-(\cite{FP}) of the Spivak normal fibration of
-$M$ \dots
-\end{dual}
-
-\begin{dual}\backup
-\begin{thm}[Johnston \cite{Jo}]
-\dots
-\end{thm}
-\end{dual}
-
-\begin{dual}
-Actually \cite{Jo}*{(5.2)} is for $m\geq 7$,
-but we can improve to $m\geq 6$ by a slight
-variation of the proof as described below.
-\end{dual}
-
-\begin{dual}
-(This type of surgery on a Poincar\'e space
-is in the tradition of Lowell Jones
-\cite{Jn}.)
-\end{dual}
-
-\bibliographystyle{amsxport}
-\bibliography{jr}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex b/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex
deleted file mode 100644
index 15167b3b9f1..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/cite-xs.tex
+++ /dev/null
@@ -1,19 +0,0 @@
-\documentclass{amsart}
-\usepackage{amsrefs}
-
-\begin{document}
-
-\section{Introduction}
-
-A single cite \cite{MR1451594}
-and a multiple \cites{Weyl,Gould,Rob,MR95f:17013,Ser77}.
-And then with an option in the middle:
-\citelist{\cite{Rob} \cite{Gould} \cite{MR95f:17013}*{Chapter 18}}.
-
-\begin{bibsection}
-\begin{biblist}
-\bibselect{gktest}
-\end{biblist}
-\end{bibsection}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt
deleted file mode 100644
index 3422ab571fb..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/classes/00readme.txt
+++ /dev/null
@@ -1,145 +0,0 @@
-00readme.txt for AMS document classes amsart/book/proc 2.0 [2004/08/06]
-
-See manifest.txt for a list of all the files in the distribution.
-
-See install.txt for installation instructions.
-
-The document classes amsart, amsbook, amsproc and related packages are
-provided by the American Mathematical Society for authors to use with
-LaTeX. They produce the overall layout and appearance of AMS
-publications.
-
-In order to use an AMS document class you need to have TeX software
-installed first. TeX is not an AMS product. If you need information on
-getting TeX see one of the following:
-
- http://www.tug.org/
- http://www.ams.org/tex/tex-resources.html
-
-Documentation for the AMS document classes is found in
-
- instr-l.pdf
- diffs-c.txt
- amsthdoc.pdf
- thmtest.tex
- thmtest.pdf
-
-which are included in the collection. Additional documentation can be
-found in the amsclass FAQ:
-
- http://www.ams.org/tex/amsclass-faq.html
-
-The recommended procedure for making a custom document class based on an
-AMS class is to make a copy of the relevant .cls file using a different
-name and edit the copy---e.g., copy amsbook.cls to mybook.cls. (In
-general we advise against using \LoadClass, unless the base class is
-frozen or changes to the base class are under your control.)
-
-For technical support:
-
- American Mathematical Society
- Technical Support
- Publications Technical Group
- P. O. Box 6248
- Providence, RI 02940-6248
- Phone: 800-321-4AMS (321-4267) (USA/Canada) or 401-455-4080
- tech-support@ams.org
-
-========================================================================
-RECENT CHANGES
-
----ams-c1.ins 2.20 2004/08/03
-Added amsmidx package.
-
----amsclass.dtx 2.20 2004/08/06
-1. Added facility for additional line(s) in copyright block.
-2. Corrected handling of section heading with no title.
-3. Got rid of spurious "Appendix" in t-of-c in \backmatter.
-4. Changed MR number formatting to use new style as on MathSciNet.
-5. Created commands for various style elements and substituted them
- for hard-coded values to simplify building derived classes.
-6. Added sectioning and otherwise cleaned up commentary.
-
----amsclass.faq - 2004/08/06
-Removed from distribution; replaced by on-line FAQ at
-http://www.ams.org/tex/amsclass-faq.html
-
----amsdtx.dtx 2.06 2004/08/06
-1. Reworked indexing commands for compatibility with doc.sty.
-2. Added option environment for enhanced indexing.
-3. Improved formatting.
-
----amsthdoc.tex 2.20 2004/08/03
-1. Substantially rewritten for clarity.
-2. Added documentation for \newtheoremstyle.
-
----instr-l.tex 2.20 2004/08/05
-Substantially rewritten for clarity and to add instructions for new
-features; see note on amsclass.dtx regarding features.
-
----mrabbrev.bib - 2004/08/05
-Removed from distribution; this is now available separately from
-http://www.ams.org/tools/mrabbrev.bib
-
----thmtest.tex 2.01 2004/08/02
-1. Corrected counter for theorems with switched headers.
-2. Added section headings for clarity.
-3. Added example ending with a display and \qedhere.
-
----upref.dtx 2.01 2004/07/29
-1. Added code to make package work with hyperref.
-2. Improved documentation.
-
----amsclass.dtx 2.14 2004/04/26 (not released)
-1. Incorporated pending changes left by Michael Downes:
- - Added trap in headings in case \thanks was set within \author,
- and added \thanks@warning.
- - Cleaned up and completed unfinished documentation.
-2. Added braces in \uppercasenonmath to limit scope.
-3. Added \contrib mechanism to handle "non-author" authors.
-4. Segregated definitions of administrative footnotes to permit easier
- customization for AMS journals.
-5. Added explicit \bibliofont to permit easy change for special uses.
-6. Changed MR number formatting to correspond to new access numbers
- used by MathSciNet.
-7. Added \@citestyle and \citeform to simplify font changes in citations.
-8. Added OT1 defaults for \DH, \dh, \DJ, \dj, required for author names.
-9. Added \markleft to permit changing of only left running head
-
----amsclass.dtx 2.13 2002/12/04 (not released)
-1. Fixed handling of theorem head punctuation with \swapnumbers.
-2. Changed \proofname to \providecommand in case it's already defined.
-3. Made \small, \Small, etc., robust.
-4. Better spacing in \l@figure to prevent overprinting of figure number.
-5. Changed handling of author names to prevent internal line breaks.
-6. Added \@noparitemfalse in \dth@everypar to prevent weird results in
- certain (rare) kinds of usage.
-7. Some other cosmetic changes.
-
----amsthdoc.tex 2.02 2000/06/06
-Use article class instead of amsldoc (which is overkill).
-
----amsldoc.cls - 2000/06/06
-Removed from distribution, no longer needed by amsthdoc.
-
----amsclass.dtx 2.07 2000/06/05
-Guard against \\ in argument of \author.
-
----amsclass.dtx 2.06 2000/06/02
-Avoid using \@elt in qed stack because LaTeX output routine falls over
-if triggered when something else is using \@elt.
-
----amsclass.dtx 2.05 2000/05/16
-1. Added \indexintro.
-2. Fixed erroneous init for thm@preskip, thm@postskip.
-
----amsclass.dtx 2.04 2000/03/10
-\newtoks fix for old versions of LaTeX. Added some commentary about \cal.
-
----amsclass.dtx 2.03 2000/01/17
-1. Removed dependency on amsgen package.
-2. Added a warning about graphics for the draft option.
-3. Improved qedhere handling for article/amsthm combination.
-
----amsclass.dtx 2.02 2000/01/17
-Some fixes for the fleqn/qedhere case.
diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/install.txt b/Master/texmf-dist/doc/latex/amslatex/classes/install.txt
deleted file mode 100644
index 87fedfdc25c..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/classes/install.txt
+++ /dev/null
@@ -1,106 +0,0 @@
-install.txt for amscls 2.20 [2004/08/05]
-
-If you have a relatively up-do-date TeX system that complies with the
-TeX Directory Structure (TDS) standard, installing according to the
-instructions in section I below is the easiest method. See
-
- http://www.tug.org/tds/tds.pdf
-
-for details on the TDS standard. If your TeX system does not comply
-with the TDS standard, please contact the manufacturer of your TeX
-system for details on how to install third-party TeX packages.
-
-The first step is to identify the TEXMF folder that contains files used
-by LaTeX. To do this, look for the file article.cls. If you find, e.g.,
-
- /usr/local/share/texmf/tex/latex/base/article.cls
-
-then we will define TEXMF to mean /usr/local/share/texmf (everything
-up to the /tex/latex/base part). On a Windows system the file location
-will probably be something like
-
- c:\sw\texmf\tex\latex\base\article.cls
-
-Then we define TEXMF to mean c:\sw\texmf. In the following
-instructions, wherever you see "TEXMF" substitute the folder name
-determined in this way.
-
-If this terminology does not make sense to you, seek assistance from
-a friend or colleague, or from the company that you bought your TeX
-system from, or contact us at
-
- tech-support@ams.org
- 800-321-4AMS (321-4267) (USA/Canada)
- 401-455-4080
-
-========================================================================
-I. Installing the easy way.
-
-1. Download the following archive file:
-
- ftp://ftp.ams.org/pub/tex/amscls.zip
-
-2. View the following files to assess the effects of the upgrade on
-your system:
-
- 00readme.txt
- install.txt (this file)
- diffs-c.txt
-
-3. Backup the old version of AMS-LaTeX, preferably by moving it out of the
-TEXMF tree.
-
-4. Extract files fromthe .zip archive using your favorite unzip tool, setting
-the extraction target directory to the texmf root directory.
-
-5. To check the end result, you should find that you now have amsmath.sty
-in the following location
-
- TEXMF/tex/latex/amscls/amsart.cls
-
-Some TeX systems also use a database to keep track of TeX input files. If
-this database is not updated, your TeX system might not find the newly
-installed files. Consult your system's documentation to determine how
-to update this database.
-
-6. Some files will appear in both the source area and another area.
-This is because the source form and the in-use form are identical.
-As distributed, the files in the source/latex/amscls area comprise a
-complete copy of the distribution from which all the other files can
-be regenerated if need be. If you need to conserve disk space, you
-could delete the files in the source area, since they are not needed
-for normal use.
-
-========================================================================
-II. Installing the not-so-easy way.
-
-Download ftp://ftp.ams.org/pub/tex/amscls.zip.
-
-Make the following directories, if not already present:
-
- TEXMF/source/latex/amscls
- TEXMF/tex/latex/amscls
- TEXMF/doc/latex/amscls
-
-Backup your old AMS-LaTeX files if they are installed, preferably moving them
-out of the TEXMF tree.
-
-Create a temporary directory and generate documentation files (these assume
-a UNIX TeX installation):
-
- - make directory /tmp/amscls
- - unzip -d /tmp/amscls amscls.zip
- - cd /tmp/amscls
- - Run latex on the file ams-c1.ins to produce .cls and .sty files
- - Run latex on *.tex
- - [optional] Run latex on *.dtx (technical documentation)
- - move *.dvi, *.pdf, *.tex to TEXMF/doc/latex/amscls
- - [optional] move *.dtx to TEXMF/doc/latex/amscls
- - [optional] convert .dvi to .ps or .pdf
- - move *.sty and *.cls to TEXMF/tex/latex/amscls
- - delete /tmp/amscls
-
-Some TeX systems also use a database to keep track of TeX input files. If
-this database is not updated, your TeX system might not find the newly
-installed files. Consult your system's documentation to determine how to
-update this database.
diff --git a/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt
deleted file mode 100644
index 9cc4cd958e7..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/classes/manifest.txt
+++ /dev/null
@@ -1,41 +0,0 @@
-
-texmf/bibtex/bst/ams/
- amsalpha.bst
- amsplain.bst
-
-texmf/doc/latex/amscls/
- amsart.template
- amsbook.template
- amsproc.template
- amsthdoc.pdf
- diffs-c.txt
- instr-l.pdf
- thmtest.pdf
-
-texmf/source/latex/amscls/
- 00readme.txt
- ams-c1.ins
- amsalpha.bst
- amsart.template
- amsbook.template
- amsclass.dtx
- amsdtx.dtx
- amsmidx.dtx
- amsplain.bst
- amsproc.template
- amsthdoc.tex
- diffs-c.txt
- install.txt
- instr-l.tex
- manifest.txt
- thmtest.tex
- upref.dtx
-
-texmf/tex/latex/amscls/
- amsart.cls
- amsbook.cls
- amsdtx.cls
- amsmidx.sty
- amsproc.cls
- amsthm.sty
- upref.sty
diff --git a/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt b/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt
deleted file mode 100644
index 55a1c98793e..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/diffs-c.txt
+++ /dev/null
@@ -1,319 +0,0 @@
-diffs-c.txt [2004/08/06]
-
-History of changes for AMS document classes, the amsthm package, and
-other packages distributed in this collection.
-
-========================================================================
-Differences in amsthm 2.20 (August 2004)
-
----Added a fallback definition for \swappedhead@plain (used in
- amsthm.sty 1.x).
-
----For \proofname, changed from \newcommand to \providecommand in case
- it's already defined.
-
----Improved the handling of \qed when the [fleqn] option is used.
-
----Avoid using \@elt in qed stack because LaTeX output routine falls
- over if triggered when something else is using \@elt.
-
-========================================================================
-Differences in amsart/amsbook/amsproc 2.20 (August 2004)
-
----Removed dependency on amsgen package.
-
----Added warning message about graphics when draft option is used.
-
----Added a check for \ifhmode when adding punctuation, and provided
- \nopunct for omitting punctuation when not wanted.
-
----Made \small, \Small, etc., robust in case they are used in a
- \caption.
-
----Changed handling of author names to prevent line breaks within
- names.
-
----For author URLs, made ~ a printable character.
-
----amsart, amsproc: Defined \@logofont and \@copyinsfont and moved font
- instructions out of \set@logo and \@setcopyright, to simplify style
- changes in derivative classes.
-
----Added \copyins to \@reinserts so that it would be included in the
- page length calculation when a float is input on the first page
-
-!! This change may affect line breaks and page breaks.
-
----Added provision for an extra line following the copyright line with
- \@extracrline (for use in derivative classes).
-
----amsart, amsproc: Added \contrib (similar to \author) to handle names
- of persons who provided, e.g., an introduction or appendix. Usage:
- \contrib[with Appendix 1 by]{John Smith}
- \contrib[and Appendix 2 by]{Henry Moore}
- \contrib{Roger Williams}
- This will be set as part of the author block:
- ...[authors]..., with Appendix 1 by John Smith, and Appendix 2
- by Henry Moore and Roger Williams
- Contributors are ignored when generating running heads.
-
----Added \thanks@warning in case \thanks is included in \author.
-
----Added \markleft to permit easy changes to left running head only.
-
----Defined \@cleartopmattertags and moved commands to do this out of
- \maketitle.
-
----Added OT1 defaults for \DH, \dh, \DJ, \dj (ordinarily in T1 only).
-
----Added braces to limit scope of \uppercasenonmath.
-
----Segregated definition of administrative footnotes (\@adminfootnotes)
- to permit easier customization for derivative document styles.
-
----amsart: When subsection has no title, made number bold.
-
----Fixed the handling of theorem head punctuation when \swapnumbers is
- used. Used \thm@headsep instead of \labelsep for theorem heads.
-
----Provided \@citestyle and \citeform to simplify change of font used
- in citation.
-
----Provided \bibliofont to allow author to make change.
-
----Provided \@bibtitlestyle, \@defaultbiblabelstyle and
- \@indextitlestyle to simplify style changes.
-
----Changed output format of \MR to recognize change in format of
- MathSciNet reference numbers; output is now all lightface instead
- of having a bold volume number.
-
-!! This change will result in a change of appearance.
-
----Reset \chaptername with \backmatter to avoid spurious "Appendix" in
- t-of-c.
-
----Added \indexintro to allow a block of text at the top of an index.
-
----Made index ragged right and suppressed hyphenation.
-
----Added \seeonly = "see" to get around unfortunate use of \see for
- "see also"; added \seealso (from makeindex) for compatibility with
- material originally set with a LaTeX document class.
-
-========================================================================
-Differences in upref 2.0 (July 2004)
-
----Package will now work with hyperref, regardless of package input
- order.
-
-========================================================================
-========================================================================
-Differences in amsthm 2.0 (November 1999)
-
----Allow line breaks in theorem headings (added \deferred@thm@head and
- related code).
-
----Make \end{proof} force end of paragraph so following text is
- indented (oversight in version 1.2).
-
-!! This change may affect line breaks and page breaks.
-
----Added \qedhere command for flush-right QED symbol in displayed
- equations.
-
----Added amsthdoc.tex documentation file (taken from amsldoc.tex).
-
----Merged amsthm.dtx into amsclass.dtx.
-
-========================================================================
-Differences in amsart/amsbook/amsproc 2.0 (November 1999)
-
----Corrected erroneous default style for labelenumi (should be parens
- instead of period); increase list left margins slightly.
-
-!! To revert to former style: \renewcommand{\labelenumi}{\theenumi.}
-
----amsart: For "swapped" theorem heads (numbers shifted to the left
- margin) the number font was changed to lightface to match subsection
- numbers. This is an AMS journal style requirement---old behavior was
- incorrect.
-
-!! This change may affect line breaks and page breaks.
