From 6c76d108053732941431a176e9a29a74d96a8587 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Thu, 13 Feb 2014 00:41:23 +0000 Subject: voss-mathmode (13feb14) git-svn-id: svn://tug.org/texlive/trunk@32953 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/voss-mathmode/Changes | 73 + .../doc/latex/voss-mathmode/Mathmode.bib | 234 + .../doc/latex/voss-mathmode/Mathmode.ist | 35 + .../doc/latex/voss-mathmode/Mathmode.ltx | 386 + .../doc/latex/voss-mathmode/Mathmode.pdf | 50285 +++++++++++++++++++ .../doc/latex/voss-mathmode/Mathmode.tex | 8205 +++ .../doc/latex/voss-mathmode/images/EuScript.eps | 1462 + .../doc/latex/voss-mathmode/images/EuScript.pdf | Bin 0 -> 34704 bytes .../doc/latex/voss-mathmode/images/amsalign.eps | 1574 + .../doc/latex/voss-mathmode/images/amsalign.pdf | Bin 0 -> 7514 bytes .../doc/latex/voss-mathmode/images/cm-crop.eps | 3421 ++ .../doc/latex/voss-mathmode/images/cm-crop.pdf | Bin 0 -> 80882 bytes .../latex/voss-mathmode/images/cmbright-crop.eps 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Mathmode.ltx|tex|bib|ist +2.32 2008-02-29 - again typos +2.31 2008-02-21 - typo +2.30 2007-12-31 - added penalty values for no breaks in inline mode +2.29 2007-11-30 - added two special symbols \Let and \teL +2.28 2007-09-25 - typo with BlueSky + - package fixltx2e with command \MakeRobust +2.27 2007-09-06 - small example for \limits +2.26 2007-05-01 - www.yandy.com -> www.pctex.com +2.25 2007-04-21 - added an example for aligned vertical dots + - typos + - added an appendix for the package file list of + the pdflatex run +2.24 2007-04-08 - added an example for a root over several lines + - fixed using \textrm inside array for cases +2.23 2007-03-30 - added \boldsymbol and \varGREEK letters +2.22 2007-02-01 - typos +2.21 2006-10-26 - added examples for package dotseqn + - one more example for split + - some typos and small changes to the structure +2.20 2006-10-08 - added examples for package cool + - new section "Tuning math typesetting" + - new subdirectory for the images +2.19 2006-10-06 - some more infos for the fleqn class option + - small fixes to the array environment + - added an example for gathered and + for boxed rows and columns of arrays + - indice in upright font shape + - a lot of modifications to the source code + - extended index +2.18 2006-09-27 - fix a problem & in align demo + - add a short section of mathtools +2.17 2006-09-25 fix problem with package showexpl +2.16 2006-08-05 typo and one more bib entry +2.15 2006-08-03 some typos, adding the missing + index and bibliography +2.14 2006-04-23 http://www.yandy.com is obsolete +2.13 2006-05-29 typos and adding a font demo section +2.12 2006-05-17 typos and changes to the bib file +2.11 2006-03-12 fix bug with \biggm +2.10 2005-12-22 new section "Problems with amsmath" +2.09 2005-10-24 fix problem with braket package +2.08 2005-10-21 example for linear equation matrix + typos +2.07 2005-10-08 update everymath subsection +2.06 2005-08-28 add an example for braces around operators with + with stacked limits +2.05 2005-08-15 add an example for vertical line spacing +2.04 2005-07-07 small changes to the text +2.03 2005-07-07 wrong references +2.02 2005-07-07 typos +2.01 2005-07-02 do not use PSTricks with pdflatex +2.00 2005-06-30 typos +1.99 2005-06-03 typos and bugfix with sqrt +1.98 2005-05-13 small tweaks +1.97 2005-05-08 small tweaks +1.96 2005-05-03 small tweaks +1.95 2005-04-23 added xlongleftrightarrow +1.94 2005-04-10 small tweaks +1.93 2005-02-22 one more example for different vertical spacing + in arrays, amsmath without usind \def\arraystretch +1.92 2005-02-02 minor changes +1.91 2005-01-30 different sizes of operators +1.90 2004-12-22 preventing linebreaks for inline mode +1.89 2004-12-08 fixed typos +1.87 2004-11-14 fixed typos +1.86 2004-11-08 fixed a small bug with inline math +1.85 2004-11-08 forgot a LateX run for the TOC +1.84 2004-11-03 fixing typos +1.83 2004-10-18 added an example for alignat + Some more bib entries +1.82 2004-10-01 TeX math macros + diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib new file mode 100644 index 00000000000..9b190ef4493 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib @@ -0,0 +1,234 @@ +@STRING{bretter = {Bretter, die die Welt bedeuten} } +@STRING{dtk = {{D}ie {\TeX}nische {K}om{\"o}die} } +@STRING{PS = {{P}ost{S}cript} } + +@Manual{MathGuide, + Title = {Short Math Guide for \LaTeX}, + Author = {Downes, Michael}, + Organization = {American Mathematical Society}, + Address = {\url{http://www.ams.org/tex/short-math-guide.html}}, + Note = {}, + year = 2002, +} + +@Manual{Notes, + Title = {Technical Notes on the \texttt{amsmath} package}, + Author = {Downes, Michael}, + Organization = {American Mathematical Society}, + Address = {\url{ftp://ftp.ams.org/pub/tex/doc/amsmath/technote.pdf}}, + Note = {}, + year = 1999, +} + +@Manual{webmath, + Title = {Web Math Formulas Using \TeX}, + Author = {Fitzgerald, J. Anthony}, + Organization = {}, + Address = {\url{http://www.unb.ca/web/Sample/math/}}, + Note = {}, + year = 1997, +} + +@article{rahtz92, + Author = {Sebastian Rahtz and Leonor Barroca}, + Title = {A style option for rotated objects in {\LaTeX}}, + journal = {TUGboat Journal}, + year = 1992, + volume = 13, + number = 2, + pages = "156--180", + month = jul, +} + +@Manual{mathwriting87, + Title= {Mathematical Writing}, + Author= {Donald {E}. {K}nuth and {T}racy {L}arrabee and {P}aul {M}. Roberts}, + Organization = {Stanford University, Computer Science Department}, + Address = {\url{http://sunburn.stanford.edu/~knuth/papers/mathwriting.tex.gz}}, + Note = {}, + year = 1987, +} + +@Manual{harvard, + Title= {An Introduction to using {\LaTeX} in the {H}arvard {M}athematics {D}epartment}, + Author= {R. Kuhn and R. Scott and L. Andreev}, + Organization = {Harvard University, Department of Mathematics}, + Address = {\url{http://abel.math.harvard.edu/computing/latex/manual/texman.html}}, + Note = {}, + year = {}, +} + +@book{graetzer00, + Title = {Math into {\LaTeX}}, + Author = {George Grtzer}, + Publisher = {Birkhuser Boston}, + Edition= {third}, + Year= {2000}, +} + +@Manual{impatient, + Title= {{\TeX} for the {I}mpatient}, + Author = {Paul W. Abrahams and Karl Berry and Kathryn Hargreaves}, + Address = {\url{http://tug.org/ftp/tex/impatient/book.pdf}}, + Note = {}, + year = {2003}, +} + +@book{knuth86, + Title = {The {\TeX}book}, + Author = {Donald E. Knuth}, + Publisher = {Addison Wesley Professional}, + Edition= {21}, + Year= {1986}, +} +@book{companion94, + Title = {The {\LaTeX} {C}ompanion}, + Author = {Michel Goosens and Frank Mittelbach and Alexander Samarin}, + Publisher = {Addison Wesley}, + Edition= {13}, + Year= {1994}, +} + +@Manual{eijkhout, + Title= {{\TeX} by {T}opic}, + Author = {Victor Eijkhout}, + Address = {\url{http://www.eijkhout.net/tbt/}}, + Note = {}, + year = {1992}, +} +@Manual{taylor00, + Title = {Commutative Diagrams in \TeX}, + Author = {Paul Taylor}, + Organization = {Department of Computer Science, Queen Mary and Westfield College}, + Address = {\url{http://www.dcs.qmw.ac.uk/~pt/diagrams/}}, + Note = {}, + year = 2000, +} +@Manual{selden00, + Title = {Math cheat sheet}, + Author = {Steve Seiden}, + Organization = {TUG}, + Address = {\url{http://www.tug.org/texshowcase/#math}}, + Note = {}, + year = 2000, +} + +@Manual{nist, + Title= {Typefaces for Symbols in Scientific +Manuscripts}, + Author = {NIST}, + Address = {\url{http://physics.nist.gov/Document/typefaces.pdf}}, + Note = {}, + year = {2004}, +} + +@Manual{expressionsI, + Title= {Ecrire des mathmatiques avec \LaTeX}, + Author = {David Cobac}, + Address = {\url{http://dcobac.free.fr/latex/prepDocMaths.pdf}}, + Note = {}, + year = {2004}, +} + +@Manual{expressionsII, + Title= {Atelier documents mathmatiques}, + Author = {David Cobac}, + Address = {\url{http://dcobac.free.fr/latex/Presentation4.pdf}}, + Note = {}, + year = {2004}, +} + +@Manual{kuester:2004, + Title= {Fonts for Mathematics}, + Author= {Johannes Kster}, + Address={\url{http://www.typoma.com/publ/20041002-atypi.pdf}}, + Note = {Vortrag auf der {AT}yp{I}-{K}onferenz in {P}rag}, + month={oct}, + year = {2004}, +} + +@Manual{kuester:2004-2, + Title= {Designing Math Fonts}, + Author= {Johannes Kster}, + Address={\url{http://www.typoma.com/publ/20040430-bachotex.pdf}}, + Note = {Vortrag auf der polnischen TeX-Konferenz BachoTeX}, + month={apr}, + year = {2004}, +} + +@article{bouchie98, + Author = {Thierry Bouche}, + Title = {Diversity in math fonts}, + journal = {TUGboat Journal}, + year = 1998, + volume = 19, + number = 2, + pages = "121--135", + Address={\url{http://www.tug.org/TUGboat/Articles/tb19-2/tb59bouc.pdf}}, +} + + @article{beccardi97, + Author = {Claudio Beccari}, + Title = {Typesetting mathematics for science + and technology according to ISO 31/XI}, + journal = {TUGboat Journal}, + year = 1997, + volume = 18, + number = 1, + pages = "39--47", + Address={\url{http://www.tug.org/TUGboat/Articles/tb18-1/tb54becc.pdf}}, +} + +@article{padovani03, + Author = {Luca Padovani}, + Title = {MathML formatting with TeX rules and TeX fonts}, + journal = {TUGboat Journal}, + year = 2003, + volume = 24, + number = 1, + pages = "53--61", + Address={\url{http://www.tug.org/TUGboat/Articles/tb24-1/padovani.pdf}}, +} + +@article{lawrence04, + Author = {Richard Lawrence}, + Title = {Math={T}ypography?}, + journal = {TUGboat Journal}, + year = 2003, + volume = 24, + number = 2, + pages = "165--168", + Address={\url{http://www.tug.org/TUGboat/Articles/tb24-2/tb77lawrence.pdf}}, +} +@Article{dtk04.2:voss, + author = {Herbert Vo{\ss}}, + title = {Farbige {M}athematik}, + journal = dtk, + year = 2004, + volume = {2/04}, + month = mar, + pages = {81--87}, + annote = bretter, + keywords = {}, +} + +@Article{dtk04.3:voss, + author = {Carole Siegfried and Herbert Vo{\ss}}, + title = {{M}athematik im {I}nline-Modus}, + journal = dtk, + year = 2004, + volume = {3/04}, + month = nov, + pages = {25--32}, + annote = bretter, + keywords = {}, +} + +@book{voss06, + Title = {\LaTeX{} in {N}aturwissenschaften \&{} {M}athematik}, + Author = {Herbert Vo\ss}, + Publisher = {Franzis Verlag}, + Edition= {first}, + Address= {Mnchen}, + Year= {2006}, +} diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist new file mode 100644 index 00000000000..a7ba26ae2f6 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist @@ -0,0 +1,35 @@ +%% +%% This is file `Letter.ist', +%% +%% The idea is from Ingo Kloeckl, Latex2e: +%% Herbert Voss 000726 +%% +%% This is a MAKEINDEX style file which should be used to +%% generate the formatted change history for use with the doc +%% package. The TeX commands used below are defined in +%% doc.sty. The commands for MAKEINDEX like `level' +%% `item_x1' are described in `` Makeindex, A General +%% Purpose, Formatter-Independent Index Processor'' by +%% Pehong Chen. +%% +headings_flag 1 % headings yes +heading_prefix "\\textbf{" % boldfont +heading_suffix "}\n" % newline +quote ">" +preamble + "\\begin{theindex}\n" +item_1 + "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}" +item_01 + "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}" +item_x1 + "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}" +item_2 + "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }" +item_12 + "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }" +item_x2 + "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }" +%% +%% +%% End of file `Letter.ist'. diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx new file mode 100644 index 00000000000..b2d5185e93f --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx @@ -0,0 +1,386 @@ +%% +%% This is file `Mathmode.ltx', +%% +%% IMPORTANT NOTICE: +%% +%% Herbert Voss +%% 2005-06-30 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% DESCRIPTION: +%% `Mathmode' is a document how the math mode works inside LaTeX +%% +\listfiles +\documentclass[11pt,a4paper,english]{article} +\usepackage{fixltx2e}%% the official fixes for LaTeX2e +\usepackage[T1]{fontenc} +\usepackage[latin1]{inputenc} +%\usepackage{lmodern} +% +\usepackage{ifpdf} +\usepackage{ifvtex} +\ifvtex\pdffalse\fi +\usepackage{comment} +\usepackage{graphicx} +\usepackage{varwidth} +\usepackage{array} +\usepackage{delarray} +\usepackage{tabularx} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{amsopn} +\usepackage{bm} +\usepackage{upgreek} +\usepackage{cancel} +\newcommand\hcancel[2][black]{\setbox0=\hbox{#2}% + \rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +\DeclareMathOperator{\Res}{Res} +\usepackage{amscd} +\usepackage{accents} +\usepackage{dsfont} +\usepackage{multirow} +\usepackage{bigdelim} +\usepackage{framed} +\usepackage{longtable} +\usepackage{varioref} +% +\ifvtex + \usepackage{pstricks} + \usepackage{pst-node} +\else\ifpdf\usepackage{xcolor}\else + \usepackage{pstricks} + \usepackage{pst-node} +\fi\fi +\usepackage{makeidx} +\makeindex +\usepackage{url} +\usepackage{setspace} +\usepackage{framed} +% +% +\DeclareMathDelimiter{\Norm} + {\mathord}{largesymbols}{"3E}{largesymbols}{"3E} +% +\makeatletter +\def\mathllap{\mathstrut\mathpalette\mathllapinternal} +%\def\mathllap{\mathpalette\mathllapinternal} +\def\mathllapinternal#1#2{% + \llap{$\mathsurround=0pt#1{#2}$}% +} +\def\clap#1{\hbox to 0pt{\hss#1\hss}} +\def\mathclap{\mathpalette\mathclapinternal} +\def\mathclapinternal#1#2{% + \clap{$\mathsurround=0pt#1{#2}$}% +} + +\def\mathrlap{\mathpalette\mathrlapinternal} +\def\mathrlapinternal#1#2{% + \rlap{$\mathsurround=0pt#1{#2}$}% +} +\def\bijmap{\ensuremath{% + \mathrlap{\rightarrowtail}\rightarrow}} +% extensible Arrow +\newcommand{\xLongLeftRightArrow}[2][]{% + \ext@arrow 0055{\LongLeftRightArrowfill@}{#1}{#2}} +\def\LongLeftRightArrowfill@{% + \arrowfill@\Leftarrow\Relbar\Rightarrow} +\newcommand\xlongleftrightarrow[2][]{% + \ext@arrow 0055{\longleftrightarrowfill@}{#1}{#2}} +\def\longleftrightarrowfill@{% + \arrowfill@\leftarrow\relbar\rightarrow} +% +% +\def\@bracketheight{2pt} +\def\underbracket{\@ifnextchar[{\@underbracket}{\@underbracket[\@bracketheight]}} +\def\@underbracket[#1]{\@ifnextchar[{\@under@bracket[#1]}{\@under@bracket[#1][0.4em]}} +\def\@under@bracket[#1][#2]#3{%\message {Underbracket: #1,#2,#3} + \mathop {\vtop {\m@th \ialign {##\crcr $\hfil \displaystyle {#3}\hfil $% + \crcr \noalign {\kern 3\p@ \nointerlineskip }\upbracketfill{#1}{#2} + \crcr \noalign {\kern 3\p@ }}}}\limits} +\def\upbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$} + \edef\@bracketheight{\the\ht\z@}\bracketend{#1}{#2} + \leaders \vrule \@height #1 \@depth \z@ \hfill + \leaders \vrule \@height #1 \@depth \z@ \hfill \bracketend{#1}{#2}$} +\def\bracketend#1#2{\vrule height #2 width #1\relax} +\def\overbracket{\@ifnextchar[{\@overbracket}{\@overbracket[\@bracketheight]}} +% +\def\@overbracket[#1]{\@ifnextchar[{\@over@bracket[#1]}{\@over@bracket[#1][0.3em]}} +\def\@over@bracket[#1][#2]#3{%\message {Overbracket: #1,#2,#3} + \mathop {\vbox {\m@th \ialign {##\crcr \noalign {\kern 3\p@ + \nointerlineskip }\downbracketfill {#1}{#2} + \crcr \noalign {\kern 3\p@ } + \crcr $\hfil \displaystyle {#3}\hfil $% + \crcr} }}\limits} +\def\downbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$} + \edef\@bracketheight{\the\ht\z@}\downbracketend{#1}{#2} + \leaders \vrule \@height #1 \@depth \z@ \hfill + \leaders \vrule \@height #1 \@depth \z@ \hfill +\downbracketend{#1}{#2}$} +\def\downbracketend#1#2{\vrule depth #2 width #1\relax} +% +\def\rightharpoondownfill@{% + \arrowfill@\relbar\relbar\rightharpoondown} +\def\rightharpoonupfill@{% + \arrowfill@\relbar\relbar\rightharpoonup} +\def\leftharpoondownfill@{% + \arrowfill@\leftharpoondown\relbar\relbar} +\def\leftharpoonupfill@{% + \arrowfill@\leftharpoonup\relbar\relbar} +\newcommand{\xrightharpoondown}[2][]{% + \ext@arrow 0359\rightharpoondownfill@{#1}{#2}} +\newcommand{\xrightharpoonup}[2][]{% + \ext@arrow 0359\rightharpoonupfill@{#1}{#2}} +\newcommand{\xleftharpoondown}[2][]{% + \ext@arrow 3095\leftharpoondownfill@{#1}{#2}} +\newcommand{\xleftharpoonup}[2][]{% + \ext@arrow 3095\leftharpoonupfill@{#1}{#2}} +\newcommand{\xleftrightharpoons}[2][]{\mathrel{% + \raise.22ex\hbox{% + $\ext@arrow 3095\leftharpoonupfill@{\phantom{#1}}{#2}$}% + \setbox0=\hbox{% + $\ext@arrow 0359\rightharpoondownfill@{#1}{\phantom{#2}}$}% + \kern-\wd0 \lower.22ex\box0}% +} +\newcommand{\xrightleftharpoons}[2][]{\mathrel{% + \raise.22ex\hbox{% + $\ext@arrow 3095\rightharpoonupfill@{\phantom{#1}}{#2}$}% + \setbox0=\hbox{% + $\ext@arrow 0359\leftharpoondownfill@{#1}{\phantom{#2}}$}% + \kern-\wd0 \lower.22ex\box0}% +} + +\usepackage[allowspaces]{empheq}% defines also harpoon macros +\usepackage{mathtools} +\usepackage{nicefrac} + +\newcommand*{\threesim}{% + \mathrel{\vcenter{\offinterlineskip + \hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}} +% +\newcounter{subequation} +% +\newlength\mtabskip\mtabskip=-1.25cm +% +\newcommand\eqnCnt[1][]{% + \refstepcounter{subequation}% + \begin{align}#1\end{align}% + \addtocounter{equation}{-1}% +} +\def\mtabLong{long} +\makeatletter +\newenvironment{mtabular}[2][\empty]{% + \parindent=0pt% + \def\@xarraycr{% + \global\stepcounter{equation}% + \setcounter{subequation}{0}% + \@ifnextchar[\@argarraycr{\@argarraycr[\mtabskip]}% + } + \let\theoldequation\theequation% + \renewcommand\theequation{\theoldequation.\alph{subequation}} + \edef\mtabOption{#1} + \setcounter{subequation}{0}% + \tabcolsep=0pt + \ifx\mtabOption\mtabLong\longtable{#2}\else\tabular{#2}\fi% +}{% + \ifx\mtabOption\mtabLong\endlongtable\else\endtabular\fi% + \let\theequation\theoldequation% + \stepcounter{equation} +} +% +\makeatother +\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}} +\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}} +%% For printing a cirumflex inside a formula +\newcommand{\mathcircumflex}[0]{\mbox{\^{}}} +\providecommand{\tabularnewline}{\\} +\usepackage{exscale} +\usepackage{relsize} +\usepackage{xspace} +\usepackage[mathscr]{eucal} +\usepackage{dsfont} +\usepackage[bottom]{footmisc} +\usepackage{esint} +\usepackage{esvect} +\usepackage{remreset} +\usepackage{calc} +\usepackage{cool} +\usepackage{xypic} +\usepackage{fancyhdr} +% +\pagestyle{fancy} +\lfoot{\footnotesize\ttfamily\jobname.tex} +\cfoot{} +\rfoot{\thepage} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} +% +\definecolor{umbra}{rgb}{0.8,0.8,0.5} +\definecolor{gray90}{gray}{0.9} +% +\addtocontents{toc}{\hfill Page\endgraf\vspace{-4ex}} +\addtocontents{lof}{\ Figure\hfill Page} +\addtocontents{lot}{\ Table\hfill Page} +\let\myPart\part +\renewcommand\part[1]{\clearpage\myPart{#1}} +% +%%%%%%%%%%%%% Math symbols %%%%%%%%%%%%%%%%% +\newcommand{\mysin}{\operatorname{mysin}} +\newcommand{\eqdef}{\ensuremath{\stackrel{\mathrm{def}}{=}}} +\newcommand{\eqexcl}{\ensuremath{\stackrel{\mathrm{!}}{=}}} +\newcommand{\eqhat}{\ensuremath{\widehat{=}}} +% +\newlength{\fullwidth} +\setlength\fullwidth{\textwidth} +\addtolength\fullwidth{\marginparsep} +\addtolength\fullwidth{\marginparwidth} +% +\newlength{\LBoxWidth} +\newcommand{\LyXBox}[1]{% + \settowidth{\LBoxWidth}{#1} + \fbox{\parbox[c]{\LBoxWidth}{#1}}\xspace% +} +\let\mpar\marginpar +\renewcommand\marginpar[1]{% + \mpar{\small #1}% +} +\newcommand{\logo}{% + \bgroup + \psset{unit=1in,linewidth=2pt} + \psline(-2.5,2.5)(-2.5,-\paperheight) + \psline(-2,2.5)(-2,-\paperheight) + \rput[lb]{90}(-2.05,-0.7\paperheight){\red\Huge\textbf{\AllTeX}} + \rput[lb]{90}(-2.15,-0.1\paperheight){\red\Huge\textbf{Documentation}} + \egroup +} +\newcommand*{\CMD}[1]{\texttt{\textbackslash#1}} +% +\makeatletter +\def\La{% + L\kern-.36em{% + \setbox0\hbox{T}% + \vbox to\ht0{% + \hbox{$\m@th$% + \csname S@\f@size\endcsname + \fontsize\sf@size\z@ + \math@fontsfalse\selectfont A}% + \vss% + }% + }% +} +\def\AllTeX{(\La\kern-.075em)\kern-.075em\TeX\xspace} +\def\AMS{American Mathematical Society\xspace} +\def\AmS{$\mathcal{A}$\kern-.1667em\lower.5ex\hbox + {$\mathcal{M}$}\kern-.125em$\mathcal{S}$\xspace} +\def\AmSmath{\AmS{}math\xspace} +\def\AmSLaTeX{\AmS-\LaTeX\xspace} +\def\AmSTeX{\AmS-\TeX\xspace} +\makeatother +% +\def\cIndex#1{\index{#1@\CMD{#1}}} +% +\usepackage{showexpl} +\lstset{language=[AlLaTeX]TeX} +% +\usepackage{microtype} +\usepackage[% + pdftitle={TeX Mathmode},% + pdfauthor={Herbert Voss},% + urlcolor=blue,% + linktocpage,% + a4paper,% + colorlinks=true]{hyperref} +\usepackage{hypcap} +\usepackage{babel} + +\def\tIndex#1{\index{#1@{\UrlFont\texttt{#1}}}} +\def\cIndex#1{\index{#1@\CMD{#1}}} +\def\pIndex#1{\index{Parameter@\textbf{Parameter}!{\UrlFont\texttt{#1}}}} +\def\PIndex#1{\texttt{#1}\index{Package@\textbf{Package}!\texttt{#1}}} +\def\Index#1{#1\index{#1}} +\def\CIndex#1{\CMD{#1}\index{#1@\CMD{#1}}\index{Macro@\textbf{Macro}!\CMD{#1}}} +\def\DIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{File@\textbf{File}!\texttt{#1}}} +\def\LIndex#1{\CMD{#1}\index{#1@\CMD{#1}}\index{Length@\textbf{Length}!\CMD{#1}}} +\def\ZIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{Counter@\textbf{Counter}!\texttt{#1}}} +\def\zIndex#1{\index{#1@\texttt{#1}}\index{Counter@\textbf{Counter}!\texttt{#1}}} +\def\FIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{Font@\textbf{Font}!\texttt{#1}}} +\def\UIndex#1{\texttt{#1} environment\index{Environment@\textbf{Environment}!\texttt{#1}}\index{#1@\texttt{#1}}} +\def\uIndex#1{\texttt{#1}\index{Environment@\textbf{Environment}!\texttt{#1}}\index{#1@\texttt{#1}}} +% +\newcommand*\eg{e.g.,\xspace} +\newcommand*\Eg{E.g.,\xspace} +\newcommand*\etc{etc.\@\xspace} +\newcommand*\dy{\,\mathrm{d}y} +\newcommand*\dx{\,\mathrm{d}x} +\newcommand*\dyx{\,\frac{\mathrm{d}y}{\mathrm{d}x}} +\newcommand*\ds{\,\mathrm{d}s} +\newcommand*\dt{\,\mathrm{d}t} +\newcommand*\dst{\,\frac{\mathrm{d}s}{\mathrm{d}t}} +% +% +\def\Mbox#1{\par +\vspace{2ex} +\noindent +\resizebox{\linewidth}{!}{\fbox{\includegraphics{#1}}}\par\medskip} + +\usepackage{braket}% there were problems when loading before other packages ... + +%------------------------------------------ Index macros ------------------------------------- +\def\Lcs#1{{\ttfamily\textbackslash#1}% + \index{Macro!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}} +\def\LMcs#1{{\ttfamily\bfseries\textbackslash#1}% + \index{Macro!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}} +\def\Ldim#1{{\ttfamily\textbackslash#1}% + \index{Dimension!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}} +\def\LMdim#1{{\ttfamily\bfseries\textbackslash#1}% + \index{Dimension!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}} +\def\Lskip#1{{\ttfamily\textbackslash#1}% + \index{Skip!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}} +\def\LMskip#1{{\ttfamily\bfseries\textbackslash#1}% + \index{Skip!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}} + +\def\LMcsStar#1{\LMcs{#1*}} +\def\LMcsOptStar#1{{\ttfamily\bfseries\textbackslash#1\OptArg{*}}} +\def\LMctr#1{{\ttfamily\bfseries#1}} +\def\Loption#1{{\ttfamily#1}} +\def\LClass#1{{\ttfamily#1}} +\def\nxLcs#1{{\ttfamily\textbackslash#1}} +\def\Lenv#1{{\ttfamily#1}} +\def\nxLenv#1{{\ttfamily#1}} +\def\Larg#1{{\itshape\ttfamily#1}} +\def\Largb#1{{\itshape\ttfamily\{#1\}}} +\def\Larga#1{{\itshape\ttfamily<#1>}} +\def\Largr#1{{\itshape\ttfamily(#1)}} +\def\Largs#1{{\itshape\ttfamily[#1]}} +\def\LMBEG#1{{\ttfamily\textbackslash begin\{\textbf{#1}\}}} +\def\LMBEGStar#1{{\ttfamily\textbackslash begin\{\textbf{#1*}\}}} +\def\LMBEGOptStar#1{{\ttfamily\textbackslash begin\{\textbf{#1\OptArg{*}}\}}} +\def\LEND#1{{\ttfamily\textbackslash end\{#1\}}} +\def\LENDStar#1{{\ttfamily\textbackslash end\{#1*\}}} +\def\LENDOptStar#1{{\ttfamily\textbackslash end\{#1\OptArg{*}\}}} +\def\OptArg#1{{\colorbox{black!20}{\ttfamily#1}}} +\def\Coordx#1{$x_{#1}$} +\def\Coordy#1{$y_{#1}$} +\def\Coordz#1{$z_{#1}$} +\def\Coord#1{\Coordx{#1},\kern 1pt\Coordy{#1}} +\def\CAny{\Coordx{},\kern 1pt\Coordy{}} +\def\CIIIAny{\Coordx{},\kern 1pt\Coordy{},\kern 1pt\Coordz{}}% hv +% with brackets +\def\coord#1{(\Coordx{#1},\kern 1pt\Coordy{#1})} +\def\coordiii#1{(\Coordx{#1},\kern 1pt\Coordy{#1},\kern 1pt\Coordy{#1})}% hv +\def\coordx#1{($x_{#1}$)} +\def\coordy#1{($y_{#1}$)} +\def\coordz#1{($z_{#1}$)} +\def\cAny{(\Coordx{},\kern 1pt\Coordy{})} +\def\ciiiAny{(\Coordx{},\kern 1pt\Coordy{},\kern 1pt\Coordy{})}% hv + + + +\graphicspath{{images/}} +\begin{document} + +\input{Mathmode.tex} + +\end{document} diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf new file mode 100644 index 00000000000..7887070ff84 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf @@ -0,0 +1,50285 @@ +%PDF-1.4 +% +5 0 obj +<< /S /GoTo /D (part.1) >> +endobj +8 0 obj +(I Standard LaTeX math mode) +endobj +9 0 obj +<< /S /GoTo /D (section.1) >> +endobj +12 0 obj +(Introduction) +endobj +13 0 obj +<< /S /GoTo /D (section.2) >> +endobj +16 0 obj +(The Inlinemode) +endobj +17 0 obj +<< /S /GoTo /D (subsection.2.1) >> +endobj +20 0 obj +(Limits) +endobj +21 0 obj +<< /S /GoTo /D (subsection.2.2) >> +endobj +24 0 obj +(Fraction command) +endobj +25 0 obj +<< /S /GoTo 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4173 0 R 4188 0 R 4215 0 R 4246 0 R] +>> endobj +4309 0 obj << +/Type /Pages +/Count 6 +/Parent 6225 0 R +/Kids [4276 0 R 4311 0 R 4334 0 R 4367 0 R 4402 0 R 4454 0 R] +>> endobj +4528 0 obj << +/Type /Pages +/Count 6 +/Parent 6225 0 R +/Kids [4508 0 R 4530 0 R 4566 0 R 4602 0 R 4617 0 R 4638 0 R] +>> endobj +4702 0 obj << +/Type /Pages +/Count 6 +/Parent 6225 0 R +/Kids [4666 0 R 4705 0 R 4734 0 R 4811 0 R 4835 0 R 4873 0 R] +>> endobj +4920 0 obj << +/Type /Pages +/Count 6 +/Parent 6225 0 R +/Kids [4902 0 R 4922 0 R 4935 0 R 4941 0 R 4968 0 R 4983 0 R] +>> endobj +5019 0 obj << +/Type /Pages +/Count 6 +/Parent 6226 0 R +/Kids [5007 0 R 5109 0 R 5221 0 R 5311 0 R 5408 0 R 5525 0 R] +>> endobj +5633 0 obj << +/Type /Pages +/Count 6 +/Parent 6226 0 R +/Kids [5630 0 R 5735 0 R 5840 0 R 5894 0 R 5898 0 R 5946 0 R] +>> endobj +6020 0 obj << +/Type /Pages +/Count 1 +/Parent 6226 0 R +/Kids [5999 0 R] +>> endobj +6222 0 obj << +/Type /Pages +/Count 36 +/Parent 6227 0 R +/Kids [1037 0 R 1279 0 R 1418 0 R 1605 0 R 1805 0 R 1936 0 R] +>> endobj +6223 0 obj << +/Type /Pages +/Count 36 +/Parent 6227 0 R +/Kids [2141 0 R 2256 0 R 2362 0 R 2505 0 R 2650 0 R 2783 0 R] +>> endobj +6224 0 obj << +/Type /Pages +/Count 36 +/Parent 6227 0 R +/Kids [2927 0 R 3057 0 R 3172 0 R 3344 0 R 3498 0 R 3591 0 R] +>> endobj +6225 0 obj << +/Type /Pages +/Count 36 +/Parent 6227 0 R +/Kids [3764 0 R 4154 0 R 4309 0 R 4528 0 R 4702 0 R 4920 0 R] +>> endobj +6226 0 obj << +/Type /Pages +/Count 13 +/Parent 6227 0 R +/Kids [5019 0 R 5633 0 R 6020 0 R] +>> endobj +6227 0 obj << +/Type /Pages +/Count 157 +/Kids [6222 0 R 6223 0 R 6224 0 R 6225 0 R 6226 0 R] +>> endobj +6228 0 obj << +/Type /Outlines +/First 7 0 R +/Last 995 0 R +/Count 8 +>> endobj +1015 0 obj << +/Title 1016 0 R +/A 1013 0 R +/Parent 995 0 R +/Prev 1011 0 R +>> endobj +1011 0 obj << +/Title 1012 0 R +/A 1009 0 R +/Parent 995 0 R +/Prev 1007 0 R +/Next 1015 0 R +>> endobj +1007 0 obj << +/Title 1008 0 R +/A 1005 0 R +/Parent 995 0 R 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0 R +/Prev 963 0 R +/Next 971 0 R +>> endobj +963 0 obj << +/Title 964 0 R +/A 961 0 R +/Parent 959 0 R +/Next 967 0 R +>> endobj +959 0 obj << +/Title 960 0 R +/A 957 0 R +/Parent 875 0 R +/Prev 955 0 R +/Next 975 0 R +/First 963 0 R +/Last 971 0 R +/Count -3 +>> endobj +955 0 obj << +/Title 956 0 R +/A 953 0 R +/Parent 875 0 R +/Prev 935 0 R +/Next 959 0 R +>> endobj +951 0 obj << +/Title 952 0 R +/A 949 0 R +/Parent 935 0 R +/Prev 947 0 R +>> endobj +947 0 obj << +/Title 948 0 R +/A 945 0 R +/Parent 935 0 R +/Prev 943 0 R +/Next 951 0 R +>> endobj +943 0 obj << +/Title 944 0 R +/A 941 0 R +/Parent 935 0 R +/Prev 939 0 R +/Next 947 0 R +>> endobj +939 0 obj << +/Title 940 0 R +/A 937 0 R +/Parent 935 0 R +/Next 943 0 R +>> endobj +935 0 obj << +/Title 936 0 R +/A 933 0 R +/Parent 875 0 R +/Prev 907 0 R +/Next 955 0 R +/First 939 0 R +/Last 951 0 R +/Count -4 +>> endobj +931 0 obj << +/Title 932 0 R +/A 929 0 R +/Parent 907 0 R +/Prev 927 0 R +>> endobj +927 0 obj << +/Title 928 0 R 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obj << +/Title 888 0 R +/A 885 0 R +/Parent 883 0 R +/Next 891 0 R +>> endobj +883 0 obj << +/Title 884 0 R +/A 881 0 R +/Parent 875 0 R +/Prev 879 0 R +/Next 899 0 R +/First 887 0 R +/Last 895 0 R +/Count -3 +>> endobj +879 0 obj << +/Title 880 0 R +/A 877 0 R +/Parent 875 0 R +/Next 883 0 R +>> endobj +875 0 obj << +/Title 876 0 R +/A 873 0 R +/Parent 6228 0 R +/Prev 851 0 R +/Next 995 0 R +/First 879 0 R +/Last 991 0 R +/Count -10 +>> endobj +871 0 obj << +/Title 872 0 R +/A 869 0 R +/Parent 851 0 R +/Prev 867 0 R +>> endobj +867 0 obj << +/Title 868 0 R +/A 865 0 R +/Parent 851 0 R +/Prev 863 0 R +/Next 871 0 R +>> endobj +863 0 obj << +/Title 864 0 R +/A 861 0 R +/Parent 851 0 R +/Prev 859 0 R +/Next 867 0 R +>> endobj +859 0 obj << +/Title 860 0 R +/A 857 0 R +/Parent 851 0 R +/Prev 855 0 R +/Next 863 0 R +>> endobj +855 0 obj << +/Title 856 0 R +/A 853 0 R +/Parent 851 0 R +/Next 859 0 R +>> endobj +851 0 obj << +/Title 852 0 R +/A 849 0 R +/Parent 6228 0 R +/Prev 823 0 R +/Next 875 0 R +/First 855 0 R +/Last 871 0 R +/Count -5 +>> endobj +847 0 obj << +/Title 848 0 R +/A 845 0 R +/Parent 823 0 R +/Prev 843 0 R +>> endobj +843 0 obj << +/Title 844 0 R +/A 841 0 R +/Parent 823 0 R +/Prev 839 0 R +/Next 847 0 R +>> endobj +839 0 obj << +/Title 840 0 R +/A 837 0 R +/Parent 823 0 R +/Prev 835 0 R +/Next 843 0 R +>> endobj +835 0 obj << +/Title 836 0 R +/A 833 0 R +/Parent 823 0 R +/Prev 831 0 R +/Next 839 0 R +>> endobj +831 0 obj << +/Title 832 0 R +/A 829 0 R +/Parent 823 0 R +/Prev 827 0 R +/Next 835 0 R +>> endobj +827 0 obj << +/Title 828 0 R +/A 825 0 R +/Parent 823 0 R +/Next 831 0 R +>> endobj +823 0 obj << +/Title 824 0 R +/A 821 0 R +/Parent 6228 0 R +/Prev 743 0 R +/Next 851 0 R +/First 827 0 R +/Last 847 0 R +/Count -6 +>> endobj +819 0 obj << +/Title 820 0 R +/A 817 0 R +/Parent 747 0 R +/Prev 815 0 R +>> endobj +815 0 obj << +/Title 816 0 R +/A 813 0 R +/Parent 747 0 R +/Prev 811 0 R +/Next 819 0 R +>> endobj +811 0 obj << +/Title 812 0 R +/A 809 0 R +/Parent 747 0 R +/Prev 807 0 R +/Next 815 0 R +>> endobj +807 0 obj << +/Title 808 0 R +/A 805 0 R +/Parent 747 0 R +/Prev 803 0 R +/Next 811 0 R +>> endobj +803 0 obj << +/Title 804 0 R +/A 801 0 R +/Parent 747 0 R +/Prev 799 0 R +/Next 807 0 R +>> endobj +799 0 obj << +/Title 800 0 R +/A 797 0 R +/Parent 747 0 R +/Prev 795 0 R +/Next 803 0 R +>> endobj +795 0 obj << +/Title 796 0 R +/A 793 0 R +/Parent 747 0 R +/Prev 791 0 R +/Next 799 0 R +>> endobj +791 0 obj << +/Title 792 0 R +/A 789 0 R +/Parent 747 0 R +/Prev 787 0 R +/Next 795 0 R +>> endobj +787 0 obj << +/Title 788 0 R +/A 785 0 R +/Parent 747 0 R +/Prev 783 0 R +/Next 791 0 R +>> endobj +783 0 obj << +/Title 784 0 R +/A 781 0 R +/Parent 747 0 R +/Prev 779 0 R +/Next 787 0 R +>> endobj +779 0 obj << +/Title 780 0 R +/A 777 0 R +/Parent 747 0 R +/Prev 775 0 R +/Next 783 0 R +>> endobj +775 0 obj << +/Title 776 0 R +/A 773 0 R +/Parent 747 0 R +/Prev 771 0 R +/Next 779 0 R +>> endobj +771 0 obj << +/Title 772 0 R +/A 769 0 R +/Parent 747 0 R +/Prev 767 0 R +/Next 775 0 R +>> endobj +767 0 obj << +/Title 768 0 R +/A 765 0 R +/Parent 747 0 R +/Prev 763 0 R +/Next 771 0 R +>> endobj +763 0 obj << +/Title 764 0 R +/A 761 0 R +/Parent 747 0 R +/Prev 759 0 R +/Next 767 0 R +>> endobj +759 0 obj << +/Title 760 0 R +/A 757 0 R +/Parent 747 0 R +/Prev 755 0 R +/Next 763 0 R +>> endobj +755 0 obj << +/Title 756 0 R +/A 753 0 R +/Parent 747 0 R +/Prev 751 0 R +/Next 759 0 R +>> endobj +751 0 obj << +/Title 752 0 R +/A 749 0 R +/Parent 747 0 R +/Next 755 0 R +>> endobj +747 0 obj << +/Title 748 0 R +/A 745 0 R +/Parent 743 0 R +/First 751 0 R +/Last 819 0 R +/Count -18 +>> endobj +743 0 obj << +/Title 744 0 R +/A 741 0 R +/Parent 6228 0 R +/Prev 443 0 R +/Next 823 0 R +/First 747 0 R +/Last 747 0 R +/Count -1 +>> endobj +739 0 obj << +/Title 740 0 R +/A 737 0 R +/Parent 719 0 R +/Prev 735 0 R +>> endobj +735 0 obj << +/Title 736 0 R +/A 733 0 R +/Parent 719 0 R +/Prev 731 0 R +/Next 739 0 R +>> endobj +731 0 obj << +/Title 732 0 R +/A 729 0 R +/Parent 719 0 R +/Prev 727 0 R +/Next 735 0 R +>> endobj +727 0 obj << +/Title 728 0 R +/A 725 0 R +/Parent 719 0 R +/Prev 723 0 R +/Next 731 0 R +>> endobj +723 0 obj << +/Title 724 0 R +/A 721 0 R +/Parent 719 0 R +/Next 727 0 R +>> endobj +719 0 obj << +/Title 720 0 R +/A 717 0 R +/Parent 443 0 R +/Prev 635 0 R +/First 723 0 R +/Last 739 0 R +/Count -5 +>> endobj +715 0 obj << +/Title 716 0 R +/A 713 0 R +/Parent 635 0 R +/Prev 711 0 R +>> endobj +711 0 obj << +/Title 712 0 R +/A 709 0 R +/Parent 635 0 R +/Prev 707 0 R +/Next 715 0 R +>> endobj +707 0 obj << +/Title 708 0 R +/A 705 0 R +/Parent 635 0 R +/Prev 703 0 R +/Next 711 0 R +>> endobj +703 0 obj << +/Title 704 0 R +/A 701 0 R +/Parent 635 0 R +/Prev 699 0 R +/Next 707 0 R +>> endobj +699 0 obj << +/Title 700 0 R +/A 697 0 R +/Parent 635 0 R +/Prev 695 0 R +/Next 703 0 R +>> endobj +695 0 obj << +/Title 696 0 R +/A 693 0 R +/Parent 635 0 R +/Prev 691 0 R +/Next 699 0 R +>> endobj +691 0 obj << +/Title 692 0 R +/A 689 0 R +/Parent 635 0 R +/Prev 687 0 R +/Next 695 0 R +>> endobj +687 0 obj << +/Title 688 0 R +/A 685 0 R +/Parent 635 0 R +/Prev 683 0 R +/Next 691 0 R +>> endobj +683 0 obj << +/Title 684 0 R +/A 681 0 R +/Parent 635 0 R +/Prev 679 0 R +/Next 687 0 R +>> endobj +679 0 obj << +/Title 680 0 R +/A 677 0 R +/Parent 635 0 R +/Prev 675 0 R +/Next 683 0 R +>> endobj +675 0 obj << +/Title 676 0 R +/A 673 0 R +/Parent 635 0 R +/Prev 671 0 R +/Next 679 0 R +>> endobj +671 0 obj << +/Title 672 0 R +/A 669 0 R +/Parent 635 0 R +/Prev 667 0 R +/Next 675 0 R +>> endobj +667 0 obj << +/Title 668 0 R +/A 665 0 R +/Parent 635 0 R +/Prev 663 0 R +/Next 671 0 R +>> endobj +663 0 obj << +/Title 664 0 R +/A 661 0 R +/Parent 635 0 R +/Prev 659 0 R +/Next 667 0 R +>> endobj +659 0 obj << +/Title 660 0 R +/A 657 0 R +/Parent 635 0 R +/Prev 655 0 R +/Next 663 0 R +>> endobj +655 0 obj << +/Title 656 0 R +/A 653 0 R +/Parent 635 0 R +/Prev 651 0 R +/Next 659 0 R +>> endobj +651 0 obj << +/Title 652 0 R +/A 649 0 R +/Parent 635 0 R +/Prev 647 0 R +/Next 655 0 R +>> endobj +647 0 obj << +/Title 648 0 R +/A 645 0 R +/Parent 635 0 R +/Prev 643 0 R +/Next 651 0 R +>> endobj +643 0 obj << +/Title 644 0 R +/A 641 0 R +/Parent 635 0 R +/Prev 639 0 R +/Next 647 0 R +>> endobj +639 0 obj << +/Title 640 0 R +/A 637 0 R +/Parent 635 0 R +/Next 643 0 R +>> endobj +635 0 obj << +/Title 636 0 R +/A 633 0 R +/Parent 443 0 R +/Prev 535 0 R +/Next 719 0 R +/First 639 0 R +/Last 715 0 R +/Count -20 +>> endobj +631 0 obj << +/Title 632 0 R +/A 629 0 R +/Parent 535 0 R +/Prev 627 0 R +>> endobj +627 0 obj << +/Title 628 0 R +/A 625 0 R +/Parent 535 0 R +/Prev 623 0 R +/Next 631 0 R +>> endobj +623 0 obj << +/Title 624 0 R +/A 621 0 R +/Parent 535 0 R +/Prev 619 0 R +/Next 627 0 R +>> endobj +619 0 obj << +/Title 620 0 R +/A 617 0 R +/Parent 535 0 R +/Prev 615 0 R +/Next 623 0 R +>> endobj +615 0 obj << +/Title 616 0 R +/A 613 0 R +/Parent 535 0 R +/Prev 611 0 R +/Next 619 0 R +>> endobj +611 0 obj << +/Title 612 0 R +/A 609 0 R +/Parent 535 0 R +/Prev 607 0 R +/Next 615 0 R +>> endobj +607 0 obj << +/Title 608 0 R +/A 605 0 R +/Parent 535 0 R +/Prev 603 0 R +/Next 611 0 R +>> endobj +603 0 obj << +/Title 604 0 R +/A 601 0 R +/Parent 535 0 R +/Prev 599 0 R +/Next 607 0 R +>> endobj +599 0 obj << +/Title 600 0 R +/A 597 0 R +/Parent 535 0 R +/Prev 595 0 R +/Next 603 0 R +>> endobj +595 0 obj << +/Title 596 0 R +/A 593 0 R +/Parent 535 0 R +/Prev 591 0 R +/Next 599 0 R +>> endobj +591 0 obj << +/Title 592 0 R +/A 589 0 R +/Parent 535 0 R +/Prev 587 0 R +/Next 595 0 R +>> endobj +587 0 obj << +/Title 588 0 R +/A 585 0 R +/Parent 535 0 R +/Prev 583 0 R +/Next 591 0 R +>> endobj +583 0 obj << +/Title 584 0 R +/A 581 0 R +/Parent 535 0 R +/Prev 579 0 R +/Next 587 0 R +>> endobj +579 0 obj << +/Title 580 0 R +/A 577 0 R +/Parent 535 0 R +/Prev 575 0 R +/Next 583 0 R +>> endobj +575 0 obj << +/Title 576 0 R +/A 573 0 R +/Parent 535 0 R +/Prev 571 0 R +/Next 579 0 R +>> endobj +571 0 obj << +/Title 572 0 R +/A 569 0 R +/Parent 535 0 R +/Prev 567 0 R +/Next 575 0 R +>> endobj +567 0 obj << +/Title 568 0 R +/A 565 0 R +/Parent 535 0 R +/Prev 563 0 R +/Next 571 0 R +>> endobj +563 0 obj << +/Title 564 0 R +/A 561 0 R +/Parent 535 0 R +/Prev 559 0 R +/Next 567 0 R +>> endobj +559 0 obj << +/Title 560 0 R +/A 557 0 R +/Parent 535 0 R +/Prev 555 0 R +/Next 563 0 R +>> endobj +555 0 obj << +/Title 556 0 R +/A 553 0 R +/Parent 535 0 R +/Prev 551 0 R +/Next 559 0 R +>> endobj +551 0 obj << +/Title 552 0 R +/A 549 0 R +/Parent 535 0 R +/Prev 547 0 R +/Next 555 0 R +>> endobj +547 0 obj << +/Title 548 0 R +/A 545 0 R +/Parent 535 0 R +/Prev 543 0 R +/Next 551 0 R +>> endobj +543 0 obj << +/Title 544 0 R +/A 541 0 R +/Parent 535 0 R +/Prev 539 0 R +/Next 547 0 R +>> endobj +539 0 obj << +/Title 540 0 R +/A 537 0 R +/Parent 535 0 R +/Next 543 0 R +>> endobj +535 0 obj << +/Title 536 0 R +/A 533 0 R +/Parent 443 0 R +/Prev 447 0 R +/Next 635 0 R +/First 539 0 R +/Last 631 0 R +/Count -24 +>> endobj +531 0 obj << +/Title 532 0 R +/A 529 0 R +/Parent 447 0 R +/Prev 527 0 R +>> endobj +527 0 obj << +/Title 528 0 R +/A 525 0 R +/Parent 447 0 R +/Prev 523 0 R +/Next 531 0 R +>> endobj +523 0 obj << +/Title 524 0 R +/A 521 0 R +/Parent 447 0 R +/Prev 519 0 R +/Next 527 0 R +>> endobj +519 0 obj << +/Title 520 0 R +/A 517 0 R +/Parent 447 0 R +/Prev 515 0 R +/Next 523 0 R +>> endobj +515 0 obj << +/Title 516 0 R +/A 513 0 R +/Parent 447 0 R +/Prev 511 0 R +/Next 519 0 R +>> endobj +511 0 obj << +/Title 512 0 R +/A 509 0 R +/Parent 447 0 R +/Prev 507 0 R +/Next 515 0 R +>> endobj +507 0 obj << +/Title 508 0 R +/A 505 0 R +/Parent 447 0 R +/Prev 503 0 R +/Next 511 0 R +>> endobj +503 0 obj << +/Title 504 0 R +/A 501 0 R +/Parent 447 0 R +/Prev 499 0 R +/Next 507 0 R +>> endobj +499 0 obj << +/Title 500 0 R +/A 497 0 R +/Parent 447 0 R +/Prev 495 0 R +/Next 503 0 R +>> endobj +495 0 obj << +/Title 496 0 R +/A 493 0 R +/Parent 447 0 R +/Prev 491 0 R +/Next 499 0 R +>> endobj +491 0 obj << +/Title 492 0 R +/A 489 0 R +/Parent 447 0 R +/Prev 487 0 R +/Next 495 0 R +>> endobj +487 0 obj << +/Title 488 0 R +/A 485 0 R +/Parent 447 0 R +/Prev 483 0 R +/Next 491 0 R +>> endobj +483 0 obj << +/Title 484 0 R +/A 481 0 R +/Parent 447 0 R +/Prev 479 0 R +/Next 487 0 R +>> endobj +479 0 obj << +/Title 480 0 R +/A 477 0 R +/Parent 447 0 R +/Prev 475 0 R +/Next 483 0 R +>> endobj +475 0 obj << +/Title 476 0 R +/A 473 0 R +/Parent 447 0 R +/Prev 471 0 R +/Next 479 0 R +>> endobj +471 0 obj << +/Title 472 0 R +/A 469 0 R +/Parent 447 0 R +/Prev 467 0 R +/Next 475 0 R +>> endobj +467 0 obj << +/Title 468 0 R +/A 465 0 R +/Parent 447 0 R +/Prev 463 0 R +/Next 471 0 R +>> endobj +463 0 obj << +/Title 464 0 R +/A 461 0 R +/Parent 447 0 R +/Prev 459 0 R +/Next 467 0 R +>> endobj +459 0 obj << +/Title 460 0 R +/A 457 0 R +/Parent 447 0 R +/Prev 455 0 R +/Next 463 0 R +>> endobj +455 0 obj << +/Title 456 0 R +/A 453 0 R +/Parent 447 0 R +/Prev 451 0 R +/Next 459 0 R +>> endobj +451 0 obj << +/Title 452 0 R +/A 449 0 R +/Parent 447 0 R +/Next 455 0 R +>> endobj +447 0 obj << +/Title 448 0 R +/A 445 0 R +/Parent 443 0 R +/Next 535 0 R +/First 451 0 R +/Last 531 0 R +/Count -21 +>> endobj +443 0 obj << +/Title 444 0 R +/A 441 0 R +/Parent 6228 0 R +/Prev 275 0 R +/Next 743 0 R +/First 447 0 R +/Last 719 0 R +/Count -4 +>> endobj +439 0 obj << +/Title 440 0 R +/A 437 0 R +/Parent 275 0 R +/Prev 435 0 R +>> endobj +435 0 obj << +/Title 436 0 R +/A 433 0 R +/Parent 275 0 R +/Prev 431 0 R +/Next 439 0 R +>> endobj +431 0 obj << +/Title 432 0 R +/A 429 0 R +/Parent 275 0 R +/Prev 427 0 R +/Next 435 0 R +>> endobj +427 0 obj << +/Title 428 0 R +/A 425 0 R +/Parent 275 0 R +/Prev 423 0 R +/Next 431 0 R +>> endobj +423 0 obj << +/Title 424 0 R +/A 421 0 R +/Parent 275 0 R +/Prev 411 0 R +/Next 427 0 R +>> endobj +419 0 obj << +/Title 420 0 R +/A 417 0 R +/Parent 411 0 R +/Prev 415 0 R +>> endobj +415 0 obj << +/Title 416 0 R +/A 413 0 R +/Parent 411 0 R +/Next 419 0 R +>> endobj +411 0 obj << +/Title 412 0 R +/A 409 0 R +/Parent 275 0 R +/Prev 407 0 R +/Next 423 0 R +/First 415 0 R +/Last 419 0 R +/Count -2 +>> endobj +407 0 obj << +/Title 408 0 R +/A 405 0 R +/Parent 275 0 R +/Prev 391 0 R +/Next 411 0 R +>> endobj +403 0 obj << +/Title 404 0 R +/A 401 0 R +/Parent 391 0 R +/Prev 399 0 R +>> endobj +399 0 obj << +/Title 400 0 R +/A 397 0 R +/Parent 391 0 R +/Prev 395 0 R +/Next 403 0 R +>> endobj +395 0 obj << +/Title 396 0 R +/A 393 0 R +/Parent 391 0 R +/Next 399 0 R +>> endobj +391 0 obj << +/Title 392 0 R +/A 389 0 R +/Parent 275 0 R +/Prev 387 0 R +/Next 407 0 R +/First 395 0 R +/Last 403 0 R +/Count -3 +>> endobj +387 0 obj << +/Title 388 0 R +/A 385 0 R +/Parent 275 0 R +/Prev 379 0 R +/Next 391 0 R +>> endobj +383 0 obj << +/Title 384 0 R +/A 381 0 R +/Parent 379 0 R +>> endobj +379 0 obj << +/Title 380 0 R +/A 377 0 R +/Parent 275 0 R +/Prev 375 0 R +/Next 387 0 R +/First 383 0 R +/Last 383 0 R +/Count -1 +>> endobj +375 0 obj << +/Title 376 0 R +/A 373 0 R +/Parent 275 0 R +/Prev 371 0 R +/Next 379 0 R +>> endobj +371 0 obj << +/Title 372 0 R +/A 369 0 R +/Parent 275 0 R +/Prev 363 0 R +/Next 375 0 R +>> endobj +367 0 obj << +/Title 368 0 R +/A 365 0 R +/Parent 363 0 R +>> endobj +363 0 obj << +/Title 364 0 R +/A 361 0 R +/Parent 275 0 R +/Prev 351 0 R +/Next 371 0 R +/First 367 0 R +/Last 367 0 R +/Count -1 +>> endobj +359 0 obj << +/Title 360 0 R +/A 357 0 R +/Parent 351 0 R +/Prev 355 0 R +>> endobj +355 0 obj << +/Title 356 0 R +/A 353 0 R +/Parent 351 0 R +/Next 359 0 R +>> endobj +351 0 obj << +/Title 352 0 R +/A 349 0 R +/Parent 275 0 R +/Prev 347 0 R +/Next 363 0 R +/First 355 0 R +/Last 359 0 R +/Count -2 +>> endobj +347 0 obj << +/Title 348 0 R +/A 345 0 R +/Parent 275 0 R +/Prev 343 0 R +/Next 351 0 R +>> endobj +343 0 obj << +/Title 344 0 R +/A 341 0 R +/Parent 275 0 R +/Prev 311 0 R +/Next 347 0 R +>> endobj +339 0 obj << +/Title 340 0 R +/A 337 0 R +/Parent 311 0 R +/Prev 335 0 R +>> endobj +335 0 obj << +/Title 336 0 R +/A 333 0 R +/Parent 311 0 R +/Prev 331 0 R +/Next 339 0 R +>> endobj +331 0 obj << +/Title 332 0 R +/A 329 0 R +/Parent 311 0 R +/Prev 323 0 R +/Next 335 0 R +>> endobj +327 0 obj << +/Title 328 0 R +/A 325 0 R +/Parent 323 0 R +>> endobj +323 0 obj << +/Title 324 0 R +/A 321 0 R +/Parent 311 0 R +/Prev 319 0 R +/Next 331 0 R +/First 327 0 R +/Last 327 0 R +/Count -1 +>> endobj +319 0 obj << +/Title 320 0 R +/A 317 0 R +/Parent 311 0 R +/Prev 315 0 R +/Next 323 0 R +>> endobj +315 0 obj << +/Title 316 0 R +/A 313 0 R +/Parent 311 0 R +/Next 319 0 R +>> endobj +311 0 obj << +/Title 312 0 R +/A 309 0 R +/Parent 275 0 R +/Prev 279 0 R +/Next 343 0 R +/First 315 0 R +/Last 339 0 R +/Count -6 +>> endobj +307 0 obj << +/Title 308 0 R +/A 305 0 R +/Parent 279 0 R +/Prev 303 0 R +>> endobj +303 0 obj << +/Title 304 0 R +/A 301 0 R +/Parent 279 0 R +/Prev 299 0 R +/Next 307 0 R +>> endobj +299 0 obj << +/Title 300 0 R +/A 297 0 R +/Parent 279 0 R +/Prev 295 0 R +/Next 303 0 R +>> endobj +295 0 obj << +/Title 296 0 R +/A 293 0 R +/Parent 279 0 R +/Prev 291 0 R +/Next 299 0 R +>> endobj +291 0 obj << +/Title 292 0 R +/A 289 0 R +/Parent 279 0 R +/Prev 287 0 R +/Next 295 0 R +>> endobj +287 0 obj << +/Title 288 0 R +/A 285 0 R +/Parent 279 0 R +/Prev 283 0 R +/Next 291 0 R +>> endobj +283 0 obj << +/Title 284 0 R +/A 281 0 R +/Parent 279 0 R +/Next 287 0 R +>> endobj +279 0 obj << +/Title 280 0 R +/A 277 0 R +/Parent 275 0 R +/Next 311 0 R +/First 283 0 R +/Last 307 0 R +/Count -7 +>> endobj +275 0 obj << +/Title 276 0 R +/A 273 0 R +/Parent 6228 0 R +/Prev 7 0 R +/Next 443 0 R +/First 279 0 R +/Last 439 0 R +/Count -18 +>> endobj +271 0 obj << +/Title 272 0 R +/A 269 0 R +/Parent 7 0 R +/Prev 267 0 R +>> endobj +267 0 obj << +/Title 268 0 R +/A 265 0 R +/Parent 7 0 R +/Prev 259 0 R +/Next 271 0 R +>> endobj +263 0 obj << +/Title 264 0 R +/A 261 0 R +/Parent 259 0 R +>> endobj +259 0 obj << +/Title 260 0 R +/A 257 0 R +/Parent 7 0 R +/Prev 255 0 R +/Next 267 0 R +/First 263 0 R +/Last 263 0 R +/Count -1 +>> endobj +255 0 obj << +/Title 256 0 R +/A 253 0 R +/Parent 7 0 R +/Prev 251 0 R +/Next 259 0 R +>> endobj +251 0 obj << +/Title 252 0 R +/A 249 0 R +/Parent 7 0 R +/Prev 247 0 R +/Next 255 0 R +>> endobj +247 0 obj << +/Title 248 0 R +/A 245 0 R +/Parent 7 0 R +/Prev 243 0 R +/Next 251 0 R +>> endobj +243 0 obj << +/Title 244 0 R +/A 241 0 R +/Parent 7 0 R +/Prev 239 0 R +/Next 247 0 R +>> endobj +239 0 obj << +/Title 240 0 R +/A 237 0 R +/Parent 7 0 R +/Prev 235 0 R +/Next 243 0 R +>> endobj +235 0 obj << +/Title 236 0 R +/A 233 0 R +/Parent 7 0 R +/Prev 231 0 R +/Next 239 0 R +>> endobj +231 0 obj << +/Title 232 0 R +/A 229 0 R +/Parent 7 0 R +/Prev 211 0 R +/Next 235 0 R +>> endobj +227 0 obj << +/Title 228 0 R +/A 225 0 R +/Parent 211 0 R +/Prev 215 0 R +>> endobj +223 0 obj << +/Title 224 0 R +/A 221 0 R +/Parent 215 0 R +/Prev 219 0 R +>> endobj +219 0 obj << +/Title 220 0 R +/A 217 0 R +/Parent 215 0 R +/Next 223 0 R +>> endobj +215 0 obj << +/Title 216 0 R +/A 213 0 R +/Parent 211 0 R +/Next 227 0 R +/First 219 0 R +/Last 223 0 R +/Count -2 +>> endobj +211 0 obj << +/Title 212 0 R +/A 209 0 R +/Parent 7 0 R +/Prev 207 0 R +/Next 231 0 R +/First 215 0 R +/Last 227 0 R +/Count -2 +>> endobj +207 0 obj << +/Title 208 0 R +/A 205 0 R +/Parent 7 0 R +/Prev 203 0 R +/Next 211 0 R +>> endobj +203 0 obj << +/Title 204 0 R +/A 201 0 R +/Parent 7 0 R +/Prev 171 0 R +/Next 207 0 R +>> endobj +199 0 obj << +/Title 200 0 R +/A 197 0 R +/Parent 191 0 R +/Prev 195 0 R +>> endobj +195 0 obj << +/Title 196 0 R +/A 193 0 R +/Parent 191 0 R +/Next 199 0 R +>> endobj +191 0 obj << +/Title 192 0 R +/A 189 0 R +/Parent 171 0 R +/Prev 187 0 R +/First 195 0 R +/Last 199 0 R +/Count -2 +>> endobj +187 0 obj << +/Title 188 0 R +/A 185 0 R +/Parent 171 0 R +/Prev 183 0 R +/Next 191 0 R +>> endobj +183 0 obj << +/Title 184 0 R +/A 181 0 R +/Parent 171 0 R +/Prev 179 0 R +/Next 187 0 R +>> endobj +179 0 obj << +/Title 180 0 R +/A 177 0 R +/Parent 171 0 R +/Prev 175 0 R +/Next 183 0 R +>> endobj +175 0 obj << +/Title 176 0 R +/A 173 0 R +/Parent 171 0 R +/Next 179 0 R +>> endobj +171 0 obj << +/Title 172 0 R +/A 169 0 R +/Parent 7 0 R +/Prev 159 0 R +/Next 203 0 R +/First 175 0 R +/Last 191 0 R +/Count -5 +>> endobj +167 0 obj << +/Title 168 0 R +/A 165 0 R +/Parent 159 0 R +/Prev 163 0 R +>> endobj +163 0 obj << +/Title 164 0 R +/A 161 0 R +/Parent 159 0 R +/Next 167 0 R +>> endobj +159 0 obj << +/Title 160 0 R +/A 157 0 R +/Parent 7 0 R +/Prev 155 0 R +/Next 171 0 R +/First 163 0 R +/Last 167 0 R +/Count -2 +>> endobj +155 0 obj << +/Title 156 0 R +/A 153 0 R +/Parent 7 0 R +/Prev 131 0 R +/Next 159 0 R +>> endobj +151 0 obj << +/Title 152 0 R +/A 149 0 R +/Parent 131 0 R +/Prev 147 0 R +>> endobj +147 0 obj << +/Title 148 0 R +/A 145 0 R +/Parent 131 0 R +/Prev 135 0 R +/Next 151 0 R +>> endobj +143 0 obj << +/Title 144 0 R +/A 141 0 R +/Parent 135 0 R +/Prev 139 0 R +>> endobj +139 0 obj << +/Title 140 0 R +/A 137 0 R +/Parent 135 0 R +/Next 143 0 R +>> endobj +135 0 obj << +/Title 136 0 R +/A 133 0 R +/Parent 131 0 R +/Next 147 0 R +/First 139 0 R +/Last 143 0 R +/Count -2 +>> endobj +131 0 obj << +/Title 132 0 R +/A 129 0 R +/Parent 7 0 R +/Prev 127 0 R +/Next 155 0 R +/First 135 0 R +/Last 151 0 R +/Count -3 +>> endobj +127 0 obj << +/Title 128 0 R +/A 125 0 R +/Parent 7 0 R +/Prev 115 0 R +/Next 131 0 R +>> endobj +123 0 obj << +/Title 124 0 R +/A 121 0 R +/Parent 115 0 R +/Prev 119 0 R +>> endobj +119 0 obj << +/Title 120 0 R +/A 117 0 R +/Parent 115 0 R +/Next 123 0 R +>> endobj +115 0 obj << +/Title 116 0 R +/A 113 0 R +/Parent 7 0 R +/Prev 111 0 R +/Next 127 0 R +/First 119 0 R +/Last 123 0 R +/Count -2 +>> endobj +111 0 obj << +/Title 112 0 R +/A 109 0 R +/Parent 7 0 R +/Prev 99 0 R +/Next 115 0 R +>> endobj +107 0 obj << +/Title 108 0 R +/A 105 0 R +/Parent 99 0 R +/Prev 103 0 R +>> endobj +103 0 obj << +/Title 104 0 R +/A 101 0 R +/Parent 99 0 R +/Next 107 0 R +>> endobj +99 0 obj << +/Title 100 0 R +/A 97 0 R +/Parent 7 0 R +/Prev 51 0 R +/Next 111 0 R +/First 103 0 R +/Last 107 0 R +/Count -2 +>> endobj +95 0 obj << +/Title 96 0 R +/A 93 0 R +/Parent 51 0 R +/Prev 91 0 R +>> endobj +91 0 obj << +/Title 92 0 R +/A 89 0 R +/Parent 51 0 R +/Prev 67 0 R +/Next 95 0 R +>> endobj +87 0 obj << +/Title 88 0 R +/A 85 0 R +/Parent 67 0 R +/Prev 83 0 R +>> endobj +83 0 obj << +/Title 84 0 R +/A 81 0 R +/Parent 67 0 R +/Prev 79 0 R +/Next 87 0 R +>> endobj +79 0 obj << +/Title 80 0 R +/A 77 0 R +/Parent 67 0 R +/Prev 75 0 R +/Next 83 0 R +>> endobj +75 0 obj << +/Title 76 0 R +/A 73 0 R +/Parent 67 0 R +/Prev 71 0 R +/Next 79 0 R +>> endobj +71 0 obj << +/Title 72 0 R +/A 69 0 R +/Parent 67 0 R +/Next 75 0 R +>> endobj +67 0 obj << +/Title 68 0 R +/A 65 0 R +/Parent 51 0 R +/Prev 59 0 R +/Next 91 0 R +/First 71 0 R +/Last 87 0 R +/Count -5 +>> endobj +63 0 obj << +/Title 64 0 R +/A 61 0 R +/Parent 59 0 R +>> endobj +59 0 obj << +/Title 60 0 R +/A 57 0 R +/Parent 51 0 R +/Prev 55 0 R +/Next 67 0 R +/First 63 0 R +/Last 63 0 R +/Count -1 +>> endobj +55 0 obj << +/Title 56 0 R +/A 53 0 R +/Parent 51 0 R +/Next 59 0 R +>> endobj +51 0 obj << +/Title 52 0 R +/A 49 0 R +/Parent 7 0 R +/Prev 15 0 R +/Next 99 0 R +/First 55 0 R +/Last 95 0 R +/Count -5 +>> endobj +47 0 obj << +/Title 48 0 R +/A 45 0 R +/Parent 15 0 R +/Prev 43 0 R +>> endobj +43 0 obj << +/Title 44 0 R +/A 41 0 R +/Parent 15 0 R +/Prev 39 0 R +/Next 47 0 R +>> endobj +39 0 obj << +/Title 40 0 R +/A 37 0 R +/Parent 15 0 R +/Prev 35 0 R +/Next 43 0 R +>> endobj +35 0 obj << +/Title 36 0 R +/A 33 0 R +/Parent 15 0 R +/Prev 31 0 R +/Next 39 0 R +>> endobj +31 0 obj << +/Title 32 0 R +/A 29 0 R +/Parent 15 0 R +/Prev 27 0 R +/Next 35 0 R +>> endobj +27 0 obj << +/Title 28 0 R +/A 25 0 R +/Parent 15 0 R +/Prev 23 0 R +/Next 31 0 R +>> endobj +23 0 obj << +/Title 24 0 R +/A 21 0 R +/Parent 15 0 R +/Prev 19 0 R +/Next 27 0 R +>> endobj +19 0 obj << +/Title 20 0 R +/A 17 0 R +/Parent 15 0 R +/Next 23 0 R +>> endobj +15 0 obj << +/Title 16 0 R +/A 13 0 R +/Parent 7 0 R +/Prev 11 0 R +/Next 51 0 R +/First 19 0 R +/Last 47 0 R +/Count -8 +>> endobj +11 0 obj << +/Title 12 0 R +/A 9 0 R +/Parent 7 0 R +/Next 15 0 R +>> endobj +7 0 obj << +/Title 8 0 R +/A 5 0 R +/Parent 6228 0 R +/Next 275 0 R +/First 11 0 R +/Last 271 0 R +/Count -24 +>> endobj +6229 0 obj << +/Names [(AMS.12) 2887 0 R (AMS.13) 2888 0 R (AMS.14) 2889 0 R (AMS.15) 3627 0 R (AMS.16) 3633 0 R (AMS.17) 3640 0 R] +/Limits [(AMS.12) (AMS.17)] +>> endobj +6230 0 obj << +/Names [(Doc-Start) 1025 0 R (Item.1) 1358 0 R (Item.10) 1431 0 R (Item.11) 1432 0 R (Item.12) 1433 0 R (Item.13) 1434 0 R] +/Limits [(Doc-Start) (Item.13)] +>> endobj +6231 0 obj << +/Names [(Item.14) 1436 0 R (Item.15) 1437 0 R (Item.16) 1438 0 R (Item.17) 2217 0 R (Item.18) 2219 0 R (Item.19) 2367 0 R] +/Limits [(Item.14) (Item.19)] +>> endobj +6232 0 obj << +/Names [(Item.2) 1359 0 R (Item.20) 2368 0 R (Item.21) 2369 0 R (Item.3) 1360 0 R (Item.4) 1370 0 R (Item.5) 1371 0 R] +/Limits [(Item.2) (Item.5)] +>> endobj +6233 0 obj << +/Names [(Item.6) 1373 0 R (Item.7) 1428 0 R (Item.8) 1429 0 R (Item.9) 1430 0 R (appendix.A) 1014 0 R (cite.MathGuide) 2784 0 R] +/Limits [(Item.6) (cite.MathGuide)] +>> endobj +6234 0 obj << +/Names [(cite.Notes) 4992 0 R (cite.beccardi97) 4987 0 R (cite.bouchie98) 4988 0 R (cite.companion94) 4996 0 R (cite.dtk04.2:voss) 5018 0 R (cite.dtk04.3:voss) 5017 0 R] +/Limits [(cite.Notes) (cite.dtk04.3:voss)] +>> endobj +6235 0 obj << +/Names [(cite.eijkhout) 4994 0 R (cite.expressionsI) 4990 0 R (cite.expressionsII) 4989 0 R (cite.graetzer00) 4997 0 R (cite.harvard) 5000 0 R (cite.impatient) 4986 0 R] +/Limits [(cite.eijkhout) (cite.impatient)] +>> endobj +6236 0 obj << +/Names [(cite.knuth86) 4213 0 R (cite.kuester:2004) 5011 0 R (cite.kuester:2004-2) 5010 0 R (cite.lawrence04) 5012 0 R (cite.mathwriting87) 4998 0 R (cite.nist) 5013 0 R] +/Limits [(cite.knuth86) (cite.nist)] +>> endobj 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[(equation.47.8) 3659 0 R (equation.47.9) 3660 0 R (equation.54.1) 4100 0 R (equation.6.21) 1795 0 R (equation.6.22) 1804 0 R (equation.6.23) 1815 0 R] +/Limits [(equation.47.8) (equation.6.23)] +>> endobj +6259 0 obj << +/Names [(equation.6.23a) 1816 0 R (equation.6.23b) 1817 0 R (equation.61.1) 4264 0 R (equation.61.2) 4279 0 R (equation.61.3) 4280 0 R (equation.61.4) 4291 0 R] +/Limits [(equation.6.23a) (equation.61.4)] +>> endobj +6260 0 obj << +/Names [(equation.61.5) 4292 0 R (equation.61.6) 4299 0 R (equation.61.7) 4300 0 R (equation.62.1) 4314 0 R (equation.62.2) 4337 0 R (equation.63.1) 4517 0 R] +/Limits [(equation.61.5) (equation.63.1)] +>> endobj +6261 0 obj << +/Names [(equation.63.2) 4542 0 R (equation.65.1) 4620 0 R (equation.65.10) 4718 0 R (equation.65.2) 4621 0 R (equation.65.3) 4622 0 R (equation.65.4) 4623 0 R] +/Limits [(equation.63.2) (equation.65.4)] +>> endobj +6262 0 obj << +/Names [(equation.65.5) 4669 0 R (equation.65.6) 4675 0 R (equation.65.7) 4676 0 R 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[(lstlisting.-142) 2675 0 R (lstlisting.-143) 2685 0 R (lstlisting.-144) 2710 0 R (lstlisting.-145) 2730 0 R (lstlisting.-146) 2742 0 R (lstlisting.-147) 2753 0 R] +/Limits [(lstlisting.-142) (lstlisting.-147)] +>> endobj +6276 0 obj << +/Names [(lstlisting.-148) 2759 0 R (lstlisting.-149) 2768 0 R (lstlisting.-15) 1459 0 R (lstlisting.-150) 2781 0 R (lstlisting.-151) 2799 0 R (lstlisting.-152) 2801 0 R] +/Limits [(lstlisting.-148) (lstlisting.-152)] +>> endobj +6277 0 obj << +/Names [(lstlisting.-153) 2803 0 R (lstlisting.-154) 2815 0 R (lstlisting.-155) 2822 0 R (lstlisting.-156) 2824 0 R (lstlisting.-157) 2838 0 R (lstlisting.-158) 2847 0 R] +/Limits [(lstlisting.-153) (lstlisting.-158)] +>> endobj +6278 0 obj << +/Names [(lstlisting.-159) 2859 0 R (lstlisting.-16) 1473 0 R (lstlisting.-160) 2890 0 R (lstlisting.-161) 2906 0 R (lstlisting.-162) 2908 0 R (lstlisting.-163) 2910 0 R] +/Limits [(lstlisting.-159) (lstlisting.-163)] +>> endobj +6279 0 obj << +/Names [(lstlisting.-164) 2914 0 R (lstlisting.-165) 2923 0 R (lstlisting.-166) 2933 0 R (lstlisting.-167) 2947 0 R (lstlisting.-169) 2952 0 R (lstlisting.-17) 1480 0 R] +/Limits [(lstlisting.-164) (lstlisting.-17)] +>> endobj +6280 0 obj << +/Names [(lstlisting.-170) 2966 0 R (lstlisting.-171) 2968 0 R (lstlisting.-172) 2973 0 R (lstlisting.-173) 2983 0 R (lstlisting.-174) 2988 0 R (lstlisting.-175) 3004 0 R] +/Limits [(lstlisting.-170) (lstlisting.-175)] +>> endobj +6281 0 obj << +/Names [(lstlisting.-176) 3014 0 R (lstlisting.-177) 3034 0 R (lstlisting.-178) 3043 0 R (lstlisting.-179) 3053 0 R (lstlisting.-180) 3065 0 R (lstlisting.-181) 3076 0 R] +/Limits [(lstlisting.-176) (lstlisting.-181)] +>> endobj +6282 0 obj << +/Names [(lstlisting.-182) 3095 0 R (lstlisting.-184) 3117 0 R (lstlisting.-186) 3132 0 R (lstlisting.-188) 3144 0 R (lstlisting.-19) 1491 0 R (lstlisting.-190) 3150 0 R] +/Limits [(lstlisting.-182) (lstlisting.-190)] +>> endobj +6283 0 obj << +/Names [(lstlisting.-191) 3161 0 R 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endobj +6371 0 obj << +/Names [(lstnumber.-166.7) 2940 0 R (lstnumber.-166.8) 2941 0 R (lstnumber.-166.9) 2942 0 R (lstnumber.-167.1) 2948 0 R (lstnumber.-167.2) 2949 0 R (lstnumber.-167.3) 2950 0 R] +/Limits [(lstnumber.-166.7) (lstnumber.-167.3)] +>> endobj +6372 0 obj << +/Names [(lstnumber.-169.1) 2954 0 R (lstnumber.-169.2) 2955 0 R (lstnumber.-169.3) 2956 0 R (lstnumber.-169.4) 2957 0 R (lstnumber.-169.5) 2958 0 R (lstnumber.-17.1) 1481 0 R] +/Limits [(lstnumber.-169.1) (lstnumber.-17.1)] +>> endobj +6373 0 obj << +/Names [(lstnumber.-17.2) 1482 0 R (lstnumber.-17.3) 1484 0 R (lstnumber.-17.4) 1485 0 R (lstnumber.-17.5) 1486 0 R (lstnumber.-17.6) 1487 0 R (lstnumber.-17.7) 1488 0 R] +/Limits [(lstnumber.-17.2) (lstnumber.-17.7)] +>> endobj +6374 0 obj << +/Names [(lstnumber.-17.8) 1489 0 R (lstnumber.-17.9) 1490 0 R (lstnumber.-170.1) 2967 0 R (lstnumber.-171.1) 2969 0 R (lstnumber.-171.2) 2970 0 R (lstnumber.-171.3) 2971 0 R] +/Limits [(lstnumber.-17.8) (lstnumber.-171.3)] +>> endobj +6375 0 obj << +/Names [(lstnumber.-172.1) 2974 0 R (lstnumber.-173.1) 2984 0 R (lstnumber.-174.1) 2989 0 R (lstnumber.-174.2) 2990 0 R (lstnumber.-174.3) 2991 0 R (lstnumber.-174.4) 2992 0 R] +/Limits [(lstnumber.-172.1) (lstnumber.-174.4)] +>> endobj +6376 0 obj << +/Names [(lstnumber.-174.5) 2993 0 R (lstnumber.-174.6) 2994 0 R (lstnumber.-174.7) 2995 0 R (lstnumber.-174.8) 2996 0 R (lstnumber.-175.1) 3005 0 R (lstnumber.-175.2) 3006 0 R] +/Limits [(lstnumber.-174.5) (lstnumber.-175.2)] +>> endobj +6377 0 obj << +/Names [(lstnumber.-175.3) 3007 0 R (lstnumber.-175.4) 3008 0 R (lstnumber.-175.5) 3009 0 R (lstnumber.-175.6) 3010 0 R (lstnumber.-175.7) 3011 0 R (lstnumber.-175.8) 3012 0 R] +/Limits [(lstnumber.-175.3) (lstnumber.-175.8)] +>> endobj +6378 0 obj << +/Names [(lstnumber.-175.9) 3013 0 R (lstnumber.-176.1) 3015 0 R (lstnumber.-176.10) 3029 0 R (lstnumber.-176.11) 3030 0 R (lstnumber.-176.12) 3031 0 R (lstnumber.-176.13) 3032 0 R] +/Limits [(lstnumber.-175.9) (lstnumber.-176.13)] +>> endobj +6379 0 obj << +/Names [(lstnumber.-176.2) 3016 0 R (lstnumber.-176.3) 3017 0 R (lstnumber.-176.4) 3018 0 R (lstnumber.-176.5) 3019 0 R (lstnumber.-176.6) 3020 0 R (lstnumber.-176.7) 3021 0 R] +/Limits [(lstnumber.-176.2) (lstnumber.-176.7)] +>> endobj +6380 0 obj << +/Names [(lstnumber.-176.8) 3022 0 R (lstnumber.-176.9) 3028 0 R (lstnumber.-177.1) 3035 0 R (lstnumber.-177.2) 3036 0 R (lstnumber.-177.3) 3037 0 R (lstnumber.-177.4) 3038 0 R] +/Limits [(lstnumber.-176.8) (lstnumber.-177.4)] +>> endobj +6381 0 obj << +/Names [(lstnumber.-177.5) 3039 0 R (lstnumber.-177.6) 3040 0 R (lstnumber.-177.7) 3041 0 R (lstnumber.-177.8) 3042 0 R (lstnumber.-178.1) 3044 0 R (lstnumber.-178.2) 3045 0 R] +/Limits [(lstnumber.-177.5) (lstnumber.-178.2)] +>> endobj +6382 0 obj << +/Names [(lstnumber.-178.3) 3046 0 R (lstnumber.-178.4) 3047 0 R (lstnumber.-179.1) 3054 0 R (lstnumber.-179.2) 3055 0 R (lstnumber.-180.1) 3066 0 R (lstnumber.-180.2) 3067 0 R] +/Limits [(lstnumber.-178.3) (lstnumber.-180.2)] +>> endobj +6383 0 obj << +/Names [(lstnumber.-180.3) 3068 0 R (lstnumber.-181.1) 3077 0 R (lstnumber.-181.10) 3086 0 R (lstnumber.-181.11) 3087 0 R (lstnumber.-181.12) 3088 0 R (lstnumber.-181.13) 3089 0 R] +/Limits [(lstnumber.-180.3) (lstnumber.-181.13)] +>> endobj +6384 0 obj << +/Names [(lstnumber.-181.14) 3090 0 R (lstnumber.-181.2) 3078 0 R (lstnumber.-181.3) 3079 0 R (lstnumber.-181.4) 3080 0 R (lstnumber.-181.5) 3081 0 R (lstnumber.-181.6) 3082 0 R] +/Limits [(lstnumber.-181.14) (lstnumber.-181.6)] +>> endobj +6385 0 obj << +/Names [(lstnumber.-181.7) 3083 0 R (lstnumber.-181.8) 3084 0 R (lstnumber.-181.9) 3085 0 R (lstnumber.-182.1) 3096 0 R (lstnumber.-182.10) 3105 0 R (lstnumber.-182.11) 3106 0 R] +/Limits [(lstnumber.-181.7) (lstnumber.-182.11)] +>> endobj +6386 0 obj << +/Names [(lstnumber.-182.12) 3107 0 R (lstnumber.-182.13) 3108 0 R (lstnumber.-182.2) 3097 0 R (lstnumber.-182.3) 3098 0 R (lstnumber.-182.4) 3099 0 R (lstnumber.-182.5) 3100 0 R] +/Limits [(lstnumber.-182.12) (lstnumber.-182.5)] +>> endobj +6387 0 obj << +/Names [(lstnumber.-182.6) 3101 0 R (lstnumber.-182.7) 3102 0 R (lstnumber.-182.8) 3103 0 R (lstnumber.-182.9) 3104 0 R (lstnumber.-184.1) 3118 0 R (lstnumber.-184.10) 3127 0 R] +/Limits [(lstnumber.-182.6) (lstnumber.-184.10)] +>> endobj +6388 0 obj << +/Names [(lstnumber.-184.2) 3119 0 R (lstnumber.-184.3) 3120 0 R (lstnumber.-184.4) 3121 0 R (lstnumber.-184.5) 3122 0 R (lstnumber.-184.6) 3123 0 R (lstnumber.-184.7) 3124 0 R] +/Limits [(lstnumber.-184.2) (lstnumber.-184.7)] +>> endobj +6389 0 obj << +/Names [(lstnumber.-184.8) 3125 0 R (lstnumber.-184.9) 3126 0 R (lstnumber.-186.1) 3133 0 R (lstnumber.-186.10) 3142 0 R (lstnumber.-186.11) 3143 0 R (lstnumber.-186.2) 3134 0 R] +/Limits [(lstnumber.-184.8) (lstnumber.-186.2)] +>> endobj +6390 0 obj << +/Names [(lstnumber.-186.3) 3135 0 R (lstnumber.-186.4) 3136 0 R (lstnumber.-186.5) 3137 0 R (lstnumber.-186.6) 3138 0 R (lstnumber.-186.7) 3139 0 R (lstnumber.-186.8) 3140 0 R] +/Limits [(lstnumber.-186.3) (lstnumber.-186.8)] +>> endobj +6391 0 obj << +/Names [(lstnumber.-186.9) 3141 0 R (lstnumber.-188.1) 3145 0 R (lstnumber.-188.2) 3146 0 R (lstnumber.-188.3) 3147 0 R (lstnumber.-188.4) 3148 0 R (lstnumber.-188.5) 3149 0 R] +/Limits [(lstnumber.-186.9) (lstnumber.-188.5)] +>> endobj +6392 0 obj << +/Names [(lstnumber.-19.1) 1493 0 R (lstnumber.-19.2) 1494 0 R (lstnumber.-19.3) 1495 0 R (lstnumber.-190.1) 3151 0 R (lstnumber.-190.2) 3152 0 R (lstnumber.-190.3) 3153 0 R] +/Limits [(lstnumber.-19.1) (lstnumber.-190.3)] +>> endobj +6393 0 obj << +/Names [(lstnumber.-190.4) 3154 0 R (lstnumber.-191.1) 3162 0 R (lstnumber.-191.2) 3163 0 R (lstnumber.-191.3) 3164 0 R (lstnumber.-191.4) 3165 0 R (lstnumber.-192.1) 3167 0 R] +/Limits [(lstnumber.-190.4) (lstnumber.-192.1)] +>> endobj +6394 0 obj << +/Names [(lstnumber.-192.2) 3168 0 R (lstnumber.-192.3) 3169 0 R (lstnumber.-192.4) 3170 0 R (lstnumber.-192.5) 3171 0 R (lstnumber.-194.1) 3180 0 R (lstnumber.-194.2) 3181 0 R] +/Limits [(lstnumber.-192.2) (lstnumber.-194.2)] +>> endobj +6395 0 obj << +/Names [(lstnumber.-194.3) 3182 0 R (lstnumber.-194.4) 3183 0 R (lstnumber.-194.5) 3184 0 R (lstnumber.-196.1) 3193 0 R (lstnumber.-196.2) 3194 0 R (lstnumber.-196.3) 3195 0 R] +/Limits [(lstnumber.-194.3) (lstnumber.-196.3)] +>> endobj +6396 0 obj << +/Names [(lstnumber.-196.4) 3196 0 R (lstnumber.-196.5) 3197 0 R (lstnumber.-196.6) 3198 0 R (lstnumber.-196.7) 3199 0 R (lstnumber.-198.1) 3201 0 R (lstnumber.-198.2) 3202 0 R] +/Limits [(lstnumber.-196.4) (lstnumber.-198.2)] +>> endobj +6397 0 obj << +/Names [(lstnumber.-198.3) 3203 0 R (lstnumber.-198.4) 3204 0 R (lstnumber.-198.5) 3205 0 R (lstnumber.-198.6) 3206 0 R (lstnumber.-198.7) 3207 0 R (lstnumber.-198.8) 3208 0 R] +/Limits [(lstnumber.-198.3) (lstnumber.-198.8)] +>> endobj +6398 0 obj << +/Names [(lstnumber.-200.1) 3215 0 R (lstnumber.-200.2) 3216 0 R (lstnumber.-202.1) 3218 0 R 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3313 0 R (lstnumber.-212.1) 3321 0 R (lstnumber.-212.2) 3322 0 R (lstnumber.-214.1) 3324 0 R] +/Limits [(lstnumber.-210.1) (lstnumber.-214.1)] +>> endobj +6403 0 obj << +/Names [(lstnumber.-214.2) 3325 0 R (lstnumber.-214.3) 3326 0 R (lstnumber.-216.1) 3328 0 R (lstnumber.-216.2) 3329 0 R (lstnumber.-216.3) 3330 0 R (lstnumber.-218.1) 3332 0 R] +/Limits [(lstnumber.-214.2) (lstnumber.-218.1)] +>> endobj +6404 0 obj << +/Names [(lstnumber.-218.2) 3333 0 R (lstnumber.-218.3) 3334 0 R (lstnumber.-218.4) 3335 0 R (lstnumber.-22.1) 1516 0 R (lstnumber.-220.1) 3341 0 R (lstnumber.-220.2) 3342 0 R] +/Limits [(lstnumber.-218.2) (lstnumber.-220.2)] +>> endobj +6405 0 obj << +/Names [(lstnumber.-220.3) 3343 0 R (lstnumber.-222.1) 3350 0 R (lstnumber.-222.2) 3351 0 R (lstnumber.-222.3) 3352 0 R (lstnumber.-222.4) 3353 0 R (lstnumber.-222.5) 3354 0 R] +/Limits [(lstnumber.-220.3) (lstnumber.-222.5)] +>> endobj +6406 0 obj << +/Names [(lstnumber.-222.6) 3355 0 R (lstnumber.-222.7) 3356 0 R 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[(lstnumber.-245.7) 3513 0 R (lstnumber.-246.1) 3515 0 R (lstnumber.-246.2) 3516 0 R (lstnumber.-246.3) 3517 0 R (lstnumber.-246.4) 3518 0 R (lstnumber.-246.5) 3519 0 R] +/Limits [(lstnumber.-245.7) (lstnumber.-246.5)] +>> endobj +6419 0 obj << +/Names [(lstnumber.-246.6) 3520 0 R (lstnumber.-246.7) 3521 0 R (lstnumber.-247.1) 3528 0 R (lstnumber.-247.10) 3537 0 R (lstnumber.-247.11) 3538 0 R (lstnumber.-247.12) 3539 0 R] +/Limits [(lstnumber.-246.6) (lstnumber.-247.12)] +>> endobj +6420 0 obj << +/Names [(lstnumber.-247.13) 3540 0 R (lstnumber.-247.2) 3529 0 R (lstnumber.-247.3) 3530 0 R (lstnumber.-247.4) 3531 0 R (lstnumber.-247.5) 3532 0 R (lstnumber.-247.6) 3533 0 R] +/Limits [(lstnumber.-247.13) (lstnumber.-247.6)] +>> endobj +6421 0 obj << +/Names [(lstnumber.-247.7) 3534 0 R (lstnumber.-247.8) 3535 0 R (lstnumber.-247.9) 3536 0 R (lstnumber.-248.1) 3549 0 R (lstnumber.-249.1) 3551 0 R (lstnumber.-249.2) 3552 0 R] +/Limits [(lstnumber.-247.7) (lstnumber.-249.2)] +>> endobj +6422 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endobj +6430 0 obj << +/Names [(lstnumber.-257.1) 3608 0 R (lstnumber.-257.2) 3609 0 R (lstnumber.-257.3) 3610 0 R (lstnumber.-257.4) 3611 0 R (lstnumber.-257.5) 3612 0 R (lstnumber.-257.6) 3613 0 R] +/Limits [(lstnumber.-257.1) (lstnumber.-257.6)] +>> endobj +6431 0 obj << +/Names [(lstnumber.-258.1) 3620 0 R (lstnumber.-258.2) 3621 0 R (lstnumber.-258.3) 3622 0 R (lstnumber.-258.4) 3623 0 R (lstnumber.-258.5) 3624 0 R (lstnumber.-258.6) 3625 0 R] +/Limits [(lstnumber.-258.1) (lstnumber.-258.6)] +>> endobj +6432 0 obj << +/Names [(lstnumber.-258.7) 3626 0 R (lstnumber.-259.1) 3630 0 R (lstnumber.-259.2) 3631 0 R (lstnumber.-259.3) 3632 0 R (lstnumber.-26.1) 1562 0 R (lstnumber.-26.10) 1571 0 R] +/Limits [(lstnumber.-258.7) (lstnumber.-26.10)] +>> endobj +6433 0 obj << +/Names [(lstnumber.-26.11) 1572 0 R (lstnumber.-26.12) 1573 0 R (lstnumber.-26.13) 1574 0 R (lstnumber.-26.14) 1575 0 R (lstnumber.-26.15) 1576 0 R (lstnumber.-26.16) 1577 0 R] +/Limits [(lstnumber.-26.11) (lstnumber.-26.16)] +>> endobj +6434 0 obj << +/Names [(lstnumber.-26.17) 1578 0 R (lstnumber.-26.18) 1579 0 R (lstnumber.-26.2) 1563 0 R (lstnumber.-26.3) 1564 0 R (lstnumber.-26.4) 1565 0 R (lstnumber.-26.5) 1566 0 R] +/Limits [(lstnumber.-26.17) (lstnumber.-26.5)] +>> endobj +6435 0 obj << +/Names [(lstnumber.-26.6) 1567 0 R (lstnumber.-26.7) 1568 0 R (lstnumber.-26.8) 1569 0 R (lstnumber.-26.9) 1570 0 R (lstnumber.-260.1) 3636 0 R (lstnumber.-260.2) 3637 0 R] +/Limits [(lstnumber.-26.6) (lstnumber.-260.2)] +>> endobj +6436 0 obj << +/Names [(lstnumber.-260.3) 3638 0 R (lstnumber.-261.1) 3644 0 R (lstnumber.-261.2) 3645 0 R (lstnumber.-261.3) 3646 0 R (lstnumber.-261.4) 3654 0 R (lstnumber.-261.5) 3655 0 R] +/Limits [(lstnumber.-260.3) (lstnumber.-261.5)] +>> endobj +6437 0 obj << +/Names [(lstnumber.-261.6) 3656 0 R (lstnumber.-262.1) 3732 0 R (lstnumber.-262.2) 3733 0 R (lstnumber.-262.3) 3734 0 R (lstnumber.-262.4) 3735 0 R (lstnumber.-262.5) 3736 0 R] +/Limits [(lstnumber.-261.6) (lstnumber.-262.5)] +>> endobj +6438 0 obj << +/Names [(lstnumber.-262.6) 3737 0 R (lstnumber.-262.7) 3738 0 R (lstnumber.-262.8) 3739 0 R (lstnumber.-264.1) 3742 0 R (lstnumber.-264.10) 3751 0 R (lstnumber.-264.11) 3752 0 R] +/Limits [(lstnumber.-262.6) (lstnumber.-264.11)] +>> endobj +6439 0 obj << +/Names [(lstnumber.-264.2) 3743 0 R (lstnumber.-264.3) 3744 0 R (lstnumber.-264.4) 3745 0 R (lstnumber.-264.5) 3746 0 R (lstnumber.-264.6) 3747 0 R (lstnumber.-264.7) 3748 0 R] +/Limits [(lstnumber.-264.2) (lstnumber.-264.7)] +>> endobj +6440 0 obj << +/Names [(lstnumber.-264.8) 3749 0 R (lstnumber.-264.9) 3750 0 R (lstnumber.-265.1) 3760 0 R (lstnumber.-265.2) 3761 0 R (lstnumber.-267.1) 3763 0 R (lstnumber.-268.1) 3773 0 R] +/Limits [(lstnumber.-264.8) (lstnumber.-268.1)] +>> endobj +6441 0 obj << +/Names [(lstnumber.-268.2) 3774 0 R (lstnumber.-268.3) 3775 0 R (lstnumber.-268.4) 3776 0 R (lstnumber.-268.5) 3777 0 R (lstnumber.-269.1) 4103 0 R (lstnumber.-27.1) 1591 0 R] +/Limits [(lstnumber.-268.2) (lstnumber.-27.1)] +>> endobj +6442 0 obj << +/Names [(lstnumber.-27.2) 1592 0 R (lstnumber.-27.3) 1593 0 R (lstnumber.-27.4) 1594 0 R (lstnumber.-27.5) 1595 0 R (lstnumber.-270.1) 4105 0 R (lstnumber.-270.10) 4118 0 R] +/Limits [(lstnumber.-27.2) (lstnumber.-270.10)] +>> endobj +6443 0 obj << +/Names [(lstnumber.-270.11) 4119 0 R (lstnumber.-270.12) 4120 0 R (lstnumber.-270.13) 4121 0 R (lstnumber.-270.14) 4122 0 R (lstnumber.-270.2) 4106 0 R (lstnumber.-270.3) 4107 0 R] +/Limits [(lstnumber.-270.11) (lstnumber.-270.3)] +>> endobj +6444 0 obj << +/Names [(lstnumber.-270.4) 4108 0 R (lstnumber.-270.5) 4109 0 R (lstnumber.-270.6) 4110 0 R (lstnumber.-270.7) 4111 0 R (lstnumber.-270.8) 4112 0 R (lstnumber.-270.9) 4117 0 R] +/Limits [(lstnumber.-270.4) (lstnumber.-270.9)] +>> endobj +6445 0 obj << +/Names [(lstnumber.-271.1) 4124 0 R (lstnumber.-271.10) 4133 0 R (lstnumber.-271.11) 4134 0 R (lstnumber.-271.12) 4135 0 R (lstnumber.-271.13) 4136 0 R (lstnumber.-271.14) 4137 0 R] +/Limits [(lstnumber.-271.1) (lstnumber.-271.14)] +>> endobj +6446 0 obj << +/Names [(lstnumber.-271.15) 4138 0 R (lstnumber.-271.16) 4139 0 R (lstnumber.-271.17) 4140 0 R (lstnumber.-271.18) 4141 0 R (lstnumber.-271.19) 4142 0 R (lstnumber.-271.2) 4125 0 R] +/Limits [(lstnumber.-271.15) (lstnumber.-271.2)] +>> endobj +6447 0 obj << +/Names [(lstnumber.-271.20) 4143 0 R (lstnumber.-271.21) 4144 0 R (lstnumber.-271.22) 4145 0 R (lstnumber.-271.23) 4146 0 R (lstnumber.-271.24) 4147 0 R (lstnumber.-271.25) 4148 0 R] +/Limits [(lstnumber.-271.20) (lstnumber.-271.25)] +>> endobj +6448 0 obj << +/Names [(lstnumber.-271.26) 4149 0 R (lstnumber.-271.27) 4150 0 R (lstnumber.-271.28) 4151 0 R (lstnumber.-271.29) 4152 0 R (lstnumber.-271.3) 4126 0 R (lstnumber.-271.30) 4153 0 R] +/Limits [(lstnumber.-271.26) (lstnumber.-271.30)] +>> endobj +6449 0 obj << +/Names [(lstnumber.-271.4) 4127 0 R (lstnumber.-271.5) 4128 0 R (lstnumber.-271.6) 4129 0 R (lstnumber.-271.7) 4130 0 R (lstnumber.-271.8) 4131 0 R (lstnumber.-271.9) 4132 0 R] +/Limits [(lstnumber.-271.4) (lstnumber.-271.9)] +>> endobj +6450 0 obj << +/Names [(lstnumber.-272.1) 4162 0 R (lstnumber.-272.2) 4163 0 R (lstnumber.-272.3) 4164 0 R (lstnumber.-272.4) 4165 0 R (lstnumber.-272.5) 4166 0 R (lstnumber.-273.1) 4169 0 R] +/Limits [(lstnumber.-272.1) (lstnumber.-273.1)] +>> endobj +6451 0 obj << +/Names [(lstnumber.-273.2) 4170 0 R (lstnumber.-273.3) 4171 0 R (lstnumber.-274.1) 4177 0 R (lstnumber.-274.2) 4178 0 R (lstnumber.-274.3) 4179 0 R (lstnumber.-274.4) 4180 0 R] +/Limits [(lstnumber.-273.2) (lstnumber.-274.4)] +>> endobj +6452 0 obj << +/Names [(lstnumber.-275.1) 4182 0 R (lstnumber.-275.2) 4183 0 R (lstnumber.-275.3) 4184 0 R (lstnumber.-277.1) 4192 0 R (lstnumber.-277.2) 4193 0 R (lstnumber.-279.1) 4195 0 R] +/Limits [(lstnumber.-275.1) (lstnumber.-279.1)] +>> endobj +6453 0 obj << +/Names [(lstnumber.-279.2) 4196 0 R (lstnumber.-28.1) 1597 0 R (lstnumber.-28.10) 1615 0 R (lstnumber.-28.11) 1616 0 R (lstnumber.-28.12) 1617 0 R (lstnumber.-28.13) 1618 0 R] +/Limits [(lstnumber.-279.2) (lstnumber.-28.13)] +>> endobj +6454 0 obj << +/Names [(lstnumber.-28.14) 1619 0 R (lstnumber.-28.2) 1598 0 R (lstnumber.-28.3) 1599 0 R (lstnumber.-28.4) 1600 0 R (lstnumber.-28.5) 1601 0 R (lstnumber.-28.6) 1602 0 R] +/Limits [(lstnumber.-28.14) (lstnumber.-28.6)] +>> endobj +6455 0 obj << +/Names [(lstnumber.-28.7) 1603 0 R (lstnumber.-28.8) 1604 0 R (lstnumber.-28.9) 1614 0 R (lstnumber.-281.1) 4198 0 R (lstnumber.-281.2) 4199 0 R (lstnumber.-282.1) 4201 0 R] +/Limits [(lstnumber.-28.7) (lstnumber.-282.1)] +>> endobj +6456 0 obj << +/Names [(lstnumber.-282.2) 4202 0 R (lstnumber.-282.3) 4203 0 R (lstnumber.-282.4) 4204 0 R (lstnumber.-282.5) 4205 0 R (lstnumber.-282.6) 4206 0 R (lstnumber.-284.1) 4208 0 R] +/Limits [(lstnumber.-282.2) (lstnumber.-284.1)] +>> endobj +6457 0 obj << +/Names [(lstnumber.-284.2) 4209 0 R (lstnumber.-284.3) 4210 0 R (lstnumber.-284.4) 4211 0 R (lstnumber.-284.5) 4212 0 R (lstnumber.-286.1) 4219 0 R (lstnumber.-286.2) 4220 0 R] +/Limits [(lstnumber.-284.2) (lstnumber.-286.2)] +>> endobj +6458 0 obj << +/Names [(lstnumber.-286.3) 4221 0 R (lstnumber.-286.4) 4222 0 R (lstnumber.-288.1) 4224 0 R (lstnumber.-288.10) 4233 0 R (lstnumber.-288.11) 4234 0 R (lstnumber.-288.2) 4225 0 R] +/Limits [(lstnumber.-286.3) (lstnumber.-288.2)] +>> endobj +6459 0 obj << +/Names [(lstnumber.-288.3) 4226 0 R (lstnumber.-288.4) 4227 0 R (lstnumber.-288.5) 4228 0 R (lstnumber.-288.6) 4229 0 R (lstnumber.-288.7) 4230 0 R (lstnumber.-288.8) 4231 0 R] +/Limits [(lstnumber.-288.3) (lstnumber.-288.8)] +>> endobj +6460 0 obj << +/Names [(lstnumber.-288.9) 4232 0 R (lstnumber.-29.1) 1622 0 R (lstnumber.-29.2) 1623 0 R (lstnumber.-29.3) 1624 0 R (lstnumber.-29.4) 1625 0 R (lstnumber.-29.5) 1626 0 R] +/Limits [(lstnumber.-288.9) (lstnumber.-29.5)] +>> endobj +6461 0 obj << +/Names [(lstnumber.-29.6) 1627 0 R (lstnumber.-290.1) 4236 0 R (lstnumber.-290.2) 4237 0 R (lstnumber.-290.3) 4238 0 R (lstnumber.-290.4) 4239 0 R (lstnumber.-290.5) 4240 0 R] +/Limits [(lstnumber.-29.6) (lstnumber.-290.5)] +>> endobj +6462 0 obj << +/Names [(lstnumber.-290.6) 4241 0 R (lstnumber.-290.7) 4242 0 R (lstnumber.-290.8) 4243 0 R (lstnumber.-290.9) 4244 0 R (lstnumber.-292.1) 4250 0 R (lstnumber.-292.10) 4259 0 R] +/Limits [(lstnumber.-290.6) (lstnumber.-292.10)] +>> endobj +6463 0 obj << +/Names [(lstnumber.-292.11) 4260 0 R (lstnumber.-292.12) 4261 0 R (lstnumber.-292.2) 4251 0 R (lstnumber.-292.3) 4252 0 R (lstnumber.-292.4) 4253 0 R (lstnumber.-292.5) 4254 0 R] +/Limits [(lstnumber.-292.11) (lstnumber.-292.5)] +>> endobj +6464 0 obj << +/Names [(lstnumber.-292.6) 4255 0 R (lstnumber.-292.7) 4256 0 R (lstnumber.-292.8) 4257 0 R (lstnumber.-292.9) 4258 0 R (lstnumber.-293.1) 4263 0 R (lstnumber.-294.1) 4266 0 R] +/Limits [(lstnumber.-292.6) (lstnumber.-294.1)] +>> endobj +6465 0 obj << +/Names [(lstnumber.-294.2) 4267 0 R (lstnumber.-294.3) 4268 0 R (lstnumber.-294.4) 4269 0 R (lstnumber.-294.5) 4270 0 R (lstnumber.-294.6) 4271 0 R (lstnumber.-294.7) 4272 0 R] +/Limits [(lstnumber.-294.2) (lstnumber.-294.7)] +>> endobj +6466 0 obj << +/Names [(lstnumber.-294.8) 4273 0 R (lstnumber.-294.9) 4274 0 R (lstnumber.-295.1) 4282 0 R (lstnumber.-295.2) 4283 0 R (lstnumber.-295.3) 4284 0 R (lstnumber.-295.4) 4285 0 R] +/Limits [(lstnumber.-294.8) (lstnumber.-295.4)] +>> endobj +6467 0 obj << +/Names [(lstnumber.-295.5) 4286 0 R (lstnumber.-295.6) 4287 0 R (lstnumber.-295.7) 4288 0 R (lstnumber.-295.8) 4289 0 R (lstnumber.-295.9) 4290 0 R (lstnumber.-296.1) 4294 0 R] +/Limits [(lstnumber.-295.5) (lstnumber.-296.1)] +>> endobj +6468 0 obj << +/Names [(lstnumber.-296.2) 4295 0 R (lstnumber.-296.3) 4296 0 R (lstnumber.-296.4) 4297 0 R (lstnumber.-296.5) 4298 0 R (lstnumber.-297.1) 4302 0 R (lstnumber.-297.2) 4303 0 R] +/Limits [(lstnumber.-296.2) (lstnumber.-297.2)] +>> endobj +6469 0 obj << +/Names [(lstnumber.-297.3) 4304 0 R (lstnumber.-297.4) 4305 0 R (lstnumber.-297.5) 4306 0 R (lstnumber.-297.6) 4307 0 R (lstnumber.-297.7) 4308 0 R (lstnumber.-298.1) 4316 0 R] +/Limits [(lstnumber.-297.3) (lstnumber.-298.1)] +>> endobj +6470 0 obj << +/Names [(lstnumber.-298.10) 4325 0 R (lstnumber.-298.11) 4326 0 R (lstnumber.-298.12) 4327 0 R (lstnumber.-298.13) 4328 0 R (lstnumber.-298.14) 4329 0 R (lstnumber.-298.15) 4330 0 R] +/Limits [(lstnumber.-298.10) (lstnumber.-298.15)] +>> endobj +6471 0 obj << +/Names [(lstnumber.-298.16) 4331 0 R (lstnumber.-298.17) 4332 0 R (lstnumber.-298.2) 4317 0 R (lstnumber.-298.3) 4318 0 R (lstnumber.-298.4) 4319 0 R (lstnumber.-298.5) 4320 0 R] +/Limits [(lstnumber.-298.16) (lstnumber.-298.5)] +>> endobj +6472 0 obj << +/Names [(lstnumber.-298.6) 4321 0 R (lstnumber.-298.7) 4322 0 R (lstnumber.-298.8) 4323 0 R (lstnumber.-298.9) 4324 0 R (lstnumber.-299.1) 4339 0 R (lstnumber.-299.10) 4348 0 R] +/Limits [(lstnumber.-298.6) (lstnumber.-299.10)] +>> endobj +6473 0 obj << +/Names [(lstnumber.-299.11) 4349 0 R (lstnumber.-299.12) 4350 0 R (lstnumber.-299.13) 4351 0 R (lstnumber.-299.14) 4352 0 R (lstnumber.-299.15) 4353 0 R (lstnumber.-299.16) 4354 0 R] +/Limits [(lstnumber.-299.11) (lstnumber.-299.16)] +>> endobj +6474 0 obj << +/Names [(lstnumber.-299.17) 4355 0 R (lstnumber.-299.18) 4356 0 R (lstnumber.-299.19) 4357 0 R (lstnumber.-299.2) 4340 0 R (lstnumber.-299.20) 4358 0 R (lstnumber.-299.21) 4359 0 R] +/Limits [(lstnumber.-299.17) (lstnumber.-299.21)] +>> endobj +6475 0 obj << +/Names [(lstnumber.-299.22) 4360 0 R (lstnumber.-299.23) 4361 0 R (lstnumber.-299.24) 4362 0 R (lstnumber.-299.25) 4363 0 R (lstnumber.-299.26) 4364 0 R (lstnumber.-299.27) 4365 0 R] +/Limits [(lstnumber.-299.22) (lstnumber.-299.27)] +>> endobj +6476 0 obj << +/Names [(lstnumber.-299.3) 4341 0 R (lstnumber.-299.4) 4342 0 R (lstnumber.-299.5) 4343 0 R (lstnumber.-299.6) 4344 0 R (lstnumber.-299.7) 4345 0 R (lstnumber.-299.8) 4346 0 R] +/Limits [(lstnumber.-299.3) (lstnumber.-299.8)] +>> endobj +6477 0 obj << +/Names [(lstnumber.-299.9) 4347 0 R (lstnumber.-3.1) 1378 0 R (lstnumber.-3.10) 1394 0 R (lstnumber.-3.2) 1379 0 R (lstnumber.-3.3) 1380 0 R (lstnumber.-3.4) 1388 0 R] +/Limits [(lstnumber.-299.9) (lstnumber.-3.4)] +>> endobj +6478 0 obj << +/Names [(lstnumber.-3.5) 1389 0 R (lstnumber.-3.6) 1390 0 R (lstnumber.-3.7) 1391 0 R (lstnumber.-3.8) 1392 0 R (lstnumber.-3.9) 1393 0 R (lstnumber.-30.1) 1631 0 R] +/Limits [(lstnumber.-3.5) (lstnumber.-30.1)] +>> endobj +6479 0 obj << +/Names [(lstnumber.-30.10) 1645 0 R (lstnumber.-30.2) 1632 0 R (lstnumber.-30.3) 1633 0 R (lstnumber.-30.4) 1634 0 R (lstnumber.-30.5) 1640 0 R (lstnumber.-30.6) 1641 0 R] +/Limits [(lstnumber.-30.10) (lstnumber.-30.6)] +>> endobj +6480 0 obj << +/Names [(lstnumber.-30.7) 1642 0 R (lstnumber.-30.8) 1643 0 R (lstnumber.-30.9) 1644 0 R (lstnumber.-300.1) 4371 0 R (lstnumber.-300.2) 4372 0 R (lstnumber.-300.3) 4373 0 R] +/Limits [(lstnumber.-30.7) (lstnumber.-300.3)] +>> endobj +6481 0 obj << +/Names [(lstnumber.-300.4) 4374 0 R (lstnumber.-300.5) 4375 0 R (lstnumber.-300.6) 4376 0 R (lstnumber.-300.7) 4377 0 R (lstnumber.-301.1) 4379 0 R (lstnumber.-301.10) 4388 0 R] +/Limits [(lstnumber.-300.4) (lstnumber.-301.10)] +>> endobj +6482 0 obj << +/Names [(lstnumber.-301.11) 4389 0 R (lstnumber.-301.12) 4390 0 R (lstnumber.-301.13) 4391 0 R (lstnumber.-301.14) 4392 0 R (lstnumber.-301.15) 4393 0 R (lstnumber.-301.16) 4394 0 R] +/Limits [(lstnumber.-301.11) (lstnumber.-301.16)] +>> endobj +6483 0 obj << +/Names [(lstnumber.-301.17) 4395 0 R (lstnumber.-301.18) 4396 0 R (lstnumber.-301.19) 4397 0 R (lstnumber.-301.2) 4380 0 R (lstnumber.-301.20) 4398 0 R (lstnumber.-301.21) 4399 0 R] +/Limits [(lstnumber.-301.17) (lstnumber.-301.21)] +>> endobj +6484 0 obj << +/Names [(lstnumber.-301.3) 4381 0 R (lstnumber.-301.4) 4382 0 R (lstnumber.-301.5) 4383 0 R (lstnumber.-301.6) 4384 0 R (lstnumber.-301.7) 4385 0 R (lstnumber.-301.8) 4386 0 R] +/Limits [(lstnumber.-301.3) (lstnumber.-301.8)] +>> endobj +6485 0 obj << +/Names [(lstnumber.-301.9) 4387 0 R (lstnumber.-302.1) 4406 0 R (lstnumber.-302.10) 4415 0 R (lstnumber.-302.11) 4416 0 R (lstnumber.-302.12) 4417 0 R (lstnumber.-302.13) 4418 0 R] +/Limits [(lstnumber.-301.9) (lstnumber.-302.13)] +>> endobj +6486 0 obj << +/Names [(lstnumber.-302.14) 4419 0 R (lstnumber.-302.15) 4420 0 R (lstnumber.-302.2) 4407 0 R (lstnumber.-302.3) 4408 0 R (lstnumber.-302.4) 4409 0 R (lstnumber.-302.5) 4410 0 R] +/Limits [(lstnumber.-302.14) (lstnumber.-302.5)] +>> endobj +6487 0 obj << +/Names [(lstnumber.-302.6) 4411 0 R (lstnumber.-302.7) 4412 0 R (lstnumber.-302.8) 4413 0 R (lstnumber.-302.9) 4414 0 R (lstnumber.-303.1) 4422 0 R (lstnumber.-303.10) 4460 0 R] +/Limits [(lstnumber.-302.6) (lstnumber.-303.10)] +>> endobj +6488 0 obj << +/Names [(lstnumber.-303.11) 4461 0 R (lstnumber.-303.12) 4462 0 R (lstnumber.-303.13) 4463 0 R (lstnumber.-303.14) 4464 0 R (lstnumber.-303.15) 4465 0 R (lstnumber.-303.16) 4466 0 R] +/Limits [(lstnumber.-303.11) (lstnumber.-303.16)] +>> endobj +6489 0 obj << +/Names [(lstnumber.-303.17) 4467 0 R (lstnumber.-303.18) 4468 0 R (lstnumber.-303.19) 4469 0 R (lstnumber.-303.2) 4423 0 R (lstnumber.-303.20) 4470 0 R (lstnumber.-303.21) 4471 0 R] +/Limits [(lstnumber.-303.17) (lstnumber.-303.21)] +>> endobj +6490 0 obj << +/Names [(lstnumber.-303.22) 4472 0 R (lstnumber.-303.23) 4473 0 R (lstnumber.-303.3) 4424 0 R (lstnumber.-303.4) 4425 0 R (lstnumber.-303.5) 4426 0 R (lstnumber.-303.6) 4427 0 R] +/Limits [(lstnumber.-303.22) (lstnumber.-303.6)] +>> endobj +6491 0 obj << +/Names [(lstnumber.-303.7) 4457 0 R (lstnumber.-303.8) 4458 0 R (lstnumber.-303.9) 4459 0 R (lstnumber.-305.1) 4475 0 R (lstnumber.-305.10) 4484 0 R (lstnumber.-305.2) 4476 0 R] +/Limits [(lstnumber.-303.7) (lstnumber.-305.2)] +>> endobj +6492 0 obj << +/Names [(lstnumber.-305.3) 4477 0 R (lstnumber.-305.4) 4478 0 R (lstnumber.-305.5) 4479 0 R (lstnumber.-305.6) 4480 0 R (lstnumber.-305.7) 4481 0 R (lstnumber.-305.8) 4482 0 R] +/Limits [(lstnumber.-305.3) (lstnumber.-305.8)] +>> endobj +6493 0 obj << +/Names [(lstnumber.-305.9) 4483 0 R (lstnumber.-307.1) 4486 0 R (lstnumber.-307.2) 4487 0 R (lstnumber.-307.3) 4488 0 R (lstnumber.-307.4) 4489 0 R (lstnumber.-307.5) 4490 0 R] +/Limits [(lstnumber.-305.9) (lstnumber.-307.5)] +>> endobj +6494 0 obj << +/Names [(lstnumber.-307.6) 4491 0 R (lstnumber.-307.7) 4492 0 R (lstnumber.-307.8) 4493 0 R (lstnumber.-307.9) 4494 0 R (lstnumber.-309.1) 4496 0 R (lstnumber.-309.10) 4505 0 R] +/Limits [(lstnumber.-307.6) (lstnumber.-309.10)] +>> endobj +6495 0 obj << +/Names [(lstnumber.-309.2) 4497 0 R (lstnumber.-309.3) 4498 0 R (lstnumber.-309.4) 4499 0 R (lstnumber.-309.5) 4500 0 R (lstnumber.-309.6) 4501 0 R (lstnumber.-309.7) 4502 0 R] +/Limits [(lstnumber.-309.2) (lstnumber.-309.7)] +>> endobj +6496 0 obj << +/Names [(lstnumber.-309.8) 4503 0 R (lstnumber.-309.9) 4504 0 R (lstnumber.-310.1) 4512 0 R (lstnumber.-310.2) 4513 0 R (lstnumber.-310.3) 4514 0 R (lstnumber.-310.4) 4515 0 R] +/Limits [(lstnumber.-309.8) (lstnumber.-310.4)] +>> endobj +6497 0 obj << +/Names [(lstnumber.-310.5) 4516 0 R (lstnumber.-311.1) 4519 0 R (lstnumber.-311.10) 4533 0 R (lstnumber.-311.11) 4534 0 R (lstnumber.-311.12) 4535 0 R (lstnumber.-311.13) 4536 0 R] +/Limits [(lstnumber.-310.5) (lstnumber.-311.13)] +>> endobj +6498 0 obj << +/Names [(lstnumber.-311.14) 4537 0 R (lstnumber.-311.15) 4538 0 R (lstnumber.-311.16) 4539 0 R (lstnumber.-311.17) 4540 0 R (lstnumber.-311.18) 4541 0 R (lstnumber.-311.2) 4520 0 R] +/Limits [(lstnumber.-311.14) (lstnumber.-311.2)] +>> endobj +6499 0 obj << +/Names [(lstnumber.-311.3) 4521 0 R (lstnumber.-311.4) 4522 0 R (lstnumber.-311.5) 4523 0 R (lstnumber.-311.6) 4524 0 R (lstnumber.-311.7) 4525 0 R (lstnumber.-311.8) 4526 0 R] +/Limits [(lstnumber.-311.3) (lstnumber.-311.8)] +>> endobj +6500 0 obj << +/Names [(lstnumber.-311.9) 4527 0 R (lstnumber.-312.1) 4544 0 R (lstnumber.-312.10) 4553 0 R (lstnumber.-312.11) 4554 0 R (lstnumber.-312.2) 4545 0 R (lstnumber.-312.3) 4546 0 R] +/Limits [(lstnumber.-311.9) (lstnumber.-312.3)] +>> endobj +6501 0 obj << +/Names [(lstnumber.-312.4) 4547 0 R (lstnumber.-312.5) 4548 0 R (lstnumber.-312.6) 4549 0 R (lstnumber.-312.7) 4550 0 R (lstnumber.-312.8) 4551 0 R (lstnumber.-312.9) 4552 0 R] +/Limits [(lstnumber.-312.4) (lstnumber.-312.9)] +>> endobj +6502 0 obj << +/Names [(lstnumber.-313.1) 4556 0 R (lstnumber.-313.10) 4570 0 R (lstnumber.-313.2) 4557 0 R (lstnumber.-313.3) 4558 0 R (lstnumber.-313.4) 4559 0 R (lstnumber.-313.5) 4560 0 R] +/Limits [(lstnumber.-313.1) (lstnumber.-313.5)] +>> endobj +6503 0 obj << +/Names [(lstnumber.-313.6) 4561 0 R (lstnumber.-313.7) 4562 0 R (lstnumber.-313.8) 4563 0 R (lstnumber.-313.9) 4569 0 R (lstnumber.-314.1) 4572 0 R (lstnumber.-314.10) 4581 0 R] +/Limits [(lstnumber.-313.6) (lstnumber.-314.10)] +>> endobj +6504 0 obj << +/Names [(lstnumber.-314.11) 4582 0 R (lstnumber.-314.12) 4583 0 R 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0 R (lstnumber.-53.6) 1757 0 R (lstnumber.-53.7) 1758 0 R (lstnumber.-53.8) 1759 0 R (lstnumber.-53.9) 1760 0 R] +/Limits [(lstnumber.-53.4) (lstnumber.-53.9)] +>> endobj +6575 0 obj << +/Names [(lstnumber.-55.1) 1793 0 R (lstnumber.-57.1) 1797 0 R (lstnumber.-57.2) 1798 0 R (lstnumber.-57.3) 1799 0 R (lstnumber.-57.4) 1800 0 R (lstnumber.-57.5) 1801 0 R] +/Limits [(lstnumber.-55.1) (lstnumber.-57.5)] +>> endobj +6576 0 obj << +/Names [(lstnumber.-58.1) 1819 0 R (lstnumber.-58.2) 1820 0 R (lstnumber.-58.3) 1821 0 R (lstnumber.-58.4) 1822 0 R (lstnumber.-58.5) 1823 0 R (lstnumber.-58.6) 1824 0 R] +/Limits [(lstnumber.-58.1) (lstnumber.-58.6)] +>> endobj +6577 0 obj << +/Names [(lstnumber.-6.1) 1400 0 R (lstnumber.-6.2) 1401 0 R (lstnumber.-60.1) 1827 0 R (lstnumber.-60.2) 1828 0 R (lstnumber.-60.3) 1829 0 R (lstnumber.-60.4) 1830 0 R] +/Limits [(lstnumber.-6.1) (lstnumber.-60.4)] +>> endobj +6578 0 obj << +/Names [(lstnumber.-60.5) 1831 0 R (lstnumber.-62.1) 1834 0 R (lstnumber.