-
----Overfull \vbox messages for every other page: increased headheight
-
----Added openany option for amsbook
-
----Moved erroneously placed \endgroup in \curraddr, \email and \urladdr
-
----Added a year option to \subjclass (default to 1991 for backward
- compatibility).
-
----For \cleardoublepage, use \pagestyle{empty} for blank pages.
-
----Empty argument of \thanks: do nothing instead of printing an empty
- footnote.
-
----Clear up contradictory font size commands for abstract; always
- \Small,
-
----Omit final punctuation for \section{} head containing only a number.
-
----Added \contentsnamefont to make changes easier.
-
----Read a .cfg file.
-
----Changed \parindent\z@ to \@parboxrestore in \@serieslogo to avoid
- side effects depending on context of pagebreaks.
-
----Use \protect instead of \@nx in \@secmark.
-
----Moved \thispagestyle{firstpage} closer to beginning of \maketitle to
- assure that the logo will be set on the first page if long abstract
- breaks to second page (for derivative classes that don't box the
- abstract).
-
----Added support for paragraph, subparagraph.
-
----In \partrunhead, added \ignorespaces, \unskip.
-
----In \@starttoc, set \parskip to zero.
-
----In \indexchap, rearranged commands to fix vertical spacing for
- title; wrong \baselineskip was being used, resulting in title 6pt
- too low.
-
----Footnote failure in minipage: Changed \@makefnmark so that it
- doesn't use math mode.
-
----Added figure* and table* environments
-
----Revised \@cflci to do the right thing with drop folio at the end of
- a two-column page.
-
----Incorporate amsthm package by direct embedding instead of
- \RequirePackage.
-
----Added missing default definition for \MRhref.
-
----Use \MakeTextUppercase if available to handle latin-1 characters in
- author names.
-
----amsbook: Print keywords and date info on title-page obverse if
- given.
-
----Added various features for AMS in-house use: \dateposted, e-only
- option, \Mc, etc.
-
-========================================================================
-Differences in amsart/amsbook/amsproc 1.2 (January 1995)
-
----Documentation
-
-The documentation for the AMS documentclasses, formerly contained in
-amslatex.tex, is now found in instr-l.tex in the amslatex/classes area.
-This is a copy of the file instr-l.tex that is found in the author-info
-area of e-math.ams.org. That area contains additional information
-pertaining specifically to the submission of LaTeX or AmS-TeX documents
-to AMS publications.
-
----New documentclass "amsproc".
-
-A document class amsproc has been added for books that consist of a
-collection of articles, such as the proceedings of a conference.
-
----Different placement of "abstract" environment.
-
-The abstract should now be entered *before* the \maketitle command.
-This provides maximum control over the position and vertical spacing
-when printing the abstract information at different places, as required
-by different AMS publications---for example, in some publications the
-abstract may be required to fall between certain other elements in the
-beginning section of a document, or it may be postponed to the end of
-the document, or it might even be omitted entirely. If an abstract is
-entered after \maketitle, it will still be printed, but with a warning
-(and possibly in the wrong place or with wrong spacing).
-
----Treatment of the @ character.
-
-As the AMS document classes automatically load the amsmath package, all
-changes for amsmath 1.2 affect the AMS classes also. Note in particular
-that the @ character is no longer a special command prefix, so to
-produce a printed @ in an e-mail address you should now write simply
-@ instead of @@.
-
----The nonbreaking dash commands @-, @--, @--- are no longer available
-because @ as a special command prefix has disappeared. An alternative
-\nobreakdash command is provided in the amsmath package.
-
----Added "nomath" option.
-
-The AMS document classes now take an option nomath that suppresses
-the automatic loading of the amsmath package. This is sometimes helpful
-in converting a pre-existing document to AMS style if you only want to
-do a quick conversion without attempting to deal with any of the math.
-
----Theorem handling.
-
-Theorem setup is now handled by the amsthm package instead of the
-"theorem" package. \theorembodyfont, \theoremheaderfont, etc are not
-used any more. See amsldoc.tex and thmtest.tex for details.
-
----The old environments pf, pf* are superseded by a single proof
-environment. It takes an optional argument to specify an alternative
-heading text.
-
-If you are converting an older document to run with \documentclass
-instead of \documentstyle, here is how you could provide
-backward-compatible definitions for pf and pf*:
-
- \newenvironment{pf}{\proof[\proofname]}{\endproof}
- \newenvironment{pf*}[1]{\proof[#1]}{\endproof}
-
----\small now produces 9pt text; \tiny now produces 6pt text
-
-Formerly \small produced the same typesize as \footnotesize (8pt). Now
-they produce different sizes, normally 9 and 8 respectively. Also the
-range of typesize-changing commands is filled out to include, below
-\normalsize, the following: \small, \Small, \SMALL, \tiny, \Tiny.
-\footnotesize and \scriptsize are retained as synonyms of \Small and
-\SMALL respectively. As it stands \tiny no longer produces the same
-typesize as it did before (now 6 instead of 5), except in compatibility
-mode. This might affect some existing documents if they are updated to
-use \documentclass instead of \documentstyle. Similarly, \large now
-produces 11pt if the base size is 10pt, where formerly it produced
-12pt.
-
-New commands \larger and \smaller are provided for changing the
-typesize relative to the current size. These commands take an optional
-integer argument to specify how many steps to go up or down: \larger[2]
-means go up two sizes, and \larger without an optional argument is the
-same as \larger[1]. The list of sizes is a standard progression of
-type sizes and associated linespacing values as defined by the
-documentclass. If you need finer control over type size or linespacing,
-consult the LaTeX documentation about the \fontsize command.
-
----Extra documentclass options 8pt, 9pt, 11pt, 12pt
-
----The \qed symbol is now an open square
-
-The \qed symbol is no longer a filled black square, but an open square,
-and it is positioned at the right margin, instead of at a fixed
-horizontal distance from the preceding text. If the \qed command is
-used inside a displayed equation, however, it will be placed at a fixed
-distance from the preceding material (correct placement in this case is
-limited by some technical difficulties).
-
----The command \rom was renamed to \upn.
-
-The command \rom, for making numbers and punctuation roman/upright in
-italic text, has been renamed \upn ``upright punctuation or number''.
-It will in most cases suffice to leave this refinement undone until a
-document is sent to a publisher for final typesetting, and furthermore,
-certain publications at the AMS now use special in-house italic fonts
-that have upright numbers and punctuation built in, making the use of
-\upn unnecessary even then. For general preprint-type use, this
-refinement is one that most users probably won't care to bother with.
-
-========================================================================
diff --git a/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt b/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt
deleted file mode 100644
index 0bfa0ff69d4..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/diffs-m.txt
+++ /dev/null
@@ -1,552 +0,0 @@
-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; see
-http://ctan.tug.org/info/compan-rev/ch8.pdf).
-
----New documentclass amsproc
-
-A new documentclass amsproc was added for collections of articles, such as
-the proceedings of a conference.
diff --git a/Master/texmf-dist/doc/latex/amslatex/exercise.thm b/Master/texmf-dist/doc/latex/amslatex/exercise.thm
deleted file mode 100644
index 93929b3beb0..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/exercise.thm
+++ /dev/null
@@ -1,8 +0,0 @@
-%% LaTeX2e file `exercise.thm'
-%% generated by the `filecontents' environment
-%% from source `thmtest' on 2005/02/14.
-%%
-\def\th@exercise{%
- \normalfont % body font
- \thm@headpunct{:}%
-}
diff --git a/Master/texmf-dist/doc/latex/amslatex/gktest.ltb b/Master/texmf-dist/doc/latex/amslatex/gktest.ltb
deleted file mode 100644
index 4236749372b..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/gktest.ltb
+++ /dev/null
@@ -1,440 +0,0 @@
-\documentclass{amsbook}
-\usepackage{amsrefs}
-\providecommand{\cyr}{}
-\providecommand{\cprime}{\textprime}
-\providecommand{\germ}{\mathfrak }
-
-\begin{document}
-\begin{bibdiv}
-\begin{biblist}
-
-\bib{MR58:27738}{book}{
- author={Andrews, G.~E.},
- title={The theory of partitions},
- publisher={Encyclopedia of Mathematics and its Applications, Vol. 2,
- Addison-Wesley, Mass.-London-Amsterdam},
- date={1976},
-}
-
-\bib{MR90b:82001}{book}{
- author={Baxter, R.~J.},
- title={Exactly solved models in statistical mechanics},
- publisher={Academic Press Inc.},
- address={London},
- date={1989},
- ISBN={0-12-083182-1},
-}
-
-\bib{MR1451594}{article}{
- author={Benkart, G.},
- author={Kang, S.-J.},
- author={Melville, D.},
- title={Quantized enveloping algebras for Borcherds superalgebras},
- date={1998},
- ISSN={0002-9947},
- journal={Trans. Amer. Math. Soc.},
- volume={350},
- number={8},
- pages={3297\ndash 3319},
-}
-
-\bib{MR95d:17023}{article}{
- author={Benkart, G.},
- author={Kang, S.-J.},
- author={Misra, K.~C.},
- title={Indefinite Kac-Moody algebras of classical type},
- date={1994},
- ISSN={0001-8708},
- journal={Adv. Math.},
- volume={105},
- number={1},
- pages={76\ndash 110},
-}
-
-\bib{MR93d:17017}{article}{
- author={Chari, V.},
- author={Pressley, A.},
- title={Quantum affine algebras},
- date={1991},
- ISSN={0010-3616},
- journal={Comm. Math. Phys.},
- volume={142},
- number={2},
- pages={261\ndash 283},
-}
-
-\bib{MR26:2519}{book}{
- author={Curtis, Charles~W.},
- author={Reiner, Irving},
- title={Representation theory of finite groups and associative algebras},
- publisher={Interscience Publishers, a division of John Wiley \& Sons, New
- York-London},
- date={1962},
- review={\MR{26 \#2519}},
-}
-
-\bib{Dr86}{incollection}{
- author={Drinfel$'$d, V.~G.},
- title={Quantum Groups},
- date={1987},
-conference={
- title={Proceedings of the International Congress of Mathematicians},
- address={Berkeley},
- date={1986}
-},
- publisher={American Mathematical Society, Providence},
- pages={798\ndash 820},
-}
-
-\bib{MR94d:17032}{article}{
- author={Feingold, A.~J.},
- author={Frenkel, I.~B.},
- author={Ries, J.~F.~X.},
- title={Representations of hyperbolic Kac-Moody algebras},
- date={1993},
- ISSN={0021-8693},
- journal={J. Algebra},
- volume={156},
- number={2},
- pages={433\ndash 453},
-}
-
-\bib{MR84f:17004}{article}{
- author={Frenkel, I.~B.},
- author={Kac, V.~G.},
- title={Basic representations of affine Lie algebras and dual resonance
- models},
- date={1981},
- ISSN={0020-9910},
- journal={Invent. Math.},
- volume={62},
- number={1},
- pages={23\ndash 66},
-}
-
-\bib{Gould}{article}{
- author={Gould, M.~D.},
- author={Zhang, R.~B.},
- author={Bracken, A.~J.},
- title={Quantum double construction for graded Hopf algebras},
- date={1993},
- journal={Bull. Austral. Math. Soc.},
- volume={47},
- pages={353\ndash 375},
-}
-
-\bib{MR1633090}{article}{
- author={Hong, J.},
- author={Kang, S.-J.},
- author={Miwa, T.},
- author={Weston, R.},
- title={Mixing of ground states in vertex models},
- date={1998},
- ISSN={0305-4470},
- journal={J. Phys. A},
- volume={31},
- number={28},
- pages={L515\ndash L525},
-}
-
-\bib{Jac1}{book}{
- author={Jacobson, N.},
- title={Basic algebra II},
- publisher={W. H. Freeman and Company},
- address={San Francisco},
- date={1980},
- ISBN={0-7167-1079-X (v. 2)},
-}
-
-\bib{MR98k:17037}{article}{
- author={Jeong, K.},
- author={Kang, S.-J.},
- author={Lee, H.},
- title={Lie-admissible algebras and Kac-Moody algebras},
- date={1997},
- ISSN={0021-8693},
- journal={J. Algebra},
- volume={197},
- number={2},
- pages={492\ndash 505},
-}
-
-\bib{Joseph}{book}{
- author={Joseph, A.},
- title={Quantum groups and their primitive ideals},
- publisher={Springer-Verlag},
- address={Berlin},
- date={1995},
- ISBN={3-540-57057-8},
-}
-
-\bib{Kac90}{book}{
- author={Kac, V.~G.},
- title={Infinite dimensional Lie algebras},
- edition={3},
- publisher={Cambridge University Press},
- address={Cambridge},
- date={1990},
- ISBN={0-521-37215-1; 0-521-46693-8},
-}
-
-\bib{KMW}{incollection}{
- author={Kac, V.~G.},
- author={Moody, R.~V.},
- author={Wakimoto, M.},
- title={On ${E}\sb {10}$},
- date={1988},
-conference={
- title={Differential geometrical methods in theoretical physics},
- address={Como},
- date={1987}
-},
- publisher={Kluwer Acad. Publ.},
- address={Dordrecht},
- pages={109\ndash 128},
-}
-
-\bib{Ka93-1}{article}{
- author={Kang, S.-J.},
- title={Root multiplicities of the hyperbolic Kac-Moody Lie algebra
- $HA\sp{(1)}\sb 1$},
- date={1993},
- ISSN={0021-8693},
- journal={J. Algebra},
- volume={160},
- number={2},
- pages={492\ndash 523},
-}
-
-\bib{MR94d:17033}{article}{
- author={Kang, S.-J.},
- title={On the hyperbolic Kac-Moody Lie algebra $HA\sb 1\sp
- {(1)}$},
- date={1994},
- ISSN={0002-9947},
- journal={Trans. Amer. Math. Soc.},
- volume={341},
- number={2},
- pages={623\ndash 638},
-}
-
-\bib{MR97e:17041}{incollection}{
- author={Kang, S.-J.},
- title={Root multiplicities of graded Lie algebras},
- date={1996},
-conference={
- title={Lie algebras and their representations},
- address={Seoul},
- date={1995},
-},
- publisher={Amer. Math. Soc.},
- address={Providence, RI},
- pages={161\ndash 176},
-}
-
-\bib{MR1641035}{article}{
- author={Kang, S.-J.},
- author={Kashiwara, M.},
- title={Quantized affine algebras and crystals with core},
- date={1998},
- ISSN={0010-3616},
- journal={Comm. Math. Phys.},
- volume={195},
- number={3},
- pages={725\ndash 740},
-}
-
-\bib{MR93g:17027}{article}{
- author={Kang, S.-J.},
- author={Kashiwara, M.},
- author={Misra, K.~C.},
- author={Miwa, T.},
- author={Nakashima, T.},
- author={Nakayashiki, A.},
- title={Vertex models and crystals},
- date={1992},
- ISSN={0764-4442},
- journal={C. R. Acad. Sci. Paris S\'er. I Math.},
- volume={315},
- number={4},
- pages={375\ndash 380},
-}
-
-\bib{MR1464137}{article}{
- author={Kang, S.-J.},
- author={Kim, M.-H.},
- title={Borcherds superalgebras and a monstrous Lie superalgebra},
- date={1997},
- ISSN={0025-5831},
- journal={Math. Ann.},
- volume={307},
- number={4},
- pages={677\ndash 694},
-}
-
-\bib{MR95f:17013}{article}{
- author={Kang, S.-J.},
- author={Misra, K.~C.},
- title={Crystal bases and tensor product decompositions of $U\sb q(G\sb
- 2)$-modules},
- date={1994},
- ISSN={0021-8693},
- journal={J. Algebra},
- volume={163},
- number={3},
- pages={675\ndash 691},
-}
-
-\bib{Kash90}{article}{
- author={Kashiwara, M.},
- title={Crystalizing the $q$-analogue of universal enveloping algebras},
- date={1990},
- journal={Comm. Math. Phys.},
- volume={133},
- pages={249\ndash 260},
-}
-
-\bib{Keng82}{book}{
- author={Keng, H.~L.},
- title={Introduction to number theory},
- publisher={Springer-Verlag},
- date={1982},
-}
-
-\bib{Wang}{article}{
- author={Li, W.~L.},
- title={Classification of generalized Cartan matrices of hyperbolic
- type},
- date={1988},
- journal={Chinese Ann. Math. Ser. B},
- volume={9},
- number={1},
- pages={68\ndash 77},
-}
-
-\bib{MR98a:20041}{incollection}{
- author={Littelmann, P.},
- title={An effective method to classify nilpotent orbits},
- date={1996},
-conference={
- title={Algorithms in algebraic geometry and applications},
- address={Santander},
- year={1994}
-},
- publisher={Birkh\"auser},
- address={Basel},
- pages={255\ndash 269},
-}
-
-\bib{MR2000d:17019}{article}{
- author={Littelmann, P.},
- title={Bases canoniques et applications},
- date={1998},
- ISSN={0303-1179},
- journal={Ast\'erisque},
- number={252},
- pages={Exp.\ No.\ 847, 5, 287\ndash 306},
- note={S\'eminaire Bourbaki. Vol.\ 1997/98},
-}
-
-\bib{MR92d:16032}{article}{
- author={Littelmann, P.},
- author={Procesi, C.},
- title={On the Poincar\'e series of the invariants of binary forms},
- date={1990},
- ISSN={0021-8693},
- journal={J. Algebra},
- volume={133},
- number={2},
- pages={490\ndash 499},
-}
-
-\bib{MR92g:20067}{incollection}{
- author={Littelmann, Peter},
- title={Good filtrations, decomposition rules and standard monomial
- theory},
- date={1991},
-conference={
- title={Computational aspects of Lie group representations and
- related topics},
- address={Amsterdam},
- date={1990}
-},
- publisher={Math. Centrum Centrum Wisk. Inform.},
- address={Amsterdam},
- pages={89\ndash 106},
-}
-
-\bib{MR92b:14027}{incollection}{
- author={Littelmann, Peter},
- author={Procesi, Claudio},
- title={Equivariant cohomology of wonderful compactifications},
- date={1990},
-conference={
- title={Operator algebras, unitary representations, enveloping
- algebras, and invariant theory},
- address={Paris},
- date={1989}
-},
- publisher={Birkh\"auser Boston},
- address={Boston, MA},
- pages={219\ndash 262},
-}
-
-\bib{MR94m:17016}{book}{
- author={Lusztig, G.},
- title={Introduction to quantum groups},
- publisher={Birkh\"auser Boston Inc.},
- address={Boston, MA},
- date={1993},
- ISBN={0-8176-3712-5},
-}
-
-\bib{Nak96}{article}{
- author={Nakayashiki, A.},
- title={Fusion of the $q$-vertex operators and its applications
- to solvable vertex models},
- date={1996},
- ISSN={0010-3616},
- journal={Commun. Math. Phys.},
- volume={177},
- number={2},
- pages={27\ndash 62},
-}
-
-\bib{Rob}{article}{
- author={Robinson, D.},
- title={On representations of the symmetric group},
- date={1938},
- journal={Amer. J. Math.},
- volume={60},
- pages={745\ndash 760},
-}
-
-\bib{Ser77}{book}{
- author={Serre, J.-P.},
- title={Linear representations of finite groups},
- publisher={Springer-Verlag},
- date={1977},
-}
-
-\bib{Weyl}{book}{
- author={Weyl, H.},
- title={Classical groups},
- edition={2},
- publisher={Princeton University Press},
- date={1946},
-}
-
-\bib{Young4}{article}{
- author={Young, A.},
- title={On quantitative substitutional analysis IV},
- date={1929},
- journal={Proc. Lond. Math. Soc. (2)},
- volume={31},
- pages={253\ndash 272},
-}
-
-\end{biblist}
-\end{bibdiv}
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/install.txt b/Master/texmf-dist/doc/latex/amslatex/install.txt
deleted file mode 100644
index e03f5411a1e..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/install.txt
+++ /dev/null
@@ -1,69 +0,0 @@
-install.txt for amsrefs 2.0 [2004-06-30]
-
-Preliminary note: The normal destination directory for amsrefs.sty in a
-standard TDS structure would be texmf/tex/latex/amscls (see step 3
-below). In the future, the amsrefs package will be integrated more
-thoroughly into the amscls distribution, but the current release has to
-be provided in the form of a separate distribution for those who already
-have the amscls distrib but not amsrefs.