-62.2) 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1238 0 R (page.60) 2626 0 R] +/Limits [(page.56) (page.60)] +>> endobj +6624 0 obj << +/Names [(page.61) 2637 0 R (page.62) 2655 0 R (page.63) 2683 0 R (page.64) 2706 0 R (page.65) 2727 0 R (page.66) 2752 0 R] +/Limits [(page.61) (page.66)] +>> endobj +6625 0 obj << +/Names [(page.67) 2767 0 R (page.68) 2791 0 R (page.69) 2797 0 R (page.7) 1278 0 R (page.70) 2813 0 R (page.71) 2832 0 R] +/Limits [(page.67) (page.71)] +>> endobj +6626 0 obj << +/Names [(page.72) 2871 0 R (page.73) 2905 0 R (page.74) 2932 0 R (page.75) 2964 0 R (page.76) 2982 0 R (page.77) 3003 0 R] +/Limits [(page.72) (page.77)] +>> endobj +6627 0 obj << +/Names [(page.78) 3027 0 R (page.79) 3051 0 R (page.8) 1312 0 R (page.80) 3064 0 R (page.81) 3075 0 R (page.82) 3094 0 R] +/Limits [(page.78) (page.82)] +>> endobj +6628 0 obj << +/Names [(page.83) 3116 0 R (page.84) 3131 0 R (page.85) 3160 0 R (page.86) 3178 0 R (page.87) 3191 0 R (page.88) 3213 0 R] +/Limits [(page.83) (page.88)] +>> endobj +6629 0 obj << +/Names [(page.89) 3288 0 R (page.9) 1332 0 R (page.90) 3319 0 R (page.91) 3339 0 R (page.92) 3348 0 R (page.93) 3385 0 R] +/Limits [(page.89) (page.93)] +>> endobj +6630 0 obj << +/Names [(page.94) 3405 0 R (page.95) 3421 0 R (page.96) 3445 0 R (page.97) 3497 0 R (page.98) 3505 0 R (page.99) 3526 0 R] +/Limits [(page.94) (page.99)] +>> endobj +6631 0 obj << +/Names [(part.1) 6 0 R (part.2) 274 0 R (part.3) 442 0 R (part.4) 742 0 R (part.5) 822 0 R (part.6) 850 0 R] +/Limits [(part.1) (part.6)] +>> endobj +6632 0 obj << +/Names [(part.7) 874 0 R (part.8) 994 0 R (section*.1) 1080 0 R (section*.18) 998 0 R (section*.19) 4944 0 R (section*.2) 2114 0 R] +/Limits [(part.7) (section*.2)] +>> endobj +6633 0 obj << +/Names [(section*.20) 1002 0 R (section*.21) 4971 0 R (section*.22) 1006 0 R (section*.23) 1010 0 R (section*.24) 5112 0 R (section*.25) 5901 0 R] +/Limits [(section*.20) (section*.25)] +>> endobj +6634 0 obj << +/Names [(section*.3) 2119 0 R (section*.4) 2127 0 R (section*.5) 2128 0 R 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(section.34) 386 0 R (section.35) 390 0 R (section.36) 406 0 R] +/Limits [(section.31) (section.36)] +>> endobj +6640 0 obj << +/Names [(section.37) 410 0 R (section.38) 422 0 R (section.39) 426 0 R (section.4) 98 0 R (section.40) 430 0 R (section.41) 434 0 R] +/Limits [(section.37) (section.41)] +>> endobj +6641 0 obj << +/Names [(section.42) 438 0 R (section.43) 446 0 R (section.44) 534 0 R (section.45) 634 0 R (section.46) 718 0 R (section.47) 746 0 R] +/Limits [(section.42) (section.47)] +>> endobj +6642 0 obj << +/Names [(section.48) 826 0 R (section.49) 830 0 R (section.5) 110 0 R (section.50) 834 0 R (section.51) 838 0 R (section.52) 842 0 R] +/Limits [(section.48) (section.52)] +>> endobj +6643 0 obj << +/Names [(section.53) 846 0 R (section.54) 854 0 R (section.55) 858 0 R (section.56) 862 0 R (section.57) 866 0 R (section.58) 870 0 R] +/Limits [(section.53) (section.58)] +>> endobj +6644 0 obj << +/Names [(section.59) 878 0 R (section.6) 114 0 R (section.60) 882 0 R (section.61) 898 0 R (section.62) 906 0 R (section.63) 934 0 R] +/Limits [(section.59) (section.63)] +>> endobj +6645 0 obj << +/Names [(section.64) 954 0 R (section.65) 958 0 R (section.66) 974 0 R (section.67) 978 0 R (section.68) 990 0 R (section.7) 126 0 R] +/Limits [(section.64) (section.7)] +>> endobj +6646 0 obj << +/Names [(section.8) 130 0 R (section.9) 154 0 R (subequation.1) 4814 0 R (subequation.2) 4816 0 R (subsection.10.1) 162 0 R (subsection.10.2) 166 0 R] +/Limits [(section.8) (subsection.10.2)] +>> endobj +6647 0 obj << +/Names [(subsection.11.1) 174 0 R (subsection.11.2) 178 0 R (subsection.11.3) 182 0 R (subsection.11.4) 186 0 R (subsection.11.5) 190 0 R (subsection.14.1) 214 0 R] +/Limits [(subsection.11.1) (subsection.14.1)] +>> endobj +6648 0 obj << +/Names [(subsection.14.2) 226 0 R (subsection.2.1) 18 0 R (subsection.2.2) 22 0 R (subsection.2.3) 26 0 R (subsection.2.4) 30 0 R (subsection.2.5) 34 0 R] +/Limits [(subsection.14.2) (subsection.2.5)] +>> endobj +6649 0 obj << +/Names [(subsection.2.6) 38 0 R (subsection.2.7) 42 0 R (subsection.2.8) 46 0 R (subsection.22.1) 262 0 R (subsection.25.1) 282 0 R (subsection.25.2) 286 0 R] +/Limits [(subsection.2.6) (subsection.25.2)] +>> endobj +6650 0 obj << +/Names [(subsection.25.3) 290 0 R (subsection.25.4) 294 0 R (subsection.25.5) 298 0 R (subsection.25.6) 302 0 R (subsection.25.7) 306 0 R (subsection.26.1) 314 0 R] +/Limits [(subsection.25.3) (subsection.26.1)] +>> endobj +6651 0 obj << +/Names [(subsection.26.2) 318 0 R (subsection.26.3) 322 0 R (subsection.26.4) 330 0 R (subsection.26.5) 334 0 R (subsection.26.6) 338 0 R (subsection.29.1) 354 0 R] +/Limits [(subsection.26.2) (subsection.29.1)] +>> endobj +6652 0 obj << +/Names [(subsection.29.2) 358 0 R (subsection.3.1) 54 0 R (subsection.3.2) 58 0 R (subsection.3.3) 66 0 R (subsection.3.4) 90 0 R (subsection.3.5) 94 0 R] +/Limits [(subsection.29.2) (subsection.3.5)] +>> endobj +6653 0 obj << +/Names [(subsection.30.1) 366 0 R (subsection.33.1) 382 0 R (subsection.35.1) 394 0 R (subsection.35.2) 398 0 R (subsection.35.3) 402 0 R (subsection.37.1) 414 0 R] +/Limits [(subsection.30.1) (subsection.37.1)] +>> endobj +6654 0 obj << +/Names [(subsection.37.2) 418 0 R (subsection.4.1) 102 0 R (subsection.4.2) 106 0 R (subsection.43.1) 450 0 R (subsection.43.10) 486 0 R (subsection.43.11) 490 0 R] +/Limits [(subsection.37.2) (subsection.43.11)] +>> endobj +6655 0 obj << +/Names [(subsection.43.12) 494 0 R (subsection.43.13) 498 0 R (subsection.43.14) 502 0 R (subsection.43.15) 506 0 R (subsection.43.16) 510 0 R (subsection.43.17) 514 0 R] +/Limits [(subsection.43.12) (subsection.43.17)] +>> endobj +6656 0 obj << +/Names [(subsection.43.18) 518 0 R (subsection.43.19) 522 0 R (subsection.43.2) 454 0 R (subsection.43.20) 526 0 R (subsection.43.21) 530 0 R (subsection.43.3) 458 0 R] +/Limits [(subsection.43.18) (subsection.43.3)] +>> endobj +6657 0 obj << +/Names [(subsection.43.4) 462 0 R (subsection.43.5) 466 0 R (subsection.43.6) 470 0 R (subsection.43.7) 474 0 R (subsection.43.8) 478 0 R (subsection.43.9) 482 0 R] +/Limits [(subsection.43.4) (subsection.43.9)] +>> endobj +6658 0 obj << +/Names [(subsection.44.1) 538 0 R (subsection.44.10) 574 0 R (subsection.44.11) 578 0 R (subsection.44.12) 582 0 R (subsection.44.13) 586 0 R (subsection.44.14) 590 0 R] +/Limits [(subsection.44.1) (subsection.44.14)] +>> endobj +6659 0 obj << +/Names [(subsection.44.15) 594 0 R (subsection.44.16) 598 0 R (subsection.44.17) 602 0 R (subsection.44.18) 606 0 R (subsection.44.19) 610 0 R (subsection.44.2) 542 0 R] +/Limits [(subsection.44.15) (subsection.44.2)] +>> endobj +6660 0 obj << +/Names [(subsection.44.20) 614 0 R (subsection.44.21) 618 0 R (subsection.44.22) 622 0 R (subsection.44.23) 626 0 R (subsection.44.24) 630 0 R (subsection.44.3) 546 0 R] +/Limits [(subsection.44.20) (subsection.44.3)] +>> endobj +6661 0 obj << +/Names [(subsection.44.4) 550 0 R (subsection.44.5) 554 0 R (subsection.44.6) 558 0 R (subsection.44.7) 562 0 R (subsection.44.8) 566 0 R (subsection.44.9) 570 0 R] +/Limits [(subsection.44.4) (subsection.44.9)] +>> endobj +6662 0 obj << +/Names [(subsection.45.1) 638 0 R (subsection.45.10) 674 0 R (subsection.45.11) 678 0 R (subsection.45.12) 682 0 R (subsection.45.13) 686 0 R (subsection.45.14) 690 0 R] +/Limits [(subsection.45.1) (subsection.45.14)] +>> endobj +6663 0 obj << +/Names [(subsection.45.15) 694 0 R (subsection.45.16) 698 0 R (subsection.45.17) 702 0 R (subsection.45.18) 706 0 R (subsection.45.19) 710 0 R (subsection.45.2) 642 0 R] +/Limits [(subsection.45.15) (subsection.45.2)] +>> endobj +6664 0 obj << +/Names [(subsection.45.20) 714 0 R (subsection.45.3) 646 0 R (subsection.45.4) 650 0 R (subsection.45.5) 654 0 R (subsection.45.6) 658 0 R (subsection.45.7) 662 0 R] +/Limits [(subsection.45.20) (subsection.45.7)] +>> endobj +6665 0 obj << +/Names [(subsection.45.8) 666 0 R (subsection.45.9) 670 0 R (subsection.46.1) 722 0 R (subsection.46.2) 726 0 R (subsection.46.3) 730 0 R (subsection.46.4) 734 0 R] +/Limits [(subsection.45.8) (subsection.46.4)] +>> endobj +6666 0 obj << +/Names [(subsection.46.5) 738 0 R (subsection.47.1) 750 0 R (subsection.47.10) 786 0 R (subsection.47.11) 790 0 R (subsection.47.12) 794 0 R (subsection.47.13) 798 0 R] +/Limits [(subsection.46.5) (subsection.47.13)] +>> endobj +6667 0 obj << +/Names [(subsection.47.14) 802 0 R (subsection.47.15) 806 0 R (subsection.47.16) 810 0 R (subsection.47.17) 814 0 R (subsection.47.18) 818 0 R (subsection.47.2) 754 0 R] +/Limits [(subsection.47.14) (subsection.47.2)] +>> endobj +6668 0 obj << +/Names [(subsection.47.3) 758 0 R (subsection.47.4) 762 0 R (subsection.47.5) 766 0 R (subsection.47.6) 770 0 R (subsection.47.7) 774 0 R (subsection.47.8) 778 0 R] +/Limits [(subsection.47.3) (subsection.47.8)] +>> endobj +6669 0 obj << +/Names [(subsection.47.9) 782 0 R (subsection.6.1) 118 0 R (subsection.6.2) 122 0 R (subsection.60.1) 886 0 R (subsection.60.2) 890 0 R (subsection.60.3) 894 0 R] +/Limits [(subsection.47.9) (subsection.60.3)] +>> endobj +6670 0 obj << +/Names [(subsection.61.1) 902 0 R (subsection.62.1) 910 0 R (subsection.62.2) 914 0 R (subsection.62.3) 918 0 R (subsection.62.4) 922 0 R (subsection.62.5) 926 0 R] +/Limits [(subsection.61.1) (subsection.62.5)] +>> endobj +6671 0 obj << +/Names [(subsection.62.6) 930 0 R (subsection.63.1) 938 0 R (subsection.63.2) 942 0 R (subsection.63.3) 946 0 R (subsection.63.4) 950 0 R (subsection.65.1) 962 0 R] +/Limits [(subsection.62.6) (subsection.65.1)] +>> endobj +6672 0 obj << +/Names [(subsection.65.2) 966 0 R (subsection.65.3) 970 0 R (subsection.67.1) 982 0 R (subsection.67.2) 986 0 R (subsection.8.1) 134 0 R (subsection.8.2) 146 0 R] +/Limits [(subsection.65.2) (subsection.8.2)] +>> endobj +6673 0 obj << +/Names [(subsection.8.3) 150 0 R (subsubsection.11.5.1) 194 0 R (subsubsection.11.5.2) 198 0 R (subsubsection.14.1.1) 218 0 R (subsubsection.14.1.2) 222 0 R (subsubsection.26.3.1) 326 0 R] +/Limits [(subsection.8.3) (subsubsection.26.3.1)] +>> endobj +6674 0 obj << +/Names [(subsubsection.3.2.1) 62 0 R (subsubsection.3.3.1) 70 0 R (subsubsection.3.3.2) 74 0 R (subsubsection.3.3.3) 78 0 R (subsubsection.3.3.4) 82 0 R (subsubsection.3.3.5) 86 0 R] +/Limits [(subsubsection.3.2.1) (subsubsection.3.3.5)] +>> endobj +6675 0 obj << +/Names [(subsubsection.8.1.1) 138 0 R (subsubsection.8.1.2) 142 0 R (table.1) 1417 0 R (table.10) 2194 0 R (table.11) 2226 0 R (table.12) 2249 0 R] +/Limits [(subsubsection.8.1.1) (table.12)] +>> endobj +6676 0 obj << +/Names [(table.13) 2257 0 R (table.14) 2269 0 R (table.15) 2381 0 R (table.16) 2744 0 R (table.17) 2798 0 R (table.18) 2821 0 R] +/Limits [(table.13) (table.18)] +>> endobj +6677 0 obj << +/Names [(table.19) 3071 0 R (table.2) 1855 0 R (table.20) 2258 0 R (table.21) 4098 0 R (table.22) 4167 0 R (table.23) 4861 0 R] +/Limits [(table.19) (table.23)] +>> endobj +6678 0 obj << +/Names [(table.3) 1854 0 R (table.4) 1938 0 R (table.5) 1950 0 R (table.6) 2063 0 R (table.7) 1937 0 R (table.8) 1382 0 R] +/Limits [(table.3) (table.8)] +>> endobj +6679 0 obj << +/Names [(table.9) 2188 0 R] +/Limits [(table.9) (table.9)] +>> endobj +6680 0 obj << +/Kids [6229 0 R 6230 0 R 6231 0 R 6232 0 R 6233 0 R 6234 0 R] +/Limits [(AMS.12) (cite.dtk04.3:voss)] +>> endobj +6681 0 obj << +/Kids [6235 0 R 6236 0 R 6237 0 R 6238 0 R 6239 0 R 6240 0 R] +/Limits [(cite.eijkhout) (equation.25.49)] +>> endobj +6682 0 obj << +/Kids [6241 0 R 6242 0 R 6243 0 R 6244 0 R 6245 0 R 6246 0 R] +/Limits [(equation.25.50) (equation.26.85)] +>> endobj +6683 0 obj << +/Kids [6247 0 R 6248 0 R 6249 0 R 6250 0 R 6251 0 R 6252 0 R] +/Limits [(equation.26.86) (equation.35.4)] +>> endobj +6684 0 obj << +/Kids [6253 0 R 6254 0 R 6255 0 R 6256 0 R 6257 0 R 6258 0 R] +/Limits [(equation.35.5) (equation.6.23)] +>> endobj +6685 0 obj << +/Kids [6259 0 R 6260 0 R 6261 0 R 6262 0 R 6263 0 R 6264 0 R] +/Limits [(equation.6.23a) (equation.67.3)] +>> endobj +6686 0 obj << +/Kids [6265 0 R 6266 0 R 6267 0 R 6268 0 R 6269 0 R 6270 0 R] +/Limits [(equation.67.4) (lstlisting.-116)] +>> endobj +6687 0 obj << +/Kids [6271 0 R 6272 0 R 6273 0 R 6274 0 R 6275 0 R 6276 0 R] +/Limits [(lstlisting.-117) (lstlisting.-152)] +>> endobj +6688 0 obj << +/Kids [6277 0 R 6278 0 R 6279 0 R 6280 0 R 6281 0 R 6282 0 R] +/Limits [(lstlisting.-153) (lstlisting.-190)] +>> endobj +6689 0 obj << +/Kids [6283 0 R 6284 0 R 6285 0 R 6286 0 R 6287 0 R 6288 0 R] +/Limits [(lstlisting.-191) (lstlisting.-247)] +>> endobj +6690 0 obj << +/Kids [6289 0 R 6290 0 R 6291 0 R 6292 0 R 6293 0 R 6294 0 R] +/Limits [(lstlisting.-248) (lstlisting.-286)] +>> endobj +6691 0 obj << +/Kids [6295 0 R 6296 0 R 6297 0 R 6298 0 R 6299 0 R 6300 0 R] +/Limits [(lstlisting.-288) (lstlisting.-324)] +>> endobj +6692 0 obj << +/Kids [6301 0 R 6302 0 R 6303 0 R 6304 0 R 6305 0 R 6306 0 R] +/Limits [(lstlisting.-325) (lstlisting.-78)] +>> endobj +6693 0 obj << +/Kids [6307 0 R 6308 0 R 6309 0 R 6310 0 R 6311 0 R 6312 0 R] +/Limits [(lstlisting.-79) (lstnumber.-105.4)] +>> endobj +6694 0 obj << +/Kids [6313 0 R 6314 0 R 6315 0 R 6316 0 R 6317 0 R 6318 0 R] +/Limits [(lstnumber.-105.5) (lstnumber.-113.1)] +>> endobj +6695 0 obj << +/Kids [6319 0 R 6320 0 R 6321 0 R 6322 0 R 6323 0 R 6324 0 R] +/Limits [(lstnumber.-113.2) (lstnumber.-122.4)] +>> endobj +6696 0 obj << +/Kids [6325 0 R 6326 0 R 6327 0 R 6328 0 R 6329 0 R 6330 0 R] +/Limits [(lstnumber.-122.5) (lstnumber.-13.4)] +>> endobj +6697 0 obj << +/Kids [6331 0 R 6332 0 R 6333 0 R 6334 0 R 6335 0 R 6336 0 R] +/Limits [(lstnumber.-131.1) (lstnumber.-134.7)] +>> endobj +6698 0 obj << +/Kids [6337 0 R 6338 0 R 6339 0 R 6340 0 R 6341 0 R 6342 0 R] +/Limits [(lstnumber.-134.8) (lstnumber.-139.3)] +>> endobj +6699 0 obj << +/Kids [6343 0 R 6344 0 R 6345 0 R 6346 0 R 6347 0 R 6348 0 R] +/Limits [(lstnumber.-139.4) (lstnumber.-143.7)] +>> endobj +6700 0 obj << +/Kids [6349 0 R 6350 0 R 6351 0 R 6352 0 R 6353 0 R 6354 0 R] +/Limits [(lstnumber.-143.8) (lstnumber.-149.11)] +>> endobj +6701 0 obj << +/Kids [6355 0 R 6356 0 R 6357 0 R 6358 0 R 6359 0 R 6360 0 R] +/Limits [(lstnumber.-149.12) (lstnumber.-157.8)] +>> endobj +6702 0 obj << +/Kids [6361 0 R 6362 0 R 6363 0 R 6364 0 R 6365 0 R 6366 0 R] +/Limits [(lstnumber.-158.1) (lstnumber.-161.1)] +>> endobj +6703 0 obj << +/Kids [6367 0 R 6368 0 R 6369 0 R 6370 0 R 6371 0 R 6372 0 R] +/Limits [(lstnumber.-162.1) (lstnumber.-17.1)] +>> endobj +6704 0 obj << +/Kids [6373 0 R 6374 0 R 6375 0 R 6376 0 R 6377 0 R 6378 0 R] +/Limits [(lstnumber.-17.2) (lstnumber.-176.13)] +>> endobj +6705 0 obj << +/Kids [6379 0 R 6380 0 R 6381 0 R 6382 0 R 6383 0 R 6384 0 R] +/Limits [(lstnumber.-176.2) (lstnumber.-181.6)] +>> endobj +6706 0 obj << +/Kids [6385 0 R 6386 0 R 6387 0 R 6388 0 R 6389 0 R 6390 0 R] +/Limits [(lstnumber.-181.7) (lstnumber.-186.8)] +>> endobj +6707 0 obj << +/Kids [6391 0 R 6392 0 R 6393 0 R 6394 0 R 6395 0 R 6396 0 R] +/Limits [(lstnumber.-186.9) (lstnumber.-198.2)] +>> endobj +6708 0 obj << +/Kids [6397 0 R 6398 0 R 6399 0 R 6400 0 R 6401 0 R 6402 0 R] +/Limits [(lstnumber.-198.3) (lstnumber.-214.1)] +>> endobj +6709 0 obj << +/Kids [6403 0 R 6404 0 R 6405 0 R 6406 0 R 6407 0 R 6408 0 R] +/Limits [(lstnumber.-214.2) (lstnumber.-228.1)] +>> endobj +6710 0 obj << +/Kids [6409 0 R 6410 0 R 6411 0 R 6412 0 R 6413 0 R 6414 0 R] +/Limits [(lstnumber.-228.2) (lstnumber.-242.4)] +>> endobj +6711 0 obj << +/Kids [6415 0 R 6416 0 R 6417 0 R 6418 0 R 6419 0 R 6420 0 R] +/Limits [(lstnumber.-242.5) (lstnumber.-247.6)] +>> endobj +6712 0 obj << +/Kids [6421 0 R 6422 0 R 6423 0 R 6424 0 R 6425 0 R 6426 0 R] +/Limits [(lstnumber.-247.7) (lstnumber.-251.3)] +>> endobj +6713 0 obj << +/Kids [6427 0 R 6428 0 R 6429 0 R 6430 0 R 6431 0 R 6432 0 R] +/Limits [(lstnumber.-251.4) (lstnumber.-26.10)] +>> endobj +6714 0 obj << +/Kids [6433 0 R 6434 0 R 6435 0 R 6436 0 R 6437 0 R 6438 0 R] +/Limits [(lstnumber.-26.11) (lstnumber.-264.11)] +>> endobj +6715 0 obj << +/Kids [6439 0 R 6440 0 R 6441 0 R 6442 0 R 6443 0 R 6444 0 R] +/Limits [(lstnumber.-264.2) (lstnumber.-270.9)] +>> endobj +6716 0 obj << +/Kids [6445 0 R 6446 0 R 6447 0 R 6448 0 R 6449 0 R 6450 0 R] +/Limits [(lstnumber.-271.1) (lstnumber.-273.1)] +>> endobj +6717 0 obj << +/Kids [6451 0 R 6452 0 R 6453 0 R 6454 0 R 6455 0 R 6456 0 R] +/Limits [(lstnumber.-273.2) (lstnumber.-284.1)] +>> endobj +6718 0 obj << +/Kids [6457 0 R 6458 0 R 6459 0 R 6460 0 R 6461 0 R 6462 0 R] +/Limits [(lstnumber.-284.2) (lstnumber.-292.10)] +>> endobj +6719 0 obj << +/Kids [6463 0 R 6464 0 R 6465 0 R 6466 0 R 6467 0 R 6468 0 R] +/Limits [(lstnumber.-292.11) (lstnumber.-297.2)] +>> endobj +6720 0 obj << +/Kids [6469 0 R 6470 0 R 6471 0 R 6472 0 R 6473 0 R 6474 0 R] +/Limits [(lstnumber.-297.3) (lstnumber.-299.21)] +>> endobj +6721 0 obj << +/Kids [6475 0 R 6476 0 R 6477 0 R 6478 0 R 6479 0 R 6480 0 R] +/Limits [(lstnumber.-299.22) (lstnumber.-300.3)] +>> endobj +6722 0 obj << +/Kids [6481 0 R 6482 0 R 6483 0 R 6484 0 R 6485 0 R 6486 0 R] +/Limits [(lstnumber.-300.4) (lstnumber.-302.5)] +>> endobj +6723 0 obj << +/Kids [6487 0 R 6488 0 R 6489 0 R 6490 0 R 6491 0 R 6492 0 R] +/Limits [(lstnumber.-302.6) (lstnumber.-305.8)] +>> endobj +6724 0 obj << +/Kids [6493 0 R 6494 0 R 6495 0 R 6496 0 R 6497 0 R 6498 0 R] +/Limits [(lstnumber.-305.9) (lstnumber.-311.2)] +>> endobj +6725 0 obj << +/Kids [6499 0 R 6500 0 R 6501 0 R 6502 0 R 6503 0 R 6504 0 R] +/Limits [(lstnumber.-311.3) (lstnumber.-314.16)] +>> endobj +6726 0 obj << +/Kids [6505 0 R 6506 0 R 6507 0 R 6508 0 R 6509 0 R 6510 0 R] +/Limits [(lstnumber.-314.17) (lstnumber.-317.16)] +>> endobj +6727 0 obj << +/Kids [6511 0 R 6512 0 R 6513 0 R 6514 0 R 6515 0 R 6516 0 R] +/Limits [(lstnumber.-317.17) (lstnumber.-319.17)] +>> endobj +6728 0 obj << +/Kids [6517 0 R 6518 0 R 6519 0 R 6520 0 R 6521 0 R 6522 0 R] +/Limits [(lstnumber.-319.18) (lstnumber.-320.3)] +>> endobj +6729 0 obj << +/Kids [6523 0 R 6524 0 R 6525 0 R 6526 0 R 6527 0 R 6528 0 R] +/Limits [(lstnumber.-320.4) (lstnumber.-322.1)] +>> endobj +6730 0 obj << +/Kids [6529 0 R 6530 0 R 6531 0 R 6532 0 R 6533 0 R 6534 0 R] +/Limits [(lstnumber.-322.2) (lstnumber.-324.4)] +>> endobj +6731 0 obj << +/Kids [6535 0 R 6536 0 R 6537 0 R 6538 0 R 6539 0 R 6540 0 R] +/Limits [(lstnumber.-324.5) (lstnumber.-329.100)] +>> endobj +6732 0 obj << +/Kids [6541 0 R 6542 0 R 6543 0 R 6544 0 R 6545 0 R 6546 0 R] +/Limits [(lstnumber.-329.101) (lstnumber.-329.37)] +>> endobj +6733 0 obj << +/Kids [6547 0 R 6548 0 R 6549 0 R 6550 0 R 6551 0 R 6552 0 R] +/Limits [(lstnumber.-329.38) (lstnumber.-329.7)] +>> endobj +6734 0 obj << +/Kids [6553 0 R 6554 0 R 6555 0 R 6556 0 R 6557 0 R 6558 0 R] +/Limits [(lstnumber.-329.70) (lstnumber.-34.12)] +>> endobj +6735 0 obj << +/Kids [6559 0 R 6560 0 R 6561 0 R 6562 0 R 6563 0 R 6564 0 R] +/Limits [(lstnumber.-34.13) (lstnumber.-42.4)] +>> endobj +6736 0 obj << +/Kids [6565 0 R 6566 0 R 6567 0 R 6568 0 R 6569 0 R 6570 0 R] +/Limits [(lstnumber.-42.5) (lstnumber.-53.11)] +>> endobj +6737 0 obj << +/Kids [6571 0 R 6572 0 R 6573 0 R 6574 0 R 6575 0 R 6576 0 R] +/Limits [(lstnumber.-53.12) (lstnumber.-58.6)] +>> endobj +6738 0 obj << +/Kids [6577 0 R 6578 0 R 6579 0 R 6580 0 R 6581 0 R 6582 0 R] +/Limits [(lstnumber.-6.1) (lstnumber.-70.4)] +>> endobj +6739 0 obj << +/Kids [6583 0 R 6584 0 R 6585 0 R 6586 0 R 6587 0 R 6588 0 R] +/Limits [(lstnumber.-70.5) (lstnumber.-84.2)] +>> endobj +6740 0 obj << +/Kids [6589 0 R 6590 0 R 6591 0 R 6592 0 R 6593 0 R 6594 0 R] +/Limits [(lstnumber.-85.1) (lstnumber.-90.1)] +>> endobj +6741 0 obj << +/Kids [6595 0 R 6596 0 R 6597 0 R 6598 0 R 6599 0 R 6600 0 R] +/Limits [(lstnumber.-90.2) (lstnumber.-94.2)] +>> endobj +6742 0 obj << +/Kids [6601 0 R 6602 0 R 6603 0 R 6604 0 R 6605 0 R 6606 0 R] +/Limits [(lstnumber.-94.3) (page.11)] +>> endobj +6743 0 obj << +/Kids [6607 0 R 6608 0 R 6609 0 R 6610 0 R 6611 0 R 6612 0 R] +/Limits [(page.110) (page.142)] +>> endobj +6744 0 obj << +/Kids [6613 0 R 6614 0 R 6615 0 R 6616 0 R 6617 0 R 6618 0 R] +/Limits [(page.143) (page.33)] +>> endobj +6745 0 obj << +/Kids [6619 0 R 6620 0 R 6621 0 R 6622 0 R 6623 0 R 6624 0 R] +/Limits [(page.34) (page.66)] +>> endobj +6746 0 obj << +/Kids [6625 0 R 6626 0 R 6627 0 R 6628 0 R 6629 0 R 6630 0 R] +/Limits [(page.67) (page.99)] +>> endobj +6747 0 obj << +/Kids [6631 0 R 6632 0 R 6633 0 R 6634 0 R 6635 0 R 6636 0 R] +/Limits [(part.1) (section.2)] +>> endobj +6748 0 obj << +/Kids [6637 0 R 6638 0 R 6639 0 R 6640 0 R 6641 0 R 6642 0 R] +/Limits [(section.20) (section.52)] +>> endobj +6749 0 obj << +/Kids [6643 0 R 6644 0 R 6645 0 R 6646 0 R 6647 0 R 6648 0 R] +/Limits [(section.53) (subsection.2.5)] +>> endobj +6750 0 obj << +/Kids [6649 0 R 6650 0 R 6651 0 R 6652 0 R 6653 0 R 6654 0 R] +/Limits [(subsection.2.6) (subsection.43.11)] +>> endobj +6751 0 obj << +/Kids [6655 0 R 6656 0 R 6657 0 R 6658 0 R 6659 0 R 6660 0 R] +/Limits [(subsection.43.12) (subsection.44.3)] +>> endobj +6752 0 obj << +/Kids [6661 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mode 100644 index 00000000000..cf4e9f7ca5b --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.tex @@ -0,0 +1,8205 @@ +%% +%% This is file `Mathmode.tex', +%% +%% IMPORTANT NOTICE: +%% +%% Herbert Voss +%% 2007-04-21 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% DESCRIPTION: +%% `Mathmode' is a document how the math mode works inside LaTeX +%% +\def\MathmodeVersion{2.32} +%\ifvtex\title{\logo Math mode - v.\MathmodeVersion}\else + \ifpdf\title{Math mode - v.\MathmodeVersion}\else + \title{\logo Math mode - v.\MathmodeVersion}\fi%\fi +% +\author{Herbert Vo\ss\footnote{\sloppy Thanks for the feedback to: + Hendri Adriaens; Juan Mari Alberdi; + Heiko Bauke; Neal Becker; Andrea Blomenhofer; Alexander Boronka; Walter Brown; + Christian Faulhammer; Jos\'e{} Luis G\'omez Dans; + Zongbao Fang; + Sabine Glaser; Sven Gleich; + Azzam Hassam; Gernot Hassenpflug; Henning Heinze; Martin Hensel; Mathias Hoffmann; + Jon Kirwan; + Morten H\o{}gholm; M. Kalidoss; Dan Lasley; + Angus Leeming; Vladimir Lomov; Tim Love; Dan Luecking; + Hendrik Maryns; Heinz Mezera; + David Neuway; + Luis Trucco Passadore; Joachim Punter; + Carl Riehm; Will Robertson; Christoph Rumsm\"uller; + Jos\'e{} Carlos Santos; Arnaud Schmittbuhl; + Rainer Schpf; Jens Schwaiger; Uwe Siart; Martin Sievers; Heiko Stamer; Uwe St\"ohr; + Carsten Thiel; + Juan Luis Varona; + David Weenink; + Philipp Wook; + Michael Zedler; + Zou Yuan-Chuan; + and last but not least a special thanks to Monika Hattenbach for her + excellent job of proofreading. +}} +\date{\today} + +\maketitle + +\begin{abstract} +It is often said that \TeX{} was designed for mathematical or technical purposes. +This may be true when we remember the reasons why Donald Knuth created \TeX{}. But nowadays +there are many examples in which \TeX\ is + used for publications with no mathematical or technical background content. However, +%we have to consider, that +writing publications with such %a lot of mathematical +material is one of the important advantages of \TeX{}. Because it +seems impossible to +know all existing macros and options of \AllTeX{} and the several additional packages, +especially of \AmSmath. This is the reason why I have attempted to gather +all the relevant +%I tried to collect all important +facts in this paper. An advanced german version of this paper is available as a book \cite{voss06}. + +\vspace{3cm} +\noindent Please report typos or any other comments to this documentation to +\href{mailto:voss@perce.de}{voss@perce.de}. +%\noindent This document was written with the \LaTeX{} editor \verb+Kile 1.8+ +%\verb+(Qt 3.3+ \verb+KDE 3.4)+ +%\href{http://sourceforge.net/projects/kile/}{http://sourceforge.net/projects/kile/} +%and the PDF output was built with the Linux version of \texttt{V\TeX/Free}, Version 8.46 +%(\href{http://www.micropress-inc.com/linux/}{http://www.micropress-inc.com/linux/}) + +This file can be redistributed and/or modified under the terms +of the \LaTeX\ Project Public License Distributed from \verb+CTAN+ archives +in directory \url{CTAN://macros/latex/base/lppl.txt}. + +\end{abstract} + + + +\clearpage +\tableofcontents{} + +\part{Standard \protect\LaTeX{} math mode} + +\section{Introduction} +The following sections describe all the math commands which are available +without any additional package. Most of them also work with special +packages and some of them are redefined. +At first some important facts for typesetting math expressions. + +\section{The Inlinemode}\label{sec:The-Inlinemode} +As the name says there are always math expressions which are in a standard +textline, like this one: $f(x)=\int_{a}^{b}\frac{\sin x}{x}\,\mathrm{d}x$. There +are no limitations for the height of the math expressions, so that +the layout may be very lousy if you insert a big matrix in an inline mode +like this: +$\underline{A}=\left[\begin{array}{ccc} +a & b & c\\ +d & e & f\\ +g & h & i\end{array}\right]$. In this case it is better to use the \verb|\smallmatrix| environment +$\underline{A}=\left[\begin{smallmatrix}% +a & b & c\cr +d & e & f\cr +g & h & i\end{smallmatrix}\right]$ from the \AmSmath{} package (see section \vref{sec:ams-matrix}) or the +displaymath mode\index{Display math mode} (section~\vref{display}). + +This inline mode is possible with three different commands: + +\bigskip +\begin{minipage}{0.35\fullwidth} +\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt] +$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt] +\begin{math} + \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1) +\end{math} +\end{minipage}\hfill +\begin{minipage}{0.62\fullwidth} +\begin{lstlisting} +\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt] +$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt] +\begin{math} + \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1) +\end{math} +\end{lstlisting} +\end{minipage} + +\begin{enumerate} +\item \CMD{( ... }\CMD{)} \marginpar{\CMD{(}...\CMD{)}}, the problem is that \verb+\(+ is +not a robust macro (see section~\vref{subsec:mathInTitles}). +\item \verb+$ ... $+ \marginpar{\$...\$} +\item \CMD{begin\{math\}} ... \CMD{end\{math\}}, also not robust% +\marginpar{\CMD{begin\{math\}}\\...\\\CMD{end\{math\}}} +\end{enumerate} + +\index{*@\texttt{\textbackslash\char040}}\index{*@\texttt{\textbackslash\char041}} +In general \verb+$...$+ is the best choice, but this does not work in environments like \verb+verbatim+ +or \verb+alltt+. In this case \verb+\(...\)+ works.\index{$@\texttt{\$}} + + +\subsection{Limits}\label{sub:Limits-Inline} + +In the inline mode the \Index{limits} are by default only in +super\index{Superscript} or subscript mode\index{Subscript} and +the fractions\index{Fraction} are always in the \Index{scriptstyle}% +\footnote{See section \vref{sec:Styles}.}\index{scriptstyle} +font size. For +example: $\int_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$, which is not too +big for the textline. You % +\marginpar{\CMD{limits}}can change this with the command \CIndex{limits}, +which must follow a math operator\footnote{To define a new operator see +page~\pageref{OperatorNames}}\index{Math operator} like % +\marginpar{\CMD{int}\\\CMD{lim}\\\CMD{prod}\\\CMD{sum}} + an integral (\CIndex{int}), a sum (\CIndex{sum}), +a product (\CIndex{prod}) or a limes +(\CIndex{lim}). But this $\int\limits_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$ +(\lstinline|$\int\limits_{1}^...|) %$ +does not look very nice in a text line when it appears between two lines, +especially when there are multiline limits.\footnote{For more +information about limits see section~\vref{sub:Multiple-Limits} or section~\vref{sec:limit-AMS}.} + + +\subsection{Fraction command}\label{sub:fraction command} + +For inlined formulas the fractions\index{Fraction} are by default +in the scriptstyle\index{scriptstyle@\textbackslash scriptstyle} (see tabular~\vref{cap:Mathstyles}), +which is good for typesetting $y=\frac{a}{b+1}$, because the +linespacing % +\marginpar{\CMD{frac}}is nearly the same, but not optimal, when the formula shows some important +facts. There are two solutions to get a better reading: + +\begin{enumerate} +\item choose the display mode instead of the inline mode, which is the better +one; +\item set the fontstyle to \CIndex{displaystyle}, which makes +the fraction $y={\displaystyle\frac{a}{b+1}}$ more readable but +the linespacing increases which is always a bad solution and should +only be used when the first solution makes no sense.\footnote{For an abbreviation see +section~\vref{sec:ams-fraction}, there is a special \CIndex{dfrac} macro.} + +\bigskip +\begin{minipage}{0.25\fullwidth} +$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$ +\end{minipage}\hfill +\begin{minipage}{0.72\fullwidth} +\begin{lstlisting} +$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$ +\end{lstlisting} +\end{minipage} +\end{enumerate} + + +\subsection[Math in Chapter/Section Titles]{\label{inline-chapter}Math in \CIndex{part}, +\CIndex{chapter}, \CIndex{section}, +... titles like $f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}\label{subsec:mathInTitles} + +All commands which appear in positions like contents, index, header, +... must be robust\footnote{% +\texttt{robust} means that the macro is not expanded before it is moved +into for example the tableofcontents file (\texttt{*.toc}). No robustness is +often a problem, when a macro is part of another macro.} +which is the case for \verb+$...$+ but not for \verb+\(...\)+. +The latest package \PIndex{fixltx2e} defines an macro for declaring +existing commands to be robust. The package itself does this already for: + +\begin{lstlisting} +\MakeRobust\( +\MakeRobust\) +\MakeRobust\[ +\MakeRobust\] +\MakeRobust\makebox +\MakeRobust\savebox +\MakeRobust\framebox +\MakeRobust\parbox +\MakeRobust\rule +\MakeRobust\raisebox +\end{lstlisting} + + +If you do not have any contents, index, a.s.o. +you can write the mathstuff in \CIndex{chapter}, \CIndex{section}, +a.s.o without any restriction. Otherwise use \verb+\protect\(+ and \verb+\protect\)+ or the +\verb+$...$+ version.\index{$@\texttt{\$}} + +The whole math expression appears in the default font shape and not +in bold like the other text. Section~\vref{sec:titleItem} describes how the math +expressions can be printed also in bold. + +\marginpar{\CMD{texorpdfstring}}% +There are problems with the \PIndex{hyperref} package when there is no +text part in a title. It is possible with the command \CIndex{texorpdfstring} +to tell \verb+hyperref+ to use different +commands, one for the title and another one for the bookmarks: + +\begin{verbatim} +\texorpdfstring{}{} +\end{verbatim} + + +\begin{minipage}{\fullwidth} +\begin{lstlisting} +\texorpdfstring{$\int f(x)\,\mathrm{d}x$}{Integral function} +\end{lstlisting} +\end{minipage} + + + +\subsection{Equation numbering} + +It is obvious that the numbering of inline mathstuff makes no sense! + +\subsection{Framed math} +With the \CIndex{fbox} macro everything of inline math can be framed\index{Framed inline +math}\index{boxed inline math}, like the following one: + +\bigskip +\begin{minipage}{0.325\fullwidth} +\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} +\end{minipage}\hfill +\begin{minipage}{0.67\fullwidth} +\begin{lstlisting} +\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} +\end{lstlisting} +\end{minipage} + +%$ + +Parameters are the width of \LIndex{fboxsep} and \LIndex{fboxrule}, the predefined values +from the file \verb|latex.ltx| are: + +\bigskip +\begin{minipage}{\fullwidth} +\begin{lstlisting} +\fboxsep = 3pt +\fboxrule = .4pt +\end{lstlisting} +\end{minipage} + +The same is possible with the \CIndex{colorbox} +\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} +from the color package. + +\bigskip +\begin{minipage}{\fullwidth} +\begin{lstlisting} +\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} +\end{lstlisting} +\end{minipage} + +%$ + +\subsection{Linebreak}\label{subsec:linebreak} + +\LaTeX{} can break an inline formula only when a relation symbol ($=, <, >, \ldots$) or a +binary operation symbol ($+,-, \ldots$) exists and at least one of these symbols appears at +the outer level of a formula. +Thus \verb|$a+b+c$| can be broken across lines, but \verb|${a+b+c}$| not.\index{$@\texttt{\$}} + +\begin{itemize} +\item The default: \hspace{1cm} +$f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots + +a_ix^i +a_2x^2 +a_1x^1 +a_0$ +\item The same inside a group \{...\}: +${f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots + +a_ix^i +a_2x^2 +a_1x^1 +a_0}$ + +\item Without any symbol: \hspace{4cm} +$f(x)=a_n\left(a_{n-1}\left(a_{n-2}\left(\ldots\right)\ldots\right)\ldots\right)$ +\end{itemize} + +If it is not possible to have any mathsymbol, then split the inline formula in two +or more pieces (\verb|$...$ $...$|). If you do not want a linebreak for the whole +document, you can set in the preamble: +\begin{verbatim} +\relpenalty=9999 +\binoppenalty=9999 +\end{verbatim} + +\noindent +which is the extreme case of grudgingly allowing breaks in extreme cases, or +% +\begin{verbatim} +\relpenalty=10000 +\binoppenalty=10000 +\end{verbatim} +% +for absolutely no breaks. + +\subsection{Whitespace}\label{subsec:whitespace} +\LaTeX{} defines the length \LIndex{mathsurround} with the default value of +\verb|0pt|. This length is added before and after an inlined math expression +(see table~\vref{tab:whitespace}). + +\begin{table}[htb] +\hspace*{-0.1\linewidth}% +\begin{tabular}{@{}cc@{}} +foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & +\begin{minipage}{0.7\linewidth} +\begin{lstlisting} +foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar +\end{lstlisting} +\end{minipage}\tabularnewline +% +foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar & +\begin{minipage}{0.7\linewidth} +\begin{lstlisting} +foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar +\end{lstlisting} +\end{minipage}\tabularnewline +\setlength{\mathsurround}{20pt}foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & +\begin{minipage}{0.7\linewidth} +\begin{lstlisting} +\setlength{\mathsurround}{20pt} +foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar +\end{lstlisting} +\end{minipage} +\end{tabular} +% +\caption{Meaning of \CMD{mathsurround}}\label{tab:whitespace} +\end{table} + +%$ + +\subsection{\AmSmath for the inline mode} + +None of the \AmSmath-functions are available in inline mode. + +\section{Displaymath mode}\label{display} +This means, that every formula gets its own paragraph (line). There are +some differences in the layout to the one from the title +of \ref{inline-chapter}. + + +\subsection{\texttt{equation} environment} + +For example: + +\bigskip\noindent +\begin{tabular}{cc} +\begin{minipage}{0.35\linewidth} +\begin{equation} + f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) +\end{equation} +\end{minipage} & +\begin{minipage}{0.63\linewidth} +\begin{lstlisting} +\begin{equation} + f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) +\end{equation} +\end{lstlisting} +\end{minipage} +\end{tabular} + +\bigskip +The delimiters\index{Delimiter} +\CMD{begin\{equation\} ... }\CMD{end\{equation\}} are the only difference to the inline version. +There are some equivalent commands for the display-math mode: + +\begin{enumerate} +\marginpar{\CMD{begin\{displaymath\}}\\ +\ldots\\ +\CMD{end\{displaymath\}}}% +\item \CMD{begin\{displaymath\}}\ldots\CMD{end\{displaymath\}}, same as +\CMD{[} \ldots \CMD{]} +% +\item \CMD{[\ldots}\CMD{]}. (see above) the short form of a displayed formula, no number% +\marginpar{\texttt{\textbackslash[\ldots\textbackslash{}]}} +\[ +f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) +\] +% +displayed, no number. Same as 1. +% +\item \CMD{begin\{equation\}\ldots}\CMD{end\{equation\}}% +\marginpar{\CMD{begin\{equation\}}\\ +\ldots\\ +\CMD{end\{equation\}}}% +% +\begin{equation} +f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) +\end{equation} +% +displayed, a sequential equation number, which may be reset when +starting a new chapter or section. + + +\begin{enumerate} +\item There is only \textbf{one} equation number for the whole environment. +\item \marginpar{\CMD{nonumber}}There exists no star-version of the equation environment +because \CIndex{[}\ldots\CIndex{]} is the equivalent. With the tag +\CIndex{nonumber} it is possible to suppress the equation number: + +\begin{minipage}{0.5\linewidth} +\begin{equation} + f(x)= [...] \nonumber +\end{equation} +\end{minipage}% +\begin{minipage}{0.6\linewidth} +\begin{lstlisting} +\begin{equation} + f(x)= [...] \nonumber +\end{equation} +\end{lstlisting} +\end{minipage} +% +\end{enumerate} +\end{enumerate} + + +\subsection{\texttt{eqnarray} environment}\label{display:eqnarray} + +This is by default an array with three columns and as many rows as +you like. \marginpar{\CMD{begin\{eqnarray\}}\\ +...\\ +\CMD{end\{eqnarray\}}} It is nearly the same as an array with a \verb|rcl| column definition. + +It is \textbf{not possible} to change the internal behaviour of the \verb|eqnarray| environment without +rewriting the environment. +It is always an impli\-cit array with \textbf{three} columns and the horizontal +alignment \verb|right-center-left (rcl)| and small \textbf{symbol} sizes for the +middle column. All this can not be changed by the user without rewriting +the whole environment in \verb|latex.ltx|. + +\bigskip\noindent +\begin{tabular}{cc} +\begin{minipage}{0.35\linewidth} +\begin{eqnarray*} +\mathrm{left} & \mathrm{middle} & \mathrm{right}\\ +\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}} +\end{eqnarray*} +\end{minipage} & +\begin{minipage}{0.63\linewidth} +\begin{lstlisting} +\begin{eqnarray*} +\mathrm{left} & \mathrm{middle} & \mathrm{right}\\ +\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}} +\end{eqnarray*} +\end{lstlisting} +\end{minipage} +\end{tabular} + +\bigskip +The \UIndex{eqnarray} should not be used as an array. As seen in the above +example the typesetting is wrong for the middle column. The numbering of eqnarray +environments is always for every row, means, +that four lines get four different equation numbers (for the labels see +section~\vref{sec:Labels}): + +\bigskip +\begin{minipage}{0.5\columnwidth} +\begin{eqnarray} +y & = & d\label{eq:2}\\ +y & = & cx+d\\ +y & = & bx^{2}+cx+d\\ +y & = & ax^{3}+bx^{2}+cx+d\label{eq:5} +\end{eqnarray} +\end{minipage}\hfill +\begin{minipage}{0.43\columnwidth} +\begin{lstlisting} +\begin{eqnarray} +y & = & d\label{eq:2}\\ +y & = & cx+d\\ +y & = & bx^{2}+cx+d\\ +y & = & ax^{3}+bx^{2}+cx+d\label{eq:5} +\end{eqnarray} +\end{lstlisting} +\end{minipage} + + +\medskip +Toggling numbering off/on for \textbf{all} rows is possible +with the starred version of eqnarray. + +\medskip +\begin{minipage}{0.45\columnwidth} +\begin{eqnarray*} +y & = & d\label{eq:3}\\ +y & = & cx+d\\ +y & = & bx^{2}+cx+d\\ +y & = & ax^{3}+bx^{2}+cx+d\label{eq:4} +\end{eqnarray*} +\end{minipage} +\begin{minipage}{0.53\columnwidth} +\begin{lstlisting} +\begin{eqnarray*} +y & = & d\label{eq:3}\\ +y & = & cx+d\\ +y & = & bx^{2}+cx+d\\ +y & = & ax^{3}+bx^{2}+cx+d\label{eq:4} +\end{eqnarray*} +\end{lstlisting} +\end{minipage} + +\medskip +Toggling off/on for \textbf{single} rows is possible with the above +mentioned \CIndex{nonumber} tag at the end of a row +(before the newline command). For example: + +\medskip +\begin{minipage}{0.45\columnwidth} +\begin{eqnarray} + y & = & d\nonumber \\ + y & = & cx+d\nonumber \\ + y & = & bx^{2}+cx+d\nonumber \\ + y & = & ax^{3}+bx^{2}+cx+d +\end{eqnarray} +\end{minipage} +\begin{minipage}{0.53\columnwidth} +\begin{lstlisting} +\begin{eqnarray} + y & = & d\nonumber \\ + y & = & cx+d\nonumber \\ + y & = & bx^{2}+cx+d\nonumber \\ + y & = & ax^{3}+bx^{2}+cx+d +\end{eqnarray} +\end{lstlisting} +\end{minipage} + + +\subsubsection{Short commands}\label{subsec:shortcommand} +It is possible to define short commands for the \UIndex{eqnarray} +% +\begin{lstlisting} +\makeatletter +\newcommand{\be}{% + \begingroup +% \setlength{\arraycolsep}{2pt} + \eqnarray% + \@ifstar{\nonumber}{}% +} +\newcommand{\ee}{\endeqnarray\endgroup} +\makeatother +\end{lstlisting} + +\makeatletter +\newcommand{\be}{% + \begingroup +% \setlength{\arraycolsep}{2pt} + \eqnarray% + \@ifstar{\nonumber}{}% +} +\newcommand{\ee}{\endeqnarray\endgroup} +\makeatother + +Now you can write the whole equation as + + +\begin{LTXexample}[width=0.5\columnwidth,wide] +\be + f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x +\ee +\end{LTXexample} + +\medskip +\noindent or, if you do not want to have a numbered equation as + +\begin{LTXexample}[width=0.5\columnwidth,wide] +\be* + f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x +\ee +\end{LTXexample} + + +\subsection{Equation numbering}\label{sub:Equationnumbering} + +For all equations which can have one or % +\marginpar{\CMD{nonumber}}more equation numbers (for every line/row) the numbering +for the whole equation can be disabled with switching from the unstarred to the star +version. This is still for the whole formula and doesn't work for single rows. +In this case use the \CIndex{nonumber} tag. + +\begin{itemize} +\item This doc is written with the article-class, which counts the equations +continuously over all parts/sections. You can change this behaviour +in different ways (see the following subsections). +\item In standard \LaTeX{} it is a problem with too long equations and the +equation number, which may be printed with the equation one upon the other. In this case +use the \AmSmath package, where the number is set above or below +of a too long equation (see equation~\vref{eq:braces}). +\item For counting subequations see section~\vref{ams:subeqn}. +\end{itemize} + +\subsubsection{Changing the style} + +\marginpar{\CMD{theequation}}% +With the beginning of Section \vref{sec:alignat environment} the +counting changes from ``\ref{eq:IntoSection}{}'' into the new style +``\ref{eq:newCounting}''. The command sequence is + +\begin{lstlisting} +\renewcommand\theequation{\thepart-\arabic{equation}} +\end{lstlisting} + +See section~\vref{sec:Equation-numbering} for the \AmSmath command. + + +\subsubsection{Resetting a counter style} + +Removing a given reset is possible with the \PIndex{remreset}.% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/supported/carlisle/remreset.sty}{CTAN://macros/latex/contrib/supported/carlisle/remreset.sty}} Write into the % +\marginpar{\CMD{@removefromreset}} preamble + +\begin{lstlisting} +\makeatletter +\@removefromreset{equation}{section} +\makeatother +\end{lstlisting} +or anywhere in the text. + +Now the equation counter is no longer reset when a new section starts. +You can see this after section~\vref{split}. + + +\subsubsection{Equation numbers on the left side} + +Choose package \PIndex{leqno}% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/unpacked/leqno.sty}{CTAN://macros/latex/unpacked/leqno.sty}} +or have a look at your document class, if such an option exists. + +\subsubsection{Changing the equation number style} +The number style can be changed with a redefinition of + +\begin{verbatim} +\def\@eqnnum{{\normalfont \normalcolor (\theequation)}} +\end{verbatim} + +For example: if you want the numbers not in parentheses write + +\begin{lstlisting} +\makeatletter +\def\@eqnnum{{\normalfont \normalcolor \theequation}} +\makeatother +\end{lstlisting} + +For \AmSmath there is another macro, see section~\ref{sec:Equation-numbering} on +page~\pageref{sec:Equation-numbering}. + +\subsubsection{More than one equation counter} +You can have more than the default equation counter. With the following code you +can easily toggle between roman and arabic equation counting. +\makeatletter +%Roman counter +\newcounter{roem} +\renewcommand{\theroem}{\roman{roem}} + +% save the original counter +\newcommand{\c@org@eq}{} +\let\c@org@eq\c@equation +\newcommand{\org@theeq}{} +\let\org@theeq\theequation + +%\setroem sets roman counting +\newcommand{\setroem}{ + \let\c@equation\c@roem + \let\theequation\theroem} + +%\setarab the arabic counting +\newcommand{\setarab}{ + \let\c@equation\c@org@eq + \let\theequation\org@theeq} +\makeatother + +\begin{lstlisting} +%code by Heiko Oberdiek +\makeatletter +%Roman counter +\newcounter{roem} +\renewcommand{\theroem}{\roman{roem}} + +% save the original counter +\newcommand{\c@org@eq}{} +\let\c@org@eq\c@equation +\newcommand{\org@theeq}{} +\let\org@theeq\theequation + +%\setroem sets roman counting +\newcommand{\setroem}{ + \let\c@equation\c@roem + \let\theequation\theroem} + +%\setarab the arabic counting +\newcommand{\setarab}{ + \let\c@equation\c@org@eq + \let\theequation\org@theeq} +\makeatother +\end{lstlisting} + +The following examples show how it works: + +\noindent +\begin{minipage}{1.2\linewidth} +\begin{minipage}{0.38\linewidth} +\begin{align} +f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\ +g(x) &= \int\frac{1}{x}\,\mathrm{d}x +\end{align} +% +\setroem +% +\begin{align} +F(x) &=-\cos x\\ +G(x) &=\ln x\label{eq:rom1} +\end{align} +% +\setarab +% +\begin{align} +f^{\prime} (x) &= \sin x\\ +g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2} +\end{align} +\end{minipage}\hfill +\begin{minipage}{0.58\linewidth} +\begin{lstlisting} +\begin{align} +f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\ +g(x) &= \int\frac{1}{x}\,\mathrm{d}x +\end{align} +% +\setroem +% +\begin{align} +F(x) &=-\cos x\\ +G(x) &=\ln x\label{eq:rom1} +\end{align} +% +\setarab +% +\begin{align} +f^{\prime} (x) &= \sin x\\ +g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2} +\end{align} +\end{lstlisting} +\end{minipage} +\end{minipage} + +\medskip +There can be references to these equations in the usual way, like eq.\ref{eq:arab1}, +\ref{eq:arab2} and for the roman one eq.