-
-------------------------------------------------------------------------
-The first step is to identify the primary location for LaTeX input files
-on your system. Typical examples are
-
- /usr/local/share/texmf/tex/latex... (Unix)
-
- C:\SWP30\TCITeX\TeX\LaTeX... (Windows)
-
-We define "ROOT" to mean everything preceding the "/tex/latex" part. In
-the second example, this would be "C:\SWP30\TCITeX". ROOT will normally
-end in "texmf"; if it doesn't you may need to consult the documentation
-for your TeX system to find out what to use. In the following
-instructions, wherever you see ROOT substitute the actual directory or
-folder name that is used on your system.
-
-If this terminology doesn't make sense to you, seek assistance from
-a friend or colleague, or from the company that you bought your TeX
-system from, or contact us at
-
- tech-support@ams.org
- 800-321-4AMS (321-4267) (USA/Canada)
- 401-455-4080
-
-If you have multiple texmf trees (as discussed, for example, in the
-teTeX documentation), you may want to install amsrefs using the
-TEXMFLOCAL tree as the value of ROOT. In due course when you upgrade to
-a newer TeX system, we expect that you will find amsrefs already
-incorporated into the TEXMFMAIN tree as part of the tex/latex/amscls
-area, at which point you will no longer need the copy in your TEXMFLOCAL
-tree.
-
-------------------------------------------------------------------------
-1. Download the following archive file:
-
- ftp://ftp.ams.org/pub/tex/amsrefs.zip
-
-2. Extract files using the texmf root directory as the destination. Some
-typical examples:
-
-WinZip: Click on "Extract" and then in the "Extract to" box, enter
- c:\sw\texmf (or whatever ROOT is on your system)
-
-unzip: unzip amsrefs.zip -d ROOT
-
-3. Please note that although the source files for amsrefs unpack into
-the ROOT/source/latex/amsrefs area at the present time [2001-12-28], the
-other files unpack into .../latex/amscls because that is the natural
-location for them.
-
-To check the end result, you should find that you now have amsrefs.sty
-in the following location (substituting \ or : for / if appropriate):
-
- ROOT/tex/latex/amscls/amsrefs.sty
-
-If you have a teTeX system you may need to rerun mktexlsr [known in
-earlier versions of teTeX as "texhash"].
-
-For a MikTeX system the command would be "initexmf -u", or look for
-"Refresh the Filename Database" in the MikTeX menus (this may be
-somewhat version-dependent).
diff --git a/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf b/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf
deleted file mode 100644
index 76fabaa0e54..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/instr-l.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/instr-l.tex b/Master/texmf-dist/doc/latex/amslatex/instr-l.tex
deleted file mode 100644
index 30aa283237b..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/instr-l.tex
+++ /dev/null
@@ -1,1233 +0,0 @@
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "instr-l.tex",
-%%% version = "2.20",
-%%% date = "2004/08/06",
-%%% time = "16:17:21 EDT",
-%%% checksum = "60855 1233 6587 50183",
-%%% author = "American Mathematical Society",
-%%% copyright = "Copyright 1994, 2004 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,
-%%% Publications Technical Group,
-%%% 201 Charles Street,
-%%% Providence, RI 02904,
-%%% 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, AMS, amslatex, ams-latex, author instructions",
-%%% supported = "yes",
-%%% abstract = "These are instructions for preparing documents for
-%%% submission to the AMS, using amsmath and AMS LaTeX
-%%% document classes.",
-%%% 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)
-[1995/06/01]% LaTeX date must be June 1995 or later
-\documentclass{amsart}
-
-\hyphenation{man-u-script man-u-scripts over-view pre-par-ing which-ever}
-
-%% Define macros for text substitution and for presentation of examples
-\newcommand{\AMS}{American Mathematical Society}
-\def\latex/{{\protect\LaTeX}}
-\def\latexe/{{\protect\LaTeXe}}
-\def\amslatex/{{\protect\AmS-\protect\LaTeX}}
-\def\tex/{{\protect\TeX}}
-\def\amstex/{{\protect\AmS-\protect\TeX}}
-\def\bibtex/{{Bib\protect\TeX}}
-\def\makeindx/{\textit{MakeIndex}}
-
-\newcommand{\filnam}[1]{\mbox{\texttt{\ignorespaces#1\unskip}}}
-\let\fn=\filnam
-\let\cls=\filnam
-\let\env=\filnam
-\let\pkg=\filnam
-\def\opt#1{\filnam{[#1]}}
-
-%% For this manual, add a section number to the references header, and
-%% include that section header in the contents list.
-\makeatletter
-\def\thebibliography#1{\section\refname
- \normalfont\small\labelsep .5em\relax
- \list{\@arabic\c@enumiv.}{\settowidth\labelwidth{#1.}%
- \leftmargin\labelwidth \advance\leftmargin\labelsep
- \usecounter{enumiv}}%
- \sloppy \clubpenalty4000\relax \widowpenalty\clubpenalty
- \sfcode`\.\@m}
-%
-%% Turn off series logo and copyright note
-\let\serieslogo@\relax
-\let\@setcopyright\relax
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Table of contents customizations
-
-\let\tocori=\tableofcontents
-\def\tableofcontents{\tocori
- \skip@\lastskip \vskip-\lastskip
- \addtocontents{toc}{\protect\tocpatch}%
- \vskip\skip@ \relax}
-
-\def\tocsection#1#2#3{%
- \indentlabel{\@ifnotempty{#2}{\tocnbox{\hss#1 #2.\quad}}}#3}
-\let\tocnbox=\hbox
-\def\tocpatch{%
- \@xp\let\csname r@tocindent2\@xp\endcsname\csname r@tocindent1\endcsname
- \def\tocnbox{\hbox to\@tempdima}}
-%% In this document, subsections are unnumbered, but we want an indent
-%% to be used.
-\def\tocsubsection#1#2#3{\hbox to\leftskip{}#3}
-\def\l@subsection{\@tocline{2}{0pt}{.5pc}{}{}}
-\makeatother
-
-\newdimen\exindent
-\exindent=3\parindent
-%% Add a high penalty to discourage line breaks within an example
-%% without absolutely prohibiting them.
-{\obeylines
- \gdef^^M{\par\penalty9999 }%
- \gdef\beginexample#1{\medskip\bgroup %
- \def\(##1){\makebox[0pt]{\normalfont\mdseries##1}}%
- \def~{\char`\~}\def\\{\char`\\}%
- \normalfont\ttfamily\frenchspacing %
- \parindent=0pt#1\leftskip=\exindent\obeylines}
-}% end \obeylines
-\def\endexample{\endgraf\egroup\medskip}
-\newdimen\exboxwidth
-\exboxwidth=3in
-\def\exbox#1#2{\noindent \hangindent=\exboxwidth
- \makebox[0pt][r]{\null\normalfont\mdseries#1\unskip\enspace}%
- \makebox[\exboxwidth][l]{\normalfont\ttfamily\ignorespaces#2}%
- \normalfont\mdseries\ignorespaces}
-
-\newcommand\cn[1]{\mbox{\def\\{\char`\\}%
- \normalfont\ttfamily\\\ignorespaces#1\unskip}}
-\let\ttcs=\cn
-\newcommand\ttcsb[2]{%
- \mbox{\def\\{\char`\\}%
- \normalfont\ttfamily
- \\begin\{\ignorespaces#1\unskip\}\ignorespaces#2\unskip}}
-\newcommand\ttcse[1]{\mbox{\def\\{\char`\\}%
- \normalfont\ttfamily\\end\{\ignorespaces#1\unskip\}}}
-\def\{{\char`\{\relax}
-\def\}{\char`\}\relax}
-
-%% Provide a meta-command facility; provide an alternate escape
-%% character so it can be used within the verbatim environment.
-
-\catcode`\|=0
-\begingroup \catcode`\>=13 % in LaTeX2e verbatim env makes > active
-\gdef\?#1>{{\normalfont$\langle$\textup{#1}$\rangle$}}
-\gdef\0{\relax}
-\endgroup
-\def\<#1>{{\normalfont$\langle$\textup{#1}$\rangle$}}
-\newcommand{\Dimen}{\<dimen>}
-\newcommand{\tab}{\textsc{tab}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%% Provide a dummy titlepage, saving maketitle for the article title.
-%% Table of contents goes onto the inside front cover.
-
-\def\instrversion{2.20}
-\def\instrdate{August 2004}
-
-\begin{document}
-
-\thispagestyle{empty}
-\vspace*{1.5in}
-\begin{center}
- {\huge\bfseries Instructions\\[2pt] for Preparation\\[2pt]
- of Papers\\[2pt] and Monographs
- \par\vspace{\baselineskip}
- \amslatex/
- \par}
- \vspace{3\baselineskip}
- \Large
- Version \instrversion\\[4pt] \instrdate
-\end{center}
-\newpage
-
-\thispagestyle{empty}
-\tableofcontents
-\newpage
-
-\setcounter{page}{1}
-
-\title [ELECTRONIC MANUSCRIPTS: \amslatex/]
- {Instructions for Preparation\\
- of Papers and Monographs: \amslatex/}
-\dedicatory{%
- \mbox{\normalfont\mdseries\small Version \instrversion: \instrdate}}
-
-\maketitle
-
-\section{Introduction}
-
-This manual is directed mainly to authors preparing material for
-publication by the AMS, using \amslatex/ document classes. As such,
-it deals with the AMS publishing style. Since these document classes
-are also used by authors who are not submitting items to the AMS,
-the manual also covers topics of more general relevance. However, it
-assumes familiarity with standard \latex/ techniques and conventions,
-and contains only material specific to AMS packages.
-
-Links to information useful in preparing manuscripts and graphics
-can be found on the AMS Author Resource Center web page \cite{ARC}\@.
-That information supplements this manual, and we recommend that you
-review it.
-
-The AMS produces three major types of publications: journals (both
-print and electronic), proceedings volumes, and monographs. There
-is a core AMS document class for each: \cls{amsart}, \cls{amsproc}
-and \cls{amsbook}, respectively. For most journals or book series,
-there is a specific author package, based on one of the core classes.
-If the specific publication is known, the appropriate author package
-should be obtained from the AMS web server \cite{AP} and used for
-preparation of manuscripts. In addition, there is a separate package
-for editors of proceedings volumes \cite{EP}, with facilities for
-preparing material that does not fit into the normal ``article''
-category.
-
-If the specific publication is not known, an appropriate generic AMS
-document class can be used:
-
-\begin{itemize}
-\item \pkg{gen-j-l} for journal articles (based on \pkg{amsart})
-\item \pkg{gen-p-l} for articles in book proceedings (based on \pkg{amsproc})
-\item \pkg{gen-m-l} for monographs (based on \pkg{amsbook})
-\end{itemize}
-
-The tagging of elements in a manuscript---title, author(s), section
-headings, theorems, etc.--- is consistent through all author packages.
-Thus a manuscript prepared using the appropriate generic document
-class can be modified trivially to use the specific package, simply by
-updating the \cn{documentclass} statement. For example, to specify
-the \textit{Contemporary Mathematics} proceedings series:
-\begin{verbatim}
-\documentclass{conm-p-l}
-\end{verbatim}
-
-Each author package contains an electronic version of this manual,
-class files, sample documents, and a \texttt{README} file that
-contains information about each of the files in the package.
-
-When an AMS author package is used, both \latex/ and a recent version
-of \amslatex/ must be installed on the computer being used for
-manuscript preparation. The AMS Author Resource Center web page
-\cite{ARC} has a link to download the most recent version of
-\amslatex/. The version number appears at the top of the file
-\pkg{amsmath.sty} (and other files in the collection), and is also
-reported in the log file of a \latex/ run; make sure you have
-version 2.0 or later.
-
-\section{Article preparation}
-
-We first address articles intended for journals and proceedings.
-Monographs are addressed in a separate section (see
-page~\pageref{s:mono}).
-
-\subsection*{Starting a new article}\label{ss:newamsart}
-%%
-Individual articles generally have the following structure:
-\begin{itemize}
-\item \verb+\documentclass{...}+
-\item preamble (for document-specific customizations)
-\item \verb+\begin{document}+
-\item top matter information
-\item \verb+\maketitle+ (to set the top matter)
-\item article body
-\item reference list
-\item \verb+\end{document}+
-\end{itemize}
-A detailed template file (included in each package) provides
-a complete set of commands for the article top matter, and the
-instructions for using them. The most efficient way to start a
-new article is to make a copy of the template and fill it in.
-
-
-\section{The preamble}
-
-The area between the \verb+\documentclass+ statement and the line
-\verb+\begin{document}+ is referred to as the ``preamble''. This is
-the place to load external packages and define document-specific
-commands.
-
-Available \cn{documentclass} options are described in the file
-\filnam{amsclass.dtx}. Process this file with \latex/ to obtain a
-version with human-readable documentation. One option does need to
-be mentioned here: \opt{psamsfonts}; include this option as
-\begin{verbatim}
-\documentclass[psamsfonts]{...}
-\end{verbatim}
-to ensure correct sizing of fonts in environments other than normal text.
-
-\subsection*{Packages}
-%%
-The AMS document classes incorporate the code for the AMS theorem
-(\pkg{amsthm}) package and automatically load the \pkg{amsmath}
-package. It is not necessary to request either one explicitly.
-The user guides for these packages \cite{ATP,AMP} contain the details,
-which will not be repeated here. The \pkg{amsfonts} package is loaded
-as well, unless the \opt{noamsfonts} option is specified; see the
-AMSFonts User's Guide \cite{AFG} for the features provided.
-
-Not all publicly available packages are compatible with the AMS
-document classes. For this reason, we mention some that are:
-\begin{itemize}
-\item \pkg{amssymb} provides names for additional symbols from the
- AMS symbol fonts; see \cite{AFG} for details.
-\item \pkg{amsmidx} supports multiple indexes for a book; see
- page~\pageref{ss:indexing}.
-\item \pkg{graphicx} is part of the \latex/ suite, preferred for
- inclusion of graphics.
-\item \pkg{longtable} facilitates tables longer than one page.
-\item \pkg{upref} forces cross-references with \cn{ref} to roman;
- see ``Roman type'', page~\pageref{ss:roman}.
-\item \pkg{xypic} is recommended for creating commutative diagrams.
-\end{itemize}
-
-There are several packages that cause particular problems for AMS
-production. Their use should be avoided if possible:
-\begin{itemize}
-\item \pkg{psfrag}, for applying labels externally to included graphics,
- may result in a PostScript that can't be converted properly to PDF.
-\item \pkg{epsfig} has been superseded by \pkg{graphicx}.
-\end{itemize}
-
-Don't load any packages that aren't actually needed.
-
-
-\subsection*{New commands}
-%%
-Place all definitions for new commands in the preamble. This includes
-instructions to access fonts that are not already defined in the AMS
-document classes or \pkg{amsmath}, such as a new math alphabet (see
-\cite{AMP}).
-
-Always use \cn{newcommand}; this will let you know if the name you
-have chosen has already been used. Do not redefine any command from
-\latex/, \pkg{amsmath}, or any AMS document class, as this could cause
-problems in AMS production. New definitions may be used to provide
-shorthand forms for mathematical expressions that are used frequently,
-but do not use new definitions for text; for articles posted on-line,
-this will prevent indexing software from identifying relevant
-references.
-
-Use commands and environments provided by the AMS document classes
-and standard packages whenever applicable---for example, you should
-use the AMS \env{proof} environment rather than define your own
-alternative.
-
-When the file is complete, remove any commands that haven't been used.
-
-
-\section{Top matter}\label{s:topmatter}
-
-The top matter associated with an article includes information that
-would appear in a bibliographic reference to the paper, plus additional
-information about the author(s), subject classifications, key words,
-acknowledgments of support, and the abstract.
-
-
-\subsection*{Summary of tags and elements}
-%%
-Table 1 lists the top matter commands provided by \amslatex/
-version 2.0 and later. Not every tag is necessary for each paper.
-The table shows which tags are necessary and which are optional.
-Requirements for monographs are somewhat different and are described
-later. The template file included in every author package contains
-all the necessary tags and instructions for using them.
-
-\begin{table}[ht]
-\caption{Top matter tags}
-\begin{minipage}{\textwidth}
-\begin{verbatim}
-\documentclass{amsart}
-|?preamble commands, such as |ttcs|bgroup|0newcommand|egroup, etc.>
-
-\begin{document}
-\end{verbatim}
-\begin{center}
-\begin{tabular}{lcc}
-\ & \multicolumn{2}{c}{Required by}\\
-\ & Journals & Books \\
-\verb+\title[...]{...}+ & yes\rlap{${}^1$} & yes\rlap{${}^1$} \\
-
-\verb+\author[...]{...}+ & yes\rlap{${}^1$} & yes\rlap{${}^1$} \\
-\verb+\contrib[...]{...}+ & no\rlap{${}^2$} & --- \\
-\verb+\address{...}+ & yes & yes \\
-\verb+\curraddr{...}+ & no & no \\
-\verb+\email{...}+ & no & no \\
-\verb+\urladdr{...}+ & no & no \\
-\verb+\dedicatory{...}+ & no & no \\
-\verb+\date{...}+ & ---\rlap{${}^3$} & --- \\
-\verb+\thanks{...}+ & no & no \\
-\verb+\translator{...}+ & ---\rlap{${}^3$} & ---\rlap{${}^3$} \\
-\verb+\keywords{...}+ & no & no \\
-\verb+\subjclass[2000]{...}+ & yes & yes \\
-\verb+\begin{abstract}...\end{abstract}+ & yes\rlap{${}^4$} & no \\
-\verb+\maketitle+ & yes & yes \\
-\end{tabular}
-\end{center}
-\vspace*{1pc}
-
-{\Small
-${}^1$ If no short form is needed, omit the brackets.
-
-${}^2$ For contributors, see details on page~\pageref{ss:contrib}.
-
-${}^3$ If this is necessary, it will be filled in by the AMS staff.
-
-${}^4$ For the \textit{Journal of the American Mathematical Society},
-abstracts are optional.
-\par
-}
-\end{minipage}
-\vspace{.25\baselineskip}
-\hrule width \textwidth
-\vspace{.5\baselineskip}
-\end{table}
-
-\subsection*{Title}
-%%
-For AMS journal articles, capitalize only the first word and proper
-nouns in the title. For articles in an AMS proceedings volume,
-capitalize the first and last words of the title and all nouns,
-pronouns, adjectives, adverbs, and verbs. Articles, conjunctions, and
-prepositions should be lowercased unless they are the first or last
-word of the title. These rules should be followed even if the
-publication in which the article appears has another style. The style
-for the particular publication will be generated automatically when
-the article is processed at the AMS.
-
-A multiline title may be left for \latex/ to break, or a desired break
-may be indicated by \cn{\\}.
-
-Unless the title is very short, provide a form of the title suitable
-for use in running heads. This should be entered in brackets between the
-tag \cn{title} and the full title:
-\verb+\title[+short title\verb+]{+full title\verb+}+.
-Do not use author-defined macros in the title.
-
-\subsection*{Author information}\label{ss:authorinfo}
-%%
-Enter the name(s) of the author(s) with the tag \cn{author}, using
-standard capitalization for proper names. Use a separate \cn{author}
-command for each author. Names will be combined by \latex/ according
-to the dictates of the document class. See also ``contributors'',
-below.
-
-If the author name(s) cannot fit in the space available for the running
-head, enter a shortened form for each name in [brackets]
-between the tag \cn{author} and the full name. Acceptable shortened
-forms use initials for all but the surname(s). For example,
-\begin{verbatim}
-\author[J. Smith]{Joseph Smith}
-\end{verbatim}
-If the list of shortened author names is still too long for the running
-head (including a reasonable space for the page number), it can be
-shortened as in the following example, as a last resort:
-\begin{trivlist}
-\item\relax
-\verb+\markleft{J. SMITH ET AL.}+
-\end{trivlist}
-
-\noindent
-Note that \cn{markleft} is available only for \amslatex/ versions 2.20
-and later; it is not a basic \latex/ command.
-Data provided with \cn{markleft\{\}} \emph{must} be in all capital letters
-(except for included math). Place \cn{markleft\{\}} before the first
-\cn{author} in your file.
-
-For each author you should provide one or more addresses. Tag them
-as follows, grouping them in this order by author:
-\begin{verbatim}
-\address{...} |rm address where the research was carried out |tt
-\curraddr{...} |rm current address, if different from the research address |tt
-\email{...} |rm address for electronic mail |tt
-\urladdr{...} |rm URL address (optional)
-\end{verbatim}
-Do \emph{not} include any addresses within the scope of an
-\cn{author\{\}} command (this is different from basic \latex/).
-Do not use abbreviations in addresses.
-
-The main address should be divided by \cn{\\} into segments that
-correspond to address lines for use on an envelope. When typeset, the
-lines will be strung together separated by commas, but the division by
-\cn{\\} will be useful to a person preparing an envelope to return
-proofs.
-
-Addresses are considered part of the top matter, but in AMS articles
-they are ordinarily printed at the end of the article following the
-bibliography (this is different from basic \latex/). Suitable labels
-will indicate the current, e-mail, and URL addresses, typically
-\textit{Current address}:, \textit{E-mail address}:, \textit{URL}:,
-respectively.
-
-If \texttt{\textasciitilde} is needed in a URL address, enter it
-directly as \texttt{\textasciitilde} if you are using \amslatex/
-version 2.20 or later; otherwise, see the Author FAQ \cite{AF}
-for instructions.
-
-\subsection*{Contributors
- {\mdseries (new with version 2.20)}}\label{ss:contrib}
-%%
-Contributors are much like authors, but are responsible for only
-a portion of an article, e.g., an appendix or auxiliary tables.
-The bracketed portion is not optional; it gives the exact text that
-will be printed to indicate the nature of the contribution:
-\begin{verbatim}
-\contrib[with an appendix by]{William Rogers}
-\end{verbatim}
-Multiple contributors and contributions are input like this:
-\begin{verbatim}
-\contrib[with Appendix A by]{William Rogers}
-\contrib[]{Henry Taylor}
-\contrib[and Appendix B by]{John Henderson}
-\end{verbatim}
-Note the empty brackets on the second line. Multiple contributors
-indicated in this way will be combined and ``andified'' appropriately.
-Contributors will not be included in running heads. Addresses provided
-for contributors will be treated the same as for regular authors.
-
-\subsection*{Dedication}
-%%
-Use the tag \cn{dedicatory} for such things as ``Dedicated to
-Professor X on the occasion of his eightieth birthday.'' If the
-dedication is longer than one line, you may indicate a break with
-\cn{\\}.
-
-\subsection*{Acknowledgments of support and other first-page footnotes}
-%%
-Use the command \cn{thanks} to acknowledge grants and other kinds of
-support or for other general information not covered by one of the
-more specific commands such as \cn{keywords} or \cn{subjclass}. Enter
-\cn{thanks} immediately following the address(es) for the relevant
-author, \emph{not} within the scope of the \cn{author\{\}} command
-(this is different from basic \latex/). Like \cn{address}, \cn{thanks}
-can appear more than once in the top matter. Each occurrence will be
-printed as an unnumbered footnote at the bottom of the first page of
-the article.
-
-\subsection*{Subject information}
-%%
-Subject classifications and key words, like acknowledg-\linebreak ments, are
-part of the top matter and appear as unnumbered footnotes at the bottom of
-the first page.
-
-Subject classifications may be primary (the major topic(s) of the
-paper) or secondary (subject areas covered by ancillary results,
-motivation or origin of problems discussed, intended or potential
-field of application, or other significant aspects worthy of notice).
-At least one primary subject classification is \textbf{required}.
-Additional primaries and secondaries are optional.
-
-\begin{samepage}
-These classifications are entered as
-\begin{verbatim}
-\subjclass[2000]{Primary |?primary class>; Secondary |?secondary classes>}
-\end{verbatim}
-(Omitting \texttt{[2000]} will cause the 1991 Subject Classification
-to be cited.)
-\end{samepage}
-
-To determine the classifications, use the 2000 Mathematics Subject
-Classification scheme that appears in annual indexes of \textit{Mathematical
-Reviews} beginning in 1999. It can also be accessed on the Web at URL:
-\texttt{http://www.ams.org/msc/} or obtained in printed form from
-Customer Services.
-Please use the full number; the two-digit code from the Contents of
-\textit{Mathematical Reviews} is \textbf{not} sufficient.
-
-Key words are not required but may be provided by an author if desired.
-They should be tagged as \cn{keywords\{...\}}.
-
-\subsection*{Abstract}
-%%
-With an AMS document class, place the abstract before \cn{maketitle},
-contrary to the practice with the basic \latex/ document classes.
-This is necessary to ensure that the abstract can always be printed in
-the proper location and style. If the abstract is given after
-\cn{maketitle}, it will be printed in place and generate a warning
-message.
-
-Input the abstract text between \verb+\begin{abstract}...\end{abstract}+.
-It may comprise multiple paragraphs and include displayed material if
-appropriate. The length of the abstract depends primarily on the
-length of the paper itself and on the difficulty of summarizing the
-material. An upper limit of about 150 words for short papers and 300
-words for long papers is suggested. Do not use author-defined macros
-or \cn{ref} in the abstract.
-
-
-\section{Document body (all document classes)}
-
-\subsection*{Linking for the Web}
-%%
-All AMS primary journals are posted on-line. Electronic
-manuscripts prepared in \latex/ for any AMS journal should be tagged
-for maximum linking on the Web. For use of \cn{label}, \cn{ref},
-and \cn{cite}, see \cite{LC}; for \cn{eqref}, see \cite{AMP}.
-
-\subsection*{Headings}
-%%
-Four levels of headings are provided to permit logical sectioning of
-a manuscript. These headings are applicable to individual articles
-and to chapters of a monograph. (Headings specific to monographs are
-listed under \textit{Monograph formatting}.)
-
-\begin{verbatim}
-\specialsection{...}
-\section[...]{...}
-\subsection[...]{...}
-\subsubsection[...]{...}
-\end{verbatim}
-
-\cn{specialsection} is for long articles that need extra divisions
-(e.g., parts) at a level above the \cn{section} level.
-
-Explicit line breaks are obtained by \verb+\\+ in first-level section
-headings.
-
-Any heading may be given a label to allow references to be made to it,
-by including a \cn{label\{...\}} command with a unique identifier
-directly \emph{after} the heading. References are made using the
-command \cn{ref\{...\}} and the same identifier. For example,
-\begin{verbatim}
-\section{Monograph formatting}
-\label{s:mono}
-\end{verbatim}
-will establish a label for this section that can be referred to with
-\cn{ref\{s:mono\}}. Cross references of
-this sort will require \latex/ to be run at least twice for proper
-resolution. A warning at the end of the \latex/ run, ``Cross
-references may have changed\dots\unskip'', should be heeded in this regard.
-
-
-\subsection*{Mathematical text}
-%%
-For instructions on preparing mathematical text, refer to
-\cite{AMP} and \cite{ML}. See also ``Roman type'', below.
-
-\subsection*{Lists}
-%%
-Follow usual \latex/ conventions for producing list environments.
-
-\subsection*{Theorems, lemmas, and other proclamations}
-%%
-See the manual \textit{Using the \pkg{amsthm} package} \cite{ATP}
-for details. Theorem environments following AMS style with respect to
-punctuation, spacing and paragraphing are defined in the AMS document
-classes. This is incompatible with the \latex/ \pkg{theorem} package,
-which cannot be used with the AMS document classes.
-
-Three different theorem styles are provided by AMS document classes:
-\cls{plain}, \cls{definition}, and \cls{remark}. By referring to these
-styles and using the \cn{newtheorem} command, you can build a
-complement of theorem environments appropriate for any paper or
-monograph. All \cn{newtheorem} specifications should be included in
-the preamble; a starter set is included in the template for every
-AMS author package.
-
-Theorem support is also available separately in the \pkg{amsthm} package
-for users of document classes other than those from the AMS.
-
-\subsection*{Equations}
-%%
-Check displayed equations carefully, making sure they are broken and
-aligned following the guidelines in \cite[pp. 44--48]{MIT}.
-
-\subsection*{Roman type}\label{ss:roman}
-%%
-Numbers, punctuation, (parentheses), [brackets],
-$\lbrace$braces$\rbrace$, and symbols used as labels should always be
-set in roman type. This is true even within the statement of a theorem,
-which is ordinarily set in italic type.
-
-Be careful to distinguish between roman elements that are mathematical
-in nature (e.g., ``a group of class 2''), and those that are part of
-the text (e.g., a label or a year). Mathematical expressions, no matter
-how short or insignificant, should be coded as math, by enclosing them
-within dollar signs \verb+$...$+ or \verb+\(...\)+. Roman text elements
-should be coded as \cn{textup\{...\}} in potentially nonroman
-environments such as theorems.
-
-Abbreviated forms of mathematical terms are also usually set in roman
-type to distinguish them from mathematical variables or constants.
-Use the control sequences for common mathematical functions and
-operators like \verb+log+ and \verb+lim+; use \cn{DeclareMathOperator}
-to add additional operator names (see \cite[\S5]{AMP}).
-
-The style of reference citations, though publication-dependent, is
-usually roman. To ensure consistency and support linking for the Web,
-\textbf{always} use the standard \latex/ \cn{cite} command when citing
-a reference. Internal references with the \cn{ref} command are not
-automatically roman in non-roman environments, but can be forced by
-using the \pkg{upref} package (part of the \amslatex/ collection).
-
-\subsection*{Exercises}
-%%
-Exercises are produced using the \env{xca} and \env{xcb} environments.
-\env{xca} may be used in any publication, but must be defined in
-the document preamble with \cn{theoremstyle\{definition\}} and the
-\cn{newtheorem} command; it is used for exercises that occur within a
-section. \env{xcb} is defined only for monographs and is used for
-exercises that occur at the end of a chapter.
-
-\subsection*{Indexing facilities}
-\label{ss:indexing}
-%%
-The tags needed for \makeindx/ are already included in AMS document
-classes. Do not include the \pkg{makeidx} package, but do put the
-command \cn{makeindex} in the preamble to launch a single index.
-See \cite[chapter 11]{LC} and \cite[chapter 11]{GL} for use of
-\makeindx/.