\ref{eq:rom1}. + + +\subsection{Labels}\label{sec:Labels} + +Every numbered equation can have a label\index{Label} to which a +reference\index{Reference} is possible. + +\begin{itemize} +\item There is one restriction for the label names, they cannot include +one of \LaTeX{}'s command characters.\footnote{\$ \_ \^{} \textbackslash{} \& \% \{ \}} +\item The label names are replaced by the equation number. +\end{itemize} +% +\marginpar{\CMD{tag}}If you do not want a reference to the equation number but to a self +defined name then use the \AmS{}math command \CMD{tag{...}}, +which is described in section \vref{sec:Labels-and-Tags}\index{tag@\textbackslash tag}. + +\subsection{Frames}\label{sec:Frames} +Similiar to the inline mode, displayed equations can also be framed with +the \CIndex{fbox} command, like equation \ref{eq:frame0}. +The only difference is +the fact, that the equation must be packed into a parbox or minipage. It is +nearly the same for a colored box, where the \verb|\fbox{...}| has to be +replaced with \verb|\colorbox{yellow}{...}|. The package \verb|color.sty| must +be loaded and --important -- the \PIndex{calc} package to get a correct boxwidth. + +\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% +\begin{equation}\label{eq:frame0} +f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1 +\end{equation}% +}} + +\medskip +\begin{lstlisting} +\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% +\begin{equation}\label{eq:frame0} + f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1 +\end{equation}% +}} +\end{lstlisting} + + +If the equation number should not be part of the frame, then it is a bit +complicated. There is one tricky solution, which puts an unnumbered equation +just beside an empty numbered equation. The \verb|\hfill| is only useful for +placing the equation number right aligned, which is not the default. The +following four equations \ref{eq:frame2}-\ref{eq:frame5} are the same, +only the second one written with the \verb|\myMathBox| macro which has the +border and background color as optional arguments with the defaults +\verb|white| for background and \verb|black| for the frame. If there is only +one optional argument, then it is still the one for the frame color (\ref{eq:frame3}). + +\makeatletter +\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}} +\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}} +\def\my@MBoxii[#1][#2]#3#4{% + \par\noindent% + \fcolorbox{#1}{#2}{% + \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}% + }% + \parbox{\labelwidth}{% + \begin{eqnarray}\label{#4}\end{eqnarray}% + }% + \par% +} +\makeatother + +\begin{lstlisting} +\makeatletter +\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}} +\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}} +\def\my@MBoxii[#1][#2]#3#4{% + \par\noindent% + \fcolorbox{#1}{#2}{% + \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}% + }% + \parbox{\labelwidth}{% + \begin{eqnarray}\label{#4}\end{eqnarray}% + }% + \par% +} +\makeatother +\end{lstlisting} + +\begin{equation}\label{eq:frame2} + f(x)=x^2 +x +\end{equation} +\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3} +\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4} +\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5} + +\medskip +\begin{lstlisting} +\begin{equation}\label{eq:frame2} + f(x)=x^2 +x +\end{equation} +\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3} +\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4} +\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5} +\end{lstlisting} + +If you are using the \AmSmath package, then try the solutions from section +\vref{sec:ams-frames}. + +\section{\texttt{array} environment} +\marginpar{\CMD{begin\{array\}}\\...\\\CMD{end\{array\}}} +This is simply the same as the \UIndex{eqnarray} only with the +possibility of variable rows \textbf{and} columns and the fact, that +the whole formula has only \textbf{one} equation number and that the +\verb|array| environment can only be part of another math environment, +like the \UIndex{equation} or the \UIndex{displaymath}. With \verb+@{}+ before the +first and after the last column the additional space \LIndex{arraycolsep} +is not used, which maybe important when using left aligned equations. + +\begin{equation} +\left.% +\begin{array}{@{}r@{\quad}ccrr@{}} + \textrm{a}) & y & = & c & (constant)\\ + \textrm{b}) & y & = & cx+d & (linear)\\ + \textrm{c}) & y & = & bx^{2}+cx+d & (square)\\ + \textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic) +\end{array}% +\right\} \textrm{Polynomes} +\end{equation} + + +\begin{lstlisting} +\begin{equation} +\left.% +\begin{array}{@{}r@{\quad}ccrr@{}} + \textrm{a}) & y & = & c & (constant)\\ + \textrm{b}) & y & = & cx+d & (linear)\\ + \textrm{c}) & y & = & bx^{2}+cx+d & (square)\\ + \textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic) +\end{array}% +\right\} \textrm{Polynomes} +\end{equation} +\end{lstlisting} + + +The horizontal alignment of the columns is the same as the one from the +\UIndex{tabular}. + +For arrays with delimiters see section~\vref{delarray}. + +\subsection{Cases structure} + +If you do not want to use the \AmSmath package then write your own +cases structure\index{cases@\textbackslash cases} with the \verb|array| environment: + +\begin{LTXexample}[pos=b] +\begin{equation} +x=\left\{ \begin{array}{cl} +0 & \textrm{if }A=\ldots\\ +1 & \textrm{if }B=\ldots\\ +x & \textrm{this runs with as much text as you like, but without an raggeright text.}\end{array}\right. +\end{equation} +\end{LTXexample} + + +It is obvious, that we need a \CMD{parbox} if the text is longer than the possible linewidth. + +\begin{LTXexample}[pos=b] +\begin{equation} +x = \left\{% + \begin{array}{l>{\raggedright}p{.5\textwidth}}% + 0 & if $A=\ldots$\tabularnewline + 1 & if $B=\ldots$\tabularnewline + x & \parbox{0.5\columnwidth}{this runs with as much text as you like, % + because an automatic linebreak is given with % + a raggedright text. Without this % + \raggedright command, you'll get a formatted % + text like the following one ... but with a parbox ... it works} + \end{array}% + \right. % +\end{equation} +\end{LTXexample} + + + +\subsection{\texttt{arraycolsep}}\label{sec:arraycolsep} +\marginpar{\CMD{arraycolsep}}% +All the foregoing math environments use the array to typeset the math +expression. The predefined separation between two columns is the length +\LIndex{arraycolsep}|, which is set by nearly all document classes to \verb|5pt|, +which seems to be too big. The following equation is typeset with the +default value and the second one with \verb|\arraycolsep=1.4pt| + + +\bgroup +\fboxsep=0pt +\def\xstrut{\vphantom{\int\frac{\sin x}{x}}} +\begin{eqnarray*} +\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x} +\end{eqnarray*} + +\vspace{-2ex} +\arraycolsep=1.4pt +\begin{eqnarray*} +\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x} +\end{eqnarray*} +\egroup + +If this modification should be valid for all arrays/equations, then write it into the +preamble, otherwise put it into a group or define your own environment as done +in section~\vref{subsec:shortcommand}. + +\begin{lstlisting} +\bgroup +\arraycolsep=1.4pt +\begin{eqnarray} +f(x) & = & \int\frac{\sin x}{x}\,\mathrm{d}x +\end{eqnarray} +\egroup +\end{lstlisting} + +\begin{lstlisting} +\makeatletter +\newcommand{\be}{% + \begingroup + \setlength{\arraycolsep}{1.4pt} +[ ... ] +\end{lstlisting} + +\section{Matrix}\label{sec:matrix} +\marginpar{\CMD{begin\{matrix\}}\\\ldots\\\CMD{end\{matrix\}}\\\CMD{bordermatrix}}% +\TeX{} knows two macros and \LaTeX{} one more for typesetting a +matrix\index{bordermatrix@\textbackslash bordermatrix}: + +\begin{LTXexample} +$\begin{matrix} + A & B & C \\ + d & e & f \\ + 1 & 2 & 3 \\ +\end{matrix}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix{% + & 0 & 1 & 2 \cr + 0 & A & B & C \cr + 1 & d & e & f \cr + 2 & 1 & 2 & 3 \cr +}$ +\end{LTXexample} + +\iffalse % smallmatrix belongs to amsmath +\begin{minipage}{0.4\textwidth} +\begin{center} +$ +\begin{smallmatrix}% + A & B & C \\ + d & e & f \\ + 1 & 2 & 3 +\end{smallmatrix} +$ +\end{center} +\end{minipage}\hfill +\begin{minipage}{0.4\textwidth} +\begin{lstlisting} +\begin{smallmatrix}% + A & B & C \\ + d & e & f \\ + 1 & 2 & 3 +\end{smallmatrix} +\end{lstlisting} +\end{minipage} +\fi + +The first two macros are listed here for some historical reason, because the +\UIndex{array} or especially the +\AmSmath package offers the same or better macros/environments. Nevertheless it is +possible to redefine the \CIndex{bordermatrix} macro to get other parentheses and a star +version which takes the left top part as matrix: + +\makeatletter +\newif\if@borderstar +\def\bordermatrix{\@ifnextchar*{% + \@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}% +} +\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}} +\def\@bordermatrix@ii[#1]#2{% +\begingroup + \m@th\@tempdima8.75\p@\setbox\z@\vbox{% + \def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}% + \ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace % + \hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut % + \hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit % + \strut\cr}}% + \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{% + $\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1% + \if@borderstar\kern2pt\else\kern -\wd\@ne\fi% + \global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}% + \vcenter{\if@borderstar\else\kern -\ht\@ne\fi% + \unvbox\z@\kern-\if@borderstar2\fi\baselineskip}% + \if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $% + }\null \;\vbox{\kern\ht\@ne\box\tw@}% +\endgroup +} +\makeatother + +\begin{LTXexample} +$\bordermatrix{% + & 1 & 2 \cr +1 & x1 & x2 \cr +2 & x3 & x4 \cr +3 & x5 & x6 +}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix[{[]}]{% + & 1 & 2 \cr +1 & x1 & x2 \cr +2 & x3 & x4 \cr +3 & x5 & x6 +}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix[\{\}]{% + & 1 & 2 \cr +1 & x1 & x2 \cr +2 & x3 & x4 \cr +3 & x5 & x6 +}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix*{% + x1 & x2 & 1 \cr + x3 & x4 & 2 \cr + x5 & x6 & 3 \cr + 1 & 2 +}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix*[{[]}]{% + x1 & x2 & 1 \cr + x3 & x4 & 2 \cr + x5 & x6 & 3 \cr + 1 & 2 +}$ +\end{LTXexample} +\vspace{-10pt} +\begin{LTXexample} +$\bordermatrix*[\{\}]{% + x1 & x2 & 1 \cr + x3 & x4 & 2 \cr + x5 & x6 & 3 \cr + 1 & 2 +}$ +\end{LTXexample} + + +There is now an optional argument for the parenthesis with \verb|()| as the +default one. To get such a behaviour, write into the preamble: + +\begin{lstlisting}[xleftmargin=-0.75cm,xrightmargin=-0.75cm] +\makeatletter +\newif\if@borderstar +\def\bordermatrix{\@ifnextchar*{% + \@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}% +} +\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}} +\def\@bordermatrix@ii[#1]#2{% +\begingroup + \m@th\@tempdima8.75\p@\setbox\z@\vbox{% + \def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}% + \ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace % + \hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut % + \hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit % + \strut\cr}}% + \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}% + \setbox\tw@\hbox{% + $\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1% + \if@borderstar\kern2pt\else\kern -\wd\@ne\fi% + \global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}% + \vcenter{\if@borderstar\else\kern -\ht\@ne\fi% + \unvbox\z@\kern-\if@borderstar2\fi\baselineskip}% + \if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $% + }\null \;\vbox{\kern\ht\@ne\box\tw@}% +\endgroup +} +\makeatother +\end{lstlisting} + +The \UIndex{matrix} macro cannot be used together with the \AmSmath package, it redefines +this environment (see section~\vref{sec:ams-matrix}). + +\section{Super/Subscript and limits}\label{sec:limits} +Writing $a_{min}$ and $a_{max}$ gives the same depth for the \Index{subscript}, but +writing them in \Index{upright mode} with \verb+\mbox+ gives a different +depth: $a_{\mbox{min}}$ and $a_{\mbox{max}}$. +The problem is the different height, which can be modified in several ways +\begin{itemize} +\item \verb+$a_{\mbox{\vphantom{i}max}}+: $a_{\mbox{min}}$ and $a_{\mbox{\vphantom{i}max}}$; +\item \verb+$a_{\mathrm{max}}+: $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$; +\item \verb+$a_{\max}+: $a_{\min}$ and $a_{\max}$. Both are predefined + operators (see section~\vref{sec:ltxOperators}). +\end{itemize} +%$ + +\subsection{Multiple limits}\label{sub:Multiple-Limits} + +\marginpar{\CMD{atop}}% +For general information about limits\index{Limits} read section +\vref{sub:Limits-Inline}. With the \TeX\ command \CIndex{atop} +multiple limits for a \CIndex{sum} or \CIndex{prod} are possible. The syntax is: + +\begin{LTXexample}[width=0.4\linewidth] +\[ {above \atop below} \] +\end{LTXexample} + +\noindent which is nearly the same as a fraction without a rule. This can +be enhanced to \verb|a\atop b\atop c| and so on. For equation \ref{eq:atop} do the following steps: + +\begin{LTXexample}[width=0.4\linewidth] +\begin{equation}\label{eq:atop} +\sum_{{1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}% +}a_{ij}b_{jk}c_{ki} +\end{equation} +\end{LTXexample} + + +\bigskip +\marginpar{\CMD{shortstack}}% +which is not the best solution because the space between the lines +is too big. +The \AmSmath package provides several commands for +limits (section~\vref{sec:limit-AMS}) and the \CIndex{underset} and \CIndex{overset} +commands (see section~\vref{sec:misc-AMS}). + +\subsection{Problems} + +\begin{equation}\label{eq:disp-limits} +\fboxsep=0pt\fboxrule=0.1pt +\boxed{\sum_{ + {{1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}% + }}% +}\boxed{a_{ij}b_{jk}c_{ki}} +\end{equation} + +The equation \ref{eq:disp-limits} shows that the horizontal alignment +is not optimal, because the math expression on the right follows at the +end of the limits which are a unit together with the sum symbol. There +is an elegant solution with \AmSmath, described in subsection +\vref{subsec:ams-limits}. If you do not want to use \AmSmath, +then use \CIndex{makebox}. But there is a problem when the general fontsize +is increased, \CMD{makebox} knows nothing about the actual math font +size. Equation \ref{eq:disp-limits2} shows the effect and equation +\ref{eq:disp-limits3} the view without the boxes. + +\vspace{\abovedisplayskip} +\begin{subequations} +\begin{minipage}{0.45\textwidth} +\begin{equation}\label{eq:disp-limits2} +\fboxsep=0pt\fboxrule=0.1pt +\boxed{\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}% + }% +}\boxed{a_{ij}b_{jk}c_{ki}} +\end{equation} +\end{minipage}\hfill +\begin{minipage}{0.45\textwidth} +\begin{equation}\label{eq:disp-limits3} +\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}}a_{ij}b_{jk}c_{ki} +\end{equation} +\end{minipage} +\end{subequations} + +\medskip +\begin{lstlisting} +\begin{equation} +\sum_{\makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}}a_{ij}b_{jk}c_{ki} +\end{equation} +\end{lstlisting} + + + +\section{Roots}\label{sec:Roots} + +The square root\index{Root} \CIndex{sqrt} is the default +for \LaTeX{} and the $n$-th root can be inserted with the optional +parameter \CMD{sqrt[n]\{\ldots\}}. +\marginpar{\CMD{sqrt}}. + +\begin{center} +\begin{tabular}{cc} + \verb|\sqrt{x}| & $\sqrt{x}$\\ + \verb|\sqrt[3]{x}| & $\sqrt[3]{x}$ +\end{tabular} +\end{center} + +There is a different typesetting in roots. Equation~\vref{eq:root1} +has different heights for the roots, whereas equation~\vref{eq:root2} +has the same one. This is possible with the % +\marginpar{\CMD{vphantom}}% +\CIndex{vphantom} command, +which reserves the vertical space (without a horizontal one) of the +parameter height. + +\begin{LTXexample}[width=0.35\linewidth,wide] +\begin{equation} + \sqrt{a}\,% + \sqrt{T}\,% + \sqrt{2\alpha k_{B_1}T^i}\label{eq:root1} +\end{equation} +\end{LTXexample} + + +\vspace{-10pt} +\begin{LTXexample}[width=0.35\linewidth,wide] +\begin{equation}\label{eq:root2} + \sqrt{a\vphantom{k_{B_1}T^i}}\,% + \sqrt{T\vphantom{k_{B_1}T^i}}\,% + \sqrt{2\alpha k_{B_1}T^i} +\end{equation} +\end{LTXexample} + + +The typesetting looks much better, especially when the formula +has different roots in a row, like equation~\vref{eq:root1}. Using +\AmSmath with the \CIndex{smash} command% +\footnote{The \CMD{smash} command exists also in \LaTeX{} +but without an optional argument, which makes the use for roots possible.} +gives some more possibilities for the typesetting of roots (see section~\vref{sec:Roots-ams}). + + +\section[Brackets, braces \ldots]{Brackets, braces and parentheses}\label{sec:Brackets,-Braces-and} + +This is one of the major problems inside the math mode, because there is often a need for different +brackets, braces and parentheses in different size. At first we had to admit, that +there is a difference between the characters ``\verb|()[]/\| +$\lbrace\rbrace$ +| +$\Vert$ +$\lfloor\rfloor$ +$\lceil\rceil$ +$\langle\rangle$ +$\uparrow\Uparrow$ +$\downarrow\Downarrow$ +$\updownarrow\Updownarrow${}'' +and their use as an argument % +\marginpar{\CMD{leftX}\\\CMD{rightX}} of the \CIndex{left} and \CIndex{right} +command, where \LaTeX{} stretches the size in a way that everything between +the pair of left and right parentheses is smaller than the parentheses themselves. In some cases% +\footnote{See section \vref{cap:Use-of-the-vphantom} for example.} +it may be useful to choose a fixed height, which is possible with +the \CMD{big}-series. Instead of writing \CMD{leftX} +or \CMD{rightX} one of the following commands can +be chosen: + +\medskip +\marginpar{\CMD{bigX}\\\CMD{BigX}\\\CMD{biggX}\\\CMD{BiggX}} +\index{big@\textbackslash big}\index{Big@\textbackslash Big}% +\index{bigg@\textbackslash bigg}\index{Bigg@\textbackslash Bigg} +\begin{tabular}{rl} +default & ()[]/\textbackslash$\lbrace\rbrace$|$\Vert$ $\lfloor\rfloor$ +$\lceil\rceil$ $\langle\rangle$ $\uparrow\Uparrow$ $\downarrow\Downarrow$% +$\updownarrow\Updownarrow$\\[2pt] +\CMD{bigX} & $\big(\big)$ $\big[\big]$ +$\bigl/\big\backslash\big\{\big\}$ +$\big|$ $\big\Vert$ $\big\lfloor\big\rfloor$ $\big\lceil\big\rceil$ +$\big\langle\big\rangle$ $\big\uparrow\big\Uparrow$ $\big\downarrow\big\Downarrow$ +$\big\updownarrow\big\Updownarrow$\\[2pt] +\CMD{BigX} & $\Big(\Big)$ +$\Big[\Big]$ $\Bigl/\Big\backslash\Big\{\Big\}$ +$\Big|$ $\Big\Vert$ $\Big\lfloor\Big\rfloor$ +$\Big\lceil\Big\rceil$ $\Big\langle\Big\rangle$ +$\Big\uparrow\Big\Uparrow$ $\Big\downarrow\Big\Downarrow$ +$\Big\updownarrow\Big\Updownarrow$\\[4pt] +\CMD{biggX} & $\bigg(\bigg)$ +$\bigg[\bigg]$ $\biggl/\bigg\backslash\bigg\{\bigg\}$% +$\bigg|$ $\bigg\Vert$ $\bigg\lfloor\bigg\rfloor$ $\bigg\lceil\bigg\rceil$ +$\bigg\langle\bigg\rangle$ $\bigg\uparrow\bigg\Uparrow$ +$\bigg\downarrow\bigg\Downarrow$ $\bigg\updownarrow\bigg\Updownarrow$\\[8pt] +\CMD{BiggX} & $\Bigg(\Bigg)$ +$\Bigg[\Bigg]$ $\Biggl/\Bigg\backslash\Bigg\{\Bigg\}$ +$\Bigg|$ $\Bigg\Vert$ $\Bigg\lfloor\Bigg\rfloor$ +$\Bigg\lceil\Bigg\rceil$ $\Bigg\langle\Bigg\rangle$ +$\Bigg\uparrow\Bigg\Uparrow$ $\Bigg\downarrow\Bigg\Downarrow$% +$\Bigg\updownarrow\Bigg\Updownarrow$ +\end{tabular} + +\medskip{} +Only a few commands can be written in a short form like \CMD{big(}. +The ``X{}'' has to be replaced with one of the following characters +or commands from table~\vref{tab:big}, which shows the parentheses +character, its code for the use with one of the ``big{}'' commands +and an example with the code for that. + +\marginpar{\CMD{biglX}\\\CMD{bigrX}}% +For all commands there exists a left/right version \CIndex{bigl}, +\CIndex{bigr}, \CIndex{Bigl} and so on, which only makes sense when writing things like: + +\begin{LTXexample}[width=0.3\linewidth,wide] +\begin{align} + \biggl)\times \frac{a}{b} \times\biggr( +\end{align} +\begin{align} + \bigg)\times \frac{a}{b} \times\bigg( +\end{align} +\end{LTXexample} + +\LaTeX{} takes the \verb|\biggl)| as a \Index{mathopen symbol}, which has by default +another horizontal spacing. + +In addition to the above commands there exist some more: +\CIndex{bigm}, \CIndex{Bigm}, \CIndex{biggm} and \CIndex{Biggm}, +which work as the standard ones (without the addtional ``m{}'') +but add some more horizontal space% +\marginpar{\CMD{bigmX}\\\CMD{bigmX}} % +between the delimiter and the formula before and after (see +table~\vref{cap:Difference-between-the-bigg}). + + + +%$3\bigg|a^2-b^2-c^2\bigg|+2$ +%$3\biggm|a^2-b^2-c^2\biggm|+2$ + +\begin{table}[htb] +\begin{LTXexample} +$\bigg(\displaystyle\frac{1}{3}\bigg|\frac{3}{4}\bigg)$ +\end{LTXexample} +\vspace{-15pt} +\begin{LTXexample} +$\bigg(\displaystyle\frac{1}{3}\biggm|\frac{3}{4}\bigg)$ +\end{LTXexample} +\caption{Difference between the default +\CMD{bigg} and the \CMD{biggm} command}\label{cap:Difference-between-the-bigg} +\end{table} + + +\newcommand{\xstrut}{\rule{0pt}{0.55cm}} +{\setlength{\hangindent}{-\marginparwidth} +\begin{longtable}{l>{\raggedright}p{2.4cm}l>{\raggedright}p{5.7cm}} +Char & Code & Example & Code\tabularnewline +\hline +\endhead +\xstrut$(\ )$ & ( ) & % + $3\Big(a^{2}+b^{c^{2}}\Big)$ & % + \texttt{3\CMD{Big}( a\^{}2+b\^{}\{c\^{}2\}\CMD{Big})}\tabularnewline +% +\xstrut$[\ ]$ & {[} {]}& +$3\Big[a^{2}+b^{c^{2}}\Big]$& +\texttt{3\CMD{Big}{[} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}{]}}\tabularnewline +% +\xstrut$/\ \backslash$ & \texttt{/}\CMD{backslash} & $3\Big/a^{2}+b^{c^{2}}\Big\backslash$ & +\texttt{3\CMD{Big}/ a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{backslash}}\tabularnewline +% +\xstrut$\{\ \}$ & \CMD{\{}\CMD{\}}\\ + & $3\Big\{ a^{2}+b^{c^{2}}\Big\}$ & +\texttt{3\CMD{Big}\CMD{\{} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{\}}}\tabularnewline +% +\xstrut$\vert\ \Vert$ & | \CMD{Vert} & $3\Big|a^{2}+b^{c^{2}}\Big\Vert$ & \texttt{3\CMD{Big}|a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{Vert}}\tabularnewline +% +\xstrut$\lfloor\ \rfloor$ & \CMD{lfloor} \CMD{rfloor} & % + $3\Big\lfloor a^{2}+b^{c^{2}}\Big\rfloor$ & % + \texttt{3\CMD{Big}\CMD{lfloor} a\^{}2+b\^{}\{c\^{}2\} + \CMD{Big}\CMD{rfloor}}\tabularnewline +% +\xstrut$\lceil\ \rceil$ & \CMD{lceil}\CMD{rceil} & + $3\Big\lceil a^{2}+b^{c^{2}}\Big\rceil$ & + \texttt{3\CMD{Big}\CMD{lceil} a\^{}2+b\^{}\{c\^{}2\} \CMD{Big}% + \CMD{rceil}}\tabularnewline +% +\xstrut$\langle\ \rangle$ & \CMD{langle}\CMD{rangle} & + $3\Big\langle a^{2}+b^{c^{2}}\Big\rangle$ & + \texttt{3\CMD{Big}\CMD{langle} a\^{}2+b\^{}\{c\^{}2\}% + \CMD{Big}\CMD{rangle}}\tabularnewline +% +\xstrut$\uparrow\ \Uparrow$ & + \CMD{uparrow} \CMD{Uparrow} & + $3\Big\uparrow a^{2}+b^{c^{2}}\Big\Uparrow$ & + \texttt{3\CMD{Big}\CMD{uparrow} a\^{}2+b\^{}\{c\^{}2\}% + \CMD{Big}\CMD{Uparrow}}\tabularnewline +% +\xstrut$\downarrow\ \Downarrow$ & \CMD{downarrow} \CMD{Downarrow} & + $3\Big\downarrow a^{2}+b^{c^{2}}\Big\Downarrow$ & + \texttt{3\CMD{Big}\CMD{downarrow} a\^{}2+b\^{}\{c\^{}2\} + \CMD{Big}\CMD{Downarrow}}\tabularnewline +% +\xstrut$\updownarrow\ \Updownarrow$ & \CMD{updownarrow} \CMD{Updownarrow} & + $3\Big\updownarrow a^{2}+b^{c^{2}}\Big\Updownarrow$ & + \texttt{3\CMD{Big}\CMD{updownarrow} a\^{}2+b\^{}\{c\^{}2\} + \CMD{Big}\CMD{Updownarrow}}\tabularnewline +& & &\\ +\caption{Use of the different parentheses for the ``big{}'' commands} \label{tab:big}\tabularnewline +\end{longtable}} + + +\subsection{Examples} +\subsubsection{Braces over several lines}\label{cap:Use-of-the-vphantom} +The following equation in the single line mode looks like + + +\begin{equation} +\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i{\mskip\medmuskip} +\def\;{\mskip\thickmuskip} +\def\!{\mskip-\thinmuskip} +\end{verbatim} +In math mode there is often a need for additional tiny spaces between variables, +\eg $L\dfrac{di}{dt}$ written with a tiny space between $L$ and +$\dfrac{di}{dt}$ looks nicer: $L\:\dfrac{di}{dt}$. Table~\ref{cap:Spaces-in-math mode} +shows a list of all commands for horizontal space which can be used +in math mode. The ``space{}'' is seen ``between{}'' the boxed a +and b. For all examples a is \verb+\boxed{a}+ and +b is \verb+\boxed{b}+. The short forms for some +\marginpar{\CMD{hspace}\\ +\CMD{hphantom}\\ +\CMD{kern}} +spaces may cause problems with other packages. In this case use the +long form of the commands. + +\subsection{Problems}\label{space:problems} +Using \CIndex{hphantom} in mathmode depends to on object. \CIndex{hphantom} +reserves only the space of +the exact width without any additional space. In the following example the second line is +wrong: \verb+& \hphantom{\rightarrow} b\\+. It does not reserve any additional space. + +\begin{LTXexample}[width=0.15\linewidth,wide] +\begin{align*} +a & \rightarrow b\\ + & \hphantom{\rightarrow} b\\ + & \mkern\thickmuskip\hphantom{\rightarrow}\mkern\thickmuskip b\\ + & \mathrel{\hphantom{\rightarrow}} b +\end{align*} +\end{LTXexample} + +This only works when the math symbol is a mathrel one, otherwise you have to change the +horizontal space to \CIndex{medmuskip} or \CIndex{thinmuskip} or to use an empty group after +the \CIndex{hphantom} command. For more informations +about the math objects look into \verb+fontmath.ltx+ or \PIndex{amssymb} or use the \CIndex{show} +macro, which prints out the type of the mathsymbol, \eg \verb+\show\rightarrow+ with the +output: + +\begin{lstlisting} +> \rightarrow=\mathchar"3221. +l.20 \show\rightarrow +\end{lstlisting} + +The first digit represents the type: + +\begin{tabular}{l@{ : }l} +0 & ordinary\\ +1 & large operator\\ +2 & binary operation\\ +3 & relation\\ +4 & opening\\ +5 & closing\\ +6 & punctuation\\ +7 & variable family +\end{tabular} + + +%\iffalse +\begingroup +\thinmuskip=3mu +\medmuskip=4mu plus 2mu minus 4mu +\thickmuskip=5mu plus 5mu + +\medskip +Grouping a math symbol can change the behaviour in horizontal spacing. Compare +$50\mkern\thinmuskip\times\mkern\thinmuskip10^{12}$ and $50{\times}10^{12}$, the first one is typeset with +\verb+$50\times10^{12}$+ and the second one with \verb+$50{\times}10^{12}$+. +\endgroup +%\fi +Another possibilty is to use the \PIndex{numprint} package.\footnote{% +\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/numprint/}% +{CTAN://macros/latex/contrib/numprint/}} + +\subsection{Dot versus comma}\label{subsec:dot-comma} +\marginpar{\CMD{mathpunct}\\\CMD{mathord}}% +In difference to a \Index{decimal point} and a \Index{comma} as a marker of thousands a lot of +countries prefer it vice versa. To get the same behaviour the meaning of \Index{dot} and +comma has to be changed: + + +\begin{align} +1,234,567.89 & \text{ default}\\ +1.234.567,89 & \text{ vice versa, wrong spacing}\label{eq:comma}\\ +1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing} +\end{align} + + +\begin{lstlisting} +%\usepackage{amsmath} +1,234,567.89 & \text{ default}\\ +1.234.567,89 & \text{ vice versa, wrong spacing}\\ +1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing} +\end{lstlisting} + +The original definitions from \verb+fontmath.ltx+\footnote{% +Located in \url{texmf/tex/latex/base/}} are + +\begin{verbatim} +\DeclareMathSymbol{,}{\mathpunct}{letters}{"3B} +\DeclareMathSymbol{.}{\mathord}{letters}{"3A} +\end{verbatim} + +\noindent\CIndex{mathord} and \CIndex{mathpunct} +can be changed for a documentwide other behaviour. In the above equation~\ref{eq:comma} +the comma is only set in a pair of braces \verb+{,}+, which is the same as writing +\verb+\mathord{,}+ because \LaTeX{} handles everything +inside of parenthises as a formula, which gets the same spacing. + +It is also possible to use the package \PIndex{icomma}\footnote{% +\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/was/}% +{CTAN:// macros/latex/contrib/was/}} for a documentwide +correct spacing. + +\subsection{Vertical whitespace}\label{subsec:vwhitespace} +\subsubsection{Before/after math expressions}\label{subsubsec:displayskip} + +There are four predefined lengths, which control the vertical whitespace +of displayed formulas: +\begin{verbatim} +\abovedisplayskip=12pt plus 3pt minus 9pt +\abovedisplayshortskip=0pt plus 3pt +\belowdisplayskip=12pt plus 3pt minus 9pt +\belowdisplayshortskip=7pt plus 3pt minus 4pt +\end{verbatim} +\index{abovedisplayskip@\textbackslash abovedisplayskip} +\index{abovedisplayshortskip@\textbackslash abovedisplayshortskip} +\index{belowdisplayskip@\textbackslash belowdisplayskip} +\index{belowdisplayshortskip@\textbackslash belowdisplayshortskip} +The short skips are used if the formula starts behind the end of the foregoing +last line. Only for demonstration the shortskips +are set to \verb|0pt| in the following examples and the normal skips to +\verb|20pt| without any glue: + +\medskip +\noindent\fbox{\begin{minipage}{\linewidth-2\fboxsep-2\fboxrule} +\abovedisplayshortskip=0pt +\belowdisplayshortskip=0pt +\abovedisplayskip=20pt +\belowdisplayskip=20pt +\noindent The line ends before. +\begin{equation} +f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x +\end{equation} +\noindent The line doesn't end before the formula. +\begin{equation} +f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x +\end{equation} +\noindent And the next line starts as usual with some text ... +\end{minipage}} + +\medskip +\begin{lstlisting} +\abovedisplayshortskip=0pt +\belowdisplayshortskip=0pt +\abovedisplayskip=20pt +\belowdisplayskip=20pt +\noindent The line ends before. +\begin{equation} + f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x +\end{equation} +\noindent The line doesn't end before the formula. +\begin{equation} + f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x +\end{equation} +\noindent And the next line starts as usual with some text ... +\end{lstlisting} +%$ + + +\marginpar{\texttt{fleqn} class option}% +When using the \verb+fleqn+\index{fleqn@\texttt{fleqn}} classoption for left +aligned equations the math environments \uIndex{equation} +and \CIndex{[}\ldots\CIndex{]} are typeset as a list. This is the reason why the +vertical space is defined by the length registers for a list, especially +\LIndex{topsep}, instead of \LIndex{abovedisplayskip} and \LIndex{belowdisplayskip}. +This doesn't effect the \UIndex{eqnarray}. + + +\subsubsection{Inside math expressions}\label{subsec:vspacing} + +\paragraph{\CMD{\textbackslash []}} +This works inside the math mode in the same way as in the text mode. + + +\paragraph{\CMD{jot}}\marginpar{\CMD{jot}} +The vertical space between the lines for all math expressions which allow multiple +lines can be changed with the length \LIndex{jot}, which is predefined as + +\begin{verbatim} +\newdimen\jot \jot=3pt +\end{verbatim} + +The following three formulas show this for the default value, \verb|\setlength\jot{0pt}| +and \verb|\setlength\jot{10pt}|. + +\begin{minipage}{0.3\linewidth} +\begin{eqnarray*} + y & = & d\\ + y & = & c\frac{1}{x}+d\\ + y & = & b\frac{1}{x^{2}}+cx+d\\ +\end{eqnarray*} +\end{minipage}\hfill +\begin{minipage}{0.3\linewidth} +\setlength\jot{0pt} +\begin{eqnarray*} + y & = & d\\ + y & = & c\frac{1}{x}+d\\ + y & = & b\frac{1}{x^{2}}+cx+d\\ +\end{eqnarray*} +\end{minipage}\hfill +\begin{minipage}{0.3\linewidth} +\setlength\jot{10pt} +\begin{eqnarray*} + y & = & d\\ + y & = & c\frac{1}{x}+d\\ + y & = & b\frac{1}{x^{2}}+cx+d\\ +\end{eqnarray*} +\end{minipage} + +Defining a new environment with a parameter makes things easier, because changes to the +length are locally. +\begin{lstlisting} +\newenvironment{mathspace}[1]{% + \setlength{\jot}{#1}% + \ignorespaces% +}{% + \ignorespacesafterend% +} +\end{lstlisting} + +\paragraph{\CMD{arraystretch}}\cIndex{arraystretch} +\marginpar{\CMD{arraystretch}}% +The vertical space between the lines for all math expressions which contain an +\UIndex{array} can be changed with the command +\CIndex{arraystretch}, which is predefined +as +\begin{verbatim} +\renewcommand\arraystretch{1} +\end{verbatim} + +Renewing this definition is global to all following math expressions, so it should be used +in the same way as \LIndex{jot}. + +\paragraph{\CMD{vskip}}\index{Vertical spacing}\index{Spacing!vertical} +Another spacing for single lines is possible with the \CIndex{vskip} macro: + +\begin{LTXexample}[width=0.4\linewidth] +\[ +\begin{pmatrix} +0 & 1 & 1 & 0 & 0 & 1 \\ +1 & 0 & 0 & 1 & 1 & 0 \\ +\noalign{\vskip2pt} +0 & 1 & 1 & 0 & \dfrac{1}{\sqrt{2}} & 1\\ +\noalign{\vskip2pt} +1 & 0 & 1 & 0 & 1 & 0 \\ +0 & 1 & 0 & 1 & 0 & 1 \\ +\end{pmatrix} +\] +\end{LTXexample} + + + +\paragraph{Package \texttt{setspace}} +To have all formulas with another vertical spacing, one can choose +the package \PIndex{setspace} and redefining some of the math macros, \eg + +\begingroup +\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}} +\let\endArray\endarray + +\begin{lstlisting} +\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}} +\let\endArray\endarray +\end{lstlisting} + +\begin{LTXexample}[width=0.25\linewidth] +\[ +\begin{Array}[2]{cc} +a =&b\\ +a =&b\\ +a =&b +\end{Array} +\] + +text $\begin{Array}{cc} +a =&b\\ +a =&b\\ +a =&b +\end{Array}$ text +\end{LTXexample} +\endgroup + +\section{Styles}\label{sec:Styles} + +\begin{table}[htb] +\newlength\formula +\settowidth{\formula}{$f(t)=\frac{T}{2\pi }\int \frac{1}{\sin \frac{\omega }{t}}dt$} +\begin{tabular}{l|ll} +Mode & Inline & Displayed\\\hline +default & $f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt$& +\begin{minipage}{\formula}\[ +f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt\] +\end{minipage}\\ +\CMD{displaystyle} & +${\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& +\begin{minipage}{\formula}\[ +{\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] +\end{minipage}\\ +\CMD{scriptstyle} & +${\scriptstyle {\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}$& +\begin{minipage}{\formula}\[ +{\textstyle {\scriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}\] +\end{minipage}\tabularnewline +\CMD{scriptscriptstyle} & +${\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& +\begin{minipage}{\formula}\[ +{\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] +\end{minipage}\tabularnewline +\CMD{textstyle} & +${\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& +\begin{minipage}{\formula}\[ +{\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] +\end{minipage} +\end{tabular} +\caption{Math styles}\label{cap:Mathstyles} +\end{table} +%$ +\makeatletter +\newenvironment{smallequation}[1]{% + \skip@=\baselineskip + #1% + \baselineskip=\skip@ + \equation +}{\endequation \ignorespacesafterend} +\makeatother + +This depends on the environment in which they are used. An inline +formula has a default math % +\marginpar{\CMD{textstyle}\\ +\CMD{displaystyle}\\ +\CMD{scriptstyle}\\ +\CMD{scripscriptstyle}} fontsize called \CIndex{textstyle}, +which is smaller than the one for a display formula (see section~\ref{display}), which is called +\CIndex{displaystyle}. +Beside this predefinition there are two other special fontstyles for +math, \CIndex{scriptstyle} and \CIndex{scriptscriptstyle}. +They are called ``style{}'' in difference to ``size{}'', because +they have a dynamic character, their real fontsize belongs to the +environment in which they are used. A fraction for example is by default in scriptstyle when it is in an +inline formula like this $\frac{a}{b}$, which can be changed to +${\displaystyle \frac{a}{b}}$. +This may be in some cases useful but it looks in general ugly because +the line spacing is too big. +These four styles\index{Style} are predefined and together in a +logical relationship. It is no problem to use the other styles like +\Index{large}, \CIndex{Large}, \ldots\ \textbf{outside} the math environment. +For example a fraction written with \CIndex{Huge}: {\Huge$\frac{a}{b}$} +(\verb|\Huge$\frac{a}{b}$|). This may cause some problems when you want to write +a displayed formula in another fontsize\index{Fontsize}, because it also affects the interline spacing of +the preceding part of the paragraph. +If you end the paragraph, you get problems with spacing and page breaking +above the equations. So it is better to declare the font size and then +restore the baselines: +\begin{smallequation}{\tiny} +\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5 +\end{smallequation} +\begin{lstlisting} +\makeatletter +\newenvironment{smallequation}[1]{% + \skip@=\baselineskip + #1% + \baselineskip=\skip@ + \equation +}{\endequation \ignorespacesafterend} +\makeatother + +\begin{smallequation}{\tiny} +\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5 +\end{smallequation} +\end{lstlisting} +If you use this the other way round for huge fontsizes, don't forget to load package +\PIndex{exscale} (see section~\vref{sec:exscale}). Also see this section for diffent symbol sizes. + + + +\section{Dots\label{sec:Dots}} + +\marginpar{\CMD{cdots}\\ +\CMD{dots}\\ +\CMD{dotsb}\\ +\CMD{dotsc}\\ +\CMD{dotsi}\\ +\CMD{dotsm}\\ +\CMD{dotso}\\ +\CMD{ldots}\\ +\CMD{vdots}}% +In addition to the above decorations there are some more different +dots which are single commands and not by default over/under a letter. +It is not easy to see the differences between some of them. Dots from +lower left to upper right are possible with +\verb|\reflectbox{$\ddots$}|\index{reflectbox@\textbackslash reflectbox} +\reflectbox{$\ddots$} + +\begin{table}[htb] +\centering +\begin{tabular}{*{5}{rc}} +\CMD{cdots}\index{cdots@\textbackslash cdots}&$\cdots$ & +\CMD{ddots}\index{ddots@\textbackslash ddots}&$\ddots$ & +\CMD{dotsb}\index{dotsb@\textbackslash dotsb}&$\dotsb$ & +\CMD{dotsc}\index{dotsc@\textbackslash dotsc}&$\dotsc$ & +\CMD{dotsi}\index{dotsi@\textbackslash dotsi}&$\dotsi$ \\\hline +\CMD{dotsm}\index{dotsm@\textbackslash dotsm}&$\dotsm$ & +\CMD{dotso}\index{dotso@\textbackslash dotso}&$\dotso$ & +\CMD{ldots}\index{ldots@\textbackslash ldots}&$\ldots$ & +\CMD{vdots}\index{vdots@\textbackslash vdots}&$\vdots$ +\end{tabular} +\caption{Dots in math mode} +\end{table} + + + +\section{Accents}\label{sec:Accents} + +The letter ``a{}'' is only for demonstration. The table \ref{cap:Accents-in-math mode} +shows all in standard \LaTeX{} available accents and also the ones placed under a character. +With package \PIndex{amssymb} it is easy to define new accents. For +more information see section~\vref{amssymb} or +other possibilities at section \vref{sec:package-accent}. + + +\begin{table}[htb] +\makebox[\textwidth]{% +\begin{tabular}{rc|rc|rc} +\CIndex{acute}\index{acute@\textbackslash acute} &$\acute{a}$& +\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$& +\CIndex{breve}\index{breve@\textbackslash breve} & $\breve{a}$\\ +\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$& +\CIndex{breve}\index{breve@\textbackslash breve} &$\breve{a}$\tabularnewline +\CIndex{check}\index{check@\textbackslash check} &$\check{a}$& +\CIndex{dddot} \index{dddot@\textbackslash dddot}&$\dddot{a}$& +\CIndex{ddot}\index{ddot@\textbackslash ddot}&$\ddot{a}$\tabularnewline +\CIndex{dot}\index{dot@\textbackslash dot}&$\dot{a}$& +\CIndex{grave}\index{grave@\textbackslash grave}&$\grave{a}$& +\CIndex{hat}\index{hat@\textbackslash hat}&$\hat{a}$\tabularnewline +\CIndex{mathring}\index{mathring@\textbackslash mathring}&$\mathring{a}$& +\CIndex{overbrace}\index{overbrace@\textbackslash overbrace}&$\overbrace{a}$& +\CIndex{overleftarrow}\index{overleftarrow@\textbackslash overleftarrow}&$\overleftarrow{a}$\tabularnewline +\CIndex{overleftrightarrow}\index{overleftrightarrow@\textbackslash overleftrightarrow}&$\overleftrightarrow{a}$& +\CIndex{overline}\index{overline@\textbackslash overline}&$\overline{a}$& +\CIndex{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}&$\overrightarrow{a}$\tabularnewline +\CIndex{tilde}\index{tilde@\textbackslash tilde}&$\tilde{a}$& +\CIndex{underbar}\index{underbar@\textbackslash underbar}&$\underbar{a}$& +\CIndex{underbrace}\index{underbrace@\textbackslash underbrace}&$\underbrace{a}$\tabularnewline +\CIndex{underleftarrow}\index{underleftarrow@\textbackslash underleftarrow}&$\underleftarrow{a}$& +\CIndex{underleftrightarrow}\index{underleftrightarrow@\textbackslash underleftrightarrow}& +$\underleftrightarrow{a}$& +\CIndex{underline}\index{underline@\textbackslash underline}&$\underline{a}$\tabularnewline +\CIndex{underrightarrow}\index{underrightarrow@\textbackslash underrightarrow}&$\underrightarrow{a}$& +\CIndex{vec}\index{vec@\textbackslash vec}&$\vec{a}$& +\CIndex{widehat}\index{widehat@\textbackslash widehat}&$\widehat{a}$\tabularnewline +\CIndex{widetilde}\index{widetilde@\textbackslash widetilde}&$\widetilde{a}$ & & & & +\end{tabular}% +} +\caption{Accents in math mode}\label{cap:Accents-in-math mode} +\end{table} + +The letters \verb+i+ and \verb+j+ can be substituted with the macros \CIndex{imath} +and \CIndex{jmath} when an accents is placed over these letters and the dot should +disappear: $\vec{\imath}\ \dddot{\jmath}$ (\verb+$\vec{\imath}\ \dddot{\jmath}$+). + +Accents can be used in different ways, \eg strike a single character with a horizontal line like +\verb+$\mathaccent`-A$+: $\mathaccent`-A$ or \verb+$\mathaccent\mathcode`-A$+: $\mathaccent\mathcode`-A$. +In section~\vref{cancel.sty} is a better solution for more than one character. + +\subsection{Over- and underbrackets} +There are no \CIndex{underbracket} and \CIndex{overbracket} +commands in the list of accents. They can be defined in the preamble +with the following code. + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1cm] +\makeatletter +\def\underbracket{% + \@ifnextchar[{\@underbracket}{\@underbracket [\@bracketheight]}% +} +\def\@underbracket[#1]{% + \@ifnextchar[{\@under@bracket[#1]}{\@under@bracket[#1][0.4em]}% +} +\def\@under@bracket[#1][#2]#3{%\message {Underbracket: #1,#2,#3} + \mathop{\vtop{\m@th \ialign {##\crcr $\hfil \displaystyle {#3}\hfil $% + \crcr \noalign {\kern 3\p@ \nointerlineskip }\upbracketfill {#1}{#2} + \crcr \noalign {\kern 3\p@ }}}}\limits} +\def\upbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$} + \edef\@bracketheight{\the\ht\z@}\bracketend{#1}{#2} + \leaders \vrule \@height #1 \@depth \z@ \hfill + \leaders \vrule \@height #1 \@depth \z@ \hfill \bracketend{#1}{#2}$} +\def\bracketend#1#2{\vrule height #2 width #1\relax} +\makeatother +\end{lstlisting} +%$ +\begin{enumerate} +\item \verb/\underbrace{...}/ is an often used command: +\begin{eqnarray} +\underbrace{{x^{2}+2x+1}} & = & f(x)\\ +\left(x+1\right)^{2}\,\,\,\nonumber +\end{eqnarray} + +\item Sometimes an under\textbf{bracket} is needed, which can be used in + more ways than \verb/\underbrace{...}/. An example for \verb/\underbracket{...}/: + + +\begin{eqnarray*} +\textrm{Hate Science }& \underbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4} + \underbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7} + \underbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\ + & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high} + \end{eqnarray*} + + +\end{enumerate} + +\subsubsection{Use of \CMD{underbracket\{...\}}} + +The \verb/\underbracket{...}/ command has two optional parameters: + +\begin{itemize} +\item the line thickness in any valid latex unit, \eg \verb/1pt/ +\item the height of the edge brackets, \eg \verb/1em/ +\end{itemize} +using without any parameters gives the same values for thickness and +height as predefined for the \CIndex{underbrace} command. + + +\vspace{0.3cm} +\begin{center} +\begin{tabular}{|c|c|c|} +\hline +1.& \verb/$\underbracket{foo~bar}$/ & $\underbracket{foo~bar}$ \tabularnewline\hline +2.