-
-A package for multiple indexes, \pkg{amsmidx}, is included in the
-\amslatex/ collection beginning with version 2.20. Unlike other
-multiple-index packages, \pkg{amsmidx} is compatible with the AMS
-document classes. To use this package, put these commands into the
-preamble:
-\begin{verbatim}
-\usepackage{amsmidx}
-\makeindex{|?name of first index file>}
-\makeindex{|?name of second index file>}
-\end{verbatim}
-To identify index entries in the text:
-\begin{verbatim}
-\index{|?name of index file>}{|?index term>}
-\end{verbatim}
-In the backmatter, where the indexes are to appear:
-\begin{verbatim}
-\Printindex{|?name of first index file>}{|?title of first index>}
-\Printindex{|?name of second index file>}{|?title of second index>}
-\end{verbatim}
-Note the capitalization of the \cn{Printindex} command.
-
-\section{Floating objects: Figures and tables}
-
-Figures and tables are usually handled as floating inserts. Such
-items are often so large that fitting them into the document at the
-point of reference may cause problems with pagination. Placing such
-items into a floating insert allows them to be repositioned
-automatically by \latex/ as required for good pagination.
-
-A floating insert generally contains one of these possibilities:
-\begin{itemize}
-\item \latex/ code that produces an object such as a table or
- commutative diagram;
-\item a command to incorporate an item produced by another application
- (most often an Encapsulated PostScript (EPS) file produced by a
- graphics utility; see \textit{Electronic graphics},
- page~\pageref{ss:electronicgraphics}).
-\end{itemize}
-
-If a figure is described by \latex/ code (e.g., using \pkg{xypic} or
-the \env{picture} environment), it should be included directly in the
-file.
-
-\subsection*{Placement}
-%%
-Floats should
-\begin{enumerate}
-\item be numbered consistently throughout the paper (figures and tables
- are numbered separately),
-\item be placed at the top or bottom of the page,
-\item have an in-text reference, and
-\item definitely appear within the same section as their first text
- reference.
-\end{enumerate}
-
-A figure or table should not precede its first text reference unless
-they both appear on the same page spread. When a figure or table is
-an integral part of text, it may appear unnumbered in place in the
-middle of text.
-
-Figures and tables should be allowed to float according to the \latex/
-defaults preset by the document class. If you are submitting a file
-that will be processed at the AMS (this applies to all journal
-articles), you could introduce major problems with pagination if you
-hard-set your figures and tables by using the \verb+[h!]+ option.
-Production problems will be avoided when you use the appropriate
-author package class file and avoid using figure or table options.
-For electronic manuscripts, the final placement of inserts will be
-determined by the AMS editorial staff, on the basis of the most
-appropriate page layout.
-
-\subsection*{Captions}
-%%
-Captions for floating inserts are usually positioned above a table and
-below a figure. The following is the general structure used to specify
-a figure insert, with a caption at the bottom:
-\begin{verbatim}
-\begin{figure}
-\includegraphics{|?file name of |tt.eps|rm| file>}|quad|rm or|tt|quad|?code for the insertion>
-\caption{|?caption text>}
-\label{|?reference label>}|quad|rm (optional)|tt
-\end{figure}
-\end{verbatim}
-
-This is the general structure for a table insert, with a caption at
-the top:
-\begin{verbatim}
-\begin{table}
-\caption{|?caption text>}
-\label{|?reference label>}|quad|rm (optional)|tt
-|?code for the insertion body>
-\end{table}
-\end{verbatim}
-
-Caption headings (e.g., ``\textsc{Table 3.1.}''\ or
-``\textsc{Figure 7.}'')\ will be supplied automatically. The
-\<caption text> is any appropriate descriptive text, and may be
-omitted if no descriptive text is desired. (The style of the caption
-differs from the basic \latex/ caption style.) A reference label
-should usually be associated with the caption, and must be given
-\emph{after} the caption. A reference in text to the figure or table
-has the form \cn{ref\{\<reference label>\}}.
-
-\latex/ packages for captions may appear to work with the AMS document
-classes, but the caption style doesn't usually match the AMS style.
-
-\subsection*{Electronic graphics}\label{ss:electronicgraphics}
-%%
-Graphics created by applications other than \latex/ may be submitted
-to the AMS in an electronic format. This includes output from
-graphics applications as well as scanned photographs or other
-computer-generated images. The AMS requires such graphics in
-Encapsulated PostScript (EPS) format.
-
-Use the \pkg{graphicx} package (part of the \pkg{graphics} bundle
-of \latex/) to embed references to EPS graphics directly in a \latex/
-file; see the manual, \filnam{grfguide.tex} \cite{GB}. Another
-valuable reference is the manual ``Using EPS Graphics in \latexe/
-Documents'' \cite{EG}.
-
-Other packages are not recommended, as there are numerous areas of
-incompatibility which may result in the need for manual intervention,
-delaying processing and increasing the cost.
-
-The EPS files will not be physically included in the \latex/ file.
-You must submit a separate file for each graphic along with the \latex/
-document. No matter what method is used to produce a graphic, it is
-necessary to provide a paper copy to the AMS for verification. Double
-check to make sure the electronic and paper versions are the same.
-
-\subsection*{Compatibility requirements for graphics}
-There are two important requirements that must be observed when
-embedding graphics.
-
-\emph{Omit path names} for the included files. Instead of
-\begin{verbatim}
-\includegraphics*{/usr/joe/book/figures/fig1.ps}
-\end{verbatim}
-use just the name of the file:
-\begin{verbatim}
-\includegraphics*{fig1.ps}
-\end{verbatim}
-The easiest way to do this is to place the graphics files in the
-same directory as the file(s) being {\TeX}ed.
-
-Do not use the \cn{graphicspath\{\<directory list>\}} command to
-establish a path. This will result in the path being included in
-the DVI file, which will be impossible to process at the AMS\@.
-It may be possible to specify a path using one of the environments
-recognized by the {\TeX} engine (\fn{TEXINPUTS}, for example);
-instructions for setting these environments should be in the
-documentation for your system.
-
-Graphics commands must be compatible with the \textit{dvips} output
-driver. This is particularly important if you are submitting a DVI
-file for a camera-ready publication. The method is specific to the
-graphics package you are using; a typical method is to use a file
-\filnam{graphics.cfg} containing the line \cn{ExecuteOptions\{dvips\}}
-when you run \latex/ to create the DVI or PostScript file to send to
-the AMS.
-
-\subsection*{Technical requirements for graphics}
-%%
-If you scale a figure before submitting it, remember that line weights
-also scale. The lightest line weight that will reproduce clearly at
-high resolution is 0.5pt after scaling. Do \emph{not} specify
-``hairline'' weight, as this will be nearly invisible at high
-resolution and will disappear in the printing process. If a rule line
-is screened, its weight should be no less than 1 point \emph{after}
-scaling.
-
-Graded line weights should increase in increments of at least 0.5pt.
-Increments less than this are insufficiently distinguishable at high
-resolution.
-
-Screened fills should be screened not less than 15\% (less will print
-as white) and not greater than 85\% (greater will print as black).
-
-Ideally, text included in graphics files should be font outlines
-rather than bitmaps, because the AMS typesets its publications on a
-high-resolution imagesetter, not a laser printer. Text or lines in
-graphics which are 300dpi bitmaps (which look fine in the
-laser-printed output of your article) may appear poor in quality next
-to the high-resolution text of AMS publications. If bitmaps of
-characters are part of bitmapped line art files, output will be
-satisfactory if the bitmapped characters are at 1200dpi.
-
-\subsection*{Color graphics}
-%%
-AMS publications are ordinarily printed in black and white.
-Use of color requires explicit permission from the AMS.
-
-Color figures should have the resolution of at least 266 pixels per
-inch when printed at 100\%, and must also be suitable for printing
-as grayscale. The files must be in EPS format
-
-
-\section{Bibliographic references}
-%%
-\subsection*{Using \protect\bibtex/ to prepare a bibliography}%
-An author may find it convenient to maintain a file of references in
-\bibtex/ form, as described in \textit{The \latex/ Companion}
-\cite[Section 13.2]{LC}. Two \bibtex/ styles are provided:
-
-\begingroup
-\exindent=2\parindent
-\beginexample{\exboxwidth=1.05in}
-\exbox{}{amsplain.bst} will produce numeric labels; preferred for articles;
-\exbox{}{amsalpha.bst} will produce labels constructed from the %
- author name(s)\newline and year of publication.
-\endexample
-\endgroup
-
-\noindent
-Both will translate references in a \bibtex/ input (\filnam{.bib})
-file to \latex/ input in a \filnam{.bbl} file in the form appropriate
-for AMS publications, including all necessary formatting instructions.
-This method of preparing bibliographies is therefore recommended.
-
-To access a \bibtex/ bibliography in a paper or monograph, include these
-instructions in the appropriate place in the input file:
-\begin{verbatim}
-\bibliographystyle{|?style>}|qquad|rm(|tt|0amsplain |rm or|tt amsalpha|rm)|tt
-\bibliography{|?name of bibliography |bgroup|tt.bib|egroup| file>}
-\end{verbatim}
-
-Running \bibtex/ on the \filnam{.bib} file will produce a \filnam{.bbl}
-file. The \filnam{.bib} file may have any name the author finds convenient;
-however, the \filnam{.bbl} file must have the same name as the source file
-for a monograph from which it is input, so it may be necessary for the
-author to rename it. For an article, after the bibliography has been
-completed (including processing by \bibtex/), the contents of the
-\filnam{.bbl} file should be inserted into the main article input file,
-replacing the \cn{bibliographystyle} and \cn{bibliography} statements.
-
-Items in the bibliography are usually ordered alphabetically by author.
-\bibtex/ processing may alter this order, especially if the
-\filnam{amsalpha} style is used.
-
-All categories of bibliographic entries listed in
-\cite[Table 13.1]{LC} are supported in the two AMS \bibtex/ styles.
-In addition to the fields listed in Table 13.1, a \verb+language+
-field is provided for use in identifying the original language of an
-item whose title has been translated.
-
-The \pkg{harvard} package (available from CTAN) provides an
-author-year style that is compatible with the AMS document classes.
-This should ordinarily be used only for monographs on historical
-topics.
-
-Standard abbreviations for periodicals should be obtained from
-\cite{ASMR}\@.
-
-\subsection*{Preparing a bibliography without \protect\bibtex/}
-%%
-The references section of a paper is contained between the commands
-\begin{verbatim}
-\begin{thebibliography}{|?model label>}
-\end{thebibliography}
-\end{verbatim}
-This environment is resolved as an unnumbered section in an article
-or an unnumbered chapter in a monograph, following AMS publication
-specifications. The indentation for the labels is set to an
-appropriate width using the model given with the \cn{begin} command.
-Thus the widest label in the bibliography should be used as the model;
-for example, \verb+99+ will provide space for a 2-digit numeric label.
-
-For the proper order of reference elements and use of fonts and
-punctuation, look at an issue or volume in the journal or book series
-for which your document is intended and follow the examples you see
-there. More examples are given in \cite{MIT}.
-
-\subsubsection*{Reference input}
-%%
-Begin each item with the command \cn{bibitem\{\<bibitem label>\}}.
-The \latex/ default is to number references automatically; however,
-other labels may be used by inserting an optional key argument in
-square brackets between the command and the internal label:
-\begin{verbatim}
-\bibitem[ABC]{Arno1994}
-\end{verbatim}
-The item label and the key need not be identical. Whatever appears
-within the \verb+[ ]+ is what prints; whatever is within the curly
-braces is used for linking and must not include any math or special
-characters.
-
-Give at least one full name; initials and last name is an acceptable
-form. If a subsequent reference is by the same author(s), use
-\cn{bysame} instead of the name(s).
-
-For examples, refer to \cite{MIT}.
-
-
-\section{Monograph formatting}\label{s:mono}
-
-A monograph is a long work by a single author or co-authors on a
-single subject. Each chapter should be prepared as a separate file,
-as should the bibliography. In addition, a ``driver'' file should be
-used to input all the others. These files should be given meaningful
-names, so that when they are transmitted to the AMS, there will be no
-question about which file represents which chapter. For example, a
-monograph by author Grey might be composed of files named
-\filnam{grey.tex} (the driver file), \filnam{grey-ch1.tex},
-\filnam{grey-ch2.tex}, \dots, \filnam{grey-ch12.tex},
-\filnam{grey-appa.tex}, etc., and \filnam{grey-bib.tex}.
-If the author name is a common one, please include something to make
-it unique, such as first initials.
-
-Information that identifies the author(s), the subject matter of the
-monograph, acknowledgments of support, and so forth, will appear in the
-front matter of the book. Place this information in the driver file,
-and use the tags shown below. Most of these are the same as the tags
-associated with the top matter of an article; see the \textit{Top
-matter} section (page~\pageref{s:topmatter}) for explanations and an
-indication of which tags are required.
-
-\subsection*{Starting a new monograph}\label{s:newamsbook}
-%%
-The driver file for a monograph is generally made up of the following:
-\begin{itemize}
-\item \verb+\documentclass{...}+
-\item preamble (where extra definitions might go)
-\item \verb+\begin{document}+
-\item \verb+\frontmatter+
-\item title page and copyright page information
-\item \verb+\maketitle+ (to set the title page and copyright page; see note)
-\item \verb+\include+ files (e.g., preface, introduction)
-\item \verb+\mainmatter+
-\item \verb+\include+ files (e.g., main chapters, appendices)
-\item \verb+\backmatter+
-\item commands for bibliography, index
-\item \verb+\end{document}+
-\end{itemize}
-
-\noindent
-Note: The title and copyright pages are for information only, so that
-a printed copy can be associated with the correct author(s). The final
-copy will be prepared at the AMS.
-
-For a typical driver file, see the template for \cls{amsbook}, included
-in the \amslatex/ collection.
-
-Instructions for preparing a dedication page are given in the AMS
-Author FAQ \cite{AF}.
-
-The table of contents will be produced automatically from a
-\filnam{.toc} file produced anew in each run of \latex/. Since there is
-no \filnam{.toc} before the first run, the body of the table of contents
-will be empty on the first run. It is AMS style to include only
-first-level heads, chapter titles, and part titles in the table of
-contents.
-
-Chapters in AMS book series start on right-hand (odd-numbered) pages.
-Blank pages will be provided as necessary at the end of earlier material
-to accomplish this.
-
-
-\subsection*{Chapter titles}
-%%
-Chapter titles should be capitalized as follows: the first and last
-words of the title and all nouns, pronouns, adjectives, adverbs, and
-verbs should be capitalized. Articles, conjunctions, and prepositions
-should be lowercased unless they are the first or last word of the title.
-
-There are three common variations of the chapter title. The form with
-a chapter number is most common:
-\begin{verbatim}
-\chapter{Matrix Algebras}
-\end{verbatim}
-
-The second variation is an appendix, where the word ``Appendix''
-replaces the word ``Chapter''. Use the command \cn{appendix} before
-the first \cn{chapter} command in a sequence of appendix chapters.
-\begin{verbatim}
-\appendix
-\chapter{Poisson Integral}
-\end{verbatim}
-In addition to ``Appendix'', the counter will produce letters ``A'',
-``B'', ``C'', etc.,\ instead of numbers.
-
-The third variation is used for an element such as a preface or
-introduction, which has no pretitle text at all. For this, use the
-\cn{chapter*} command:
-\begin{verbatim}
-\chapter*{Preface}
-\end{verbatim}
-Unlike the \latex/ \cls{book} class, the AMS document classes will
-place entries for unnumbered chapters in the table of contents, as
-required by AMS style.
-
-\subsection*{Monograph running heads}
-%%
-The chapter title is used for the left running head and section
-headings for the right running head. The chapter title repeats if
-there are no sections. If the text of a section heading is too long
-to fit as a running head, use the square-bracket option to specify a
-shortened form for use in the running heads:
-
-\begin{verbatim}
-\section[Fourier coefficients of periodic functions]
- {Fourier coefficients of continuous periodic functions
- of bounded entropy norm}
-\end{verbatim}
-
-If the chapter title is too long to fit as a running head, a shortened
-form can be supplied in a similar way. Full chapter titles and section
-headings will be used in the table of contents (this is different from
-basic \latex/).
-
-\subsection*{Numbering of figures and tables}
-%%
-The preferred AMS style for numbering figures and tables is to start
-numbering from 1 within each chapter, and to include both the chapter
-and element number in the printed caption heading. For example, the
-first figure in Chapter 5 would be numbered ``\textsc{Figure} 5.1''.
-The \cls{amsbook} document class resets figure and table numbers
-automatically, but does not include the chapter number in the printed
-caption. To add the chapter number, place these lines in the preamble
-of the driver file:
-\begin{verbatim}
-\numberwithin{figure}{chapter}
-\numberwithin{table}{chapter}
-\end{verbatim}
-
-
-\section{Getting help}
-
-Many questions raised by authors are answered in the AMS Author FAQ
-\cite{AF}. Please check that before asking for assistance.
-
-If you encounter difficulties in preparing or submitting your
-manuscript in electronic form after it has been accepted for
-publication by the appropriate editorial board, you can ask for help
-from the \AMS\ at:
-
-\penalty-100
-\begin{samepage}
-\beginexample{\normalfont\mdseries}
-Technical Support
-Publications Technical Group
-201 Charles Street
-Providence, RI 02904-2294
-\vspace{3pt}
-Phone: 800-321-4267, ext.\ 4080 \quad or \quad 401-455-4080
-E-mail: {\texttt{tech-support@ams.org}}
-\endexample
-\end{samepage}
-
-\noindent
-Please supply the name of the journal or book series, the editor's
-name if the manuscript is for a proceedings volume, and a concise
-explanation of the problem.
-
-
-\begin{thebibliography}{[ASMR]}
-
-\bibitem[AF]{AF} AMS Author FAQ,
-\texttt{http://www.ams.org/authors/author-faq.html}
-
-\bibitem[AFG]{AFG} \textit{AMSFonts{} version~\textup{2.2d} user's guide},
-Amer. Math. Soc., Providence, RI, 2002.
-PDF file linked from \texttt{http://www.ams.org/tex/amsfonts.html}
-
-\bibitem[AMP]{AMP} \textit{User's guide for the \pkg{amsmath} package
-\textup{(}version~\textup{2.0)}}, Amer. Math. Soc., Providence, RI, 2004.
-PDF file linked from \texttt{http://www.ams.org/tex/amslatex.html}
-
-\bibitem[AP]{AP} Author packages for publishing with the AMS,\\
-\texttt{http://www.ams.org/tex/author-info.html}
-
-\bibitem[ARC]{ARC} AMS Author Resource Center,
-\texttt{http://www.ams.org/authors/}
-
-\bibitem[ASMR]{ASMR} \textit{Abbreviations of names of serials reviewed in
-Mathematical Reviews}, Amer. Math. Soc., Providence, RI,
-revised annually; searchable on-line at\\
-\texttt{http://www.ams.org/msnhtml/serials-list/annser\_frames.html}.
-
-\bibitem[ATP]{ATP} \textit{Using the \pkg{amsthm} package,
-version~\textup{2.0}}, Amer. Math. Soc., Providence, RI, 2004.\\
-PDF file linked from \texttt{http://www.ams.org/tex/amslatex.html}
-
-\bibitem[EG]{EG} Keith Reckdahl, ``Using EPS graphics in \latexe/
-documents'', available in electronic form as \texttt{info/epslatex.ps}
-or \filnam{.pdf} from\newline
-\texttt{http://www.ctan.org/tex-archive/}
-
-\bibitem[EP]{EP} Guide to AMS editor's package,
-\texttt{http://www.ams.org/authors/editpkg.html}
-
-\bibitem[GB]{GB} David Carlisle, ``Packages in the `graphics' bundle'',
-available in electronic form as
-\filnam{macros/latex/required/graphics/grfguide.tex} or \filnam{.ps}
-from\\ \texttt{http://www.ctan.org/tex-archive/}
-
-\bibitem[GL]{GL} Helmut Kopka and Patrick Daly, \textit{A Guide to
- \latex/}, 4th ed., Addison-Wesley, Reading, MA, 2004.
-
-\bibitem[HBW]{HBW} Nicholas J. Higham, \textit{Handbook of Writing for
-the Mathematical Sciences}, 2nd ed., SIAM, Philadelphia, PA, 1998.
-
-\bibitem[HWM]{HWM}
-Norman E. Steenrod, Paul R. Halmos, Menahem M. Schiffer, and Jean A.
-Dieudonn\'e, \textit{How to Write Mathematics}, 5th printing 1995,
-Amer. Math. Soc., Providence, RI, 1973.
-
-\bibitem[Joy]{Joy} M. D. Spivak, \textit{The Joy of \tex/},
-2nd revised ed., Amer. Math. Soc., Providence, RI, 1990.
-
-\bibitem[LC]{LC} Frank Mittelbach and Michel Goossens, with
-Johannes Braams, David Carlisle and Chris Rowley,
-\textit{The \latex/ Companion}, 2nd ed., Addison-Wesley Co.,
-Reading, MA, 2004.
-
-\bibitem[LGC]{LGC} Michel Goossens, Sebastian Rahtz, and Frank Mittelbach,
-\textit{The \latex/ graphics Companion}, Addison-Wesley Co., Reading,
-MA, 1997.
-
-\bibitem[MIT]{MIT} Ellen E. Swanson, updated by Arlene O'Sean and
-Antoinette Schleyer, \textit{Mathematics into Type},
-Updated ed., Amer. Math. Soc., Providence, RI, 1999.
-
-\bibitem[ML]{ML} George Gr\"{a}tzer, \textit{Math into \latex/},
-3rd ed., Birkh\"{a}user, Boston, MA/Springer Verlag, NY, 2000.
-
-\bibitem[MSC]{MSC} \textit{\textup{2000} Mathematics subject classification},
-Amer. Math. Soc., Providence, RI, 1999; searchable on-line at
-\texttt{http://www.ams.org/msc/}.
-
-\end{thebibliography}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/amslatex/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/manifest.txt
deleted file mode 100644
index ffeebfacf43..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/manifest.txt
+++ /dev/null
@@ -1,56 +0,0 @@
-
-texmf/bibtex/bst/ams/
- amsra.bst
- amsrn.bst
- amsrs.bst
- amsru.bst
- amsry.bst
-
-texmf/doc/latex/amscls/
- amsrdoc.pdf
- amsrefs.faq
- amsrefs.pdf
- changes.pdf
- cite-xa.tex
- cite-xb.tex
- cite-xh.tex
- cite-xs.tex
- gktest.ltb
- jr.bib
- mathscinet.pdf
- textcmds.pdf
-
-texmf/source/latex/amsrefs/
- 00readme.txt
- ams-r1.ins
- amsrdoc.pdf
- amsrefs.dtx
- amsrefs.faq
- amsrefs.pdf
- amsxport.dtx
- changes.pdf
- cite-xa.tex
- cite-xb.tex
- cite-xh.tex
- cite-xs.tex
- gktest.ltb
- ifoption.dtx
- install.txt
- jr.bib
- manifest.txt
- mathscinet.dtx
- mathscinet.pdf
- pcatcode.dtx
- rkeyval.dtx
- textcmds.dtx
- textcmds.pdf
-
-texmf/tex/latex/amscls/
- amsrbeta.sty
- amsrefs.sty
- ifoption.sty
- mathscinet.sty
- pcatcode.sty
- rkeyval.sty
- rkvbeta.sty
- textcmds.sty
diff --git a/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt b/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt
deleted file mode 100644
index 080ed622537..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/math/00readme.txt
+++ /dev/null
@@ -1,123 +0,0 @@
-00readme.txt for amsmath 2.0 [2004/08/06] American Mathematical Society
-
-See manifest.txt for a list of all the files in the distribution.
-
-See install.txt for installation instructions. [Installing from an
-archive file such as ftp://ftp.ams.org/pub/tex/amsmath.zip is
-recommended.]
-
-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 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.
-
-In order to use amsmath you need to have TeX installed first. TeX is not
-an AMS product. For information on getting TeX see one of the following:
-
- http://www.tug.org/
- http://www.ams.org/tex/tex-resources.html
-
-The primary documentation for amsmath is in
-
- amsldoc.pdf
-
-Additional documentation files include:
-
- diffs-m.txt
- subeqn.pdf
- technote.pdf
- testmath.pdf
-
-which are included in the collection. Additional documentation can be
-found in the amsmath FAQ:
-
- http://www.ams.org/tex/amsmath-faq.html
-
-For technical support:
-
- American Mathematical Society
- Technical Support
- Publications Technical Group
- P. O. Box 6248
- Providence, RI 02940-6248
- Phone: 800-321-4AMS (321-4267) (USA/Canada) or 401-455-4080
- tech-support@ams.org
-
-For submitting bug reports, however, users are encouraged to use the
-standard LaTeX bug reporting system: Issue the command
-
- latex latexbug.tex
-
-and follow the resulting instructions (selecting the "amslatex" category
-when the list of possible categories is shown).
-
-========================================================================
-RECENT CHANGES (REVERSE ORDER)
-
----amsmath.faq - 2004/08/06
-Removed from distribution; replaced by on-line FAQ at
-http://www.ams.org/tex/amsmath-faq.html
-
----amsmath.dtx 2.13 2000/07/18:
-
-After the numbering patches in 2.11, \notag failed in certain
-circumstances: introduce some more auxiliary functions to sort things
-out, and redefine \nonumber.
-
----amstext.dtx 2.01 2000/06/29:
-
-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.
-
----amsmath.dtx 2.12 2000/06/06:
-
-Fix transposed lines in 2.11 patch.
-
----amsdtx.dtx - 2000/06/02:
-
-Move to the amscls distribution.
-
----amsmath.dtx 2.11 2000/06/02:
-
-Prevent "Arithmetic overflow" error by guarding against divide-by-zero
-in \x@calc@shift@lc (align environment).
-
----amsmath.dtx 2.10 2000/05/25:
-
-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.
-
----amsmath.dtx 2.09 2000/04/21:
-
-Ensure good catcodes for " etc.
-
----amsmath.dtx 2.08 2000/03/16:
-
-Fixed erroneous tag placement on split with fleqn/tbtags options.
-
----amsmath.dtx 2.07 2000/03/15:
-
-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.
-
----amsmath.dtx 2.06 2000/03/10:
-
-Change \MathAccent to \mathaccentV so \DeclareMathAccent won't give an
-error when redefining an accent.
-
----amsmath.dtx 2.05 2000/01/06:
-
-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/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls b/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls
deleted file mode 100644
index 96a50814c8f..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/math/amsdtx.cls
+++ /dev/null
@@ -1,517 +0,0 @@
-%%
-%% This is file `amsdtx.cls',
-%% generated with the docstrip utility.
-%%
-%% The original source files were:
-%%
-%% amsdtx.dtx (with options: `amsdtx')
-%%
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "amsdtx.dtx",
-%%% version = "2.06",
-%%% date = "2004/08/06",
-%%% time = "12:18:49 EDT",
-%%% checksum = "19929 1192 3506 39423",
-%%% author = "Michael J. Downes, updated by David M. Jones",
-%%% copyright = "Copyright 1996, 1999, 2004
-%%% 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,
-%%% Publications Technical Group,
-%%% 201 Charles Street,
-%%% Providence, RI 02904,
-%%% 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, amslatex, ams-latex, user documentation",
-%%% supported = "yes",
-%%% abstract = "This is the source for two document classes, amsdtx
-%%% and amsldoc, used to produce AMS user documentation
-%%% or technical documentation.",
-%%% 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)
-[1995/06/01]% LaTeX date must be June 1995 or later
-\ProvidesClass{amsdtx}[2004/08/06 v2.06]
-\DeclareOption*{\PassOptionsToClass{\CurrentOption}{book}}
-\ProcessOptions
-\LoadClass{book}
-\IfFileExists{url.sty}{%
- \RequirePackage{url}\relax
- \@gobble
-}{%
- \@firstofone
-}
-{
- \DeclareRobustCommand{\url}[1]{%
- \def\@tempa{#1}%
- \texttt{\urlsetup $\expandafter\strip@prefix\meaning\@tempa$}%
- }%
- \def\urlsetup{%
- \check@mathfonts \textfont\@ne\the\font \textfont\z@\the\font
- \urlfix +\urlfix\=\urlfix\:\urlfix\-\urlfix\.\urlfix\,\urlfix\;%
- \urlbreak\&\urlbreak\/\urlbreak\?%
- }%
- \def\urlbreak#1{%
- \mathcode`#1="8000
- \begingroup \lccode`\~=`#1 \lowercase{\endgroup \edef~}%
- {\mathchar\number`#1\penalty\hyphenpenalty}%
- }%
- \def\urlfix#1{%
- \mathcode`#1=`#1\relax
- }%
-}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\providecommand{\qq}[1]{\textquotedblleft#1\/\textquotedblright}
-\providecommand{\mdash}{\textemdash\penalty\exhyphenpenalty}
-\providecommand{\ndash}{\textendash\penalty\exhyphenpenalty}
-\let\@xp\expandafter
-\newcommand*{\autoindex}[1]{%
- \index{#1\ifcodeline@index\encapchar usage\fi}%
-}
-\newcommand{\ntt}{\normalfont\ttfamily}
-\newcommand*{\indexcs}[1]{%
- \@xp\@xp\@xp\@indexcs\@xp\@nobslash\string#1\@nil
-}
-\def\@indexcs#1\@nil{%
- \autoindex{#1\actualchar
- \string\verb\quotechar*\verbatimchar
- \@xp\@bothoftwo\string\ #1\@empty
- \verbatimchar
- }%
-}
-\def\@bothoftwo#1#2{#1#2}
-\def\category@index#1#2{%
- {\ntt#2}%
- \@category@index{#1}{#2}%
-}
-\def\@category@index#1#2{%
- \autoindex{%
- #2\actualchar\string\texttt{#2}%
- \ifx\@nil#1\@nil\else\space#1\fi
- }%
-}
-\chardef\bslchar=`\\ % p. 424, TeXbook
-\newcommand{\addbslash}{\expandafter\@addbslash\string}
-\def\@addbslash#1{\bslchar\@nobslash#1}
-\newcommand{\nobslash}{\expandafter\@nobslash\string}
-\def\@nobslash#1{\ifnum`#1=\bslchar\else#1\fi}
-\def\@boxorbreak{%
- \leavevmode
- \ifmmode\hbox\else\ifdim\lastskip=\z@\penalty9999 \fi\fi
-}
-\DeclareRobustCommand{\cs}[1]{%
- \@boxorbreak{%
- \ntt
- \addbslash#1\@empty
- \@xp\@xp\@xp\@indexcs\@xp\@nobslash\string#1\@nil
- }%
-}
-\let\cn\cs
-\DeclareRobustCommand{\cls}{\category@index{class}}
-\DeclareRobustCommand{\pkg}{\category@index{package}}
-\DeclareRobustCommand{\opt}{\category@index{option}}
-\DeclareRobustCommand{\env}[1]{{\ntt#1}\SpecialEnvIndex{#1}}
-\DeclareRobustCommand{\fn}{\category@index{}}
-\DeclareRobustCommand{\bst}{\category@index{\string\BibTeX{} style}}
-\DeclareRobustCommand{\cnt}{\category@index{counter}}
-\DeclareRobustCommand{\fnt}{\category@index{font}}
-\def\allowtthyphens{\begingroup
- \fontencoding{OT1}\fontfamily{cmtt}%
- \expandafter\let\csname OT1+cmtt\endcsname\relax
- \try@load@fontshape
- \endgroup
- \expandafter\let\csname OT1+cmtt\endcsname\@empty
-}
-\hfuzz2pc
-\vbadness9999 \hbadness5000
-\def\AmS{{\protect\usefont{OMS}{cmsy}{m}{n}%
- A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
-\def\latex/{{\protect\LaTeX}}
-\def\amslatex/{{\protect\AmS-\protect\LaTeX}}
-\def\tex/{{\protect\TeX}}
-\def\amstex/{{\protect\AmS-\protect\TeX}}
-\def\bibtex/{{Bib\protect\TeX}}
-\def\makeindx/{MakeIndex}
-\def\xypic/{XY\mbox{-}pic}
-\newcommand{\Textures}{\textit{Textures}}
-\def\<#1>{\textit{$\langle$#1\/$\rangle$}}
-\def\@listi{%
- \leftmargin\leftmargini
- \topsep 3\p@ \@plus2\p@ \@minus\p@
- \parsep \p@ \@plus\p@ \itemsep\parsep
-}
-\let\@listI\@listi
-\@listi
-\def\@listii{%
- \leftmargin\leftmarginii
- \labelwidth\leftmarginii \advance\labelwidth-\labelsep
- \topsep\p@\@plus\p@ \@minus\p@
- \parsep\z@skip \itemsep\z@skip
-}
-\def\@listiii{%
- \leftmargin\leftmarginiii
- \labelwidth\leftmarginiii \advance\labelwidth-\labelsep
- \topsep\z@skip \parsep\z@skip \itemsep\z@skip
-}
-\newenvironment{histnote}{%
- \trivlist\item[\hspace{\labelsep}\bfseries Historical Note:]%
-}{%
- \endtrivlist
-}
-\def\@starttoc#1{\begingroup
- \let\autoindex\@gobble
- \makeatletter
- \@input{\jobname.#1}\if@filesw
- \expandafter\newwrite\csname tf@#1\endcsname
- \immediate\openout
- \csname tf@#1\endcsname \jobname.#1\relax
- \fi \global\@nobreakfalse \endgroup}
-\newcommand*{\secref}[1]{\S\ref{#1}}
-\newcommand{\qc}[1]{}% check for prior definition
-\edef\qc#1{\noexpand\protect\expandafter\noexpand\csname qc \endcsname
- \noexpand\protect#1}
-\@namedef{qc }#1#2{\begingroup\ntt
- \ifx\ #2\char`\ \else\escapechar\m@ne\string#2\fi\endgroup}
-\DeclareRobustCommand{\qcat}{\qc\@}%
-\DeclareRobustCommand{\qcamp}{\qc\&}%
-\DeclareRobustCommand{\qcbang}{\qc\!}%
-\DeclareRobustCommand{\arg}[1]{{\ntt\##1}}
-\def\ncn#1{{\let\index\@gobble\cn{#1}}}
-
-\DeclareRobustCommand{\cnbang}{%
- \ncn{\!}\index{"!@{\ntt\bslchar\qcbang}}}
-\DeclareRobustCommand{\cnat}{%
- \ncn{\!}\index{"@@{\ntt\bslchar\qcat}}}
-\def\5{\penalty500 }
-\newcommand{\errexa}{\par\noindent\textit{Example}:\ }
-\newcommand{\errexpl}{\par\noindent\textit{Explanation}:\ }
-\renewcommand\chapter{\par \@afterindentfalse
- \secdef\@chapter\@schapter}
-\def\@chapter[#1]#2{\ifnum \c@secnumdepth >\m@ne
- \if@mainmatter
- \refstepcounter{chapter}%
- \typeout{\@chapapp\space\thechapter.}%
- \addcontentsline{toc}{chapter}%
- {\protect\numberline{\thechapter}#1}%
- \else
- \addcontentsline{toc}{chapter}{#1}\fi
- \else
- \addcontentsline{toc}{chapter}{#1}
- \fi
- \chaptermark{#1}%
- \addtocontents{lof}{\protect\addvspace{10\p@}}%
- \addtocontents{lot}{\protect\addvspace{10\p@}}%
- \if@twocolumn
- \@topnewpage[\@makechapterhead{#2}]%
- \else
- \@makechapterhead{#2}%
- \@afterheading
- \fi}
-\def\@makechapterhead#1{%
- \vspace{1.5\baselineskip}%
- {\parindent \z@ \raggedright \reset@font
- \ifnum \c@secnumdepth >\m@ne
- \large\bfseries \@chapapp\space\thechapter
- \par\nobreak
- \vskip.5\baselineskip\relax
- \fi
- #1\par\nobreak
- \vskip\baselineskip
- }}
-\def\@schapter#1{\if@twocolumn
- \@topnewpage[\@makeschapterhead{#1}]%
- \else
- \@makeschapterhead{#1}%
- \@afterheading
- \fi}
-\def\@makeschapterhead#1{%
- \vspace*{1.5\baselineskip}%
- {\parindent \z@ \raggedright
- \reset@font
- \large \bfseries #1\par\nobreak
- \vskip\baselineskip
- }}
-\def\@removefromreset#1#2{\let\@tempb\@elt
- \expandafter\let\expandafter\@tempa\csname c@#1\endcsname
- \def\@elt##1{\expandafter\ifx\csname c@##1\endcsname\@tempa\else
- \noexpand\@elt{##1}\fi}%
- \expandafter\edef\csname cl@#2\endcsname{\csname cl@#2\endcsname}%
- \let\@elt\@tempb}
-\@removefromreset{footnote}{chapter}
-\def\ps@headings{%
- \let\@oddfoot\@empty\let\@evenfoot\@empty
- \def\@evenhead{\thepage\hfil{\footnotesize\leftmark{}{}}}%
- \def\@oddhead{{\footnotesize\rightmark{}{}}\hfil\thepage}%
- \let\@mkboth\markboth
- \def\chaptermark##1{%
- \markboth {\uppercase{\ifnum \c@secnumdepth >\m@ne
- \if@mainmatter
- \@chapapp\ \thechapter. \ \fi
- \fi
- ##1}}{}}%
- \def\sectionmark##1{%
- \markright {\uppercase{\ifnum \c@secnumdepth >\z@
- \thesection. \ \fi
- ##1}}}}
-\renewcommand\maketitle{\par
- \begingroup
- \renewcommand\thefootnote{\fnsymbol{footnote}}%
- \def\@makefnmark{\hbox to\z@{$\m@th^{\@thefnmark}$\hss}}%
- \long\def\@makefntext##1{\parindent 1em\noindent
- \hbox to1.8em{\hss$\m@th^{\@thefnmark}$}##1}%
- \if@twocolumn
- \ifnum \col@number=\@ne
- \@maketitle
- \else
- \twocolumn[\@maketitle]%
- \fi
- \else
- \newpage
- \global\@topnum\z@ % Prevents figures from going at top of page.