& \verb/$\underbracket[2pt]{foo~bar}$/ & $\underbracket[2pt]{foo~bar}$ \tabularnewline\hline +3.& \verb/$\underbracket[2pt][1em] {foo~bar}$/& $\underbracket[2pt][1em] {foo~bar}$\tabularnewline\hline +\end{tabular} +\end{center} + + +\subsubsection{Overbracket} + +In addition to the underbracket an overbracket is also useful, which can be used in +more ways than \verb/\overbrace{...}/. For example: + + +\begin{eqnarray*} +\textrm{Hate Science }& \overbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4} + \overbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7} + \overbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\ + & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high}\nonumber + \end{eqnarray*} + + +The \verb/\overbracket{...}/ command has two optional parameters: + +\begin{itemize} +\item the line thickness in any valid latex unit, \eg \verb/1pt/ +\item the height of the edge brackets, \eg \verb/1em/ +\end{itemize} +using without any parameters gives the same values for thickness and +height as predefined for the \CIndex{overbrace} command. + + +\vspace{0.3cm} +\begin{center}\begin{tabular}{|c|c|c|} +\hline +1.&\verb/$\overbracket {foo\ bar}$/ & $\overbracket {foo\ bar}$ \tabularnewline\hline +2.&\verb/$\overbracket[2pt] {foo\ bar}$/ &$\overbracket[2pt] {foo\ bar}$ \tabularnewline\hline +3.&\verb/$\overbracket[2pt] [1em] {foo\ bar}$/&$\overbracket[2pt] [1em] {foo\ bar}$\tabularnewline\hline +\end{tabular} +\end{center} + +%$ +\subsection{Vectors} + +Especially for vectors\index{Vector} there is the package \PIndex{esvect}% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esvect/}% + {CTAN://macros/latex/contrib/esvect/}} package, which looks better than the +\CMD{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}, \eg + +\begin{table}[!htb] +\centering +\begin{tabular}{c|c} +\textbackslash{}vv\{...\}&\textbackslash{}overrightarrow\{...\}\tabularnewline\hline +$\vv{a}$ & $\overrightarrow{a}$\tabularnewline +$\vv{abc}$ & $\overrightarrow{abc}$\tabularnewline +$\vv{\imath}$ & $\overrightarrow{\imath}$\tabularnewline +$\vv*{A}{x}$ & $\overrightarrow{A}_{x}$\tabularnewline +\end{tabular} +\caption[Vectors with package \texttt{esvec}]% + {Vectors with package \texttt{esvec} (in the right column the default one from \LaTeX{})} +\end{table} + + +Look into the documentation for more details about the package \PIndex{esvect}. + +%$ +\section{Exponents and indices}\label{sec:exponents} +The two active characters \verb|_| and \verb|^| can only be used in math mode. The +\textbf{following} character will be printed as an index (\verb|$y=a_1x+a_0$|: $y=a_1x+a_0$) +or as an exponent (\verb|$x^2+y^2=r^2$|: $x^2+y^2=r^2$). For more than the next character +put it inside of \verb|{}|, like \verb|$a_{i-1}+a_{i+1}}| +doesn't work with lower greek character. See +section \vref{sec:greek-AMS} for the \CIndex{pmb} macro, which makes it possible +to print bold lower greek\index{Greek} letters. Not all upper case letters have +own macro names. If there is no difference to the roman font, then the default +letter is used, \eg A for the upper case of +$\alpha$. Table \ref{tab:greek-letters} shows only those upper case letters +which have own macro names. Some of the lower case letters have an additional +\verb|var| option for an alternative. + +\bgroup +\tabcolsep=3pt +\begin{longtable}{lclccc} +lower & default & upper & default & \verb|\mathbf| & \verb|\mathit|\\\hline +\endhead +\verb|\alpha| & $\alpha$ \\ +\verb|\beta| & $\beta$ \\ +\verb|\gamma| & $\gamma$ + & \verb|\Gamma| & $\Gamma$ & $\mathbf{\Gamma}$ & $\mathit{\Gamma}$\\ +\verb|\delta| & $\delta$ + & \verb|\Delta| & $\Delta$ & $\mathbf{\Delta}$ & $\mathit{\Delta}$\\ +\verb|\epsilon| & $\epsilon$\\ +\verb|\varepsilon| & $\varepsilon$\\ +\verb|\zeta| & $\zeta$\\ +\verb|\eta| & $\eta$ \\ +\verb|\theta| & $\theta$ + & \verb|\Theta| & $\Theta$ & $\mathbf{\Theta}$ & $\mathit{\Theta}$\\ +\verb|\vartheta| & $\vartheta$\\ +\verb|\iota| & $\iota$\\ +\verb|\kappa| & $\kappa$\\ +\verb|\lambda| & $\lambda$ + & \verb|\Lambda| & $\Lambda$ & $\mathbf{\Lambda}$ & $\mathit{\Lambda}$\\ +\verb|\mu| & $\mu$ \\ +\verb|\nu| & $\nu$\\ +\verb|\xi| & $\xi$ + & \verb|\Xi| & $\Xi$ & $\mathbf{\Xi}$ & $\mathit{\Xi}$\\ +\verb|\pi| & $\pi$ + & \verb|\Pi| & $\Pi$ & $\mathbf{\Pi}$ & $\mathit{\Pi}$\\ +\verb|\varpi| & $\varpi$ \\ +\verb|\rho| & $\rho$\\ +\verb|\varrho| & $\varrho$\\ +\verb|\sigma| & $\sigma$ + & \verb|\Sigma| & $\Sigma$ & $\mathbf{\Sigma}$ & $\mathit{\Sigma}$\\ +\verb|\varsigma| & $\varsigma$\\ +\verb|\tau| & $\tau$\\ +\verb|\upsilon| & $\upsilon$ + & \verb|\Upsilon| & $\Upsilon$ & $\mathbf{\Upsilon}$ & $\mathit{\Upsilon}$\\ +\verb|\phi| & $\phi$ + & \verb|\Phi| & $\Phi$ & $\mathbf{\Phi}$ & $\mathit{\Phi}$\\ +\verb|\varphi| & $\varphi$\\ +\verb|\chi| & $\chi$ \\ +\verb|\psi| & $\psi$ + & \verb|\Psi| & $\Psi$ & $\mathbf{\Psi}$ & $\mathit{\Psi}$\\ +\verb|\omega| & $\omega$ + & \verb|\Omega| & $\Omega$ & $\mathbf{\Omega}$ & $\mathit{\Omega}$\\[5pt] +\caption{The greek letters}\label{tab:greek-letters}\\ +\end{longtable} +\egroup + +Bold \Index{greek} letters are possible with the package \PIndex{bm} (see section~\vref{sec:bm}) +and if they should also be upright with the package \PIndex{upgreek}: +\index{greek!upright}\index{greek!bold} + +\medskip +\verb+$\bm{\upalpha}, \bm{\upbeta} ... $+ $ \bm{\upalpha}, \bm{\upbeta} ... $ + +A useful definition maybe: + +\begin{lstlisting} +\usepackage{upgreek} +\makeatletter +\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}} +\makeatother +\end{lstlisting} + +\makeatletter +\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}} +\makeatother +Then +\verb|$\bfgreek{mu}$| will allow you to type $\bfgreek{mu}$ to obtain an upright boldface $\mu$. + + + +\section{Pagebreaks} +\marginpar{\CMD{allowdisplaybreaks}}By default a displayed formula cannot +have a pagebreak. This makes some sense, but sometimes it gives a better +typesetting when a pagebreak is possible. + +\begin{verbatim} +\allowdisplaybreaks +\end{verbatim} + +\CIndex{allowdisplaybreaks} enables \TeX{} to insert pagebreaks into +displayed formulas whenever a newline command appears.\index{Pagebreak} +With the command \CIndex{displaybreak} it is also possible to insert a +pagebreak at any place. + +\section{\CMD{stackrel}} + +\CIndex{stackrel} puts a character on top of another one which may be important if a +used symbol is not predefined. For example ``$\stackrel{\wedge}{=}$'' +(\verb|\stackrel{\wedge}{=}|). \marginpar{\CMD{stackrel}} +The syntax is + +\begin{lstlisting} +\stackrel{top}{base} +\end{lstlisting} + +Such symbols may be often needed so that a macro definition in the preamble makes some sense: + +\begin{lstlisting} +\newcommand{\eqdef}{% + \ensuremath{% + \stackrel{\mathrm{def}}{=}% + }% +} +\end{lstlisting} +% +With the \CIndex{ensuremath} command we can use the new \CIndex{eqdef} command in text +and in math mode, \LaTeX{} switches automatically in math mode, which +saves some keystrokes like the following command, which is written +without the delimiters (\texttt{\$...\$}) for the math mode \eqdef , +only \CMD{eqdef} with a space at the end. In math mode +together with another material it may look like +$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$ and as command sequence + +\begin{lstlisting} +$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$ +\end{lstlisting} + +The fontsize of the top is one size smaller than the one from the +base, but it is no problem to get both the same size, just increase the +top or decrease the base. + +\section{\CMD{choose}} + +\CIndex{choose}\index{Binom} is like \CIndex{atop} +with delimiters or like \CIndex{frac} +without the fraction line and also with delimiters. It is often used +for binomial coefficients and has the following syntax:\marginpar{\CMD{choose}} + +\begin{lstlisting} +{above \choose below} +\end{lstlisting} +The two braces are not really important but it is safe to use them. + +\begin{equation} +{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose} +\end{equation} + +\begin{lstlisting} +{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose} +\end{lstlisting} + + +See section~\vref{sub:Binoms} for the \AmSmath equivalents and enhancements. + +\section{Color in math expressions}\label{sec:color} +\index{Color}There is no difference in using colored text and colored math expressions. With +\begin{verbatim} +\usepackage{color} +\end{verbatim} + +\noindent in the preamble the macro \verb|\textcolor{}{}| exists. +\begin{equation} +\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1 +\end{equation} +\marginpar{\CMD{textcolor}} +\begin{lstlisting} +\begin{equation} +\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1 +\end{equation} +\end{lstlisting} + +If all math expressions should be printed in the same color, then it is better +to use the \verb+everydisplay+ macro (section~\vref{sec:other}). + + +\section{Boldmath}\label{sec:boldmath} + +\marginpar{\CMD{mathversion}\\\CMD{boldmath}\\\CMD{unboldmath}}% +Writing a whole formula in bold\index{boldmath@\textbackslash boldmath} is possible with the command sequence +\verb|\boldmath ... \unboldmath|, which itself must be written in textmode (outside the +formula) or with the command \verb+{\mathversion{bold} ... }+. +\index{mathversion@\textbackslash mathversion}\index{boldmath@\textbackslash +boldmath}\index{unboldmath@\textbackslash unboldmath} + +\noindent\begin{minipage}{0.49\linewidth} +\[ +\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}% + }a_{ij}b_{jk}c_{ki} +\] +\end{minipage}\hfill +\begin{minipage}{0.49\linewidth} +\boldmath +\[ +\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}% + }a_{ij}b_{jk}c_{ki} +\] +\unboldmath +\end{minipage} + +\medskip +\begin{lstlisting} +\boldmath +\[ +\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}% + }a_{ij}b_{jk}c_{ki} +\] +\unboldmath +\end{lstlisting} + +The \verb+\mathversion+ macro defines a math style which is valid for all following +math expressions. If you want to have all math in bold then use this macro instead of +\CIndex{boldmath}. But it is no problem to put \CIndex{mathversion} inside a group to hold +the changes locally. + +{\mathversion{bold}% +\begin{equation} +y(x) = ax^3+bx^2+cx+d +\end{equation}} + +\begin{lstlisting} +{\mathversion{bold}% +\begin{equation} +y(x) = ax^3+bx^2+cx+d +\end{equation}} +\end{lstlisting} + + +Single characters inside a formula can be written in bold with \CIndex{mathbf}, +but only in upright mode, which is in general not useful as shown in +equation~\ref{eq:bold}. It is better +to use package \PIndex{bm} (see section~\vref{sec:bm}). + +\begin{equation}\label{eq:bold} +\sum_{% + \makebox[0pt]{$% + {{\scriptscriptstyle 1\le j\le p\atop {% + {1\le j\le q\atop 1\le k\le r}}}}% + $}% + }a_{ij}\mathbf{b_{jk}}c_{ki} +\end{equation} + +\subsection[Bold math titles and items]{Bold math expressions as part of titles and items}\label{sec:titleItem} +By default the titles in sections, subsections, a.s.o. are printed in bold. Same for the +\verb|description| environment. The problem is that a math expression in one of these +environments is printed in default font shape, like the following example for a \verb|section| and +\UIndex{description}: + +\medskip +\fbox{% +\begin{minipage}{.75\linewidth} +\section*{\thesection\ Function $f(x)=x^2$} +\begin{description} +\item[This is $y=f(x)$] Only a demonstration. +\item[And $z=f(x,y)$] Another demonstration. +\end{description} +\end{minipage}% +} + +\medskip +With a redefinition of the \CIndex{section} and +\CIndex{item} macros it is possible to get everything in bold font. + +\medskip +\fbox{% +\begin{minipage}{.75\linewidth} +\let\itemOld\item +\makeatletter +\renewcommand\item[1][]{% + \def\@tempa{#1} + \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi% +} +\makeatother +\section*{\thesection\ \boldmath Function $f(x)=x^2$\unboldmath} +\begin{description} +\item[This is $y=f(x)$] Only a demonstration. +\item[And $z=f(x,y)$] Another demonstration. +\end{description} +\end{minipage}% +} + + +\medskip +\begin{lstlisting} +\let\itemOld\item +\makeatletter +\renewcommand\item[1][]{% + \def\@tempa{#1} + \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi% +} +\makeatother +\let\sectionOld\section +\renewcommand\section[2][\empty]{% + \boldmath\sectionOld[#1]{#2}\unboldmath% +} +\end{lstlisting} + +\section{Multiplying numbers} +When the dot is used as the decimal marker as in the United States, the preferred sign +for the multiplication of +numbers or values of quantities is a cross (\verb|\times| $\times$ ), not a half-high and +centered dot (\verb|\cdot| $\cdot$ ). + +When the comma is used as the decimal marker as in Europe, the preferred sign for the +multiplication of +numbers is the half-high dot. The multiplication of quantity symbols (or numbers in +parentheses or values of +quantities in parentheses) may be indicated in one of the following ways: $ab$, +$a\cdot b$, $a\times b$. + +For more information see ``Nist Guide to SI Units -More on Printing and Using Symbols and +Numbers in Scientific and +Technical Documents''\footnote{\url{http://physics.nist.gov/Pubs/SP811/sec10.html}} or +the German DIN 1304, Teil 1. + + +\section{Other macros}\label{sec:other} +\marginpar{\CMD{everymath}\\\CMD{everydisplay}\\\CMD{underline}}% +There are some other macros which are not mentioned in the foregoing text. Here comes +a not really complete list of these macros. +\begin{description} +\item[\CMD{everymath}] \index{everymath@\textbackslash everymath} puts the argument before +any inlined math expression, \eg \verb+\everymath{\displaysize}+. Using this macro doesn't really +make sense, when one is using footnotes because the footnote number is printed as superscript in +inline mathmode and an \CMD{everymath} will be valid, too. +\item[\CMD{everydisplay}] \index{everydisplay@\textbackslash everydisplay} puts the +argument before any displayed math expression, \eg \verb+\everydisplay{\color{blue}}+. +\item[\CMD{underline}] \index{underline@\textbackslash underline} underlines a math +expression and has to be used inside the math mode. +\[ +\underline{F(x)=\int f(x)\,\mathrm{d}x} +\] +\end{description} + + + +\part{\texorpdfstring{\AmSmath}{amsmath} package}\label{par:AMSmath-package} + +In general the \AmS packages are at least a collection of three different ones: +\begin{enumerate} +\item \verb|amsmath.sty| +\item \verb|amssymb.sty| +\item \verb|amsfonts.sty| +\end{enumerate} +In the following only the first one is described in detail. + +The \AmSmath has the following options: + +\bigskip\noindent +\begin{tabularx}{\linewidth}{@{}lX@{}} +\verb+centertags+\index{centertags} & (default) For a split equation, place +equation numbers vertically centered on the total height of the equation.\\\hline +\verb+tbtags+\index{tbtags} & `Top-or-bottom tags' For a split equation, +place equation numbers level with the last (resp. first) line, if +numbers are on the right (resp. left).\\\hline +\verb+sumlimits+\index{sumlimits} & (default) Place the subscripts and superscripts +of summation symbols above and below, in displayed equations. This +option also affects other symbols of the same type -- $\prod$, $\coprod$, +$\bigotimes$, $\bigoplus$, and so forth -- but excluding integrals +(see below).\\\hline +\verb+nosumlimits+\index{nosumlimits} & Always place the subscripts and +superscripts of summation-type symbols to the side, even in displayed +equations.\\\hline +\verb+intlimits+\index{intlimits} & Like sumlimits, but for integral symbols.\\\hline +\verb+nointlimits+\index{nointlimits} & (default) Opposite of intlimits.\\\hline +\verb+namelimits+\index{namelimits} & (default) Like sumlimits, but for +certain `operator names' such as \verb+det+, \verb+inf+, \verb+lim+, \verb+max+, \verb+min+, that traditionally +have subscripts placed underneath when they occur in a displayed equation.\\\hline +\verb+nonamelimits+\index{nonamelimits} & Opposite of namelimits.\\\hline +\end{tabularx} +\bigskip + +To use one of these package options, put the option name in the optional +argument, \eg +\verb|\usepackage[intlimits]{amsmath}|. The %%% ----- Martin ----- +\AmSmath also recognises the following options which are normally +selected (implicitly or explicitly) through the \verb|documentclass| +command, and thus need not be repeated in the option list of the \verb|\usepackage{amsmath}| statement. %%% ----- Martin ----- + +\bigskip\noindent +\begin{tabularx}{\linewidth}{@{}lX@{}} +\verb+leqno+\index{leqno} & Place equation numbers on the left.\\\hline +\verb+reqno+\index{reqno} & (default) Place equation numbers on the right.\\\hline +\verb+fleqn+\index{fleqn} & Position equations at a fixed indent from the +left margin rather than centered in the text column. \AmSmath defines the +length \CMD{mathindent} and uses it when the equations have only one +tabbing character (\verb+&+).\index{mathindent@\textbackslash mathindent}\\\hline +\end{tabularx} + +\bigskip\noindent All math environments are displayed ones, so there is no special inline +math. + +\section{\texttt{align} environments} + +There are four different align environments, described in the following +subsections. Their behaviour is shown in table \ref{cap:align}. The symbolic +code for all align environments is: + +\begin{lstlisting} +\begin{} + &= x & x &= x\\ + &= x & x &= x +\end{} +\end{lstlisting} + +\begin{table}[htb] +\caption[Comparison between the different align environments]{Comparison between the different align environments +with the same code, where the first three can have an equation number}\label{cap:align} +\begin{align*} +\framebox[0.125\columnwidth]{align} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x}&= \framebox[0.125\columnwidth]{x}\\ +\framebox[0.125\columnwidth]{align}&= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} +\end{align*} + +\begin{alignat*}{2} +\framebox[0.125\columnwidth]{alignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ +\framebox[0.125\columnwidth]{alignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} +\end{alignat*} + +\begin{flalign*} +\framebox[0.125\columnwidth]{flalign} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ +\framebox[0.125\columnwidth]{flalign} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} +\end{flalign*} + +\begin{xalignat*}{2} +\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ +\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} +\end{xalignat*} + +\begin{xxalignat}{2} +\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ +\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} +\end{xxalignat} + +\end{table} + +In difference to the \UIndex{eqnarray} from standard \LaTeX{} +(section~\ref{display:eqnarray}), the ``three'' parts +of one equation \verb+expr.-symbol-expr.+ are divided by only one ampersand %%% ----- Martin ----- +in two parts. In general the ampersand should be before the symbol to get the right spacing, +\eg \verb+y &= x+. Compare the following three equations, the second one has a wrong spacing. %%% ----- Martin ----- + + +\noindent +~\hfill\includegraphics{amsalign} + +\iffalse +\begin{minipage}{0.4\linewidth} +\begin{align} +\rnode[lt]{a}{y} &= \rnode[rt]{A}{x} +\end{align} +\vspace*{-3\abovedisplayskip} +\begin{align} +y =& x +\end{align} +\vspace*{-3\abovedisplayskip} +\begin{align} +\rnode[lb]{b}{y} ={}& \rnode[rb]{B}{x} +\end{align} +\ncline[nodesep=-10pt,linewidth=0.1pt]{A}{B} +\ncline[nodesepA=-11pt,nodesepB=-10pt,linewidth=0.1pt]{a}{b} +\end{minipage} +\hfill\begin{minipage}{0.4\linewidth} +\begin{lstlisting} + y &= x + y =& x + y ={}& x +\end{lstlisting} +\end{minipage} +\fi + +\subsection{The default \texttt{align} environment} + +The \texttt{eqnarray} environment has a not so good spacing between +the cells. Writing the equations no. \ref{eq:2} to \ref{eq:5} with +the \texttt{align} environment gives: + +\begin{align} + y & =d\label{eq:IntoSection}\\ + y & =cx+d\\ + y_{12} & =bx^{2}+cx+d\\ + y(x) & =ax^{3}+bx^{2}+cx+d +\end{align} + +\noindent The code looks like: +\begin{lstlisting} +\begin{align} + y & =d\label{eq:IntoSection}\\ + y & =cx+d\\ + y_{12} & =bx^{2}+cx+d\\ + y(x) & =ax^{3}+bx^{2}+cx+d +\end{align} +\end{lstlisting} + +\begin{itemize} +\item The \texttt{align} environment has an implicit \textbf{\{rlrl...\}} +horizontal alignment with a vertical column-alignment, \eg +\begin{LTXexample}[width=0.5\linewidth] +\begin{align*} + 1 & 2 & 3 +\end{align*} +\end{LTXexample} + +\item A nonumber-version \texttt{\small \textbackslash{}begin\{align{*}\}...\textbackslash{}end\{align{*}\}} +exists. +\item Unnumbered single rows are possible with \CMD{nonumber}. %%% ----- Martin ----- +\item The \texttt{align} environment takes the whole horizontal space if +you have more than two columns: +\begin{align} +y & =d & z & =1\\ +y & =cx+d & z & =x+1\\ +y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ +y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1 +\end{align} + +\end{itemize} +The code for this example looks like% +\begin{lstlisting} +\begin{align} + y & =d & z & =1\\ + y & =cx+d & z & =x+1\\ + y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ + y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1 +\end{align} +\end{lstlisting} + +\subsection{\texttt{alignat} environment\label{sec:alignat environment}} +\marginpar{\CMD{begin\{align\}\\...\\\CMD{end\{align\}}}} +\renewcommand{\theequation}{% + \thepart-\arabic{equation}% +} + +\begin{leftbar} +>From now the counting of the equation changes. It is introduced with a foregoing command, +which doesn't really make sense, it is only for demonstration:\\ +\verb|\renewcommand{\theequation}{\thepart-\arabic{equation}}|. +\end{leftbar} + + +This means ``align at several places{}'' and is something like +more than two \verb+align+ environment side by side. +Parameter is the number of the \verb+align+ environments, which +is not important for the user. The +above last \verb+align+ example looks like: + +\begin{alignat}{2} +y & =d & z & =1\label{eq:newCounting}\\ +y & =cx+d & z & =x+1\\ +y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ +y(x) & =ax^{3}+bx^{2}+cx+d\quad & z & =x^{3}+x^{2}+x+1\end{alignat} + + +The parameter was 2 and it is 3 for the following example: %%% ----- Martin ----- + +\begin{alignat}{3} +i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ +i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ +i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}\end{alignat} + + +For this example the code is: +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{alignat}{3} + i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ + i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ + i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} +\end{alignat} +\end{lstlisting} + +With the \verb+alignat+ environment one can easily align equations vertically +at more than one marker: + +\begin{alignat}{3} + abc &= xxx &&= xxxxxxxxxxxx &&= aaaaaaaaa \\ + ab &= yyyyyyyyyyyyyyy &&= yyyy &&= ab +\end{alignat} +\begin{lstlisting} +\begin{alignat}{3} + abc &= xxx &&= xxxxxxxxxxxx &&= aaaaaaaaa \\ + ab &= yyyyyyyyyyyyyyy &&= yyyy &&= ab +\end{alignat} +\end{lstlisting} + + + + +\begin{itemize} +\item The \texttt{alignat} environment has an implicit \{rlrl...rlrl\} +horizontal alignment with a vertical column alignment. +\item A nonumber-version \texttt{\small +\textbackslash{}begin\{alignat{*}\}...\textbackslash{}end\{alignat{*}\}} +exists. +\item Unnumbered single rows are possible with \CMD{nonumber}. %%% ----- Martin ----- +\end{itemize} + +\subsection{\texttt{flalign} environment}\label{ams:flalign} +\marginpar{\CMD{begin\{flalign\}\\...\\\CMD{end\{flalign\}}}}This is the new replacement for the \texttt{xalignat} and \texttt{xxalignat} +environments. It is nearly the same as the \texttt{xalignat} environment, only +more ``out spaced'' and ``left aligned''. + +\begin{LTXexample}[width=0.5\linewidth] +\begin{flalign} +i_{11} & =0.25\nonumber \\ +i_{21} & =\frac{1}{3}i_{11}\\ +i_{31} & =0.33i_{22} +\end{flalign} +\end{LTXexample} + +\medskip +As seen, the equations are not really left aligned, when they have only one +ampersand. In this case \verb+flalign+ has the same behaviour as the \verb+align+ +environment.\index{Alignment!left}\index{Indentation} + + +When there are more than one tabbing characters (\verb+&+), then the equations are +really left aligned. This is also an easy way to get an equation with only one +ampersand left aligned, see equation \ref{eq:leftaligned} below. +\begin{flalign} +i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ +i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ +i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} +\end{flalign} +The code looks like: + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{flalign} + i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ + i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ + i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} +\end{flalign} +\end{lstlisting} + +\medskip +This environment can be used to mix centered and left aligned\index{Left aligned} +equations without +using the document wide valid option \verb|fleqn|. +\begin{align}\label{eq:centered} + f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x +\end{align} + +\begin{flalign}\label{eq:leftaligned} + f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x & +\end{flalign} +Equation \ref{eq:leftaligned} is left aligned in fact of the second tabbing +character \verb|&|. + +\begin{lstlisting} +\begin{align}\label{eq:centered} + f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x +\end{align} + +\begin{flalign}\label{eq:leftaligned} + f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x & +\end{flalign} +\end{lstlisting} + +Another case is placing text left aligned, whereas the formulas should be right aligned. + +\begin{flalign*} + && 12(x-1)+20(y-3)+14(z-2) &= 0\\ +\text{same as } && 6x+10y+7z &= 0 +\end{flalign*} + +\begin{lstlisting} +\begin{flalign*} + && 12(x-1)+20(y-3)+14(z-2) &= 0\\ +\text{same as } && 6x+10y+7z &= 0 +\end{flalign*} +\end{lstlisting} + + +\subsection{\texttt{xalignat} environment} +\marginpar{\CMD{begin\{xalignat\}\\...\\\CMD{end\{xalignat\}}}}% +This is an obsolete macro but still supported by the \AmSmath package. +Same as \texttt{alignat} environment, only a little more ``out spaced{}''. +\begin{xalignat}{3} +i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ +i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ +i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} +\end{xalignat} +The same code looks like: + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{xalignat}{3} + i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ + i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ + i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} +\end{xalignat} +\end{lstlisting} + +\subsection{\texttt{xxalignat} environment} +\marginpar{\CMD{begin\{xxalignat\}\\...\\\CMD{end\{xxalignat\}}}}% +Like \texttt{xalignat} an obsolete macro but still supported by the \AmSmath package. +Same as \texttt{align} environment, only extremely ``out spaced{}'', +therefore no equation number! +\begin{xxalignat}{3} +i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\\ +i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ +i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} +\end{xxalignat} +The same code looks like: + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{xxalignat}{3} + i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ + i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ + i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} +\end{xxalignat} +\end{lstlisting} + + +\subsection{\texttt{aligned} environment}\label{sec:aligned} + +\marginpar{\CMD{begin\{aligned\}\\...\\\CMD{end\{aligned\}}}}In difference to the +\verb|split| environment (section \vref{split})\index{Split equation}, the +\verb|aligned| environment allows more than one horizontal alignment but has +also only one equation number: +% +\begin{equation} +\begin{aligned} + 2x+3 &= 7 & 2x+3-3 &=7-3 \\ + 2x &= 4 & \frac{2x}2 &=\frac42\\ + x &= 2 +\end{aligned} +\end{equation} + +\begin{lstlisting} +\begin{equation} +\begin{aligned} + 2x+3 &= 7 & 2x+3-3 &= 7-3 \\ + 2x &= 4 & \frac{2x}2 &= \frac42\\ + x &= 2 +\end{aligned} +\end{equation} +\end{lstlisting} + +The \verb|aligned| environment is similar to the \verb|array|\index{array} +environment, there exists no +starred version and it has only one equation number and has to be part of +another math environment, which should be \verb|equation| environment. +The advantage of \verb|aligned| is the much + better horizontal and vertical spacing. %%% ----- Martin ----- + + +\subsection{Problems} +When using one of the \verb+align+ environments, there should be no \verb+\\+ at the +end of the last line, otherwise you'll get another equation number for this +``empty{}'' line: %%% ----- Martin ----- + +\begin{LTXexample}[width=0.65\linewidth] +\begin{align} + 2x+3 &= 7\\ +\end{align} +\end{LTXexample} + +\begin{LTXexample}[width=0.65\linewidth] +\begin{align} + 2x+3 &= 7 +\end{align} +\end{LTXexample} +\section{Other environments} + + +\subsection{\texttt{gather} environment} + +\marginpar{\CMD{begin\{gather\}\\...\\\CMD{end\{gather\}}}} +This is like a multi line environment with no special horizontal alignment. +All rows are centered and can have an own equation number: +% +\begin{gather} +i_{11}=0.25\\ +i_{21}=\frac{1}{3}i_{11}\nonumber \\ +i_{31}=0.33i_{22} +\end{gather} +% +For this example the code looks like: +\begin{lstlisting} +\begin{gather} + i_{11} = 0.25\\ + i_{21} = \frac{1}{3}i_{11}\nonumber\\ + i_{31} =0.33i_{22} +\end{gather} +\end{lstlisting} + +\begin{itemize} +\item The \texttt{gather}\index{gather} environment has an implicit \texttt{\{c\}} +horizontal alignment with no vertical column alignment. It is just +like an one column array/table. +\item A nonumber-version \texttt{\small \textbackslash{}begin\{gather{*}\}...\textbackslash{}end\{gather{*}\}} +exists. +Look at section \vref{split} for an example. +\end{itemize} + +\subsection{\texttt{gathered} environment} +\marginpar{\CMD{begin\{gathered\}[c]\\...\\\CMD{end\{gathered\}}}} + +The \verb+gathered+ environment is like the \verb+aligned+ or \verb+alignat+ +\index{gathered}\index{aligned}\index{alignat} +environment. They use only so much horizontal space as the widest line needs. +In difference to the \verb+gather+ environment it must be itself inside the +math mode. +% +\begin{align} +\rule{2cm}{1pt} +\begin{gathered} +\quad i_{11}=0.25\\ +\quad i_{21}=\frac{1}{3}i_{11}\\ +\quad i_{31}=0.33i_{22} +\end{gathered} +\rule{2cm}{1pt} +\end{align} + +% +\begin{lstlisting} +\begin{align} +\rule{2cm}{1pt} +\begin{gathered} +\quad i_{11}=0.25\\ +\quad i_{21}=\frac{1}{3}i_{11}\\ +\quad i_{31}=0.33i_{22} +\end{gathered} +\rule{2cm}{1pt} +\end{align} +\end{lstlisting} +% + +The optional argument can be used for setting the vertical alignment which is +by default c (centered). It can also be t for top or b for bottom. + +\begin{align} +\rule{1cm}{1pt} +\begin{gathered}[t] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +% +\begin{gathered}[c] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +% +\begin{gathered}[b] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +\ \rule{1cm}{1pt} +\end{align} + +\begin{lstlisting} +\begin{align} +\rule{1cm}{1pt} +\begin{gathered}[t] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +% +\begin{gathered}[c] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +% +\begin{gathered}[b] +\quad A=a\\ +\quad B=b\\ +\quad C=c +\end{gathered} +\ \rule{1cm}{1pt} +\end{align} +\end{lstlisting} + + +When using a square bracket as first character inside the environment, then +everything is ignored by \AmS until a following closing bracket, because \AmS takes this +as an optional argument: +% +\begin{align} +\begin{gathered} +[A]\quad A=a\\ +[B]\quad B=b\\ +[C]\quad C=c +\end{gathered} +\end{align} +% +\begin{lstlisting} +\begin{align} +\begin{gathered} +[A]\quad A=a\\ +[B]\quad B=b\\ +[C]\quad C=c +\end{gathered} +\end{align} +\end{lstlisting} +% +The \verb+[A]+ is completely ignored, which can be avoided by using the +optional argument \verb+[c]+ or at least an empty one directly +after the \verb+\begin{gather}+. Another possibility is using the package \verb+empheq+, +which fixes this behaviour by default. +% +\begin{align} +\begin{gathered}[] +[A]\quad A=a\\ +[B]\quad B=b\\ +[C]\quad C=c +\end{gathered} +\end{align} +% +\begin{lstlisting} +\begin{align} +\begin{gathered}[] +[A]\quad A=a\\ +[B]\quad B=b\\ +[C]\quad C=c +\end{gathered} +\end{align} +\end{lstlisting} +% + + +\subsection{\texttt{multline} environment} +\marginpar{\CMD{begin\{multline\}\\...\\\CMD{end\{multline\}}}} +This is also like a multi line% +\footnote{It is no typo, the name of the environment is \texttt{multline}, no +missing i here!} environment with a special vertical alignment. The \textbf{first} +row is \textbf{left aligned}, the second and all following ones except +the last one are \textbf{centered} and the \textbf{last} line is \textbf{right +aligned}. It is often used to write extremely long formulas: + + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{multline} + A = \lim _{n\rightarrow \infty }\Delta x\left( a^{2}+\left( a^{2}+2a\Delta x + +\left( \Delta x\right) ^{2}\right)\right.\\ + +\left( a^{2}+2\cdot 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)\\ + +\left( a^{2}+2\cdot 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\ + + \ldots\\ + \left.+\left( a^{2}+2\cdot (n-1)a\Delta x +(n-1)^{2}\left( \Delta x\right) ^{2}\right) \right)\\ + = \frac{1}{3}\left( b^{3}-a^{3}\right) +\end{multline} +\end{lstlisting} +\begin{multline} +A=\lim_{n\rightarrow\infty}\Delta x\left(a^{2}+\left(a^{2}+2a\Delta x+\left(\Delta x\right)^{2}\right)\right.\label{eq:reset}\\ ++\left(a^{2}+2\cdot2a\Delta x+2^{2}\left(\Delta x\right)^{2}\right)\\ ++\left(a^{2}+2\cdot3a\Delta x+3^{2}\left(\Delta x\right)^{2}\right)\\ ++\ldots\\ +\left.+\left(a^{2}+2\cdot(n-1)a\Delta x+(n-1)^{2}\left(\Delta x\right)^{2}\right)\right)\\ +=\frac{1}{3}\left(b^{3}-a^{3}\right) +\end{multline} + + +\begin{figure}[htb] +\begin{multline} +\framebox[0.5\columnwidth]{x}\\ +\framebox[0.5\columnwidth]{x}\\ +\framebox[0.5\columnwidth]{x}\\ +\shoveright{\framebox[0.5\columnwidth]{x}}\\ +\framebox[0.5\columnwidth]{x}\\ +\framebox[0.5\columnwidth]{x} +\end{multline} +\caption{\texttt{multline} Alignment demo +(the fourth row is shifted to the right with \CMD{shoveright})} +\label{cap:multline-Alignment-Demo} +\end{figure} + +\begin{figure}[htb] +\begin{minipage}[c]{0.45\textwidth}% +\fbox{\parbox{\columnwidth}{\begin{multline} +\framebox[0.5\columnwidth]{\textrm{\textbackslash multlinegap=}}\\ +\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline} +}} +\end{minipage}% +\hfill{}\begin{minipage}[c]{0.45\textwidth}% +{\setlength{\multlinegap}{0pt}\fbox{\parbox{\columnwidth}{\begin{multline} +\framebox[0.5\columnwidth]{\textbackslash\textrm{multlinegap=}}\\ +\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline} +}}} +\end{minipage}% +\caption{\label{cap:multlinegap}Demonstration of \CMD{multlinegap} (default is 0pt)} +\end{figure} + + + +\begin{itemize} +\item A nonumber-version \CMD{begin\{multline{*}\}...}\CMD{end\{multline{*}\}} +exists. +\item By default only the last line (for right equation numbers) or the +first line (for left equation numbers) gets a number, the others can't. +\item The alignment of a single line can be changed with the command +\CMD{shoveright}\index{shoveright@\textbackslash shoveright} (figure \vref{cap:multline-Alignment-Demo}) +\item The first line and the last line have a small gap to the text border.% +\footnote{When the first (numbers left) or last line (numbers right) has an +equation number then \CMD{multlinegap} is not used +for these ones, only for the line without a number.} See figure \ref{cap:multlinegap}, where the length of \CMD{multlinegap}\index{multlinegap@\textbackslash multlinegap} +is set to \texttt{0pt} for the right one. +\end{itemize} + +\subsubsection{Examples for \texttt{multline}}\label{sec:Specials-for-multline} + +With the multline environment the equation~\vref{eq:braces} looks like: + +\begin{multline} +\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i>>> to get the correct height <<<<< + \left[ 1-e^{-pn} \right] \left[ Q \left( n \right) - pR + \left( n \right) + R'\left( n \right) \right]e^{-pn}\right.\\ + - \left.\left[-\frac{Q \left( n \right) e^{-pn}}{p} + + \frac{Q \left( 0 \right)}{p} + R \left( n \right) e^{-pn} + - A\right] pe^{-pn}\right\} = 0 +\end{multline} +\end{LTXexample} + + + +\subsection{\texttt{split} environment}\label{split} + +\marginpar{\CMD{begin\{split\}\\...\\\CMD{end\{split\}}}}% +\makeatletter +\@removefromreset{equation}{section} +\makeatother +% +\begin{leftbar} +\noindent From now on the counting of the equations changes. It is introduced with a +foregoing command, which doesn't really make sense, it is only +for demonstration: +\begin{lstlisting} +\makeatletter +\@removefromreset{equation}{section} +\makeatother +\end{lstlisting} +\end{leftbar} + + +The \verb|split| environment is like the \verb|multline|\index{multline} +or \verb|array| environment for equations longer than the column +width. Just like the array environment and in contrast to \verb|multline|, +\verb|split| can only be used as \textbf{part of another environment}. +\verb|split| itself has no own numbering, this is given by the other +environment. Without an ampersand all lines in the split environment +are right-aligned and can be aligned at a special point by using an +ampersand. In difference to the \verb|aligned| environment (section \vref{sec:aligned}), the \verb|split| environment permits more than one horizontal alignment. + +It is important that the split environment has another behaviour when used inside one of the %%% ----- Martin ----- +``old'' \LaTeX{} environments \verb+\[...\]+ or \verb+\begin{equation}+ \verb+...+\verb+ \end{equation}+, in this +case more than one horizontal alignment tabs are possible. + +\hspace*{-\marginparwidth}% +\begin{minipage}{0.5\columnwidth} +\[ +\begin{split} + \framebox[0.35\columnwidth]{x}\\ + \framebox[0.75\columnwidth]{x}\\ + \framebox[0.65\columnwidth]{x}\\ + \framebox[0.95\columnwidth]{x} +\end{split} +\] +\end{minipage}\hfill% +\begin{minipage}{0.5\columnwidth} +\footnotesize\begin{verbatim} +\[ +\begin{split} + \framebox[0.35\columnwidth]{x}\\ + \framebox[0.75\columnwidth]{x}\\ + \framebox[0.65\columnwidth]{x}\\ + \framebox[0.95\columnwidth]{x} +\end{split} +\] +\end{verbatim} +\end{minipage} +\vspace{2ex} + +\hspace*{-\marginparwidth}% +\begin{minipage}{0.5\columnwidth} +\[ +\begin{split} + \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\ + &\framebox[0.75\columnwidth]{x}\\ + &\framebox[0.65\columnwidth]{x}\\ + &\framebox[0.95\columnwidth]{x} +\end{split} +\] +\end{minipage}\hspace{1cm}% +\begin{minipage}{0.5\columnwidth} +\footnotesize% +\begin{verbatim} +\[ +\begin{split} + \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\ + &\framebox[0.75\columnwidth]{x}\\ + &\framebox[0.65\columnwidth]{x}\\ + &\framebox[0.95\columnwidth]{x} +\end{split} +\] +\end{verbatim} +\end{minipage} +\vspace{1ex} + +The following example shows the \texttt{split} environment as part +of the \texttt{equation} environment: + +\begin{equation} +\begin{split}A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\ + & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\ + & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\ + & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\ + & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE}\end{split} +\label{eq:Beispiel-Integral}\end{equation} + + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{equation} + \begin{split} + A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| + \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\ + & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| + \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\ + & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+ + \left| \frac{x^{3}}{3}- + \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\ + & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| + \frac{8}{3}-\frac{20}{2}+12- + \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\ + & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6} + \right| =\frac{7}{6}+\frac{5}{6}=2\, \textrm{FE} + \end{split} +\end{equation} +\end{lstlisting} + +\bigskip{} +The same using the \verb|array| environment with \verb|{rl}|-alignment +instead of \verb|split| gives same horizontal alignment, but another %%% ----- Martin ----- +vertical spacing% +\footnote{Can be changed with \texttt{\textbackslash renewcommand\textbackslash arraystretch\{1.5\}}} and the +symbols are only in scriptsize and not textsize:\footnote{See section \vref{sec:Styles}} %%% ----- Martin ----- + +\begin{equation} +\begin{array}{rl} +A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\ + & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\ + & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\ + & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\ + & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE} + \end{array} + \end{equation} + +Compare the following two examples for typesetting the minus sign. In the first case it +is typeset similiar to the plus character, and in the second example it is typeset +without the additional space for a binary math atom. + +\begin{minipage}{0.49\linewidth} +\begin{align} +\begin{split} +a = {} & -b + c \\ + & -d + e +\end{split} +\end{align} +% +\begin{align} +\begin{split} +a = {} & {-}b + c \\ + & {-}d + e +\end{split} +\end{align} +\end{minipage}\hfill +\begin{minipage}{0.49\linewidth} +\begin{lstlisting} +\begin{align} +\begin{split} +a = {} & -b + c \\ + & -d + e +\end{split} +\end{align} +% +\begin{align} +\begin{split} +a = {} & {-}b + c \\ + & {-}d + e +\end{split} +\end{align} +\end{lstlisting} +\end{minipage} + +\begin{itemize} +\item There exists no starred version (\texttt{\textbackslash{}begin\{split{*}\}}) %%% ----- Martin ----- +of the \texttt{split} environment. +\end{itemize} + + +\subsection{\texttt{cases} environment } + +This gives support for an often used mathematical construct.\index{cases@\textbackslash cases} +You can also choose the more than once described way to convert some +text into math, like +{\footnotesize\begin{verbatim} +$x=\begin{cases} + 0 & \text{if A=...}\\ + 1 & \text{if B=...}\\ + x & \textrm{this runs with as much text as you like, + but without an automatic linebreak, it runs out + of page....} +\end{cases}$ +\end{verbatim}} +\noindent which gives equation~\vref{eq:cases}. It is obvious what the problem +is. + +\begin{eqnarray} +x & = & \begin{cases} +0 & \text{if A=...}\\ +1 & \text{if B=...}\\ +x & \textrm{this runs with as much text as you like, but without a linebreak, it runs out of page....}\end{cases}\label{eq:cases}\end{eqnarray} + + +In this case it is better to use a parbox\index{parbox@\textbackslash parbox} +for the text part with a \texttt{flushleft} command for a better view. + +\begin{equation} +x=\begin{cases} +0 & \text{if A=...}\\ +1 & \text{if B=...}\\ +x & \parbox{5cm}{\flushleft this runs with as much text as you like, but without an automatic linebreak, it runs out of page....