- \@maketitle
- \fi
- \thispagestyle{plain}\@thanks
- \endgroup
- \setcounter{footnote}{0}%
- \let\thanks\relax
- \let\maketitle\relax\let\@maketitle\relax
- \gdef\@thanks{}\gdef\@author{}\gdef\@title{}}
-\def\@maketitle{%
- \newpage
- \null
- \vskip 2em%
- \begin{center}%
- {\LARGE \@title \par}%
- \vskip 1.5em%
- {\large
- \lineskip .5em%
- \begin{tabular}[t]{c}%
- \@author
- \end{tabular}\par}%
- \vskip 1em%
- {\large \@date}%
- \end{center}%
- \par
- \uppercase\expandafter{\expandafter\toks@\expandafter{\@title}}%
- \edef\@tempa{\noexpand\markboth{\the\toks@}{\the\toks@}}%
- \@tempa
- \vskip 1.5em}
-\renewcommand\tableofcontents{%
- \if@twocolumn
- \@restonecoltrue\onecolumn
- \else
- \@restonecolfalse
- \fi
- \subsection*{\contentsname}%
- \@starttoc{toc}%
- \if@restonecol\twocolumn\fi
- }
-\renewcommand\section{\@startsection {section}{1}{\z@}%
- {-.6\baselineskip \@plus -3\p@}%
- {.4\baselineskip}
- {\reset@font\Large\bfseries}}
-\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
- {-.3\baselineskip\@plus -2\p@}%
- {.2\baselineskip}%
- {\reset@font\large\bfseries}}
-\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
- {-.2\baselineskip\@plus -2\p@}%
- {.2\baselineskip}%
- {\reset@font\normalsize\bfseries}}
-\renewenvironment{theindex}{%
- \if@twocolumn \@restonecolfalse \else \@restonecoltrue \fi
- \columnseprule \z@ \columnsep 35\p@
- \let\autoindex\@gobble
- \twocolumn[\section*{\indexname}]%
- \addcontentsline{toc}{chapter}{\indexname}%
- \@mkboth{\uppercase{\indexname}}{\uppercase{\indexname}}%
- \thispagestyle{plain}\parindent\z@
- \parskip\z@ \@plus .3\p@\relax
- \let\item\@idxitem
-}{%
- \if@restonecol\onecolumn\else\clearpage\fi
-}
-\renewcommand{\thesection}{\arabic{section}}
-\long\def\@makecaption#1#2{%
- \addvspace\abovecaptionskip
- \begingroup
- \countdef\@parcycles=8 % local count register
- \@parcycles\z@
- \@setpar{\advance\@parcycles\@ne \ifnum\@parcycles>999
- \@@par\@parcycles\z@\fi
- \ifhmode \unskip\hskip\parfillskip\penalty-\@M\fi}%
- \@hangfrom{\textbf{#1.} }\vadjust{\penalty\m@ne}#2%
- \endgroup
- \ifhmode\unpenalty\fi\par
- \ifnum\lastpenalty=\m@ne % only one line in the caption
- \unpenalty \setbox\@tempboxa\lastbox
- \nointerlineskip
- \hbox to\hsize{\hfill\unhbox\@tempboxa\unskip\hfill}%
- \fi
- \nobreak\vskip\belowcaptionskip
-}
-\renewenvironment{table}{%
- \belowcaptionskip\abovecaptionskip \abovecaptionskip\z@skip
- \@float{table}%
-}{%
- \end@float
-}
-\renewenvironment{table*}{%
- \belowcaptionskip\abovecaptionskip \abovecaptionskip\z@skip
- \@dblfloat{table}%
-}{%
- \end@dblfloat
-}
-\setcounter{topnumber}{4}\setcounter{bottomnumber}{4}
-\setcounter{totalnumber}{4}\setcounter{dbltopnumber}{4}
-\renewcommand{\topfraction}{.97}\renewcommand{\bottomfraction}{.97}
-\renewcommand{\textfraction}{.03}\renewcommand{\floatpagefraction}{.9}
-\renewcommand{\dbltopfraction}{.97}
-\renewcommand{\dblfloatpagefraction}{.9}
-\setlength{\floatsep}{8pt plus6pt}
-\setlength{\textfloatsep}{10pt plus8pt}
-\setlength{\intextsep}{8pt plus6pt}
-\setlength{\dblfloatsep}{8pt plus6pt}
-\setlength{\dbltextfloatsep}{10pt plus8pt}
-\setlength{\@fptop}{0pt}\setlength{\@fpsep}{8pt}%
-\setlength{\@fpbot}{0pt plus 1fil}
-\setlength{\@dblfptop}{0pt}\setlength{\@dblfpsep}{8pt}%
-\setlength{\@dblfpbot}{0pt plus 1fil}
-
-\pagestyle{headings}
-\newcommand{\arrayargpatch}{%
- \let\@oldarray\@array
- \edef\@array[##1]##2{\catcode\number`\|=\number\catcode`\|
- \catcode\number`\@=\number\catcode`\@ \relax
- \let\noexpand\@array\noexpand\@oldarray
- \noexpand\@array[##1]{##2}}%
- \catcode`\|=12 \catcode`\@=12 \relax
-}
-\newenvironment{ctab}{%
- \par\topsep\medskipamount
- \trivlist\centering
- \item[]%
- \arrayargpatch
- \begin{tabular}%
-}{%
- \end{tabular}%
- \endtrivlist
-}
-\RequirePackage{doc}
-\def\AltMacroFont{\MacroFont}
-\def\SpecialMainEnvIndex#1{%
- \@bsphack
- \special@index{%
- #1\actualchar\string\texttt{#1} environment\encapchar main%
- }%
- \special@index{%
- environments:\levelchar#1%
- \actualchar\string\texttt{#1}%
- \encapchar main}%
- \@esphack
-}
-\def\SpecialEnvIndex#1{%
- \@bsphack
- \index{#1\actualchar\string\texttt{#1} environment\encapchar usage}%
- \index{%
- environments:\levelchar#1%
- \actualchar\string\texttt{#1}%
- \encapchar usage}%
- \@esphack
-}
-\def\DescribeOption{%
- \leavevmode
- \@bsphack
- \begingroup
- \MakePrivateLetters
- \Describe@Option
-}
-\def\Describe@Option#1{%
- \endgroup
- \marginpar{\raggedleft\PrintDescribeOption{#1}}%
- \SpecialOptionIndex{#1}%
- \@esphack
- \ignorespaces
-}
-\def\PrintDescribeOption#1{\strut \MacroFont #1\ }
-\def\option{%
- \let\SpecialMainEnvIndex\SpecialMainOptionIndex
-\begingroup
- \catcode`\\12
- \MakePrivateLetters \m@cro@ \iffalse}
-\def\SpecialMainOptionIndex#1{%
- \@bsphack
- \special@index{#1\actualchar\string\texttt{#1} option\encapchar main}%
- \@esphack
-}
-\def\SpecialOptionIndex{\@category@index{option}}
-\def\hDocInput#1{\MakePercentIgnore
- \begingroup
- \begingroup \lccode`\~=`\@
- \lowercase{\endgroup\long\def ~}##1##{%
- \catcode`\==12 \skipfileheader{##1}}%
- \catcode`\@=\active \catcode`\==14 % comment
- \def\filename{#1}%
- \@@input#1 \MakePercentComment}
-\def\skipfileheader#1#2 {\endgroup
- \hGetFileInfo#2 version = "??" date = "??"\@nil
- \begingroup\catcode`\==9 \catcode`\ =9 \futurelet\0\endgroup
-}
-\long\def\hGetFileInfo#1 version = "#2"#3 date = "#4"#5\@nil{%
- \def\fileversion{#2}\def\filedate{#4}}
-\DoNotIndex{\@xp,\@nx,\@empty,\newcommand,\renewcommand}
-\DoNotIndex{\newenvironment,\renewenvironment,\providecommand}
-\DoNotIndex{\if,\fi,\ifnum,\fi,\@let@token,\futurelet,\fsa@n}
-\DoNotIndex{\ignorespaces,\@tempcnta,\@tempcntb,\count@}
-\DoNotIndex{\toks@,\@ne,\advance}
-\DoNotIndex{\!,\/,\?,\@,\^,\_}
-\DoNotIndex{\@@par,\@M,\@auxout,\@bsphack,\@esphack,\@depth,\@ehc}
-\DoNotIndex{\@for,\@flushglue,\@gobble,\@gobbletwo,\@height,\@idxitem}
-\DoNotIndex{\@ifnextchar,\@ifstar,\@ifundefined,\@input,\@latexerr}
-\DoNotIndex{\@makeschapterhead,\@namedef,\@nameuse,\@nil}
-\DoNotIndex{\@nobreakfalse,\@restonecolfalse,\@restonecoltrue}
-\DoNotIndex{\@tempa,\@tempb,\@tempc,\@tempf,\@temptokena,\@themark,\@width}
-\DoNotIndex{\active,\aindex,\baselineskip,\begin,\begingroup,\box}
-\DoNotIndex{\c@page,\catcode,\chapter,\char,\chardef,\closeout}
-\DoNotIndex{\CodelineIndex,\sp,\sb,\label,\leavevmode,\mark}
-\DoNotIndex{\mark,\newinsert,\newwrite,\newtoks,\xdef}
-\DoNotIndex{\columnsep,\columnseprule,\columnwidth,\csname,\def}
-\DoNotIndex{\dimen,\do,\DocInput,\documentstyle,\edef,\em}
-\DoNotIndex{\EnableCrossrefs,\end,\endcsname,\endgroup,\endinput}
-\DoNotIndex{\everypar,\expandafter,\filedate,\fileversion}
-\DoNotIndex{\footnotesize,\gdef,\global,\glossary,\hangindent}
-\DoNotIndex{\if@filesw,\else,\fi}
-\DoNotIndex{\if@nobreak,\if@twocolumn,\if@twoside,\fi,\fi,\fi}
-\DoNotIndex{\hsize,\hskip}
-\DoNotIndex{\ifhmode,\ifmmode,\ifodd,\ifvmode,\ifx,\fi,\fi,\fi,\fi,\fi}
-\DoNotIndex{\ifcase,\ifdim,\ifeof,\iffalse,\iftrue,\fi,\fi,\fi,\fi,\fi}
-\DoNotIndex{\ifcat,\fi}
-\DoNotIndex{\immediate,\insert,\item,\jobname,\long}
-\DoNotIndex{\let,\lineskip,\marginparsep,\marginparwidth,\maxdimen}
-\DoNotIndex{\makeatletter,\noexpand,\openout,\protect,\rlap}
-\DoNotIndex{\min,\newpage,\nobreak,\normalbaselineskip}
-\DoNotIndex{\normallineskip,\p@,\par,\parfillskip,\parindent,\parskip}
-\DoNotIndex{\penalty,\relax,\section,\sin,\sloppy,\space,\string}
-\DoNotIndex{\tableofcontents,\the,\thepage,\thispagestyle,\toks,\tt}
-\DoNotIndex{\twocolumn,\uppercase,\vbox,\vrule,\vskip,\vss}
-\DoNotIndex{\write,\z@,\z@skip}
-\endinput
-%%
-%% End of file `amsdtx.cls'.
diff --git a/Master/texmf-dist/doc/latex/amslatex/math/install.txt b/Master/texmf-dist/doc/latex/amslatex/math/install.txt
deleted file mode 100644
index fb4b835f282..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/math/install.txt
+++ /dev/null
@@ -1,108 +0,0 @@
-install.txt for amsmath 2.16 [2004/08/05]
-
-If you have a relatively up-do-date TeX system that complies with the
-TeX Directory Structure (TDS) standard, installing according to the
-instructions in section I below is the easiest method. See
-
- http://www.tug.org/tds/tds.pdf
-
-for details on the TDS standard. If your TeX system does not comply
-with the TDS standard, please contact the manufactuer of your TeX
-system for details on how to install third-party TeX packages.
-
-The first step is to identify the TEXMF folder that contains files used
-by LaTeX. To do this, look for the file article.cls. If you find, e.g.,
-
- /usr/local/share/texmf/tex/latex/base/article.cls
-
-then we will define TEXMF to mean /usr/local/share/texmf (everything
-up to the /tex/latex/base part). On a Windows system the file location
-will probably be something like
-
- c:\sw\texmf\tex\latex\base\article.cls
-
-Then we define TEXMF to mean c:\sw\texmf. In the following instructions,
-wherever you see "TEXMF" substitute the folder name determined in this
-way.
-
-If this terminology does not make sense to you, seek assistance from
-a friend or colleague, or from the company that you bought your TeX
-system from, or contact us at
-
- tech-support@ams.org
- 800-321-4AMS (321-4267) (USA/Canada)
- 401-455-4080
-
-========================================================================
-I. Installing the easy way.
-
-1. Download the following archive file:
-
- ftp://ftp.ams.org/pub/tex/amsmath.zip
-
-2. View the following files to assess the effects of the upgrade on
-your system:
-
- 00readme.txt
- install.txt (this file)
- diffs-m.txt
-
-3. Backup the old version of AMS-LaTeX, preferably by moving it out of the
-TEXMF tree.
-
-4. Extract files from the .zip archive using your favorite unzip tool,
-setting the extraction target directory to the texmf root directory.
-
-5. To check the end result, you should find that you now have amsmath.sty
-in the following location
-
- TEXMF/tex/latex/amsmath/amsmath.sty
-
-Some TeX systems also use a database to keep track of TeX input files.
-If this database is not updated, your TeX system might not find the
-newly installed files. Consult your TeX system's documentation to
-determine how to update this database.
-
-6. Some files will appear in both the source area and another area.
-This is because the source form and the in-use form are identical.
-As distributed, the files in the source/latex/ams* areas comprise a
-complete copy of the distribution from which all the other files can
-be regenerated if need be. If you need to conserve disk space, you
-could delete the files in the source area, since they are not needed
-for normal use.
-
-========================================================================
-II. Installing the not-so-easy way.
-
-Download ftp://ftp.ams.org/pub/tex/amsmath.zip.
-
-Make the following directories, if not already present:
-
- TEXMF/source/latex/amsmath
- TEXMF/tex/latex/amsmath
- TEXMF/doc/latex/amsmath
-
-Backup your old AMS-LaTeX files if they are installed, preferably moving them
-out of the TEXMF tree.
-
-******** revise -- pdf file amsldoc will be included in distrib
-
-Create a temporary directory and generate documentation files (these assume
-a UNIX TeX installation):
-
- - make directory /tmp/amsmath
- - unzip -d /tmp/amscls amsmath.zip
- - cd /tmp/amsmath
- - Run latex on the file ams-m1.ins to produce .cls and .sty files
- - Run latex on *.tex
- - [optional] Run latex on *.dtx (technical documentation)
- - move *.dvi, *.pdf, *.tex to TEXMF/doc/latex/amsmath
- - [optional] move *.dtx to TEXMF/doc/latex/amsmath
- - [optional] convert .dvi to .ps or .pdf
- - move *.sty and *.cls to TEXMF/tex/latex/amsmath
- - delete /tmp/amsmath
-
-Some TeX systems also use a database to keep track of TeX input files.
-If this database is not updated, your TeX system might not find the
-newly installed files. Consult your system's documentation to determine
-how to update this database.
diff --git a/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt b/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt
deleted file mode 100644
index 2ea274a32d7..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/math/manifest.txt
+++ /dev/null
@@ -1,38 +0,0 @@
-
-texmf/doc/latex/amsmath/
- amsldoc.pdf
- diffs-m.txt
- subeqn.pdf
- technote.pdf
- testmath.pdf
-
-texmf/source/latex/amsmath/
- 00readme.txt
- ams-m1.ins
- amsbsy.dtx
- amscd.dtx
- amsdtx.cls
- amsgen.dtx
- amsldoc.cls
- amsldoc.tex
- amsmath.dtx
- amsopn.dtx
- amstex.sty
- amstext.dtx
- amsxtra.dtx
- diffs-m.txt
- install.txt
- manifest.txt
- subeqn.tex
- technote.tex
- testmath.tex
-
-texmf/tex/latex/amsmath/
- amsbsy.sty
- amscd.sty
- amsgen.sty
- amsmath.sty
- amsopn.sty
- amstex.sty
- amstext.sty
- amsxtra.sty
diff --git a/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf b/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf
deleted file mode 100644
index 2392932a506..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/mathscinet.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty b/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty
deleted file mode 100644
index 9fd19b0a06e..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/other/amsmidx.sty
+++ /dev/null
@@ -1,82 +0,0 @@
-% amsmidx.sty
-% 2001/09/26
-% preliminary version
-%
-% Package for use with AMS document classes to produce multiple indexes
-%
-% Adapted from multind.sty (version 1.1b, 31 August 1991), by F.W. Long
-
-% Modified \makeindex and \index commands to allow multiple indexes
-% The first argument of \makeindex and \index is the index file name.
-% These commands now work more like \@starttoc and \addcontentsline.
-% \index is no longer defined inside \makeindex but determines whether
-% the appropriate file is defined before writing to it.
-
-\def\makeindex#1{\begingroup
- \makeatletter
- \if@filesw \expandafter\newwrite\csname #1@idxfile\endcsname
- \expandafter\immediate\openout \csname #1@idxfile\endcsname #1.idx\relax
- \typeout{Writing index file #1.idx }\fi \endgroup}
-
-\def\index#1{\@bsphack
- \begingroup
- \def\protect##1{\string##1\space}\@sanitize
- \@wrindex{#1}}
-
-% \@wrindex now checks that the appropriate file is defined.
-
-\def\@wrindex#1#2{\let\thepage\relax
- \xdef\@gtempa{\@ifundefined{#1@idxfile}{}{%
- \expandafter\write\csname #1@idxfile\endcsname
- {\string\indexentry{#2}{\thepage}}}}%
- \endgroup\@gtempa
- \if@nobreak \ifvmode\nobreak\fi\fi
- \@esphack}
-
-% Modified \printindex command to accept the name of an index file.
-
-\renewcommand{\printindex}[1]{\@input{#1.ind}}
-
-% Alternate command with new name:
-% \Printindex locally modifies some formatting commands for an improved
-% appearance, sets the index title and reads in the requested index file.
-% #1 = file name, #2 = index title
-
-\newcommand\Printindex[2]{%
- \begingroup
- \cleardoublepage
- \def\indexname{#2}%
- \raggedright
- \hyphenpenalty=10000
- \renewcommand{\seename}{see~also}
- \renewcommand{\subitem}{\par\hangindent 3em\hspace*{1em}}
- \@input{#1.ind}%
- \endgroup
-}
-
-\endinput
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-Instructions for using amsmidx.sty
-
-Put these commands in the preamble:
-
- \usepackage{amsmidx}
- \makeindex{filename-a}
- \makeindex{filename-b}
-
-To identify the index entries in the text:
-
- \index{filename-a}{index term}
- \index{filename-b}{index term}
-
-In the backmatter, where the indexes are to appear:
-
- \Printindex{filename-a}{First Index}
- \Printindex{filename-b}{Second Index}
-
-Two files of index terms, filename-a.idx and filename-b.idx, will be
-generated. To sort the index terms, process the two .idx files
-separately with Makeindex; this will create the files filename-a.ind
-and filename-b.ind, which will in turn be input by \Printindex.
diff --git a/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf b/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf
deleted file mode 100644
index a2aa7a40fd2..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/subeqn.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/subeqn.tex b/Master/texmf-dist/doc/latex/amslatex/subeqn.tex
deleted file mode 100644
index d0fa7d9b023..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/subeqn.tex
+++ /dev/null
@@ -1,202 +0,0 @@
-%%% ====================================================================
-%%% @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}{\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/Master/texmf-dist/doc/latex/amslatex/technote.pdf b/Master/texmf-dist/doc/latex/amslatex/technote.pdf
deleted file mode 100644
index 11b67dfa4dc..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/technote.pdf
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/amslatex/technote.tex b/Master/texmf-dist/doc/latex/amslatex/technote.tex
deleted file mode 100644
index aede450621e..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/technote.tex
+++ /dev/null
@@ -1,233 +0,0 @@
-%%% ====================================================================
-%%% @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}
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-%%% ====================================================================
-%%% @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
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deleted file mode 100644
index 21193949e83..00000000000
--- a/Master/texmf-dist/doc/latex/amslatex/thmtest.tex
+++ /dev/null
@@ -1,255 +0,0 @@
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "thmtest.tex",
-%%% version = "2.01",
-%%% date = "2004/08/02",
-%%% time = "14:18:27 EDT",
-%%% checksum = "26819 255 963 8277",
-%%% author = "American Mathematical Society",
-%%% copyright = "Copyright 1996, 2004 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,
-%%% Publications Technical Group,
-%%% 201 Charles Street,
-%%% Providence, RI 02904,
-%%% 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",
-%%% supported = "yes",
-%%% keywords = "latex, amslatex, ams-latex, theorem, proof",
-%%% abstract = "This is part of the AMS-\LaTeX{} distribution.
-%%% It is a sample document illustrating the use of
-%%% the amsthm 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.",
-%%% }
-%%% ====================================================================
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Option test file, will be created during the first LaTeX run;
-% this facility is not available when using an AMS document class.
-\begin{filecontents}{exercise.thm}
-\def\th@exercise{%
- \normalfont % body font
- \thm@headpunct{:}%
-}
-\end{filecontents}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\documentclass{article}
-\title{Newtheorem and theoremstyle test}
-\author{Michael Downes\\updated by Barbara Beeton}
-
-\usepackage[exercise]{amsthm}
-
-\newtheorem{thm}{Theorem}[section]
-\newtheorem{cor}[thm]{Corollary}
-\newtheorem{prop}{Proposition}
-\newtheorem{lem}[thm]{Lemma}
-
-\theoremstyle{remark}
-\newtheorem*{rmk}{Remark}
-
-\theoremstyle{plain}
-\newtheorem*{Ahlfors}{Ahlfors' Lemma}
-
-\newtheoremstyle{note}% name
- {3pt}% Space above
- {3pt}% Space below
- {}% Body font
- {}% Indent amount (empty = no indent, \parindent = para indent)
- {\itshape}% Thm head font
- {:}% Punctuation after thm head
- {.5em}% Space after thm head: " " = normal interword space;
- % \newline = linebreak
- {}% Thm head spec (can be left empty, meaning `normal')
-
-\theoremstyle{note}
-\newtheorem{note}{Note}
-
-\newtheoremstyle{citing}% name
- {3pt}% Space above, empty = `usual value'
- {3pt}% Space below
- {\itshape}% Body font
- {}% Indent amount (empty = no indent, \parindent = para indent)
- {\bfseries}% Thm head font
- {.}% Punctuation after thm head
- {.5em}% Space after thm head: " " = normal interword space;
- % \newline = linebreak
- {\thmnote{#3}}% Thm head spec
-
-\theoremstyle{citing}
-\newtheorem*{varthm}{}% all text supplied in the note
-
-\newtheoremstyle{break}% name
- {9pt}% Space above, empty = `usual value'
- {9pt}% Space below
- {\itshape}% Body font
- {}% Indent amount (empty = no indent, \parindent = para indent)
- {\bfseries}% Thm head font
- {.}% Punctuation after thm head
- {\newline}% Space after thm head: \newline = linebreak
- {}% Thm head spec
-
-\theoremstyle{break}
-\newtheorem{bthm}{B-Theorem}
-
-\theoremstyle{exercise}
-\newtheorem{exer}{Exercise}
-
-\swapnumbers
-\theoremstyle{plain}
-\newtheorem{thmsw}{Theorem}[section]
-\newtheorem{corsw}[thmsw]{Corollary}
-\newtheorem{propsw}{Proposition}
-\newtheorem{lemsw}[thmsw]{Lemma}
-
-% Because the amsmath pkg is not used, we need to define a couple of
-% commands in more primitive terms.
-\let\lvert=|\let\rvert=|
-\newcommand{\Ric}{\mathop{\mathrm{Ric}}\nolimits}
-
-% Dispel annoying problem of slightly overlong lines:
-\addtolength{\textwidth}{8pt}
-
-\begin{document}
-\maketitle
-
-\section{Test of standard theorem styles}
-
-Ahlfors' Lemma gives the principal criterion for obtaining lower bounds
-on the Kobayashi metric.
-
-\begin{Ahlfors}
-Let $ds^2 = h(z)\lvert dz\rvert^2$ be a Hermitian pseudo-metric on
-$\mathbf{D}_r$, $h\in C^2(\mathbf{D}_r)$, with $\omega$ the associated
-$(1,1)$-form. If $\Ric\omega\geq\omega$ on $\mathbf{D}_r$,
-then $\omega\leq\omega_r$ on all of $\mathbf{D}_r$ (or equivalently,
-$ds^2\leq ds_r^2$).
-\end{Ahlfors}
-
-\begin{lem}[negatively curved families]
-Let $\{ds_1^2,\dots,ds_k^2\}$ be a negatively curved family of metrics
-on $\mathbf{D}_r$, with associated forms $\omega^1$, \dots, $\omega^k$.
-Then $\omega^i \leq\omega_r$ for all $i$.
-\end{lem}
-
-Then our main theorem:
-\begin{thm}\label{pigspan}
-Let $d_{\max}$ and $d_{\min}$ be the maximum, resp.\ minimum distance
-between any two adjacent vertices of a quadrilateral $Q$. Let $\sigma$
-be the diagonal pigspan of a pig $P$ with four legs.
-Then $P$ is capable of standing on the corners of $Q$ iff
-\begin{equation}\label{sdq}
-\sigma\geq \sqrt{d_{\max}^2+d_{\min}^2}.
-\end{equation}
-\end{thm}
-
-\begin{cor}
-Admitting reflection and rotation, a three-legged pig $P$ is capable of
-standing on the corners of a triangle $T$ iff (\ref{sdq}) holds.
-\end{cor}
-
-\begin{rmk}
-As two-legged pigs generally fall over, the case of a polygon of order
-$2$ is uninteresting.
-\end{rmk}
-
-\section{Custom theorem styles}
-
-\begin{exer}
-Generalize Theorem~\ref{pigspan} to three and four dimensions.
-\end{exer}
-
-\begin{note}
-This is a test of the custom theorem style `note'. It is supposed to have
-variant fonts and other differences.
-\end{note}
-
-\begin{bthm}
-Test of the `linebreak' style of theorem heading.
-\end{bthm}
-
-This is a test of a citing theorem to cite a theorem from some other source.
-
-\begin{varthm}[Theorem 3.6 in \cite{thatone}]
-No hyperlinking available here yet \dots\ but that's not a
-bad idea for the future.
-\end{varthm}
-
-\section{The proof environment}
-
-\begin{proof}
-Here is a test of the proof environment.
-\end{proof}
-
-\begin{proof}[Proof of Theorem \ref{pigspan}]
-And another test.
-\end{proof}
-
-\begin{proof}[Proof \textup(necessity\textup)]
-And another.
-\end{proof}
-
-\begin{proof}[Proof \textup(sufficiency\textup)]
-And another, ending with a display:
-\[
-1+1=2\,. \qedhere
-\]
-\end{proof}
-
-\section{Test of number-swapping}
-
-This is a repeat of the first section but with numbers in theorem heads
-swapped to the left.
-
-Ahlfors' Lemma gives the principal criterion for obtaining lower bounds
-on the Kobayashi metric.
-\begin{Ahlfors}
-Let $ds^2 = h(z)\lvert dz\rvert^2$ be a Hermitian pseudo-metric on
-$\mathbf{D}_r$, $h\in C^2(\mathbf{D}_r)$, with $\omega$ the associated
-$(1,1)$-form. If $\Ric\omega\geq\omega$ on $\mathbf{D}_r$,
-then $\omega\leq\omega_r$ on all of $\mathbf{D}_r$ (or equivalently,
-$ds^2\leq ds_r^2$).
-\end{Ahlfors}
-
-\begin{lemsw}[negatively curved families]
-Let $\{ds_1^2,\dots,ds_k^2\}$ be a negatively curved family of metrics
-on $\mathbf{D}_r$, with associated forms $\omega^1$, \dots, $\omega^k$.
-Then $\omega^i \leq\omega_r$ for all $i$.
-\end{lemsw}
-
-Then our main theorem:
-\begin{thmsw}
-Let $d_{\max}$ and $d_{\min}$ be the maximum, resp.\ minimum distance
-between any two adjacent vertices of a quadrilateral $Q$. Let $\sigma$
-be the diagonal pigspan of a pig $P$ with four legs.
-Then $P$ is capable of standing on the corners of $Q$ iff
-\begin{equation}\label{sdqsw}
-\sigma\geq \sqrt{d_{\max}^2+d_{\min}^2}.
-\end{equation}
-\end{thmsw}
-
-\begin{corsw}
-Admitting reflection and rotation, a three-legged pig $P$ is capable of
-standing on the corners of a triangle $T$ iff (\ref{sdqsw}) holds.
-\end{corsw}
-
-\begin{thebibliography}{99}
-\bibitem{thatone} Dummy entry.
-\end{thebibliography}
-
-\end{document}