}\end{cases}\end{equation} + + + +\begin{lstlisting} +\begin{equation} +x=\begin{cases} + 0 & \text{if A=...}\\ + 1 & \text{if B=...}\\ + x & \parbox{5cm}{% + \flushleft% + this runs with as much text as you like, + but without an automatic linebreak, + it runs out of page....}% +\end{cases} +\end{equation} +\end{lstlisting} + +\begin{leftbar} +\noindent From now on the counting of the equations changes. It is introduced +with a foregoing command, which doesn't really make sense, it is only for +demonstration: +\begin{lstlisting} +\renewcommand\theequation{\arabic{equation}} +\end{lstlisting} +\end{leftbar} + +\renewcommand\theequation{\arabic{equation}} + + +\subsection{Matrix environments}\label{sec:ams-matrix} +% +\begin{table}[htb] +\centering\begin{tabular}{rcrcrc} +\textbackslash{}Vmatrix\index{Vmatrix@\textbackslash Vmatrix}& +$\begin{Vmatrix}a & b\\ +c & d\end{Vmatrix}$& +\textbackslash{}Bmatrix\index{Bmatrix@\textbackslash Bmatrix}& +$\begin{Bmatrix}a & b\\ +c & d\end{Bmatrix}$& +\textbackslash{}matrix\index{matrix@\textbackslash matrix}& +$\begin{matrix}a & b\\ +c & d\end{matrix}$\tabularnewline +\rule{0pt}{0.85cm}\textbackslash{}vmatrix\index{vmatrix@\textbackslash vmatrix}& +$\begin{vmatrix}a & b\\ +c & d\end{vmatrix}$& +\textbackslash{}bmatrix\index{bmatrix@\textbackslash bmatrix}& +$\begin{bmatrix}a & b\\ +c & d\end{bmatrix}$& +\textbackslash{}pmatrix\index{pmatrix@\textbackslash pmatrix}& +$\begin{pmatrix}a & b\\ +c & d\end{pmatrix}$\tabularnewline[10pt] +&&&&\textbackslash{}smallmatrix\index{smallmatrix@\textbackslash smallmatrix}& +$\begin{smallmatrix}a & b\\ +c & d\end{smallmatrix}$ +\end{tabular} +\caption{Matrix environments} +\end{table} + +All matrix environments can be nested and an element may also contain +any other math environment, so that very complex structures are possible. +By default all cells have a centered alignment, which is often not the best +when having different decimal numbers or plus/minus values. Changing the +alignment to right (not for the \verb+smallmatrix+) is possible with +\marginpar{% +\texttt{matrix}\\ +\texttt{vmatrix}\\ +\texttt{Vmatrix}\\ +\texttt{bmatrix}\\ +\texttt{Bmatrix}\\ +\texttt{pmatrix}\\ +\texttt{smallmatrix}% +}% + +\begin{lstlisting} +\makeatletter +\def\env@matrix{\hskip -\arraycolsep + \let\@ifnextchar\new@ifnextchar + \array{*\c@MaxMatrixCols r}} +\makeatother +\end{lstlisting} + +The special matrix environment \verb+smallmatrix+, which decreases +horizontal and vertical space is typeset in scriptstyle. The \verb|smallmatrix| +\index{smallmatrix@\textbackslash smallmatrix} environment makes some sense +in the inline mode to decrease the line height. +For dots over several columns look for \CMD{hdotsfor} in the following section. + + + +\section{Vertical whitespace}\label{sec:ams-whitespace} +See section~\vref{subsec:vwhitespace} for the lengths which control the +vertical whitespace. There is no difference to \AmSmath. + +\section{Dots}\label{sec:ams-dots} + +In addition to section~\vref{sec:Dots} \AmSmath has two more commands +for dots: \CMD{dddot}\{...\}\footnote{already mentioned in section \ref{sec:Accents}} and \CMD{ddddot}\{...\} +\index{dddot@\textbackslash dddot}\index{ddddot@\textbackslash ddddot} + +\verb|$\dddot{y}$|: $\dddot{y}$ + +\verb|$\ddddot{y}$|: $\ddddot{y}$ + + +Another interesting dot command is \CMD{hdotsfor}\index{hdotsfor@\textbackslash hdotsfor} +with the syntax: + +\begin{lstlisting} +\hdotsfor[]{} +\end{lstlisting} + +With the spacing factor the width of the dots can be stretched or +shrinked. The number of columns allows a continuing dotted line over +more columns. Equation \ref{eq:tridiagonal} shows the definition +of a tridiagonal matrix. + +\begin{equation} +\underline{A}=\left[\begin{array}{ccccccc} +a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\ +a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\ +0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\ +\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ +\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ +0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\ +0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\ +0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn} +\end{array}\right]\label{eq:tridiagonal} +\end{equation} + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\begin{equation} +\underline{A}=\left[\begin{array}{ccccccc} +a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\ +a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\ +0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\ +\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ +\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ +0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\ +0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\ +0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn} +\end{array}\right] +\end{equation} +\end{lstlisting} + + +\section{\texttt{fraction} commands}\label{sec:ams-fraction} + + +\subsection{Standard} + +Additional to the font size problem described in subsection~\vref{sub:fraction command} +\AmSmath supports some more commands for fractions\index{Fraction}. The \CMD{frac} command +described in \cite{MathGuide}, does no more exist in \AmSmath. %%% ----- Martin ----- + +\begin{itemize} +\item The global fraction definition has five parameters\index{genfrac@\textbackslash genfrac} +\index{fraction@\textbackslash frac} +\begin{lstlisting}[xleftmargin=-1em,xrightmargin=-1em] +\genfrac{}{}{}{}{}{} +\end{lstlisting} +where thickness can have any length with a valid unit like \\ +\verb|genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}| +$\rightarrow\genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}$ +\item \CMD{cfrac}\index{cfrac@\textbackslash cfrac} (continued fraction) which is +by default set in the display mathstyle and useful for fractions like +\begin{equation} +\cfrac{1}{\sqrt{2}+\cfrac{1}{\sqrt{3}+\cfrac{1}{\sqrt{4}+\cfrac{1}{\ldots}}}}\label{cfrac} +\end{equation} +which looks with the default \CMD{frac} command like +\begin{equation} + \frac{1}{\sqrt{2}+\frac{1}{\sqrt{3}+\frac{1}{\sqrt{4}+\frac{1}{\ldots}}}} +\end{equation} +where the mathstyle decreases for every new level in the fraction. +The \CMD{cfrac} command can be called with an optional +parameter which defines the placing of the nominator, which can be +\texttt{[l]}eft, \texttt{[r]}ight or \texttt{[c]}enter (the default - see +equation~\ref{cfrac}):\\ +\begin{minipage}[c]{0.40\textwidth}% +\[ +\cfrac[l]{1}{\sqrt{2}+\cfrac[l]{1}{\sqrt{3}+\cfrac[l]{1}{\sqrt{4}+\cfrac[l]{1}{\ldots}}}} +\] +\end{minipage}% +\hfill{}\begin{minipage}[c]{0.40\textwidth}% +\[\cfrac[r]{1}{\sqrt{2}+\cfrac[r]{1}{\sqrt{3}+\cfrac[r]{1}{\sqrt{4}+\cfrac[r]{1}{\ldots}}}}\] +\end{minipage}% + +\item \CMD{dfrac}\index{dfrac@\textbackslash dfrac} +which takes by default the displaystyle\index{displaystyle@\textbackslash displaystyle}, so that +fractions in inline mode $\dfrac{1}{2}$ have the same size than in +display mode. +\item \CMD{tfrac}\index{tfrac@\textbackslash tfrac} (vice versa to \CMD{dfrac}) which takes by default +the scriptstyle\index{scriptstyle@\textbackslash scriptstyle}, so that fractions in display +mode have the same size than in inline mode. +\end{itemize} + +\[\tfrac{2}{3} \text{\hspace{0.5cm}\CMD{tfrac\{2\}\{3\}}} \] +\[\frac{2}{3} \text{\hspace{0.5cm}\CMD{frac\{2\}\{3\}}} \] + + +\subsection{Binoms}\label{sub:Binoms} + +\marginpar{\CMD{binom}\\\CMD{dbinom}\\\CMD{tbinom}}They are like fractions without a rule and its syntax is different +to the \CMD{choose} command from standard \LaTeX{} +(see section \vref{sub:fraction command}). \AmSmath{} provides three +different commands for binoms just like the ones for fractions. + +\begin{table}[htb] +\centering% +\begin{tabular}{lcl} +Command & Inlinemath & Displaymath\tabularnewline +\hline +\texttt{\textbackslash{}binom\{m\}\{n\}} & $\binom{m}{n}$& +${\displaystyle \binom{m}{n}}$\tabularnewline +\texttt{\rule{0pt}{0.75cm}\textbackslash{}dbinom\{m\}\{n\}}& +$\dbinom{m}{n}$& +${\displaystyle \dbinom{m}{n}}$\tabularnewline +\texttt{\rule{0pt}{0.5cm}\textbackslash{}tbinom\{m\}\{n\}}& +$\tbinom{m}{n}$& +${\displaystyle \tbinom{m}{n}}$\tabularnewline +\end{tabular} +\caption{binom commands} +\end{table} + + +\section{Roots}\label{sec:Roots-ams} + +The typesetting for roots\index{uproot@\textbackslash uproot} is sometimes not +the best. Some solutions for better typesetting are % +\marginpar{\CMD{leftroot}\\\CMD{uproot}}% +described in section~\vref{sec:Roots} for standard \LaTeX{}. \AmSmath +has some more commands for the $n$-th root: + +\begin{lstlisting} +\sqrt[\leftroot{}\uproot{}]{< ... >} +\end{lstlisting} + +\noindent \verb++ indicates a value for the points% +\footnote{In PostScript units (bp -- Big Points).} of which the root can be +adjusted to the left and/or to the top, \eg +$\sqrt[k_n]{a}$ (\verb+$\sqrt[k_n]{a}$+) has a too deep exponent, whereas $\sqrt[\uproot{2}k_n]{a}$ \verb+$\sqrt[\uproot{2}k_n]{a}$+ looks nicer. + + + +\subsection{Roots with \CMD{smash} command} + +\marginpar{\CMD{smash}}The default for a root\index{Root} with $\lambda_{k_{i}}$ as root +argument looks like $\sqrt{\lambda_{k_{i}}}$, which may be not the %%% ----- Martin ----- +best typesetting. It is possible to reduce the lowest point of the root +to the baseline with the \CMD{smash} command: $\sqrt{\lambda_{k_{i}}}\xrightarrow{\text{with \textbackslash smash}}\sqrt{\smash[b]{\lambda_{k_{i}}}}$ + + +The syntax of the \CMD{smash} command% +\footnote{In \texttt{latex.ltx} \CMD{smash} is defined without an optional argument.} renewed by the \AmSmath package is %%% ----- Martin ----- + +\begin{lstlisting} +\smash[]{} +\end{lstlisting} +The optional argument for the position can be: + +\begin{description} +\item [t]keeps the bottom and annihilates the top +\item [b]keeps the top and annihilates the bottom +\item [tb]annihilates top and bottom (the default) +\end{description} + +\section{Accents}\label{amssymb} + +With the macro \verb|\mathaccent| it is easy to define new accent types, for example + +\begin{lstlisting} +\def\dotcup{$\mathaccent\cdot\cup$} +\end{lstlisting} + +$\mathaccent\cdot\cup$ + +\def\curvearrowleftright{% + \ensuremath{% + \mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}% + }% +} + +Overwriting of two symbols is also possible: + +{\huge +$\curvearrowleft\curvearrowright\curvearrowleftright$} + +In this case the second symbol has to be shifted to the left for a length %%% ----- Martin ----- +of $5mu$ (mu: math unit\index{Math unit}). + +\begin{lstlisting} +\def\curvearrowleftright{% + \ensuremath{% + \mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}% + }% +} +\end{lstlisting} + +For other possibilities to define new accents see section \vref{sec:package-accent}. %%% ----- Martin ----- + +\section{\CMD{mod} command} + +In standard \LaTeX{} the modulo command is not an operator, though %%% ----- Martin ----- +it is often used in formulas. \AmSmath provides two (three) different +commands for modulo, which are listed in tabular~\vref{cap:The-modulo commands}. + +\begin{itemize} +\item They all insert some useful space before and behind the mod-operator. +\end{itemize} + +\begin{table}[htb] +\centering\begin{tabular}{rrl} +a\textbackslash{}mod\{n\^{}2\}=b& +$\rightarrow$& +$a\mod{n^{2}}=b$\tabularnewline +a\textbackslash{}pmod\{n\^{}2\}=b& +$\rightarrow$& +$a\pmod{n^{2}}=b$\tabularnewline +a\textbackslash{}pod\{n\^{}2\}=b& +$\rightarrow$& +$a\pod{n^{2}}=b$\tabularnewline +\end{tabular} +\caption{\label{cap:The-modulo commands}The modulo commands and their meaning} +\end{table} + + + +\section{Equation numbering\label{sec:Equation-numbering}} + +See section \vref{sub:Equationnumbering} for equation numbering\index{Equation!numbering}. +It is mostly the % +\marginpar{\textbackslash{}numberwithin% +}same, only one command is new to \AmSmath. If you want +a numbering like ``\ref{eq:IntoSection}{}'' then write either in the preamble %%% ----- Martin ----- +or like this example anywhere in your doc: + +\begin{lstlisting} +\numberwithin{equation}{section} +\end{lstlisting} + +\begin{leftbar} +\numberwithin{equation}{section}From now on the numbering looks like %%% ----- Martin ----- +equation \vref{eq:IntoSection}. For the book-class you can get the +same for chapters. +\end{leftbar} + +If you want to get rid of the parentheses then write in the preamble: %%% ----- Martin ----- + +\begin{lstlisting} +\makeatletter +\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}} +\makeatother +\end{lstlisting} + +Now the following four subequation numbers have no parentheses. + + + + +\makeatletter +\let\oldTagForm\tagform@ +\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}} +\makeatother + +\subsection{Subequations}\label{ams:subeqn} + +Amsmath supports this with the environment \verb|subequation|\index{Subequations}. +For example: +\begin{subequations} +\begin{align} +y & = d\\ +y & = cx+d\\ +y & = bx^{2}+cx+d\\ +y & = ax^{3}+bx^{2}+cx+d +\end{align} +\end{subequations} + +\begin{lstlisting} +\begin{subequations} +\begin{align} +y & = d\\ +y & = cx+d\\ +y & = bx^{2}+cx+d\\ +y & = ax^{3}+bx^{2}+cx+d +\end{align} +\end{subequations} +\end{lstlisting} + +\makeatletter +\let\tagform@\oldTagForm +\makeatother + + +Inside of subequations only complete other environments (\texttt{\textbackslash{}begin\{...\} +... \textbackslash{}end\{...\}}) are possible. + +\begin{lstlisting} +\renewcommand{\theequation}{% + \theparentequation{}-\arabic{equation}% +} +\end{lstlisting} + +\begin{subequations} +\renewcommand{\theequation}{% + \theparentequation -\arabic{equation}% +}% +\begin{align} +y & = d\\ +y & = cx+d\label{eq:subequation-neu}\\ +y & = bx^{2}+cx+d\\ +y & = ax^{3}+bx^{2}+cx+d +\end{align} +\end{subequations} + +A ref to a subequation is possible like the one to equation \ref{eq:subequation-neu}. +The environment chooses the same counter ``\texttt{equation}'' +but saves the old value into ``\texttt{parentequation}''. + +\newcounter{mySubCounter} +\newcommand{\twocoleqn}[2]{ + \setcounter{mySubCounter}{0}% + \let\OldTheEquation\theequation% + \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}% + \noindent% + \begin{minipage}{.49\textwidth} + \begin{equation}\refstepcounter{mySubCounter} + #1 + \end{equation} + \end{minipage}\hfill% + \addtocounter{equation}{-1}% + \begin{minipage}{.49\textwidth} + \begin{equation}\refstepcounter{mySubCounter} + #2 + \end{equation} + \end{minipage} + \let\theequation\OldTheEquation +} + +It is also possible to place two equations side by side with counting as subfigures: + +\twocoleqn{y=f(x)}{y=f(z)} + +\vspace{1ex} +In this case, the \AmSmath internal subfigure counter cannot be used and an own +counter has to be defined: + +\begin{lstlisting} +\newcounter{mySubCounter} +\newcommand{\twocoleqn}[2]{ + \setcounter{mySubCounter}{0}% + \let\OldTheEquation\theequation% + \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}% + \noindent% + \begin{minipage}{.49\textwidth} + \begin{equation}\refstepcounter{mySubCounter} + #1 + \end{equation} + \end{minipage}\hfill% + \addtocounter{equation}{-1}% + \begin{minipage}{.49\textwidth} + \begin{equation}\refstepcounter{mySubCounter} + #2 + \end{equation} + \end{minipage}% + \let\theequation\OldTheEquation +} +[ ... ] +\twocoleqn{y=f(x)}{y=f(z)} +\end{lstlisting} + + +\section{Labels and tags}\label{sec:Labels-and-Tags} + +For the \CMD{label} command\index{label@\textbackslash label} \marginpar{\textbackslash{}tag% +} +see section \vref{sec:Labels}, it is just the same behaviour. \AmSmath +allows to define own single ``equation numbers\index{Equation number}'' +with the \CMD{tag} command. +\begin{align} +f(x) & =a\tag{linear}\label{eq:linear}\\ +g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\ +h(x) & =\sin x\tag*{trigonometric} +\end{align} + +\begin{lstlisting} +\begin{align} +f(x) & =a\tag{linear}\label{eq:linear}\\ +g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\ +h(x) & =\sin x\tag*{trigonometric} +\end{align} +\end{lstlisting} + +\begin{itemize} +\item The \CMD{tag} command is also possible for unnumbered +equations, \LaTeX{} changes the behaviour when a tag is detected. +\item There exists a starred version \verb|\tag{*}{...}|, %%% ----- Martin ----- +which supresses any annotations like parentheses for equation numbers\index{Equation!number}. +\item There exist two package options for tags, \verb|ctagsplit|\index{ctagsplit} %%% ----- Martin ----- +and \verb|righttag|\index{righttag} (look at the beginning of this +part on page~\pageref{par:AMSmath-package}). +\end{itemize} + + +\section{Limits}\label{sec:limit-AMS} + +By default the sum/prod has the limits above/below and the integral +at the side. To get the same behaviour for all symbols which can have +limits load the package \AmSmath in the preamble as %%% ----- Martin ----- + +\begin{lstlisting} +\usepackage[sumlimits,intlimits]{amsmath} +\end{lstlisting} + +There exist also options for the vice versa (see page~\pageref{par:AMSmath-package}). %%% ----- Martin ----- +See also Section~\ref{sec:misc-AMS} for the additional commands \CMD{underset} and \CMD{overset}. + + + +\subsection{Multiple limits} + +For general information about limits\index{Limits} read section +\vref{sub:Limits-Inline}. Standard \LaTeX{} provides the \texttt{\textbackslash{}atop}\index{atop@\textbackslash atop} command +for multiple limits (section \vref{sub:Multiple-Limits}). \AmSmath \marginpar{\textbackslash{}substack% +} +has an additional command for that, which +can have several lines with the following syntax: +\marginpar{\CMD{begin\{Sb\}}\\...\\\CMD{end\{Sb\}}\\\CMD{begin\{Sp\}}\\...\\\CMD{end\{Sp\}}% +} + +\begin{lstlisting} +\substack{...\\...\\...} +\end{lstlisting} + +The environments described in \cite{MathGuide} + +\begin{lstlisting} +\begin{Sb} ... \end{Sb} +\begin{Sp} ... \end{Sp} +\end{lstlisting} +are obsolete and no more part of \AmSmath. + +The example equation \vref{eq:atop} with the \CMD{substack}\index{substack@\textbackslash substack} command +looks like: + +\begin{equation}\label{eq:multlimits} +\sum_{\substack{1\le i\le p\\ +1\le j\le q\\ +1\le k\le r} +}a_{ij}b_{jk}c_{ki} +\end{equation} + + +Insert these limits in the following way: +\begin{lstlisting} +\begin{equation} + \sum_{% + \substack{1\le i\le p\\ + 1\le j\le q\\ + 1\le k\le r} + }% + a_{ij}b_{jk}c_{ki} +\end{equation} +\end{lstlisting} + +\subsection{Problems}\label{subsec:ams-limits} + +There are still some problems with limits and the following math +expression. For example: + +\[ +X = \sum_{1\le i\le j\le n}X_{ij} +\] +\begin{lstlisting} +\[ +X = \sum_{1\le i\le j\le n}X_{ij} +\] +\end{lstlisting} + +\noindent does not look nice because of the long limit. Using a +\CMD{makebox} also does not really solve the problem, because +\CMD{makebox} is in \TeX{} horizontal mode and knows nothing about +the appropriate math font size, because limits have a smaller font size. +It is better to define a \CMD{mathclap}\index{mathclap@\textbackslash mathclap} macro, similiar to the two +macros \CMD{llap} and \CMD{rlap} and uses the also new defined \CMD{mathclap} macro\index{clap@\textbackslash clap}: + +\begin{lstlisting} +\def\mathllap{\mathpalette\mathllapinternal} +\def\mathllapinternal#1#2{% + \llap{$\mathsurround=0pt#1{#2}$}% $ +} +\def\clap#1{\hbox to 0pt{\hss#1\hss}} +\def\mathclap{\mathpalette\mathclapinternal} +\def\mathclapinternal#1#2{% + \clap{$\mathsurround=0pt#1{#2}$}% +} +\def\mathrlap{\mathpalette\mathrlapinternal} +\def\mathrlapinternal#1#2{% + \rlap{$\mathsurround=0pt#1{#2}$}% $ +} +\end{lstlisting} + + +Now we can write limits which have a boxwidth of 0pt and the right font +size and the following math expression appears just behind the symbol: + +\[ +X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij} +\] +\begin{lstlisting} +\[ +X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij} +\] +\end{lstlisting} + +Another problem occurs when having operators with stacked limits in braces:\index{substack@\textbackslash substack} +\index{Braces!Problems} +\index{Stacked limits} +\begin{align} +\left[\sum_{\substack{i,j\\i>j}} \dots \right] +\end{align} + +This case is not easy to handle when some other math expressions are around the braces +which should be on the same baseline. However, the following may help in some cases +to get better looking braces. + +\begin{LTXexample}[width=0.45\linewidth,wide] +\begin{align} +foo \left[\begin{array}{@{}c@{}} + \displaystyle\sum_{\substack{i,j\\i>j}} \dots + \end{array}\right] bar +\end{align} +\end{LTXexample} + + +\subsection{\CMD{sideset}} + +This is a command for a very special purpose, to combine over/under +limits with superscript/subscripts for \marginpar{\CMD{sideset}}the +sum-symbol. For example: it is not possible to place the prime +for the equation \ref{eq:sideset} near to the sum\index{sum@\textbackslash sum} symbol, +because it becomes an upper limit when writing without an preceeding \verb|{}|. +\begin{equation} +\sum_{n}{} +\end{lstlisting} + +It can place characters on all four corners of the sum-symbol: +\[ +\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T} +\] + +\begin{lstlisting} +\[ +\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T} +\] +\end{lstlisting} + +Now it is possible to write the equation \ref{eq:sideset} in a proper +way with the command \verb|\sideset{}{'}| before +the sum symbol: +\begin{equation} +\sideset{}{'}\sum_{n\mapstofill@{#1}{#2}} +\end{lstlisting} + +{\fboxsep=0pt +\verb+$\ext@arrow 0000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0000$} + +\verb+$\ext@arrow 9000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9000$} + +\verb+$\ext@arrow 0900$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0900$} + +\verb+$\ext@arrow 0009$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0009$} + +\verb+$\ext@arrow 0090$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0090$} + +\verb+$\ext@arrow 0099$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0099$} + +\verb+$\ext@arrow 9999$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9999$} +} + +% $ +\begin{itemize} +\item 1st digit: space left +\item 2nd digit: space right +\item 3rd digit: space left and right +\item 4th digit: space relativ to the tip of the ``arrow'' +\end{itemize} + +The two macros \verb+\xrightarrow+ and \verb+\xleftarrow+ are defined as: +\begin{lstlisting} +\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}} +\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}} +\end{lstlisting} + + + +\section{Frames}\label{sec:ams-frames} +\marginpar{\CMD{boxed}}% +\AmSmath knows the macro \verb|\boxed|\index{boxed@\textbackslash boxed} which can +be used for inline $a\boxed{b+c}$ and displayed math expressions: + +\begin{align} +\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1} +\end{align} + +\begin{lstlisting} +\begin{align} +\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1} +\end{align} +\end{lstlisting} + +For coloured boxes use package \verb|empheq|. For an example see section \vref{sec:empheq}. + +\section{Greek letters}\label{sec:greek-AMS} +\marginpar{\CMD{pmb}\\\CMD{boldsymbol}}% +The \AmSmath package simulates a bold font for the greek letters by writing a greek %%% ----- Martin ----- +character twice with a small kerning. This is done with the macro +\verb|\pmb{}|\index{pmb@\textbackslash pmb}\index{Bold greek letters}. The +\verb|\mathbf{}| doesn't work with lower greek character. However, +using the \CMD{boldsymbol} macro from \AmSmath{} is the better way when the font +has a bold symbol. +\index{boldsymbol@\CMD{boldsymbol}} + +Uppercase greek letters are by default in upright mode. \AmSmath\ supports also +such letters in italic mode with a preceeding \verb+var+ e.g., \verb+\varGamma+ + +\medskip +\begin{tabular}{ccc|cc} +\emph{letter} & \CMD{pmb}\verb+{letter}+ & \CMD{boldsymbol}\verb+{letter}+ & \emph{letter} & \emph{italic}\\ +$\alpha$ & $\pmb{\alpha}$ & $\boldsymbol{\alpha}$ & $\Gamma$ & $\varGamma$\\ +$\beta$ & $\pmb{\beta}$ & $\boldsymbol{\beta}$ & $\Delta$ & $\varDelta$\\ +$\gamma$ & $\pmb{\gamma}$ & $\boldsymbol{\gamma}$ & $\Theta$ & $\varTheta$\\ +$\delta$ & $\pmb{\delta}$ & $\boldsymbol{\delta}$ & $\Lambda$ & $\varLambda$\\ +$\epsilon$ & $\pmb{\epsilon}$ & $\boldsymbol{\epsilon}$ & $\Xi$ & $\varXi$\\ +$\varepsilon$ & $\pmb{\varepsilon}$ & $\boldsymbol{\varepsilon}$ & $\Pi$ & $\varPi$\\ +$\zeta$ & $\pmb{\zeta}$ & $\boldsymbol{\zeta}$ & $\Sigma$ & $\varSigma$\\ +$\eta$ & $\pmb{\eta}$ & $\boldsymbol{\eta}$ & $\Upsilon$ & $\varUpsilon$\\ +$\theta$ & $\pmb{\theta}$ & $\boldsymbol{\theta}$ & $\Phi$ & $\varPhi$\\ +$\vartheta$ & $\pmb{\vartheta}$ & $\boldsymbol{\vartheta}$ & $\Psi$ & $\varPsi$\\ +$\iota$ & $\pmb{\iota}$ & $\boldsymbol{\iota}$ & $\Omega$ & $\varOmega$\\ +$\ldots$ & $\ldots$ & $\ldots$ +\end{tabular} + + +\section{Miscellaneous commands}\label{sec:misc-AMS} + +There are several commands which can be used in math mode:\marginpar{\CMD{overset}\\\CMD{underset}} + +Some examples are shown in table~\vref{cap:Different-Mathcommands-supported-AMS}. + +\begin{table}[htb] +\centering +{\renewcommand{\arraystretch}{2} +\begin{tabular}{r|>{\raggedright}p{2cm}} +\verb|$\underset{under}{baseline}$| \index{underset@\textbackslash underset} & +$\underset{under}{baseline}$\tabularnewline +\verb|$\overset{over}{baseline}$| \index{overset@\textbackslash overset} & +$\overset{over}{baseline}$\tabularnewline +\verb+\boldsymbol{\Omega}+ & $\boldsymbol{\Omega}$ +\end{tabular}} +\caption{Different mathcommands}\label{cap:Different-Mathcommands-supported-AMS} +\end{table} + +\CMD{underset} is a useful macro for having limits under non-operators +(see page~\pageref{sec:amsopn}). %%% ----- Martin ----- +\CMD{boldsymbol} can be used for a math symbol that remains unaffected by +\CMD{mathbf} if the current math font set includes a bold version of that symbol. + + +\section{Problems with \texttt{amsmath}} +\AmSmath{} is an excellent package with some ``funny features''. +When using an \verb+align+ environment inside a \verb+gather+ environment, it should +be centered just like the other lines. This is only true, when there is a number/tag or +an additional ampersand: + + +%\begin{LTXexample}[pos=t] +\begin{gather*} + \begin{align*} + m_2 &= m_2' + m_2''\\ + &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} + \end{align*}\\ + \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ +\end{gather*} +\begin{gather*} + \begin{align*} + m_2 &= m_2' + m_2''\\ + &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<==== + \end{align*}\\ + \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ +\end{gather*} +%\end{LTXexample} + +\begin{lstlisting} +\begin{gather*} + \begin{align*} + m_2 &= m_2' + m_2''\\ + &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} + \end{align*}\\ + \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ +\end{gather*} +\begin{gather*} + \begin{align*} + m_2 &= m_2' + m_2''\\ + &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<==== + \end{align*}\\ + \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ +\end{gather*} +\end{lstlisting} + + +This effect depends to the horizontal width, which is wrong in the first example, +in fact of a missing tag or number the right whitespace is cut, but the left one +is still there. The additional ampersand prevents \AmSmath{} to change the right +margin. + +Another kind of curiousity is the following example, which depends to the +same problem of cutting whitespace only on one side. + +\bigskip\noindent% +%\begin{LTXexample}[pos=t] +\fbox{% +\begin{minipage}{10cm} +\begin{align*} + a&=b \\ c&=d +\end{align*} +\end{minipage}} + +\noindent\fbox{% +\begin{minipage}{10cm} +\noindent\begin{align*} + a&=b \\ c&=d +\end{align*} +\end{minipage}} +%\end{LTXexample} + +\bigskip +\begin{lstlisting} +\bigskip\noindent\fbox{% +\begin{minipage}{10cm} +\begin{align*} + a&=b \\ c&=d +\end{align*} +\end{minipage}} + +\noindent\fbox{% +\begin{minipage}{10cm} +\noindent\begin{align*} + a&=b \\ c&=d +\end{align*} +\end{minipage}} +\end{lstlisting} + + + +\part{\TeX{} and math} + +There is in general no need to use the \TeX{} macros, because the ones defined with \LaTeX{} +or with \AmSmath{} are much more useful. Nevertheless there may be situations, where someone %%% ----- Martin ----- +has to use one of the \TeX{} macros or special \TeX{} math length. One can not expect, that all +macros work in the usual way, a lot of them are redefined by \LaTeX{} %%% ----- Martin ----- +or \AmSmath{}. On the other hand some of these basic macros or length definitions are used +in the \TeX{} way, so it might be interesting to have all declared in a short way for some +information. + +\section{Length registers} + +\subsection{\CMD{abovedisplayshortskip}} +\cIndex{abovedisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. + +\subsection{\CMD{abovedisplayskip}} +\cIndex{abovedisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. + +\subsection{\CMD{belowdisplayshortskip}} +\cIndex{belowdisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. + +\subsection{\CMD{belowdisplayskip}} +\cIndex{belowdisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. + + +\subsection{\CMD{delimiterfactor}} +\cIndex{delimiterfactor}The height of a delimiter is often not optimally calculated by \TeX{}. In some cases it is %%% ----- Martin ----- +too short. With \verb+\delimiterfactor+ one can correct this height. The delimiterheight +is $<\textrm{calculated height}>\cdot <\textrm{\#1}>/1000$ where \verb+#1+ is the parameter of +\verb+\delimiterfactor+. The default value is $901$. + +\begin{LTXexample}[width=0.4\linewidth] +\[ +y = \left\{% + \begin{array}{ll} + x^2+2x &\textrm{if }x<0,\\ + x^3 &\textrm{if }0\le x<1,\\ + x^2+x &\textrm{if }1\le x<2,\\ + x^3-x^2 &\textrm{if }2\le x. + \end{array}% +\right. +\] +\end{LTXexample} + +\begin{LTXexample}[width=0.4\linewidth] +\[ +\delimiterfactor=1500 +y = \left\{% + \begin{array}{ll} + x^2+2x &\textrm{if }x<0,\\ + x^3 &\textrm{if }0\le x<1,\\ + x^2+x &\textrm{if }1\le x<2,\\ + x^3-x^2 &\textrm{if }2\le x. + \end{array}% +\right. +\] +\end{LTXexample} + +\subsection{\CMD{delimitershortfall}} +\cIndex{delimitershortfall}Additionally to the forgoing \verb+\delimiterfactor+ one can modify the height of the +delimiter with another value. \TeX{} makes the delimiter larger than the values of +$<\textrm{calculated height}>\cdot <\textrm{delimiterfactor}>/1000$ and $<\textrm{calculated height}>-<\textrm{delimitershortfall}>$. This makes it possible to always get different heights %%% ----- Martin ----- +of a sequence of delimiters. + +\begin{LTXexample}[width=0.3\linewidth] +$x\cdot\left(\left(x^2-y^2\right)-3\right)$\\[7pt] + +$ +\delimitershortfall-1pt +x\cdot\left(\left(x^2-y^2\right)-3\right)$ +\end{LTXexample} + +\begin{LTXexample}[width=0.2\linewidth] +$\left(\left(\left(A\right)\right)\right)$\\[7pt] + +$\delimitershortfall-1pt +\left(\left(\left(A\right)\right)\right)$ +\end{LTXexample} + + +\subsection{\CMD{displayindent}} +\cIndex{displayindent}This is the left shift amount of a line holding displayed equation. +By default it is $0pt$ but +gets the value of an indented paragraph when there is an environment like the quotation one.\index{Indentation} + +The following formula is typeset in the usual way without modifying anything. + +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] + +Now we start a quotation environment which sets \CIndex{labelwidth} to new values for a +greater %%% ----- Martin ----- +left margin. + +\begin{itemize} +\item The following formula is typeset in the usual way without modifying anything. + +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] + +\item Now we write the same equation, but now with modifying \Index{displayindent}, it is set to +the negative \verb+\leftskip+: + +\[ + \displayindent=-\labelwidth + f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x +\] +\end{itemize} + +\begin{lstlisting} +\[ + \displayindent=-\leftskip + f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x +\] +\end{lstlisting} + +\subsection{\CMD{displaywidth}} +\cIndex{displaywidth}The width of the line holding a displayed equation, which is by default +\verb+\linewidth+. In the +second example the formula is centered for a display width of \verb+0.5\linewidth+. + +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] +\[ + \displaywidth=0.5\linewidth + f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x +\] +\begin{lstlisting} +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] +\[ + \displaywidth=0.5\linewidth + f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x +\] +\end{lstlisting} + +\subsection{\CMD{mathsurround}} +\cIndex{mathsurround}Extra space added when switching in and out of the +inline math mode (see section~\ref{subsec:whitespace}). + +\subsection{\CMD{medmuskip}} +\cIndex{medmuskip}See section~\ref{subsec:mathskip} for an example. + +\subsection{\CMD{mkern}} +\cIndex{mkern}Similiar to \verb+\kern+, but adds a math kern item to the current math list. Length must be a math unit. + +\subsection{\CMD{mskip}} +\cIndex{mskip}Similiar to \verb+\skip+, but adds math glue to the current math list. Length must be a math unit. + +\subsection{\CMD{muskip}} +\cIndex{muskip}Assigns a length with a math unit to one of the 256 \verb+\muskip+ register. + +\subsection{\CMD{muskipdef}} +\cIndex{muskipdef}Defines a symbolic name for a \verb+\muskip+ register. + +\subsection{\CMD{nonscript}} +\cIndex{nonscript}Ignores immediately following glue or kern in script and +scriptscript styles, which makes a redefinition of \verb+\mathchoice+ superfluous. + +\subsection{\CMD{nulldelimiterspace}} +\cIndex{nulldelimiterspace}This is the width of a null or missing delimiter, +\eg \verb+\right.+ or for the left one. + +\subsection{\CMD{predisplaysize}} +\cIndex{predisplaystyle}Is the effective width of the line preceeding a displayed equation, whether +\verb+\abovedisplayskip+ or \verb+abovedisplayshortskip+ is used for the vertical skip. + +\subsection{\CMD{scriptspace}} +\cIndex{scriptspace}The space inserted after an exponent or index, predefined as \verb+\scriptspace=0.5pt+ %%% ----- Martin ----- + +\subsection{\CMD{thickmuskip}} +\cIndex{thickmuskip}See section~\ref{subsec:mathskip}. + +\subsection{\CMD{thinmuskip}} +\cIndex{thinmuskip}The short version for positive skip is defined as \verb+\def\,{\mskip\thinmuskip}+ and the one +for a negative skip as \verb+\def\!{\mskip-\thinmuskip}+ (see also Section~\ref{subsec:mathskip}). + + +\begin{LTXexample}[width=0.35\linewidth] +$\sqrt 2 x$ -- $\sqrt 2\,x$\\ +$\sqrt{\log x}$ -- $\sqrt{\,\log x}$\\ +$P\left({1/\sqrt n}\right)$ -- $P\left({1/ \sqrt n}\,\right)$\\[8pt] + $[0,1)$ -- $[\,0,1)$\\ +$x^2/2$ -- $x^2\!/2$\\ +\end{LTXexample} + +\begin{LTXexample}[width=0.35\linewidth] +\[\int\int_D \mathrm{d}x\mathrm{d}y \quad + \int\!\int_D \mathrm{d}x\,\mathrm{d}y\] +\[\int\!\!\int_D \mathrm{d}x\,\,\mathrm{d}y \quad + \int\!\!\!\int_D \mathrm{d}x\,\,\,\mathrm{d}y\] +\[\int\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\mathrm{d}y \quad + \int\!\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\,\mathrm{d}y\] +\[\int\!\!\!\int_D \mathrm{d}x\,\mathrm{d}y\] +\end{LTXexample} + +\subsection{\CMD{medmuskip}} +See section~\ref{subsec:mathskip}. + + +\section{Math font macros} +\subsection{\CMD{delcode}} +\cIndex{delcode}Each character has not only a \CIndex{catcode} and \CIndex{mathcode} but also +a \verb+\delcode+ +which defines for a single chracter how it should look when used as a math delimiter. + +\subsection{\CMD{delimiter}} +\cIndex{delimiter}Every character can be declared as a delimiter, but \TeX{} +must know which characters +should be used for the default and the big size. For \LaTeX{} +the macro \CIndex{DeclareMathDelimiter} should be used (see section~\vref{subsec:delim}). + +In the following example \verb+\tdela+ is the character $0x22$ ($\uparrow$) from +font number $2$ (\verb+csmy+) and character $0x78$ from font number $3$ (\verb+cmex+) +for the big version. \verb+\tdelb+ is the same vice versa ($\downarrow$). +\begin{LTXexample}[width=0.35\linewidth] +\def\tdela{\delimiter"4222378\relax} +\def\tdelb{\delimiter"5223379\relax} + +$\tdela x-y\tdelb(x+y)=x^2-y^2$ + +\[\tdela\sum_{n=0}^\infty {1\over2^n}\tdelb^2 = 4\] + +\[\left\tdela\sum_{n=0}^\infty {1\over2^n}\right\tdelb^2 = 4\] +\end{LTXexample} + +\subsection{\CMD{displaystyle}} +\cIndex{displaystyle}See section~\ref{sec:Styles} for an example. + +\subsection{\CMD{fam}} +\cIndex{fam}When \TeX{} switches into the math mode, it typesets everything using one of the 16 +possible families of fonts. \verb+\fam+ is an internal register where other macros can check which font is the actual one. At the beginning \TeX{} starts with \verb+\fam=-1+. + +\bigskip +\noindent +\includegraphics{family} +\iffalse + +\begin{center} +\begin{tabular}{ll} +\verb+\fam=-1+ & $\fam=-1 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=0+ & $\fam=0 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=1+ & $\fam=1 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=2+ & $\fam=2 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=3+ & $\fam=3 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=4+ & $\fam=4 123abcABC\alpha\beta\gamma$\\ +\verb+\fam=5+ & $\fam=5 123abcABC\alpha\beta\gamma$ +\end{tabular} +\end{center} + + +\begin{LTXexample}[width=0.3\linewidth] +$\mathrm{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] +$\mathbf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] +$\mathit{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] +$\mathtt{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] +$\mathsf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] +$\mathnormal{123abcABC\alpha\beta\gamma (\the\fam)}$ +\end{LTXexample} +\fi + +\subsection{\CMD{mathaccent}} +\cIndex{mathaccent}Requires three parameter as one number, the class, the font family and the character. + +\begin{LTXexample}[width=0.3\linewidth] +\def\dA{\mathaccent"7015\relax} +{\Large $\dA{A}$} +\end{LTXexample} + +\subsection{\CMD{mathbin}} +\cIndex{mathbin}Declares a following character as a binary symbol with another +spacing before and behind such a symbol. + +\begin{LTXexample}[width=0.3\linewidth] +{\Large +$a|b \quad a\mathbin| b$} +\end{LTXexample} + +\subsection{\CMD{mathchar}} +\cIndex{mathchar}Declares a math character by three integer numbers as Parameters, giving its class, %%% ----- Martin ----- +font family, and font position. In the following example \verb+\mathchar+ defines a +character of class 1 (big operators), font family 3 (math extension font) and number +58 (big sum character). + +\begin{LTXexample}[width=0.3\linewidth] +{\Large +$a\sum\limits_{i=1}^{\infty} b \quad + a\mathchar"1358\limits_{i=1}^{\infty} b$} +\end{LTXexample} + +\subsection{\CMD{mathchardef}} +\cIndex{mathchardef}This is in principle the same as \CIndex{mathchar}, +it only allows to make such definitions permanent. + +\begin{LTXexample}[width=0.25\linewidth] +\bgroup +\mathchardef\sum="1358 +$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$\\[5pt] +\egroup + +$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$ +\end{LTXexample} + + +\subsection{\CMD{mathchoice}} +\cIndex{mathchoice}Specifies specific subformula sizes for the 4 main styles: +\CIndex{displaystyle} -- \CIndex{textstyle} -- +\CIndex{scriptstyle} -- \CIndex{scriptscriptstyle}. + +\begin{LTXexample}[width=0.15\linewidth] +\Large +\def\myRule{{% + \color{red}% + \mathchoice{\rule{2pt}{20pt}}{\rule{1pt}{10pt}}% + {\rule{0.5pt}{5pt}}{\rule{0.25pt}{2.5pt}}% + \mkern2mu}} +$\myRule\sum\limits_{\myRule i=1}^{\myRule\infty}% + \myRule\frac{\myRule\sqrt{\myRule i+1}}{\myRule i^2}$ +\end{LTXexample} + +\subsection{\CMD{mathclose}}\label{subsec:mathclose} +\cIndex{mathclose}Assigns class 5 (closing character) to the following +parameter, which can hold a single character or a subformula. + +\begin{LTXexample}[width=0.2\linewidth] +{\large +$A:\frac{B}{C}:D$\\[5pt] +$A\mathopen:\frac{B}{C}\mathclose: D $} +\end{LTXexample} + + +\subsection{\CMD{mathcode}} +\cIndex{mathcode}A math font is far different from a text font. A lot of the characters has to be defined with +\verb+\mathcode+, which defines the character with its class, font family and character number, \eg +\verb+\mathcode`\<="313C+. It defines the character ``<''{} as a realtion symbol (class 3) from +the font family 1 and the character number 0x3C, which is 60 decimal. + +\subsection{\CMD{mathop}} +\cIndex{mathop}Assigns class 1 (large operator) to the parameter, which can be a single character or a subformula. + +\begin{LTXexample}[width=0.2\linewidth] +\[ A_{i=1}^{\infty} \] +\[ \mathop{A}_{i=1}^{\infty} \] +\end{LTXexample} + +\subsection{\CMD{mathopen}} +\cIndex{mathopen}Vice versa to \verb+\mathclose+ (see section~\ref{subsec:mathclose}). + + +\subsection{\CMD{mathord}} +\cIndex{mathord}Assigns class 0 (ordinary character) to the following parameter, which can be a single character +or a subformula. + +\begin{LTXexample}[width=0.2\linewidth] +{\large +$y = f(x)$\\[5pt] +$y \mathord= f(x)$} +\end{LTXexample} + +\subsection{\CMD{mathpunct}} +\cIndex{mathpunct}Assigns class 6 (punctuation) to the following parameter, which can be a single character +or a subformula (see section~\ref{subsec:dot-comma} for an example). + +\subsection{\CMD{mathrel}} +\cIndex{mathrel}Assigns class 3 (relation) to the following parameter, which can be a single character +or a subformula. + +\begin{LTXexample}[width=0.25\linewidth] +{\large +$x_1 o x_2 o x_3$\\[5pt] +$x_1\mathrel o x_2\mathrel o x_3$} +\end{LTXexample} + + +\subsection{\CMD{scriptfont}} +\cIndex{scriptfont}Specifies the scriptstyle font (used for super/subscript) for a family. + +\begin{LTXexample}[width=0.25\linewidth] +$A_1$ +\font\tenxii=cmr12 +\scriptfont0=\tenxii +$A_1$ +\end{LTXexample} + + +\subsection{\CMD{scriptscriptfont}} +\cIndex{scriptscriptfont}Specifies the scriptscriptstyle font for a family. + +\subsection{\CMD{scriptscriptstyle}} +\cIndex{scriptscriptstyle}Selects scriptscript style for the following characters. + +\subsection{\CMD{scriptstyle}} +\cIndex{scriptstyle}Selects script style for the following characters. + + +\subsection{\CMD{skew}} +\cIndex{skew}Especially for italic characters double accents are often misplaced. \verb+\skew+ has three arguments +\begin{description} +\item[horizontal shift:] A value in math units for the additional shift of the accent. +\item[the accent:] The symbol which is placed above the character. +\item[the character:] This is in general a single character, but can also include itself an accent. +\end{description} + +\AmSmath\ redefines the setting of double accents. This is the reason why there are only a few +cases where someone has to use \verb+\skew+ when the package \PIndex{amsmath} is loaded, like +in this document. + +\begin{LTXexample}[width=0.2\linewidth] +\large +$\tilde i$ \qquad $\tilde{A}$\\[5pt] +$\skew{3}{\tilde}{i}$ \qquad $\skew{7}{\tilde}{A}$ +\end{LTXexample} + +\subsection{\CMD{skewchar}} +\cIndex{skewchar}Is -1 or the character (reference symbol) used to fine-tune the positioning of math accents. + +\subsection{\CMD{textfont}} +\cIndex{textfont}Specifies the text font for a family. + +\subsection{\CMD{textstyle}} +\cIndex{textstyle}Selects the text style for the following characters. + + + +\section{Math macros} + + +\subsection{\CMD{above}} +\cIndex{above} +\begin{LTXexample}[width=0.2\linewidth] +$a\above0pt b$\\[8pt] + +${a\above1pt b}$\\[8pt] + +${a\above2.5pt b}$\\[8pt] + +$\displaystyle{a\above0pt b}$ +\end{LTXexample} + + + +\subsection{\CMD{abovewithdelims}} +\cIndex{abovewithdelims} +\begin{LTXexample}[width=0.2\linewidth] +$a\abovewithdelims()0pt b$\\[8pt] + +\def\fdelimA{\abovewithdelims\{)1.0pt} +${a\fdelimA b}$\\[8pt] + +\def\fdelimB{\abovewithdelims[]2.0pt} +${a\fdelimB b}$\\[8pt] + +\def\fdelimC{\abovewithdelims\{.0pt} +$\displaystyle{a\fdelimC b}$ +\end{LTXexample} + +\subsection{\CMD{atop}} +\cIndex{atop} + +\begin{LTXexample}[width=0.2\linewidth] +$a\atop b$\\[8pt] + +$({n \atop k}) = {n!\above1pt k!(n-k)!}$\\[8pt] + +$\displaystyle{a\atop b}$ +\end{LTXexample} + + +\subsection{\CMD{atopwithdelims}} +\cIndex{atopwithdelims} +\begin{LTXexample}[width=0.2\linewidth] +$a\atopwithdelims() b$\\[8pt] + +${n \atopwithdelims() k} = {n!\above1pt k!(n-k)!}$\\[8pt] + +$\displaystyle{a\atopwithdelims\{. b}$ +\end{LTXexample} + +\subsection{\CMD{displaylimits}} +\cIndex{displaylimits}Resets the conventions for using limits with operators to the standard for the used environment. + +\subsection{\CMD{eqno}}\label{subsec:eqno} +\cIndex{eqno}Puts an equation number at the right margin, the parameter can hold anything. \verb+\eqno+ places +only the parameter, but doesn't increase any equation counter. + +\begin{LTXexample}[width=0.5\linewidth] +\[ y=f(x) \eqno{(A12)} \] +\end{LTXexample} + +\subsection{\CMD{everydisplay}} +\cIndex{everydisplay}Inserts the parameter at the start of every switch to display math mode. + +\begin{LTXexample}[width=0.4\linewidth] +\everydisplay{\color{red} +} +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] +\[ g(x) = \int \frac{\sin^2 x}{x^2}\,\mathrm{d}x \] +\end{LTXexample} + +\subsection{\CMD{everymath}} +\cIndex{everymath}Same as \CIndex{everydisplay}, but now for the inline mode. +In the following example +the displaystyle is used (besides using color red) for every inline math expression. + +\bgroup +\begin{LTXexample}[width=0.45\linewidth] +\everymath{\color{red}% + \displaystyle} +\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] +Instead of $\frac{\sin x}{x}$ + now with $\frac{\cos x}{x}$: +\[ g(x) = \int \frac{\cos x}{x}\,\mathrm{d}x \] +\end{LTXexample} +\egroup + +Pay attention for side effects on footnotes and other macros which use the math mode for superscript +and other math related modes. In this case you'll get the footnotes also in red. + +\subsection{\CMD{left}} +\cIndex{left}\TeX{} calculates the size of the following delimiter needed at the left side of a formula. +Requires an additional \verb+right+. + +\subsection{\CMD{leqno}} +\cIndex{leqno}Vice versa to \verb+\eqno+ (see section~\vref{subsec:eqno}). + +\subsection{\CMD{limits}} +\cIndex{limits}Typesets limits above and/or below operators (see section~\vref{sec:limits}). + +\subsection{\CMD{mathinner}} +\cIndex{mathinner}Defines the following parameter as subformula. + +\subsection{\CMD{nolimits}} +\cIndex{nolimits}The opposite of \CIndex{limits}, instead of above/below limits are placed to the right of large +operators (class 1). + + +\subsection{\CMD{over}} +\cIndex{over}Is equivalent to the fraction macro of \LaTeX{} and equivalent to the +\verb+\overwithdelims+, see section~\vref{subsec:overwithdelims}. + +\begin{LTXexample}[width=0.2\linewidth] +$ {a\over b} \qquad {{m\over n}\over{a+b}} $ +\[ {m\over n}\over{a+b} \] +\end{LTXexample} + + +\subsection{\CMD{overline}} +\cIndex{overline}Puts a line over the following character or subformula and has the same problems with different +heights as underlines (see section~\ref{subsec:underline}). + +\begin{LTXexample}[width=0.2\linewidth] +$\overline{x}+\overline{y}=\overline{z}$\\ +\let\ol\overline +$ \ol{x} + \ol{A} = \ol{z} $\\[5pt] +\def\yPh{\vphantom{A}} +$ \ol{x\yPh} + \ol{A} = \ol{z\yPh} $ +\end{LTXexample} + +\subsection{\CMD{overwithdelims}}\label{subsec:overwithdelims} +\cIndex{overwithdelims}Is a generalized fraction command with preset fraction bar thickness. %%% ----- Martin ----- + +\begin{LTXexample}[width=0.25\linewidth] +$ {a\overwithdelims() b} \qquad {{m\over n}\overwithdelims[]{a+b}} $ +\[ {m\over n}\overwithdelims\{.{a+b} \] +\end{LTXexample} + + +\subsection{\CMD{radical}} +\cIndex{radical}Makes a radical atom from the delimiter (27-bit number) and the math field. + +\begin{LTXexample}[width=0.2\linewidth] +\def\mySqrt{\radical"0270371\relax} +$ \mySqrt{\frac{1}{7}} $\\[5pt] + +\def\mySqrt{\radical"0270372\relax} +$ \mySqrt{\frac{1}{7}} $\\[5pt] + +\def\mySqrt{\radical"0270373\relax} +$ \mySqrt{\frac{1}{7}} $\\[5pt] + +\def\mySqrt{\radical"0270374\relax} +$ \mySqrt{\frac{1}{7}} $\\[5pt] +\end{LTXexample} + +\subsection{\CMD{right}} +\cIndex{right}Opposite to \verb+\left+, makes \TeX{} calculate the size of the +delimiter needed at the right of a formula. + +\subsection{\CMD{underline}}\label{subsec:underline} +\cIndex{underline}When there is a combination of variables with and without an index, the underlines are typeset %%% ----- Martin ----- +with a different depth. Using \verb+\vphantom+ in this case is a good choice. + +\begin{LTXexample}[width=0.2\linewidth] +$\underline{x}+\underline{y}=\underline{z}$\\ + +\let\ul\underline +\def\yPh{\vphantom{y}} +$ \ul{x\yPh} + \ul{y} = \ul{z\yPh} $\\ + +$ \ul{x_1} + \ul{y_2} = \ul{z_3} $ +\end{LTXexample} + +\subsection{\CMD{vcenter}} +\cIndex{vcenter}Centers vertical material with respect to the axis. + + +\section{Math penalties} + +\subsection{\CMD{binoppenalty}} +\cIndex{binoppenalty}A penalty for breaking math expressions between lines in a paragraph. TeX breaks lines only +when the binary symbol is not the last one and when the penalty is below 10,000. + +\subsection{\CMD{displaywidowpenalty}} +\cIndex{displaywidowpenalty}The penalty which is added after the penultimate line immediately preceeding a display math formula. + +\subsection{\CMD{postdisplaypenalty}} +\cIndex{postdisplaypenalty}Is added immediately after a math display ends. + +\subsection{\CMD{predisplaypenalty}} +\cIndex{predisplaypenalty}Is added immediately before a math display starts. + +\subsection{\CMD{relpenalty}} +\cIndex{relpenalty}The penalty for a line break after a relation symbol (if a break is possible). + + +\part{Other packages} +The following sections are not a replacement for the package documentation! +\section{List of available math packages} +\markboth{Math packages}{Math packages} + +\begin{center} +\noindent +\begin{tabular}{llll} +\href{http://www.dante.de/CTAN/help/Catalogue/entries/accents.html}{accents}& +\href{http://www.dante.de/CTAN/help/Catalogue/entries/alphalph.html}{alphalph}& +\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsart.html}{amsart}& +\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsbook.html}{amsbook}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsbsy.html}{amsbsy}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscd.html}{amscd}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscls.html}{amscls}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsfonts.html}{amsfonts}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amslatex.html}{amslatex}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsltx11.html}{amsltx11}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsmath.html}{amsmath}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt.html}{amsppt}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt1.html}{amsppt1}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsproc.html}{amsproc}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssym.html}{amssym (plain TeX)}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssymb.html}{amssymb (LaTeX)}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstex.html}{amstex (Plain TeX)}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstext.html}{amstext}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsthm.html}{amsthm}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/bez123.html}{bez123}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/bitfield.html}{bitfield}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/brclc.html}{brclc}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/breqn.html}{breqn}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/cancel.html}{cancel}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/cases.html}{cases}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/comma.html}{comma}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/datenumber.html}{datenumber}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/diagxy.html}{diagxy}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/doublestroke.html}{doublestroke}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/easyeqn.html}{easyeqn}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/easybmat.html}{easybmat}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/easymat.html}{easymat}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/eqnarray.html}{eqnarray}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/esvect.html}{esvect}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/fixmath.html}{fixmath}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/fltpoint.html}{ftlpoint}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/icomma.html}{icomma}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/leftidx.html}{leftidx}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathdots.html}{mathdots}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathtools.html}{mathtools}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathematica.html}{mathematica}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/mil3.html}{mil3}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/mtbe.html}{mtbe}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/nath.html}{Nath}\\ +\href{http://www.dante.de/CTAN//help/Catalogue/entries/numprint.html}{numprint}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/random.html}{random}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/romannum.html}{romannum}& +\href{http://www.dante.de/CTAN//help/Catalogue/entries/texaide.html}{TeXaide} +\end{tabular} +\end{center} + +The following examples depend on the listed versions of the packages: %%% ----- Martin ----- + +{\small +\begin{verbatim} + amsopn.sty 1999/12/14 v2.01 operator names + bm.sty 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi) + empheq.sty 2004/08/03 v2.11 Emphasizing equations (MH) + amscd.sty 1999/11/29 v2.0 + accents.sty 2000/08/06 v1.2 Math Accent Tools + framed.sty 2002/12/29 v 0.5: framed or shaded text with page breaks + pstcol.sty 2001/06/20 v1.1 PSTricks color colompatibility (DPC) +pstricks.sty 2004/05/06 v0.2k LaTeX wrapper for `PSTricks' (RN,HV) +pstricks.tex 2003/03/07 v97 patch 15 `PSTricks' (tvz) +pst-node.sty 1997/03/25 package wrapper for PSTricks pst-node.tex +delarray.sty 1994/03/14 v1.01 array delimiter package (DPC) + xypic.sty 1999/02/16 Xy-pic version 3.7 + exscale.eps Graphic file (type veps) +\end{verbatim} +} + + +\subsection{\texttt{accents}}\label{sec:package-accent} +If you want to write for example an underlined M, then you can do it by %%% ----- Martin ----- + +\medskip +\begin{tabular}{ll} +\verb|\underline{$M$}| & \underline{$M$}\\ +\verb|\underbar{$M$}| & \underbar{$M$}\\ +\verb|\underaccent{\bar}{M}| & $\underaccent{\bar}{M}$ +\end{tabular} +\medskip + +As seen, there is no difference between \CMD{underline} and \CMD{underbar}. For %%% ----- Martin ----- +some reasons it may be better to use the \PIndex{accent} package with the +\CMD{underaccents} macro. + +\subsection{\texttt{amscd} -- commutative diagrams} + +The \PIndex{amscd} package is part of the \AmSmath bundle +or available at CTAN% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amscd.dtx}% +{CTAN://macros/latex/required/amslatex/math/amscd.dtx}} and has no options for the +\verb|\usepackage| command. +\texttt{amscd} does not support diagonal arrows but is much %%% ----- Martin ----- +easier to handle than the complex \PIndex{pstricks} package or +the \PIndex{xypic} package. On the other hand simple diagrams +can be written with the \UIndex{array} or look at \cite{taylor00}. + +\[ +\begin{CD} + R\times S\times T @>\text{restriction}>> S\times T \\ + @VprojVV @VVprojV \\ + R\times S @<<\text{inclusion}< S +\end{CD} +\] + +\begin{lstlisting} +\[ +\begin{CD} + R\times S\times T @>\text{restriction}>> S\times T \\ + @VprojVV @VVprojV \\ + R\times S @<<\text{inclusion}< S +\end{CD} +\] +\end{lstlisting} + + +\subsection{\texttt{amsopn}}\label{sec:amsopn} +With the \PIndex{amsopn} package it is very easy to declare new math operators, which are written in +upright mode: + +$\underset{s=p}{Res}\quad\text{versus}\quad\underset{s=p}{\Res}$ + +\medskip +\begin{lstlisting} +\documentclass[10pt]{article} +\usepackage{amsmath} +\usepackage{amsopn} +\DeclareMathOperator{\Res}{Res} +\begin{document} +$\underset{s=p}{Res}\quad\underset{s=p}{\Res}$ +\end{document} +\end{lstlisting} + +Table~\ref{tab:amsopn} shows the predefined operatornames of \verb+amsopn+. + +\begin{table}[htb] +\centering +\begin{tabular}{llllll} +\verb+\arccos+ & $\arccos$ & \verb+\arcsin+ & $\arcsin$ & \verb+\arctan+ & $\arctan$\\ +\verb+\arg+ & $\arg$ & \verb+\cos+ & $\cos$ & \verb+\cosh+ & $\cosh$\\ +\verb+\cot+ & $\cot$ & \verb+\coth+ & $\coth$ & \verb+\csc+ & $\csc$\\ +\verb+\deg+ & $\deg$ & \verb+\det+ & $\det$ & \verb+\dim+ & $\dim$\\ +\verb+\exp+ & $\exp$ & \verb+\gcd+ & $\gcd$ & \verb+\hom+ & $\hom$\\ +\verb+\inf+ & $\inf$ & \verb+\injlim+ & $\injlim$ & \verb+\ker+ & $\ker$\\ +\verb+\lg+ & $\lg$ & \verb+\lim+ & $\lim$ & \verb+\liminf+ & $\liminf$\\ +\verb+\limsup+ & $\limsup$ & \verb+\ln+ & $\ln$ & \verb+\log+ & $\log$\\ +\verb+\max+ & $\max$ & \verb+\min+ & $\min$ & \verb+\Pr+ & $\Pr$\\ +\verb+\projlim+& $\projlim$& \verb+\sec+ & $\sec$ & \verb+\sin+ & $\sin$\\ +\verb+\sinh+ & $\sinh$ & \verb+\sup+ & $\sup$ & \verb+\tan+ & $\tan$\\ +\verb+\tanh+ & $\tanh$ +\end{tabular} +\caption{The predefined operators of \texttt{amsopn.sty}}\label{tab:amsopn} +\end{table} + + +\subsection{\texttt{bigdel}}\label{sec:bigdelim} +This is a very useful package together with the \PIndex{multirow} package. +In the following example we need additional parentheses for a different +number of rows. This is also possible with the \UIndex{array}, +but not as easy as with the \PIndex{bigdelim} package. The trick is that you need one +separate column for a big delimiter, but with empty cells in all rows, which +the delimiter spans. + +\[ + \begin{pmatrix} + & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\ + \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\ + & \vdots\\ + & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\ + & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} & + \rdelim\}{3}{3cm}[some more text]\\ + & \vdots\\ + & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\ + & \vdots \\ + \end{pmatrix} +\] + +\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] +\[ + \begin{pmatrix} + & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\ + \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\ + & \vdots\\ + & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\ + & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} & + \rdelim\}{3}{3cm}[some more text]\\ + & \vdots\\ + & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\ + & \vdots \\ + \end{pmatrix} +\] +\end{lstlisting} + +As seen in the above listing the left big delimiter is placed in the first +column, all other rows start with second column. It is possible to use all +columns above and below the delimiter. For the \UIndex{array} +there must be two more columns defined, in case of a big delimiter left and +right. The syntax of \CIndex{ldelim} and \CIndex{rdelim} is: +% +\begin{verbatim} +\ldelim{}{}[] +\rdelim{}{}[] +\end{verbatim} + +Any delimiter which is possible for the \CIndex{left} or \CIndex{right} command +is allowed, \eg ``\verb/()[]{}|/''. The text is an optional argument and +always typeset in text mode. + +\subsection{\texttt{bm}}\label{sec:bm} +By default the math macro \CIndex{mathbf} writes everything in bold and in upright mode +$\mathbf{y=f(x)}$ (\verb|$\mathbf{y=f(x)}$|), but it should be in italic mode especially +for variables $\bm{y=f(x)}$ (\verb|$\bm{y=f(x)}$|), which is possible with the package \PIndex{bm}. +For writing a whole formula in bold have a look at section~\vref{sec:boldmath}. + + +\subsection{\texttt{braket}}\label{sec:braket} +It is available at + \href{http://www.ctan.org/tex-archive/macros/latex/contrib/other/misc/braket.sty}% +{CTAN://macros/latex/contrib/other/misc/braket.sty} +and provides several styles for writing math expressions inside brakets. For example: + +\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \] + +\begin{lstlisting} +\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \] +\end{lstlisting} + +\noindent looks not quite right and it is not really easy to get the first vertical line in the same +size as the outer braces. Some solution may be using \CIndex{vphantom}: + +\[ +\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\} +\] + +\begin{lstlisting} +\[ +\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\} +\] +\end{lstlisting} + +The package \PIndex{braket} has the macros + +\begin{lstlisting} +\Bra{} +\Ket{} +\Braket{} +\Set{} +\end{lstlisting} + +\noindent and the same with a leading lower letter, which are not really interesting. + +\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \] +\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] + +\begin{lstlisting} +\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \] +\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] +\end{lstlisting} + +The difference between the \CIndex{Set} and the \CIndex{Braket} macro is the handling of the +vertical lines. In \CIndex{Set} only the first one gets the same size as the +braces\index{Braces} and in \CIndex{Braket} all. + +\[ \Braket{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\] +\[ \Set{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\] +\begin{lstlisting} +\[\Braket{\phi | \frac{\partial^2}{\partial t^2} | \psi}\] +\[\Set{\phi | \frac{\partial^2}{\partial t^2} | \psi}\] +\end{lstlisting} + + +\CMD{Bra} and \CMD{Ket} do nothing with the inner vertical lines. + + +\subsection{\texttt{cancel}}\label{cancel.sty} +This is a nice package for canceling anything in mathmode with a slash, +backslash or a \verb+X+. To get +a horizontal line we can define an additional macro called \CIndex{hcancel} +with an optional argument +for the line color (requires package \PIndex{color}): +% +\begin{lstlisting} +\newcommand\hcancel[2][black]{\setbox0=\hbox{#2}% + \rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +\end{lstlisting} + +It is no problem to redefine the \CIndex{cancel} macros to get also colored lines. +A horizontal line for +single characters is also decribed in section~\vref{sec:Accents}. + +\medskip +\noindent +\verb+\cancel+: $f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm] +\verb+\bcancel+: $\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm] +\verb+\xcancel+: $\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm] +\verb+\hcancel+: $\hcancel{3}\qquad\hcancel[red]{1234567}$ + +\bigskip +\begin{lstlisting} +$f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm] +$\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm] +$\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm] +$\hcancel{3}\qquad\hcancel[red]{1234567}$ +\end{lstlisting} + + +\subsection{\texttt{cool}}\label{cool} +The \PIndex{cool} package defines a lot of special mathematical expressions +to use them by the macro name. The following list shows only some of +them, for more informations look at the example file, which comes with +the package. + +\bgroup +\parindent=0pt +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{Sin}\verb|{x}| & $\displaystyle \Sin{x}$\\ +\CIndex{Cos}\verb|{x}| & $\displaystyle \Cos{x}$\\ +\CIndex{Tan}\verb|{x}| & $\displaystyle \Tan{x}$\\ +\CIndex{Csc}\verb|{x}| & $\displaystyle \Csc{x}$\\ +\CIndex{Sec}\verb|{x}| & $\displaystyle \Sec{x}$\\ +\CIndex{Cot}\verb|{x}| & $\displaystyle \Cot{x}$ +\end{tabular} + +\bigskip +\Style{ArcTrig=inverse}% +\CMD{Style\{ArcTrig=inverse\}} (default) + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{ArcSin}\verb|{x}|& $\displaystyle \ArcSin{x}$\\ +\CIndex{ArcCos}\verb|{x}|& $\displaystyle \ArcCos{x}$\\ +\CIndex{ArcTan}\verb|{x}|& $\displaystyle \ArcTan{x}$ +\end{tabular} + +\bigskip +\Style{ArcTrig=arc} +\CMD{Style\{ArcTrig=arc\}} + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{ArcSin}\verb|{x}| & $\displaystyle \ArcSin{x}$\\ +\CIndex{ArcCos}\verb|{x}| & $\displaystyle \ArcCos{x}$\\ +\CIndex{ArcTan}\verb|{x}| & $\displaystyle \ArcTan{x}$\\ +\CIndex{ArcCsc}\verb|{x}| & $\displaystyle \ArcCsc{x}$\\ +\CIndex{ArcSec}\verb|{x}| & $\displaystyle \ArcSec{x}$\\ +\CIndex{ArcCot}\verb|{x}| & $\displaystyle \ArcCot{x}$ +\end{tabular} + + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{Factorial}\verb|{n}| & $\displaystyle \Factorial{n}$\\ +\CIndex{DblFactorial}\verb|{n}| & $\displaystyle \DblFactorial{n}$\\ +\CIndex{Binomial}\verb|{n}{k}| & $\displaystyle \Binomial{n}{k}$\\ +\CIndex{Multinomial}\verb|{1,2,3,4}|& $\displaystyle \Multinomial{1,2,3,4}$ +\end{tabular} + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{GammaFunc}\verb|{x}| & $\displaystyle \GammaFunc{x}$\\ +\CIndex{IncGamma}\verb|{a}{x}| & $\displaystyle \IncGamma{a}{x}$\\ +\CIndex{GenIncGamma}\verb|{a}{x}{y}|& $\displaystyle \GenIncGamma{a}{x}{y}$ \\ +\CIndex{RegIncGamma}\verb|{a}{x}|& $\displaystyle \RegIncGamma{a}{x}$ \\ +\CIndex{RegIncGammaInv}\verb|{a}{x}|& $\displaystyle \RegIncGammaInv{a}{x}$ \\ +\CIndex{GenRegIncGamma}\verb|{a}{x}{y}| & $\displaystyle \GenRegIncGamma{a}{x}{y}$\\ +\CIndex{GenRegIncGammaInv}\verb|{a}{x}{y}|& $\displaystyle \GenRegIncGammaInv{a}{x}{y}$\\ +\CIndex{Pochhammer}\verb|{a}{n}| & $\displaystyle \Pochhammer{a}{n}$ \\ +\CIndex{LogGamma}\verb|{x}| & $\displaystyle \LogGamma{x}$ +\end{tabular} + + +\bigskip + +\begin{tabular}{@{}ll@{}} +\CIndex{Hypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \Hypergeometric{0}{0}{}{}{x}$\\ +\CIndex{Hypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \Hypergeometric{0}{1}{}{b}{x}$ +\end{tabular} + + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{RegHypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \RegHypergeometric{0}{0}{}{}{x}$\\ +\CIndex{RegHypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \RegHypergeometric{0}{1}{}{b}{x}$ +\end{tabular} + + + +\bigskip +\begin{tabular}{@{}l@{}} +\CIndex{MeijerG}\verb|[a,b]{n}{p}{m}{q}{x}| \\ + \hspace*{2cm} $\displaystyle \MeijerG[a,b]{n}{p}{m}{q}{x}$ \\ +\CIndex{MeijerG}\verb|{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}| \\ + \hspace*{2cm} $\displaystyle \MeijerG{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}$ +\end{tabular} + +\index{Zeta!Functions} +\index{Polylogarithm} +\index{Zeta!Riemann} +\index{Zeta!Hurwitz} +\index{Zeta} + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{RiemannZeta}\verb|{s}| & $\displaystyle \RiemannZeta{s}$\\ +\CIndex{Zeta}\verb|{s}| & $\displaystyle \Zeta{s}$\\ +\CIndex{HurwitzZeta}\verb|{s}{a}|& $\displaystyle \HurwitzZeta{s}{a}$\\ +\CIndex{Zeta}\verb|{s,a}| & $\displaystyle \Zeta{s,a}$ \\ +\CIndex{RiemannSiegelTheta}\verb|{x}|& $\displaystyle \RiemannSiegelTheta{x}$ \\ +\CIndex{RiemannSiegelZ}\verb|{x}| & $\displaystyle \RiemannSiegelZ{x}$ \\ +\CIndex{StieltjesGamma}\verb|{n}| & $\displaystyle \StieltjesGamma{n}$ +\end{tabular} + + +\index{Mathieu!Functions} +\index{Mathieu!Characteristics} + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{MathieuC}\verb|{a}{q}{z}| & $\displaystyle \MathieuC{a}{q}{z}$ \\ +\CIndex{MathieuS}\verb|{a}{q}{z}| & $\displaystyle \MathieuS{a}{q}{z}$ +\end{tabular} + + +\bigskip +\begin{tabular}{@{}ll@{}} +\CIndex{MathieuCharacteristicA}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicA{r}{q}$ \\ +\CIndex{MathieuCharisticA}\verb|{r}{q}| & $\displaystyle \MathieuCharisticA{r}{q}$ \\ + +%%%%%%% Characteristic Value of Even Mathieu Fucntion b_r(q) +\CIndex{MathieuCharacteristicB}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicB{r}{q}$ \\ +\CIndex{MathieuCharisticB}\verb|{r}{q}|& $\displaystyle \MathieuCharisticB{r}{q}$ \\ + +%%%%%%%% Characteristic Exponent of a Mathieu Fucntion r(a,q) +\CIndex{MathieuCharacteristicExponent}\verb|{a}{q}|& $\displaystyle \MathieuCharacteristicExponent{a}{q}$\\ +\CIndex{MathieuCharisticExp}\verb|{a}{q}|& $\displaystyle \MathieuCharisticExp{a}{q}$ +\end{tabular} +\egroup + +\subsection{\texttt{delarray}}\label{delarray} + +Package \PIndex{delarray}% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/tools/delarray.dtx}{CTAN://macros/latex/required/tools/delarray.dtx}% +} supports different delimiters which are defined together with the +beginning of an array: + +\begin{lstlisting} +\begin{array}{cc} +... +\end{lstlisting} + +\noindent defines an array with two centered columns and the delimiters\\ +``\texttt{}{}'', \eg ``\texttt{()}{}''. + +\medskip{} +\begin{minipage}[c]{0.45\textwidth}% +\begin{lstlisting} +\[ +A=\begin{array}({cc}) + a & b\\ + c & d +\end{array} +\] +\end{lstlisting} + +\end{minipage}% +\hfill{}\begin{minipage}[c]{0.45\textwidth}% +\[ +A=\begin{array}({cc}) +a & b \\ +c & d +\end{array} +\] +\end{minipage}% + +\medskip{} + +The \PIndex{delarray} package expects a pair of delimiters. If you need only +one (like the cases structure) then use the dot for an ``empty'' +delimiter, \eg + +\medskip{} +\begin{minipage}[c]{0.45\textwidth}% +\begin{lstlisting} +\[ +A=\begin{array}\{{cc}. + a & b\\ + c & d +\end{array} +\] +\end{lstlisting} + +\end{minipage}% +\hfill{}\begin{minipage}[c]{0.45\textwidth}% +\[A=\begin{array}\{{cc}. +a & b \\ +c & d +\end{array}\] +\end{minipage}% + +\medskip{} + +\noindent which is a useful command for a cases structure without the \AmSmath +package, which is described in the \AmSmath part. + + +\subsection{\texttt{dotseqn}}\label{dotseqn} +This package% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/dotseqn/}% +{CTAN://macros/latex/contrib/dotseqn}} fills the space between the math +expression and the equation +number with dots. Expect problems when using this package together with \AmSmath. + +\begingroup +\makeatletter +% package couldn't be loaded, it redefines the math +% environments +\newcommand\EqnDots{\leaders\hbox{\kern4\p@ .\kern4\p@}\hfill} +\@ifundefined{mathindent}{\newdimen\mathindent \mathindent\leftmargini}{} +\renewcommand{\[}{\relax \ifmmode\@badmath \else + \begin{trivlist}% + \@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty + \item[]\leavevmode \hbox to\linewidth\bgroup $\m@th\displaystyle %$ + \hskip\mathindent\bgroup + \fi} +\renewcommand{\]}{\relax\ifmmode \egroup $\hfil% $ + \egroup \end{trivlist}% + \else \@badmath \fi} +\renewenvironment{equation}% + {\@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty + \refstepcounter{equation}\trivlist \item[]\leavevmode + \hbox to\linewidth\bgroup $\m@th% $ + \displaystyle \hskip\mathindent}% + {$\EqnDots % $ Replace `\hfil' with dotted leaders `\EqnDots'. + \displaywidth\linewidth\hbox{\@eqnnum}\egroup \endtrivlist} +\renewenvironment{eqnarray}{% + \stepcounter{equation}% + \def\@currentlabel{\p@equation\theequation}% + \global\@eqnswtrue \m@th \global\@eqcnt\z@ \tabskip\mathindent + \let\\\@eqncr \setlength\abovedisplayskip\topsep + \ifvmode \addtolength\abovedisplayskip\partopsep \fi + \addtolength\abovedisplayskip\parskip + \setlength\belowdisplayskip\abovedisplayskip + \setlength\belowdisplayshortskip\abovedisplayskip + \setlength\abovedisplayshortskip\abovedisplayskip + $$\everycr{}\halign to\linewidth% $$ + \bgroup + \hskip\@centering + $\displaystyle\tabskip\z@skip{##}$\@eqnsel&% + \global\@eqcnt\@ne \hfil${\DEQ@acs##\DEQ@acs}$\hfil&% + \global\@eqcnt\tw@ $\displaystyle{##}$\hskip\@centering\cr% + }% end of "\begin" part + {\@@eqncr + \noalign{% vertical skip up to overlay phantom line + \penalty\@M \vskip-\prevdepth + \edef\@tempa{\omit\span\omit\span\omit % span three columns + \vrule\@depth\the\prevdepth \@width\z@ % strut of proper depth + \kern-\mathindent \kern\linewidth}% % full line width + \nointerlineskip \expandafter % use saved |\@tempa| outside group + }\@tempa\cr + \egroup + \global\advance\c@equation\m@ne$$% $$ + \global\@ignoretrue + } +\def\@@eqncr{\let\reserved@a\@empty + \ifcase\@eqcnt \def\reserved@a{& &}\or \def\reserved@a{&}\fi + \reserved@a + \if@eqnsw \egroup $\EqnDots \@eqnnum $\bgroup \stepcounter{equation}% + \fi \global\@eqnswtrue\global\@eqcnt\z@\cr} +\def\DEQ@acs{\hskip\tw@\arraycolsep} +\makeatother +\begin{eqnarray} + F(x) &=& \int f(x)\,\mathrm{d}x + C +\end{eqnarray} +% +\begin{equation} + F(x)=\int f(x)\,\mathrm{d}x + C +\end{equation} +\endgroup + +\begin{lstlisting} +\begin{eqnarray} + F(x) &=& \int f(x)\,\mathrm{d}x + C +\end{eqnarray} +% +\begin{equation} + F(x)=\int f(x)\,\mathrm{d}x + C +\end{equation} +\end{lstlisting} + + +\subsection{\texttt{empheq}}\label{sec:empheq} + +This package supports different frames for math environments of the \AmSmath +package. It doesn't support all the environments from standard \LaTeX{} which %%% ----- Martin ----- +are not modified by \AmSmath, \eg \UIndex{eqnarray}. + +With the optional argument of the \UIndex{empheq} the preferred box type +can be specified. A simple one is \CIndex{fbox} + +\begin{empheq}[box=\fbox]{align} + f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1 +\end{empheq} + +\begin{lstlisting} +\begin{empheq}[box=\fbox]{align} + f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1 +\end{empheq} +\end{lstlisting} + +The same is possible with the macro \verb|\colorbox|: +\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align} + f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1 +\end{empheq} + +\begin{lstlisting} +\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align} + f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=1 +\end{empheq} +\end{lstlisting} + +The key \verb|box| can hold any possible \LaTeX{} command sequence. Boxing +subequations is also no problem, the \UIndex{empheq} works in the same way: + +\begin{subequations} +\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align} + f(x) & =\int_1^{\infty}\frac{1}{x^1}\,dt=1\\ + f(x) & =\int_2^{\infty}\frac{1}{x^2}\,dt=0.25 +\end{empheq} +\end{subequations} + +\begin{lstlisting} +\begin{subequations} +\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align} + f(x) & =\int_1^{\infty}\frac{1}{x^2}\,dt=1\\ + f(x) & =\int_2^{\infty}\frac{1}{x^2}\,dt=0.25 +\end{empheq} +\end{subequations} +\end{lstlisting} + +For more information on \PIndex{empheq} package have a look at the documentation of the package +which is available at any CTAN server. + +\subsection{\texttt{esint}}\label{sec:esint} +This is a very useful package when you want nice double or triple integral or curve +integral symbols. The ones from the \PIndex{wasysym} package% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/wasysym/}% +{CTAN://macros/latex/contrib/wasysym/}} are not the best. +\verb|esint|\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esint/}% +{CTAN://macros/latex/contrib/esint/} +\href{http://www.ctan.org/tex-archive/fonts/ps-type1/esint/}{CTAN://fonts/ps-type1/esint/}} supports the following symbols: + +\allowdisplaybreaks +\begin{align} +\text{\CMD{int}} &: \int\\ +\text{\CMD{iint}} &: \iint\\ +\text{\CMD{iiintop}} &: \iiintop\\ +\text{\CMD{iiiintop}} &: \iiiintop\\ +\text{\CMD{dotsintop}}&: \dotsintop\\ +\text{\CMD{ointop}} &: \ointop\\ +\text{\CMD{oiint}} &: \oiint\\ +\text{\CMD{sqint}} &: \sqint\\ +\text{\CMD{sqiint}} &: \sqiint\\ +\text{\CMD{ointctrclockwise}} &: \ointctrclockwise\\ +\text{\CMD{ointclockwise}} &: \ointclockwise\\ +\text{\CMD{varointclockwise}} &: \varointclockwise\\ +\text{\CMD{varointctrclockwise}} &: \varointctrclockwise\\ +\text{\CMD{fint}} &: \fint\\ +\text{\CMD{varoiint}} &: \varoiint\\ +\text{\CMD{landupint}} &: \landupint\\ +\text{\CMD{landdownint}} &: \landdownint +\end{align} + + +\subsection{\texttt{eucal} and \texttt{euscript}}\label{sec:euscript.sty} + +These packages should be part of your local \TeX{} installation, because +they come with the \AmSmath packages. Otherwise get them from CTAN% +\footnote{\href{http://www.ctan.org/tex-archive/fonts/amsfonts/latex/euscript.sty}% +{CTAN://fonts/amsfonts/latex/euscript.sty}}. They support a scriptwriting of only uppercase +letters: + +\begin{center} +\includegraphics{EuScript} +%\texttt{\textbackslash{}mathscr\{...\}}\index{EuScript@\textbackslash EuScript} +%{$\EuScript{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$} +\end{center} + +Read the documentation for the interdependence to the %%% ----- Martin ----- +\verb|\mathcal| command. For the above example the +package \PIndex{eucal} was loaded with the option \verb|mathscr|. + + +\subsection{\texttt{exscale}}\label{sec:exscale} + +The following formula is written with the default fontsize where everything +looks more or less well: + +\[ +\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,% +\,\mathrm{d}x\approx\frac{\pi}{n}\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\] + + +Writing the same with the fontsize \CIndex{huge} gives +a surprising result, which belongs to the historical development of +\LaTeX{}, the \CIndex{int} and \CIndex{sum} symbols +are not stretched. This extreme fontsize is often needed for slides +and not only written ``just for fun{}''. + +\begin{center} +\includegraphics{exscale} +\end{center} + +Using the \PIndex{exscale} package% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/base/}% +{CTAN://macros/latex/base/}} package, which should be part of any local \TeX{} +installation, all symbols get the right size. + +\begin{minipage}[c]{1.0\textwidth}% +\centering\huge\[ +\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,\mathrm{d}x\approx\frac{\pi}{n}% +\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\] +\end{minipage}% + +\subsection{\texttt{mathtools}}\label{sec:mathtools} +This package comes with a lot of additional features for typesetting math code. +Sometimes it is useful when only such equations are numbered which are +referenced in the text. This is possible with the switch \verb+\showonlyrefs+. + +Matrices are set by default with a centered horizontal alignment, which is +often not the best way. The \PIndex{mathtools} package provides a starred version of +the matrix environments which allow an optional argument for the horizontal +alignment: + +\[ +\begin{pmatrix*}[r] + 1 & -1 & 0 \\ + -1 & 1 & -1 \\ + 1 & -1 & 0 \\ +-11 & 11 &-11 \\ +\end{pmatrix*} +\] + +\begin{lstlisting} +\[ +\begin{pmatrix*}[r] + 1 & -1 & 0 \\ + -1 & 1 & -1 \\ + 1 & -1 & 0 \\ +-11 & 11 &-11 \\ +\end{pmatrix*} +\] +\end{lstlisting} + +\PIndex{mathtools} also provides some more environments for setting equations. +Very interesting is the \UIndex{lgathered}, which allows to typeset a formula in +the following way: + +\begin{LTXexample}[width=0.6\linewidth] +\begin{align} + x &= + \begin{lgathered}[t] + a + b + c \\ + d + e + + \!\begin{gathered}[t] + f + g + h \\ + i + j + k + \end{gathered} + \end{lgathered} +\end{align} +\end{LTXexample} + +The \CMD{!}\index{*@\textbackslash\char033} revokes the internal horizontal space +in front of the \UIndex{gathered}. + + + +\subsection{\texttt{nicefrac}}\label{sec:nicefrac} +Typesetting fractions\index{Fraction} in the inline mode is often a bad choice, the vertical spacing +increases in fact of the fraction. The \PIndex{nicefrac} package defines the macro +\CIndex{nicefrac}, which is used in the same way as the \CIndex{frac} command, but it +typesets the fraction with a less height: \nicefrac{2}{3} \lstinline|\nicefrac{2}{3}|. +The package is part of the \PIndex{units} package bundle and can be found in the +directory of \PIndex{units}. + + + +\subsection{\texttt{relsize}}\label{sec:relsize} +Often consecutives math operators are used, like two sum symbols, \eg +% +\[ \sum\sum_{i=1}^n i^2 \] + + +As seen the sums are of the same size. To increase the first operator size, someone +can use the \CIndex{scalebox} macro from package \UIndex{graphicx} and write an own macro %%% ----- Martin ----- +\verb+\Sum+, \eg \index{Operator!size}\index{Size!Operator} + +\begin{lstlisting} +\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}} +\[ \Sum_{j=1}\sum_{i=1}^\infty i \] +\end{lstlisting} + +\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}} +\[ \Sum_{j=1}\sum_{i=1}^\infty i \] + +Another solution is to use the \PIndex{relsize} package% +\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/ltxmisc/}{CTAN://macros/latex/ltxmisc/}} +together with the \PIndex{exscale} one. \PIndex{relsize} defines a useful macro \CIndex{mathlarger}: + +\begin{LTXexample} +\[ \mathlarger{\sum}\sum_{i=1}^n i^2 \] +\end{LTXexample} + + +\subsection{\texttt{xypic}}\label{xypic.sty} + +The \CIndex{xymatrix} macro is part of the \PIndex{xypic} package% +\footnote{\href{http://www.ctan.org/tex-archive/support/latex2html/}% +{CTAN://macros/generic/diagrams/xypic/xy-3.7/}} which can be loaded with several options +which are not so important here.% +\footnote{For more information look at the package documentation or the +package \PIndex{xy} itself, which is often saved in \texttt{/usr/share/texmf/tex/generic}}. + +\begin{equation} +\xymatrix{A\POS[];[d]**\dir{~},[];[dr]**\dir{-} & B & C\\ +D & E\POS[];[l]**\dir{.},[];[r]**\dir{~} & F\POS[];[dl]**\dir{~}\\ +G & H & I} +\label{eq:xymatrix} +\end{equation} + + +This matrix was created with + +\begin{lstlisting} +\[ +\xymatrix{ A\POS [];[d]**\dir {~},[];[dr]**\dir {-} & B & C\\ + D & E\POS [];[l]**\dir {.},[];[r]**\dir {~} & F\POS [];[dl]**\dir {~}\\ + G & H & I} +\] +\end{lstlisting} + + + + +\part{Math fonts} +Typesetting text and math is far different. There exist a lot of free text fonts without +additional math characters. This is the reason why we have to buy a commercial math font, e.\,g. +\Index{Palatino} (\PIndex{pamath}) or \Index{Helvetica} (\PIndex{hvmath}), or to +combine the free text font with another free math font. + +\section{Computer modern} +This is the default font, designed by Knuth.\index{cmr}\index{Computer modern} For the PDF output +the Type 1 fonts cm-super and BlueSky were used. + +\Mbox{cm-crop} + +\section{Latin modern} +This is the new designed font which comes with an own Type 1 version.\FIndex{lm}\index{Latin modern} + +\Mbox{lm-crop} + +\section{Palatino} +There is a free package mathpazo.\PIndex{mathpazo}\index{Palatino} + +\Mbox{pazo-crop} + +\section{Palatino -- microimp} +There is the package \PIndex{pamath} for the nonfree palatino font.\PIndex{mathpazo}\index{Palatino} + +\Mbox{pamath-crop} + +\section{cmbright} + +\Mbox{cmbright-crop} + +\section{minion} + +\Mbox{minionpro-crop} + + + +\part{Special symbols} + +In this section only those symbols are defined, which are not part of the %%% ----- Martin ----- +list of all available symbols: +\href{http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}% +{CTAN://info/symbols/comprehensive/symbols-a4.pdf}. With +\verb+fontmath.ltx+ \LaTeX{} itself defines the following special symbols for using inside math: %%% ----- Martin ----- + +\begin{table}[htb] +\centering +\begin{tabular}{l|c} +Name & Meaning\\\hline +\verb+\mathparagraph+ & $\mathparagraph$\\ +\verb+\mathsection+ & $\mathsection$\\ +\verb+\mathdollar+ & $\mathdollar$\\ +\verb+\mathsterling+ & $\mathsterling$\\ +\verb+\mathunderscore+ & $\mathunderscore$\\ +\verb+\mathellipsis+ & $\mathellipsis$\\ +\end{tabular} +\caption{Predefined math symbols from \texttt{fontmath.ltx}}\label{fontmath.ltx} +\end{table} + +\section{Integral symbols} +\index{Integral symbols} + +\def\Xint#1{\mathchoice + {\XXint\displaystyle\textstyle{#1}}% + {\XXint\textstyle\scriptstyle{#1}}% + {\XXint\scriptstyle\scriptscriptstyle{#1}}% + {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% + \!\int} +\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} + \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} +\def\ddashint{\Xint=} +\def\dashint{\Xint-} +\def\clockint{\Xint\circlearrowright} % GOOD! +\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern! +\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft} +\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}} + +\begin{center} +\begin{tabular}{lc} +Name & Symbol\\\hline +\verb|\dashint| & $\dashint$\\ +\verb|\ddashint| & $\ddashint$\\ +\verb|\clockint| & $\clockint$\\ +\verb|\counterint| & $\counterint$ +\end{tabular} +\end{center} + +%$ +For all new integral symbols limits can be used in the usual way: + +\begin{equation} +\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A +\end{equation} + +\begin{lstlisting} +\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A +\end{lstlisting} + +Put the following definitions into the preamble to use one or all of these new +integral symbols. + +\begin{lstlisting} +\def\Xint#1{\mathchoice + {\XXint\displaystyle\textstyle{#1}}% + {\XXint\textstyle\scriptstyle{#1}}% + {\XXint\scriptstyle\scriptscriptstyle{#1}}% + {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% + \!\int} +\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} + \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} +\def\ddashint{\Xint=} +\def\dashint{\Xint-} +\def\clockint{\Xint\circlearrowright} % GOOD! +\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern! +\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft} +\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}} +\end{lstlisting} + +%\clearpage +\section{Harpoons} +\LaTeX{} knows no stretchable harpoon\index{Harpoon} symbols, like \verb|\xrightarrow|. +The following code defines several harpoon symbols.% +\index{xrightharpoondown@\textbackslash xrightharpoondown} +\index{xrightharpoonup@\textbackslash xrightharpoonup} +\index{xleftharpoondown@\textbackslash xleftharpoondown} +\index{xleftharpoonup@\textbackslash xleftharpoonup} +\index{xleftrightharpoons@\textbackslash xleftrightharpoons} +\index{xrightleftharpoons@\textbackslash xrightleftharpoons}% +% +\marginpar{\CMD{xrightharpoondown}\\% +\CMD{xrightharpoonup}\\% +\CMD{xleftharpoondown}\\% +\CMD{xleftharpoonup}\\% +\CMD{xleftrightharpoons}\\% +\CMD{xrightleftharpoons}% +} + +\begin{lstlisting} +\def\rightharpoondownfill@{% + \arrowfill@\relbar\relbar\rightharpoondown} +\def\rightharpoonupfill@{% + \arrowfill@\relbar\relbar\rightharpoonup} +\def\leftharpoondownfill@{% + \arrowfill@\leftharpoondown\relbar\relbar} +\def\leftharpoonupfill@{% + \arrowfill@\leftharpoonup\relbar\relbar} +\newcommand{\xrightharpoondown}[2][]{% + \ext@arrow 0359\rightharpoondownfill@{#1}{#2}} +\newcommand{\xrightharpoonup}[2][]{% + \ext@arrow 0359\rightharpoonupfill@{#1}{#2}} +\newcommand{\xleftharpoondown}[2][]{% + \ext@arrow 3095\leftharpoondownfill@{#1}{#2}} +\newcommand{\xleftharpoonup}[2][]{% + \ext@arrow 3095\leftharpoonupfill@{#1}{#2}} +\newcommand{\xleftrightharpoons}[2][]{\mathrel{% + \raise.22ex\hbox{% + $\ext@arrow 3095\leftharpoonupfill@{\phantom{#1}}{#2}$}% + \setbox0=\hbox{% + $\ext@arrow 0359\rightharpoondownfill@{#1}{\phantom{#2}}$}% + \kern-\wd0 \lower.22ex\box0}% +} +\newcommand{\xrightleftharpoons}[2][]{\mathrel{% + \raise.22ex\hbox{% + $\ext@arrow 3095\rightharpoonupfill@{\phantom{#1}}{#2}$}% + \setbox0=\hbox{% + $\ext@arrow 0359\leftharpoondownfill@{#1}{\phantom{#2}}$}% + \kern-\wd0 \lower.22ex\box0}% +} +\end{lstlisting} + +\begin{tabular}{ll} +\verb|\xrightharpoondown[under]{over}| & $\xrightharpoondown[under]{over}$\\[10pt] +\verb|\xrightharpoonup[under]{over}| & $\xrightharpoonup[under]{over}$ \\[10pt] +\verb|\xleftharpoondown[under]{over}| & $\xleftharpoondown[under]{over}$\\[10pt] +\verb|\xleftharpoonup[under]{over}| & $\xleftharpoonup[under]{over}$ \\[10pt] +\verb|\xleftrightharpoons[under]{over}|& $\xleftrightharpoons[under]{over}$\\[10pt] +\verb|\xrightleftharpoons[under]{over}|& $\xrightleftharpoons[under]{over}$ +\end{tabular} + +%$ + +\section{Bijective mapping arrow} + +To get something like \bijmap~we can define: +\begin{lstlisting} +\def\bijmap{% + \ensuremath{% + \mathrlap{\rightarrowtail}\rightarrow% + }% +} +\end{lstlisting} + +This uses the \CIndex{mathrlap} definition from section~\vref{subsec:ams-limits}. With this +definition a huge symbol is also possible: \verb+{\Huge\bijmap}+ {\Huge\bijmap}. + +\section{Stacked equal sign} +There are several symbols stacked with an equal sign, \eg \CIndex{doteq}, \CIndex{equiv} or +\CIndex{cong} ($\doteq$, $\equiv{}$, $\cong$ ). But there are still some missing, which are +shown in table~\ref{tab:equal} and the following definitions. + +\begin{table}[htb] +\centering +\begin{tabular}{ll} +\verb+\eqdef+ & \eqdef\\ +\verb+\eqexcl+ & \eqexcl\\ +\verb+\eqhat+ & \eqhat +\end{tabular} +\caption{New symbols in combination with the equal sign}\label{tab:equal} +\end{table} + +\begin{lstlisting} +\newcommand{\eqdef}{\ensuremath{\stackrel{\mathrm{def}}{=}}} +\newcommand{\eqexcl}{\ensuremath{\stackrel{\mathrm{!}}{=}}} +\newcommand{\eqhat}{\ensuremath{\widehat{=}}} +\end{lstlisting} + +\section{Other symbols} + +\begin{minipage}{0.7\linewidth} +\begin{lstlisting} +\newcommand*{\threesim}{% + \mathrel{\vcenter{\offinterlineskip + \hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}} +$\threesim ABC$ +\end{lstlisting}% +\end{minipage}\hfill +\begin{minipage}{0.15\linewidth} +$\threesim ABC$ +\end{minipage} + + +\noindent +\begin{minipage}{0.7\linewidth} +\begin{lstlisting} +\newcommand\Let{\mathrel{\mathop:\!\!=}}% Upper case L! +\newcommand\teL{\mathrel{=\!\!\mathop:}} +$x\Let y$ $y\teL x$ +\end{lstlisting}% +\end{minipage}\hfill +\newcommand\Let{\mathrel{\mathop:\!\!=}}% Upper case L! +\newcommand\teL{\mathrel{=\!\!\mathop:}} +$x\Let y$ $y\teL x$ +\begin{minipage}{0.15\linewidth} +\end{minipage} + + +%\lstset{xrightmargin=-\marginparwidth} + +\part{Examples} +\section{Tuning math typesetting} +Chapter 18 of the \TeX book is named ,,Fine Points of Mathematics Typing``~\cite{knuth86} +and it +shows on 20 pages some more or less important facts when typesetting mathematical +expressions. Often inline formulas contain a \Index{punctuation} character like a +\Index{dot}, \Index{comma}, \Index{colon}, \etc. It is a general rule to write +those characters outside the math mode. Compare + +\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] +$a, b, c, d, e, \textrm{and }f$ \\[5pt] +$a$, $b$, $c$, $d$, $e$, and $f$ +\end{LTXexample} + +Having such math as single expressions enables \TeX\ to insert a linebreak at several +places (see Section~\vref{subsec:linebreak}). + +Writing an \Index{ellipses} as three single dots, doesn't look very nice, one should +always use the \CIndex{ldots} command: + +\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] +$1,...,10$\\[5pt] +$1,\ldots,10$ +\end{LTXexample} + +This is correct as long as on the left and right are a comma as a separator. +For sums the \CIndex{cdot} command should be used instead: + +\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] +$1+2+\cdots+10$\\[5pt] +$x_n=x_{n-1}=\cdots=n_0=1$ +\end{LTXexample} + +For a multiplication it is important which character is used, in european countries +often a centered dot. In such a case it is appropriate not to use the \CIndex{cdots} +command for a ellipsis. + +For typesetting integrals\index{Integral} or differential equations\index{differential equation} +it makes sense to define the following short macros: + +\begin{lstlisting} +\newcommand*\dy{\,\mathrm{d}y} +\newcommand*\dx{\,\mathrm{d}x} +\newcommand*\dyx{\,\frac{\mathrm{d}y}{\mathrm{d}x}} +\newcommand*\ds{\,\mathrm{d}s} +\newcommand*\dt{\,\mathrm{d}t} +\newcommand*\dst{\,\frac{\mathrm{d}s}{\mathrm{d}t}} +\end{lstlisting} + +\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] +\begin{align*} +F(x) &= \int\!f(x)\dx\\ +v(t) &= \dst\\ +a(t) &= \frac{\mathrm{d}^2s}{\mathrm{d}t^2} +\end{align*} +\end{LTXexample} + +\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] +\begin{align*} +G(t) &= \underbrace{\,\int\cdots\!\int\!\!}_D\;\dx\dy\ldots\\ +u_C(t) &= \int\!\,i_C(t)\dt +\end{align*} +\end{LTXexample} + +\bigskip +\section{Matrix} +\subsection{Identity matrix} + +There are several possibilities to write this matrix. Here is a solution +with the default array environment. + +\begin{LTXexample}[width=0.4\linewidth] +\[ +\left( + \begin{array}{ccccc} + 1\\ + & 1 & & \text{{\huge{0}}}\\ + & & 1\\ + & \text{{\huge{0}}} & & 1\\ + & & & & 1 + \end{array} +\right) +\] +\end{LTXexample} + +\subsection{System of linear equations} + +\begin{LTXexample}[pos=t] +\[ +\begin{array}{l@{\:=\:}*{5}{l@{\:+\:}}l} +y_1 & x_{11} & x_{12} & x_{13} & \dots & x_{1(n-1)} & x_{1n} \\ +y_2 & x_{21} & x_{22} & x_{23} & \dots & x_{2(n-1)} & x_{2n} \\ +\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots\\ +y_{n-1} & x_{(n-1)1} & x_{(n-1)2} & x_{(n-1)3} & \dots & x_{(n-1)3} & x_{(n-1)n}\\ +y_n & x_{n1} & x_{n2} & x_{n3} & \dots & x_{(n-1)(n-1)} & x_{nn} +\end{array} +\] +\end{LTXexample} + +\subsection{Matrix with comments on top} + + +\begin{LTXexample}[width=0.35\linewidth] +\def\rb#1{\rotatebox{90}{$\xleftarrow{#1}$}} +\begin{tabular}{c} +$\begin{matrix} +\rb{text1}&\rb{text1}&\rb{text1}&\rb{text1}\\ +\end{matrix}$\\ +$\begin{bmatrix} +X_x & Y_x & Z_x & T_x \\ +X_y & Y_y & Z_y & T_y \\ +X_z & Y_z & Z_z & T_z \\ +0 & 0 & 0 & 1 +\end{bmatrix}$ +\end{tabular} +\end{LTXexample} + +%$ + + + + +\section{Cases structure} + +\index{Cases!numbered lines}Sometimes it is better to use the array environment instead of amsmath's %%% ----- Martin ----- +cases environment. To get optimal horizontal spacing for the conditions, +there are two matrixes in series, one $3\times 1$ followed by $3\times 3$ matrix. +To minimize the horizontal space around the variable $z$ a + +\begin{lstlisting} +\addtolength{\arraycolsep}{-3pt} +\end{lstlisting} +is a useful command. + +\begin{equation} +\addtolength{\arraycolsep}{-3pt} +I(z)=\delta_{0}\left\{% + \begin{array}{lcrcl} + D+z & \quad & -D & \le z\le & -p\\ + D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)% + & \quad & -p & \le z\le & \phantom{-}p\\ + D-z & \quad & p & \le z\le & \phantom{-}D + \end{array}\right. +\end{equation} + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\addtolength{\arraycolsep}{-3pt} +I(z)=\delta_{0}\left\{% + \begin{array}{lcrcl} + D+z & \quad & -D & \le z\le & -p\\ + D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)% + & \quad & -p & \le z\le & \phantom{-}p\\ + D-z & \quad & p & \le z\le & \phantom{-}D + \end{array}\right. +\end{equation} +\end{lstlisting} + + +The \CMD{phantom}\index{phantom@\textbackslash phantom} command +replaces exactly that place with whitespace which the argument needs. + +\subsection{Cases with numbered lines} +This is not possible in an easy way, because \verb+cases+ uses the array +environment for typesetting which has by default no numbering. However, there +are some tricky ways to get numbered lines. The following three examples +use the \verb+tabular+, the \verb+tabularx+ and the \verb+array+ environment. + +\bigskip\noindent +\begin{tabular}{rc} +\ldelim\{{2}{2.75cm}[some text here] & %%% ----- Martin ----- + \parbox{{\linewidth-3cm-4\tabcolsep}}{ + \vspace*{1ex} + \begin{flalign} + x & = 2\quad\text{if }y >2 &\\ + x & = 3\quad\text{if }y \le 2& + \end{flalign}} +\end{tabular} + +\bigskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\begin{tabular}{rc} +\ldelim\{{2}{2.75cm}[some text here] & + \parbox{{\linewidth-3cm-4\tabcolsep}}{ + \vspace*{1ex} + \begin{flalign} + x & = 2\quad\text{if }y >2 &\\ + x & = 3\quad\text{if }y \le 2& + \end{flalign}} +\end{tabular} +\end{lstlisting} + + +\bigskip\noindent +\begin{tabularx}{\linewidth}{rXc} +\ldelim\{{2}{2.75cm}[some text here] %%% ----- Martin ----- + & $ x = 2\quad\text{if }y > 2 $ & \refstepcounter{equation}(\theequation)\\ + & $ x = 3\quad\text{if }y \le 2$ &\refstepcounter{equation}(\theequation) +\end{tabularx} + +\bigskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\begin{tabularx}{\linewidth}{rXc} +\ldelim\{{2}{2.75cm}[some text here] + & $x=2\quad\text{if }y>2$ &\refstepcounter{equation}(\theequation)\\ + & $x=3\quad\text{if }y\le2$&\refstepcounter{equation}(\theequation) +\end{tabularx} +\end{lstlisting} + + +\bigskip +\[ +\begin{array}{rc@{\qquad}c} +\ldelim\{{2}{2.75cm}[some text here] %%% ----- Martin ----- + & x = 2\quad\text{if }y > 2 & \refstepcounter{equation}(\theequation)\\ + & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation) +\end{array} +\] + + +\bigskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\[ +\begin{array}{rc@{\qquad}c} +\ldelim\{{2}{2.75cm}[some text here] + & x = 2\quad\text{if }y > 2 & \refstepcounter{equation}(\theequation)\\ + & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation) +\end{array} +\] +\end{lstlisting} + +%$ + +\section{Arrays} + +There is a general rule that a lot of mathematical stuff should be +divided in smaller pieces. But sometimes it is difficult to get a nice +horizontal alignment when splitting a formula. The following ones +uses the \texttt{array} environment to get a proper alignment. + + +\subsection{Quadratic equation} + +\begin{equation} +\begin{array}{rcll} +y & = & x^{2}+bx+c\\ + & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\ + & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle% + \left(\frac{b}{2}\right)^{2}+c}\\ + & & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\ + & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle% + \frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle% + \frac{b}{2}}\right)^{2}-c\right.\\ +y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle% + \frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\ +y-y_{S} & = & (x-x_{S})^{2}\\ +S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle% + \frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right) +\end{array} +\end{equation} + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\begin{equation} +\begin{array}{rcll} +y & = & x^{2}+bx+c\\ + & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\ + & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle% + \left(\frac{b}{2}\right)^{2}+c}\\ + & & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\ + & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle% +\frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle% +\frac{b}{2}}\right)^{2}-c\right.\\ +y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle% +\frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\ +y-y_{S} & = & (x-x_{S})^{2}\\ +S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle% +\frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right) +\end{array} +\end{equation} +\end{lstlisting} + + + +\subsection{Vectors and matrices} +\index{Vector} +\begin{equation} +\begin{array}{rcl} +\underline{RS} & = & \left(\begin{array}{cccccccc} +01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\ +a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\ +02 & a1 & fc & c1 & 47 & ae & 3d & 19\\ +a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\ +\\ +\left(\begin{array}{c} + s_{i,0}\\ + s_{i,1}\\ + s_{i,2}\\ + s_{i,3} +\end{array}\right) & = & \underline{RS}\cdot% +\left(\begin{array}{c} + m_{8i+0}\\ + m_{8i+1}\\ + \cdots\\ + m_{8i+6}\\ + m_{8i+7} +\end{array}\right)\\ +\\ +S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\ +\\ +S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right) +\end{array} +\end{equation} + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\begin{equation} +\begin{array}{rcl} +\underline{RS} & = & \left(\begin{array}{cccccccc} +01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\ +a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\ +02 & a1 & fc & c1 & 47 & ae & 3d & 19\\ +a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\ +\\ +\left(\begin{array}{c} + s_{i,0}\\ + s_{i,1}\\ + s_{i,2}\\ + s_{i,3} +\end{array}\right) & = & \underline{RS}\cdot% +\left(\begin{array}{c} + m_{8i+0}\\ + m_{8i+1}\\ + \cdots\\ + m_{8i+6}\\ + m_{8i+7} +\end{array}\right)\\ +\\ +S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\ +\\ +S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right) +\end{array} +\end{equation} +\end{lstlisting} + + +\subsection{Cases with (eqn)array environment} + +This solution is important when \AmSmath can't be used. %%% ----- Martin ----- + +$\lim\limits_{n->\infty}q^{n}=\left\{% + \begin{array}{lc@{\kern2pt}c@{\kern2pt}r} + \textrm{divergent}\ & q & \le & -1\\ + 0 & |q| & < & 1\\ + 1 & q & = & 1\\ + \infty & q & > & 1 + \end{array}\right.$ + +\medskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +$\lim\limits_{n->\infty}q^{n}=\left\{% + \begin{array}{lc@{\kern2pt}c@{\kern2pt}r} + \textrm{divergent}\ & q & \le & -1\\ + 0 & |q| & < & 1\\ + 1 & q & = & 1\\ + \infty & q & > & 1 + \end{array}\right.$ +\end{lstlisting} +%$ + +\subsection{Arrays inside arrays} +The array environment is a powerful one because it can be nested in several ways: + +\[ +\left( +\begin{array}{c@{}c@{}c} +\begin{array}{|cc|} +\hline +a_{11} & a_{12} \\ +a_{21} & a_{22} \\ +\hline +\end{array} & 0 & 0 \\ +0 & \begin{array}{|ccc|} + \hline + b_{11} & b_{12} & b_{13}\\ + b_{21} & b_{22} & b_{23}\\ + b_{31} & b_{32} & b_{33}\\ + \hline + \end{array} & 0 \\ +0 & 0 & \begin{array}{|cc|} + \hline + c_{11} & c_{12} \\ + c_{21} & c_{22} \\ + \hline + \end{array} \\ +\end{array} +\right) +\] + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\[ +\left( +\begin{array}{c@{}c@{}c} + \begin{array}{|cc|}\hline + a_{11} & a_{12} \\ + a_{21} & a_{22} \\\hline + \end{array} & \mathbf{0} & \mathbf{0} \\ + \mathbf{0} & + \begin{array}{|ccc|}\hline + b_{11} & b_{12} & b_{13}\\ + b_{21} & b_{22} & b_{23}\\ + b_{31} & b_{32} & b_{33}\\\hline + \end{array} & \mathbf{0} \\ + \mathbf{0} & \mathbf{0} & + \begin{array}{|cc|}\hline + c_{11} & c_{12} \\ + c_{21} & c_{22} \\\hline + \end{array} \\ +\end{array} +\right) +\] +\end{lstlisting} + +\[ +Y^1= +\begin{array}{c} + \null\\[1ex]% kann weg + \left[\begin{array}{rrrr} + 0 & 0 & 1 & 0\\ + 1 & 0 & 1 & 0\\ + 1 & 1 & 1 & 1 + \end{array}\right]\\[3ex]\hline + \begin{array}{rrrr} +% \hdotsfor{4}\\% statt \\[3ex]\hline + 2 & 1 &3 & 1 + \end{array} +\end{array} +\] + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\[ +Y^1= +\begin{array}{c} + \null\\[1ex]% only vor vertical alignment + \left[\begin{array}{rrrr} + 0 & 0 & 1 & 0\\ + 1 & 0 & 1 & 0\\ + 1 & 1 & 1 & 1 + \end{array}\right]\\[3ex]\hline + \begin{array}{rrrr} +% \hdotsfor{4}\\%( needs \AmSmath) instead of \\[3ex]\hline + 2 & 1 &3 & 1 + \end{array} +\end{array} +\] +\end{lstlisting} + +\subsection{Colored cells}\label{sub:color} +In general there is no difference in coloring tabular or array cells. The following example +shows how one can put \index{color}colors in rows, columns and cells. +\index{rowcolor@\textbackslash rowcolor}\index{columncolor@\textbackslash columncolor} + +\medskip\noindent +\includegraphics[width=\columnwidth]{colArray} + +%\[ +%\left[\, +%\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}} +% {h_{k,1,0}(n)} & {h_{k,1,1}(n)} & {h_{k,1,2}(n)} & \zero & \zero \\ +% {h_{k,2,0}(n)} & {h_{k,2,1}(n)} & {h_{k,2,2}(n)} & \zero & \zero \\ +% {h_{k,3,0}(n)} & {h_{k,3,1}(n)} & {h_{k,3,2}(n)} & \zero & \zero \\ +% {h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & {h_{k,4,2}(n)} & \zero & \zero \\ +% \zero & {h_{k,1,0}(n-1)} & {h_{k,1,1}(n-1)} & {h_{k,1,2}(n-1)} & \zero \\ +% \zero & {h_{k,2,0}(n-1)} & {h_{k,2,1}(n-1)} & {h_{k,2,2}(n-1)} & \zero \\ +% \zero & {h_{k,3,0}(n-1)} & {h_{k,3,1}(n-1)} & {h_{k,3,2}(n-1)} & \zero \\ +% \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & {h_{k,4,1}(n-1)} & {h_{k,4,2}(n-1)} & \zero \\ +% \zero & \zero & {h_{k,1,0}(n-2)} & {h_{k,1,1}(n-2)} & {h_{k,1,2}(n-2)}\\ +% \rowcolor[gray]{0.75}% +% \zero & \zero & {h_{k,2,0}(n-2)} & {h_{k,2,1}(n-2)} & {h_{k,2,2}(n-2)}\\ +% \zero & \zero & {h_{k,3,0}(n-2)} & {h_{k,3,1}(n-2)} & {h_{k,3,2}(n-2)}\\ +% \zero & \zero & {h_{k,4,0}(n-2)} & {h_{k,4,1}(n-2)} & {h_{k,4,2}(n-2)} +%\end{array} \,\right] +%\end] + + +\medskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +... +\usepackage{array} +\usepackage{colortbl} +\definecolor{umbra}{rgb}{0.8,0.8,0.5} +\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}} +\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}} +\begin{document} +\[\left[\, +\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}} + h_{k,1,0}(n) & h_{k,1,1}(n) & h_{k,1,2}(n) & \zero & \zero\\ + h_{k,2,0}(n) & h_{k,2,1}(n) & h_{k,2,2}(n) & \zero & \zero\\ + h_{k,3,0}(n) & h_{k,3,1}(n) & h_{k,3,2}(n) & \zero & \zero\\ + h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & h_{k,4,2}(n) & \zero & \zero\\ + \zero & h_{k,1,0}(n-1) & h_{k,1,1}(n-1) & h_{k,1,2}(n-1) & \zero\\ + \zero & h_{k,2,0}(n-1) & h_{k,2,1}(n-1) & h_{k,2,2}(n-1) & \zero\\ + \zero & h_{k,3,0}(n-1) & h_{k,3,1}(n-1) & h_{k,3,2}(n-1) & \zero\\ + \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & h_{k,4,1}(n-1) & h_{k,4,2}(n-1) & \zero\\ + \zero & \zero & h_{k,1,0}(n-2) & h_{k,1,1}(n-2) & h_{k,1,2}(n-2)\\ + \zero & \zero & h_{k,2,0}(n-2) & h_{k,2,1}(n-2) & h_{k,2,2}(n-2)\\ + \zero & \zero & h_{k,3,0}(n-2) & h_{k,3,1}(n-2) & h_{k,3,2}(n-2)\\ + \zero & \zero & h_{k,4,0}(n-2) & h_{k,4,1}(n-2) & h_{k,4,2}(n-2) +\end{array} \,\right]_{12\times 5}\] +... +\end{lstlisting} + + +\subsection{Boxed rows and columns} + +\begin{LTXexample}[width=0.35\linewidth] +\[ +\overrightarrow{A}=\left[ + \begin{array}{cccc} + 1 & 2 & 3 & 4\\ + 1 & 2 & 3 & 4\\\hline + \multicolumn{1}{|c}{1} & 2 & 3 & + \multicolumn{1}{c|}{4}\\\hline + 1 & 2 & 3 & 4 + \end{array}\right] +\] +\end{LTXexample} + + +\begin{LTXexample}[width=0.35\linewidth] +\[ +\overrightarrow{A}=\left[ + \begin{array}{cc|c|c}\cline{3-3} + 1 & 2 & 3 & 4\\ + 1 & 2 & 3 & 4\\ + 1 & 2 & 3 & 4\\ + 1 & 2 & 3 & 4\\\cline{3-3} + \end{array}\right] +\] +\end{LTXexample} + +\begin{LTXexample}[width=0.35\linewidth] +\[ +\overrightarrow{A}=\left[ + \begin{array}{cc|c|c}\cline{3-3} + 1 & 2 & 3 & 4\\ + 1 & 2 & 3 & 4\\\hline + \multicolumn{1}{|c}{1} & 2 & 3 & + \multicolumn{1}{c|}{4}\\\hline + 1 & 2 & 3 & 4\\\cline{3-3} + \end{array}\right] +\] +\end{LTXexample} + + + +\section{Over- and underbraces} +\subsection{Braces and roots} +To put an underbrace in a root without enlarging the root symbol is possible with +the \verb+\makebox+ macro: + +\[ z =\;\;\underbrace{\makebox[\widthof{~$x^2+y^2$}][r]{$\sqrt{x^2+y^2}$}}_{=z^2} \] + +\begin{lstlisting} +\[ +z =\;\;\underbrace{% + \makebox[\widthof{~$x^2+y^2$}][r]{% + $\sqrt{x^2+y^2}$}}_{=z^2} +\] +\end{lstlisting} + + + +\subsection{Overlapping braces} +Overlapping under- and overbraces like% +\parbox{10em}{\begin{align*} +\qquad\overbrace{\qquad\qquad}^o\qquad\\[-16pt] +\underbrace{\qquad\qquad}_{u1}\underbrace{\qquad\qquad}_{u2} +\end{align*}} needs some tricky code, because we cannot have parts of the argument inside +\verb+overbrace+\index{overbrace@\textbackslash overbrace} and also \verb+underbrace+. +\index{underbrace@\textbackslash underbrace} The following equation~\vref{eq:pqFormel} +is an example for such a construction: + +\begin{align}\label{eq:pqFormel} +y &= 2x^2 -3x +5\nonumber\\ + & \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }% + \textcolor{blue}{% + \overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- % + \left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt] + &= 2\left(\textcolor{red}{% + \underbrace{% + x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}% + }% + \underbrace{% + - \left(\frac{3}{4}\right)^2 + \frac{5}{2}}% + \right)\\ + &= 2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2} + \qquad + \ \frac{31}{16}\qquad\right)\nonumber\\ +y\textcolor{blue}{-\frac{31}{8}} + &= 2\left(x\textcolor{cyan}{-\frac{3}{4}}\right)^2\nonumber +\end{align} + +\medskip +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\begin{align}\label{eq:pqFormel} +y &= 2x^2 -3x +5\nonumber\\ + & \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }% + \textcolor{blue}{% + \overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- % + \left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt] + &= 2\left(\textcolor{red}{% + \underbrace{% + x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}% + }% + \underbrace{% + - \left(\frac{3}{4}\right)^2 + \frac{5}{2}}% + \right)\\ + &= 2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2} + \qquad + \ \frac{31}{16}\qquad\right)\nonumber\\ +y\textcolor{blue}{-\frac{31}{8}} + &= 2\left(x\textcolor{cyan}{-\frac{3}{4}}\right)^2\nonumber +\end{align} +\end{lstlisting} + +\subsection[Vertical alignment]{Vertical alignment of different braces} +When having several braces in one formula line, then it looks better when all +braces are also on the same line, \eg + +\begin{equation} + \binom{x_R}{y_R} = \underbrace{r\vphantom{\binom{A}{B}}}_{\text{Scaling}}\cdot% + \underbrace{% + \begin{pmatrix} + \sin \gamma & -\cos \gamma \\ + \cos \gamma & \sin \gamma \\ + \end{pmatrix}% + }_{\text{Rotation}} + \binom{x_K}{y_K} + + \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} +\end{equation} + +\begin{lstlisting} +\begin{equation} + \binom{x_R}{y_R} = \underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\cdot% + \underbrace{% + \begin{pmatrix} + \sin \gamma & -\cos \gamma \\ + \cos \gamma & \sin \gamma \\ + \end{pmatrix}% + }_{\text{Rotation}} + \binom{x_K}{y_K} + + \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} +\end{equation} +\end{lstlisting} + +It is again the \verb+\vphantom+ macro which reserves the needed vertical space. +Nevertheless the horizontal space around the \verb+r+ of the first underbrace and the last \verb|+| should +be decreased to get a better typesetting. This is possible with \verb+\hspace+ or +simply \verb+\kern+: + +\[ \binom{x_R}{y_R} = % + \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt% + \cdot\underbrace{% + \begin{pmatrix} + \sin \gamma & -\cos \gamma \\ + \cos \gamma & \sin \gamma \\ + \end{pmatrix}% + }_{\text{Rotation}} + \binom{x_K}{y_K} +\kern-5pt% + \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \] + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\[ \binom{x_R}{y_R} = % + \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt% + \cdot\underbrace{% + \begin{pmatrix} + \sin \gamma & -\cos \gamma \\ + \cos \gamma & \sin \gamma \\ + \end{pmatrix}% + }_{\text{Rotation}} + \binom{x_K}{y_K} +\kern-5pt% + \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \] +\end{lstlisting} + + +\subsection[Alignment]{Vertical and horizontal alignment} +The forgoing example simply uses \verb+\hspace+ to decrease the horizontal width between two +\index{underbrace@\textbackslash underbrace} underbraces. This may be okay for a single solution, but in general it is better to have some %%% ----- Martin ----- +code which works in any case. + +The following example looks simple but it needs some tricky code to get vertical and horizontal +alignment.\index{substack@\textbackslash substack} + +\def\num#1{\hphantom{#1}} +\def\vsp{\vphantom{\rangle_1}} + +\begin{equation*} + \frac{300}{5069}% + \underbrace{\longmapsto\vphantom{\frac{1}{1}}}_{% + \mathclap{\substack{% + \Delta a=271\num9\vsp \\[2pt] + \Delta b=4579\vsp\\[2pt] + \text{$1$ iteration}% + }}} \frac{29}{490}% + \underbrace{\longmapsto \frac{19}{321}\longmapsto}_{% + \mathclap{\substack{% + \Delta a=10\num{9}=\langle271\rangle_{29}\num{20}\\[2pt] + \Delta b=169=\langle4579\rangle_{490}\\[2pt] + \text{$2$ iterations} + }}} \frac{9}{152} + \underbrace{\longmapsto \frac{8}{135}\longmapsto\dots\longmapsto}_{% + \substack{% + \Delta a=1\num{7}=\langle10\rangle_{9}\num{119}\\[2pt] + \Delta b=17=\langle169\rangle_{152}\\[2pt] + \text{$8$ iterations} + }} \frac{1}{16} + \underbrace{\longmapsto\dots\longmapsto\vphantom{\frac{8}{135}}}_{% + \substack{% + \Delta a=0=\langle1\rangle_{1}\num{76} \\[2pt] + \Delta b=1=\langle17\rangle_{16} \\[2pt] + \text{$8$ iterations} + }} \frac{1}{1} +\end{equation*} + +It uses the macro \verb+\mathclap+ defined in section\vref{subsec:ams-limits} +\index{mathclap@\textbackslash mathclap}\index{vphantom@\textbackslash vphantom}\index{hphantom@\textbackslash hphantom} +, which gives a better result. %%% ----- Martin ----- +It is also possible to use \verb+\makebox[0pt]{...}+ but it works only in text mode +and this needs some more \verb+$...$+.\index{substack@\textbackslash substack} + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\def\num#1{\hphantom{#1}} +\def\vsp{\vphantom{\rangle_1}} + +\begin{equation*} + \frac{300}{5069}% + \underbrace{\longmapsto\vphantom{\frac{1}{1}}}_{% + \mathclap{\substack{% + \Delta a=271\num9\vsp \\[2pt] + \Delta b=4579\vsp\\[2pt] + \text{$1$ iteration}% + }}} \frac{29}{490}% + \underbrace{\longmapsto \frac{19}{321}\longmapsto}_{% + \mathclap{\substack{% + \Delta a=10\num{9}=\langle271\rangle_{29}\num{20}\\[2pt] + \Delta b=169=\langle4579\rangle_{490}\\[2pt] + \text{$2$ iterations} + }}} \frac{9}{152} + \underbrace{\longmapsto \frac{8}{135}\longmapsto\dots\longmapsto}_{% + \substack{% + \Delta a=1\num{7}=\langle10\rangle_{9}\num{119}\\[2pt] + \Delta b=17=\langle169\rangle_{152}\\[2pt] + \text{$8$ iterations} + }} \frac{1}{16} + \underbrace{\longmapsto\dots\longmapsto\vphantom{\frac{8}{135}}}_{% + \substack{% + \Delta a=0=\langle1\rangle_{1}\num{76} \\[2pt] + \Delta b=1=\langle17\rangle_{16} \\[2pt] + \text{$8$ iterations} + }} \frac{1}{1} +\end{equation*} +\end{lstlisting} + + +\section{Integrals}\label{sec:Integrals} +\index{underset@\textbackslash underset} +\def\Q#1#2{\frac{\partial #1}{\partial #2}} +% +The \emph{first theorem of Green} is: +\[ +\underset{\mathcal{G}\quad}\iiint\!% + \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]\mathrm{d}^{3}V% + =\underset{\mathcal{S}\quad}\oiint u\,\Q{v}{n}\,\,\mathrm{d}^{2}A +\] + +The \emph{second theorem of Green} is: + +\[ +\underset{{\mathcal{G}\quad}}\iiint\!% + \left[u\nabla^{2}v-v\nabla^{2}u\right]\mathrm{d}^{3}V% + =\underset{\mathcal{S}\quad}\oiint% + \left(u\,\Q{v}{n}-v\,\Q{u}{n}\right)\mathrm{d}^{2}A +\] + + +They are both written with the \PIndex{esint} package% +\footnote{See section~\vref{sec:Integrals}.}, which gives nice integral symbols. +The \LaTeX{} code for the first equation is: + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\[ +\underset{\mathcal{G}\quad}\iiint\!% + \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]\mathrm{d}^{3}V% + =\underset{\mathcal{S}\quad}\oiint u\,\Q{v}{n}\,\,\mathrm{d}^{2}A +\] +\end{lstlisting} + +\noindent with the following definition in the preamble for the partial derivation: + +\begin{lstlisting} +\def\Q#1#2{\frac{\partial#1}{\partial #2}} +\end{lstlisting} + +\noindent which makes things easier to write. + +%-------------------------------------------------------------------------- +\section{Horizontal alignment}\label{sec:verticalAlignment} +%-------------------------------------------------------------------------- +\subsection{Over more than one page} +%-------------------------------------------------------------------------- +Sometimes it may be useful to have a vertical alignment over the whole page with a mix of %%% ----- Martin ----- +formulas and text. Section \ref{sec:Text-in-math mode} shows the use of \CMD{intertext}. +There is another trick to get all formulas vertical aligned. Let's have the following +formulas distributed over the whole page: +% +\begin{align*} + f(x) &= a\\ + g(x) &= x2-4x\\ +f(x)-g(x) &= x2+x3+x\\ + g &= x2+x3+x4+x5+b +\end{align*} +% +They all have a different length of the left and right side. Now we want to write some +text and other objects between them, but let the alignment untouched. We choose the +longest left and the longest right side and take them for scaling with the \CMD{hphantom} +command: + +\begin{verbatim} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}} +\end{verbatim} + +This is the first (empty) line in every equation where now all other lines are aligned to +this one. For example: + +\bgroup +\medskip\noindent +\rule{\columnwidth}{1pt} +\newcommand{\x}{blah blah blah blah blah blah blah blah } +\addtolength\abovedisplayshortskip{-.5cm}% decrease the skip +\addtolength\abovedisplayskip{-.5cm} +\x\x\x +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +f(x) &= a\\ +g(x) &= x^2-4x +\end{align} +% +\x\x\x +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +f(x)-g(x) &= x^2+x^3+x +\end{align} +\x\x\x +% +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +g(x) &= x^2+x^3+x^4+x^5+b +\end{align} +\x\x\x + +\noindent +\rule{\columnwidth}{1pt} +\egroup +\medskip + +The phantom line is empty but leaves the vertical space for a line. This could be +corrected with decreasing the \CMD{abovedisplayshortskip} length and done all +inside a group. + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\newcommand{\x}{blah blah blah blah blah blah blah blah } +\bgroup +\addtolength\abovedisplayshortskip{-0.5cm}% decrease the skip +\addtolength\abovedisplayskip{-0.5cm} +\x\x\x +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +f(x) &= a\\ +g(x) &= x^2-4x +\end{align} +% +\x\x\x +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +f(x)-g(x) &= x^2+x^3+x +\end{align} +\x\x\x +% +\begin{align} +\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ +g(x) &= x^2+x^3+x^4+x^5+b +\end{align} +\x\x\x +\egroup +\end{lstlisting} + + + + +Another case of aligning equations inside an itemize environment is the following one. +With the \CIndex{makebox} macro one can have the same size on the left side of the +equal sign to get a vertical alignment. + +\newsavebox\lW +\sbox\lW{$P_{3}+P_{2}-P_{1}$}% $ + +\begin{itemize} +\item first function \\ + $\displaystyle\makebox[\wd\lW][r]{$P_1$}=\sum_a \in A$ +\item but another one \\ + $\makebox[\wd\lW][r]{$\sin\left(P_1\right)$}=blabla$ +\item or perhaps \\ + $P_{3}+P_{2}-P_{1}=blablub$ +\end{itemize} + + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\newsavebox\lW +\sbox\lW{$P_{3}+P_{2}-P_{1}$} + +\begin{itemize} +\item first function \\ + $\displaystyle\makebox[\wd\lW][r]{$P_1$}=\sum_a \in A$ +\item but another one \\ + $\makebox[\wd\lW][r]{$\sin\left(P_1\right)$}=blabla$ +\item or perhaps \\ + $P_{3}+P_{2}-P_{1}=blablub$ +\end{itemize} +\end{lstlisting} +%$ + +%-------------------------------------------------------------------------- +\subsection{Special text columns} +%-------------------------------------------------------------------------- +This one comes from Hartmut Henkel and offers a special form of placing +additional text between the equation and the \Index{equation number}. This makes only +sense when you load the documentclass with the option \verb+fleqn+. The example +places the additional text at \verb+0.5\textwidth+, changing this value is no +problem. + +\clearpage +\medskip +\noindent\rule{\linewidth}{1pt} +\begingroup +\small +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text + +\makeatletter +\@fleqntrue +\let\old@mathmargin=\@mathmargin +\@mathmargin=-1sp +\let\oldmathindent=\mathindent +\let\mathindent=\@mathmargin +\newsavebox{\myendhook} % for the tabulars +\def\tagform@#1{{(\maketag@@@{\ignorespaces#1\unskip\@@italiccorr)} + \makebox[0pt][r]{% after the equation number + \makebox[0.5\textwidth][l]{\usebox{\myendhook}}}% + \global\sbox{\myendhook}{}% empty box +}} +\makeatother +\sbox{\myendhook}{% +\begin{footnotesize}% +\begin{tabular}{@{}ll} +$a_0$ & Bohrscher Radius ($\mathrm{= 0{,}53\,\mbox{\AA}}$)\\ +$e$ & Elementarladung\\ +$N_{si}$ & Anzahl der Siliziumatome\\ +& pro Einheitsvolumen\\ +$m$ & Atomgewicht\\ +$Z$ & Kernladungszahl +\end{tabular} +\end{footnotesize}} +% +\begin{equation} +\varepsilon = \frac{E \cdot 4 \cdot \pi \cdot \varepsilon_{0} +\cdot a_0 \cdot \left( Z_i^{\frac{2}{3}} + Z_{Si}^{\frac{2}{3}} +\right)^{-\frac{1}{2}}} {Z_i \cdot Z_{Si} \cdot e2 \cdot \left( 1 ++ \frac{m_i}{m_{Si}} \right)}\,; +\end{equation} + +\sbox{\myendhook}{abc} + +\begin{equation} +a2+b2=c2 +\end{equation} + +\begin{equation} +z = 9 +\end{equation} +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text +text text text text text text text text text text text text text text + +\endgroup +\noindent\rule{\linewidth}{1pt} + +\medskip +This solution works only with \AmSmath{}, without you have to redefine the +\LaTeX{} macro, which creates the equation number. + +\begin{lstlisting}[xrightmargin=-\marginparwidth] +\newsavebox{\myendhook} % for the tabulars +\def\tagform@#1{{(\maketag@@@{\ignorespaces#1\unskip\@@italiccorr)} + \makebox[0pt][r]{% after the equation number + \makebox[0.4\textwidth][l]{\usebox{\myendhook}}% + }% + \global\sbox{\myendhook}{}% clear box content +}} +[ ... ] +\sbox{\myendhook}{% +\begin{footnotesize}% +\begin{tabular}{@{}ll} +$a_0$ & Bohrscher Radius ($\mathrm{= 0{,}53\,\mbox{\AA}}$)\\ +$e$ & Elementarladung\\ +$N_{si}$ & Anzahl der Siliziumatome\\ +& pro Einheitsvolumen\\ +$m$ & Atomgewicht\\ +$Z$ & Kernladungszahl +\end{tabular} +\end{footnotesize}} +% +\begin{equation} +\varepsilon = \frac{E \cdot 4 \cdot \pi \cdot \varepsilon_{0} +\cdot a_0 \cdot \left( Z_i^{\frac{2}{3}} + Z_{Si}^{\frac{2}{3}} +\right)^{-\frac{1}{2}}} {Z_i \cdot Z_{Si} \cdot e2 \cdot \left( 1 ++ \frac{m_i}{m_{Si}} \right)}\,; +\end{equation} +% +\sbox{\myendhook}{abc} +% +\begin{equation} a2+b2=c2 \end{equation} +% +\begin{equation} z = 9 \end{equation} +\end{lstlisting} + + +%-------------------------------------------------------------------------- +\subsection{Centered vertical dots} +%-------------------------------------------------------------------------- + +By default the vertical dots of \CMD{vdots} are aligned to the left of +the $=$ symbol and not centered.\index{vdots@\textbackslash vdots} +% +\bgroup +\newsavebox{\eqbox}% Heiko Bauke +\sbox{\eqbox}{$\null=\null$} +\newcommand{\Vdots}{\makebox[\wd\eqbox]{\vdots}} +% +\begin{align} + a_1 & = b_1 & c_1 & = d_1 \\ + a_2 & = b_2 & c_2 & = d_2 \\ + a & \Vdots b & & \Vdots \nonumber \\ + a_n & = b_n & c_n & = d_n +\end{align} +\egroup +% +\begin{lstlisting} +\usepackage{amsmath} +... + +\newsavebox{\eqbox} +\sbox{\eqbox}{$\null=\null$} +\newcommand{\Vdots}{\makebox[\wd\eqbox]{\vdots}} + +\begin{align} + a_1 & = b_1 & c_1 & = d_1 \\ + a_2 & = b_2 & c_2 & = d_2 \\ + a & \Vdots b & & \Vdots \nonumber \\ + a_n & = b_n & c_n & = d_n +\end{align} +\end{lstlisting} + + +%------------------------------------------------------------------------------ +\section{Node connections} +%------------------------------------------------------------------------------ +This is a typical application for PSTricks and it needs the package \verb+pst-node+ +and doesn't work with \verb+pdflatex+. Use \verb+vlatex+, \verb+ps4pdf+ or \verb+ps2pdf+. + +\medskip +\noindent\fbox{\includegraphics[width=\linewidth]{node}} + +\iffalse +\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% +\psset{nodesep=3pt} +\definecolor{lila}{rgb}{0.6,0.2,0.5} +\definecolor{darkyellow}{rgb}{1,0.9,0} +Die Bindungsenergie im Tr\"opfchenmodell setzt sich aus +folgenden Teilen zusammen: +\begin{itemize} +\item dem \rnode{b}{Oberfl\"achenanteil} +\item dem \rnode{a}{Volumenanteil},\\[0.75cm] +\def\xstrut{\vphantom{\frac{(A)^1}{(B)^1}}} +\begin{equation} +E = +\rnode[t]{ae}{\psframebox*[fillcolor=darkyellow, + linestyle=none]{\xstrut a_vA}} + +\rnode[t]{be}{\psframebox*[fillcolor=lightgray, + linestyle=none]{\xstrut -a_fA^{2/3}}} + +\rnode[t]{ce}{\psframebox*[fillcolor=green, + linestyle=none]{\xstrut -a_c\dfrac{Z(Z-1)}{A^{1/3}}}} + +\rnode[t]{de}{\psframebox*[fillcolor=cyan, + linestyle=none]{\xstrut -a_s\frac{(A-2Z)^2}{A}}} + +\rnode[t]{ee}{\psframebox*[fillcolor=yellow, + linestyle=none]{\xstrut E_p}} +\end{equation}\\ +\item dem \rnode{c}{Coulomb-Anteil} +\item der \rnode{d}{Symmetrieenergie} +\item sowie einem \rnode{e}{Paarbildungsbeitrag}. +\end{itemize} +\nccurve[angleA=-90,angleB=90]{->}{a}{ae} +\nccurve[angleB=45]{->}{b}{be} +\nccurve[angleB=-90]{->}{c}{ce} +\nccurve[angleB=-90]{->}{d}{de} +\nccurve[angleB=-90]{->}{e}{ee} +}} +\fi + +\medskip +\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] +\psset{nodesep=3pt} +\definecolor{lila}{rgb}{0.6,0.2,0.5} +\definecolor{darkyellow}{rgb}{1,0.9,0} +Die Bindungsenergie im Tr\"opfchenmodell setzt sich aus +folgenden Teilen zusammen: +\begin{itemize} +\item dem \rnode{b}{Oberfl\"achenanteil} +\item dem \rnode{a}{Volumenanteil},\\[1cm] +\def\xstrut{\vphantom{\frac{(A)^1}{(B)^1}}} +\begin{equation} +E = +\rnode[t]{ae}{\psframebox*[fillcolor=darkyellow, + linestyle=none]{\xstrut a_vA}} + +\rnode[t]{be}{\psframebox*[fillcolor=lightgray, + linestyle=none]{\xstrut -a_fA^{2/3}}} + +\rnode[t]{ce}{\psframebox*[fillcolor=green, + linestyle=none]{\xstrut -a_c\frac{Z(Z-1)}{A^{1/3}}}} + +\rnode[t]{de}{\psframebox*[fillcolor=cyan, + linestyle=none]{\xstrut -a_s\frac{(A-2Z)^2}{A}}} + +\rnode[t]{ee}{\psframebox*[fillcolor=yellow, + linestyle=none]{\xstrut E_p}} +\end{equation}\\[0.25cm] +\item dem \rnode{c}{Coulomb-Anteil} +\item der \rnode{d}{Symmetrieenergie} +\item sowie einem \rnode{e}{Paarbildungsbeitrag}. +\end{itemize} +\nccurve[angleA=-90,angleB=90]{->}{a}{ae} +\nccurve[angleB=45]{->}{b}{be} \nccurve[angleB=-90]{->}{c}{ce} +\nccurve[angleB=-90]{->}{d}{de} \nccurve[angleB=-90]{->}{e}{ee} +\end{lstlisting} + + + + +%----------------------------------------------------------------------------- +\section[Special Placement]{Special placement of displayed equations} +%----------------------------------------------------------------------------- + +%----------------------------------------------------------------------------- +\subsection{Formulas side by side}\label{sec:sidebyside} +%----------------------------------------------------------------------------- + +Sometimes it may be useful to have numbered formulas side by side like the following ones: + +%\begin{framed} +\begin{mtabular}{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah}]\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub}] + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt +\end{mtabular} +%\end{framed} + + +And again a default display equation: +\begin{align} +F(x) &= \int_0^\infty\dfrac{1}{x}\,\mathrm{d}x +\end{align} + +\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] +\begin{mtabular}{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah}]\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub}] + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt +\end{mtabular} +\end{lstlisting} + +The new environment \verb|mtabular| has two arguments, one optional and one which is the same +as the one from the \verb|tabular| environment. With the option \verb|long| it is possible to have %%% ----- Martin ----- +all the formulas in a \verb|longtable| environment, which allows a pagebreak. The new macro +\verb|\eqnCnt| controls the counting of these equations as subequations for one tabular +line. This macro can have an optional argument for a label. At least it counts +the equations. If the +equation number is not centered to the foregoing equation, then it needs some more horizontal +space in the tabular column. + +\begin{verbatim} +\eqnCnt[] +\end{verbatim} + +The vertical space is controlled by the length \verb|mtabskip|, which +is by default \verb|-1.25cm| and can be modified in the usual way. +To define all these macros write into the preamble: +\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] +\usepackage{amsmath} +\newcounter{subequation} +\newlength\mtabskip\mtabskip=-1.25cm +\newcommand\eqnCnt[1][]{% + \refstepcounter{subequation}% + \begin{align}#1\end{align}% + \addtocounter{equation}{-1}} +\def\mtabLong{long} +\makeatletter +\newenvironment{mtabular}[2][\empty]{% + \def\@xarraycr{% + \stepcounter{equation}% + \setcounter{subequation}{0}% + \@ifnextchar[\@argarraycr{\@argarraycr[\mtabskip]}} + \let\theoldequation\theequation% + \renewcommand\theequation{\theoldequation.\alph{subequation}} + \edef\mtabOption{#1} + \setcounter{subequation}{0}% + \tabcolsep=0pt + \ifx\mtabOption\mtabLong\longtable{#2}\else\tabular{#2}\fi% +}{% + \ifx\mtabOption\mtabLong\endlongtable\else\endtabular\fi% + \let\theequation\theoldequation% + \stepcounter{equation}} +\makeatother +\end{lstlisting} + + +As seen in equation~\ref{blub} and equation~\ref{blah}, everything of the table contents is +nonsense~\ldots And the following tabular is defined as a \Index{longtable} to enable pagebreaks. +%which is the reason for the following big skip, to show that it works. + + +%\vspace*{3cm} +%\begin{framed} +\begin{mtabular}[long]{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah2}]\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub2}] + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt +\end{mtabular} +%\end{framed} + +As seen in equation~\ref{blub2} and equation~\ref{blah2}, everything is nonsense ... + + +And again a default display equation: +\begin{align} +F(x) &= \int_0^\infty\dfrac{1}{x}\,\mathrm{d}x +\end{align} + +\begin{lstlisting}[tabsize=4] +\begin{mtabular}[long]{*{2}{m{0.375\linewidth}m{0.125\linewidth}}} +\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % + & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ +\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % + & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ +\begin{align*} c =1 \end{align*} & \eqnCnt + & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ + +[ ... ] +\end{lstlisting} + +%----------------------------------------------------------------------------- +\subsection[Itemize environment]{Formulas inside an itemize enviroment}\label{sec:itemize} +%----------------------------------------------------------------------------- +Without any modification it is not possible to get a numbered equation +at the same height as the symbol of the itemize environment\index{itemize@\texttt{itemize}}. This depends on %%% ----- Martin ----- +the \LIndex{abovedisplayskip}. The formula has to be raised up for exactly this length. + +\begin{lstlisting} +\def\itemMath#1{% + \raisebox{-\abovedisplayshortskip}{% + \parbox{0.75\linewidth}{% + \begin{equation}#1\end{equation}}}} +% +\begin{itemize} +\item \itemMath{ f = l } +\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x } +\end{itemize} +\end{lstlisting} + +\def\itemMath#1{% + \raisebox{-\abovedisplayshortskip}{% + \parbox{0.75\linewidth}{% + \begin{equation}#1\end{equation}}}} +% +\begin{itemize} +\item \itemMath{ f = l } +\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x } +\end{itemize} + + +\section{Roots} +There exists no special symbol for roots\index{Root} which are longer than one line. In such +cases the root should be split into two or more one, like $\sqrt{a\cdot b\cdot c}=\sqrt{a}\cdot\sqrt{a}\cdot\sqrt{b}\cdot\sqrt{c}$ +if possible. If nothing helps one can use \CMD{overline}\cIndex{overline} for +following lines of the root. The following example uses the \verb+multline+ environment +to get only one equation number: + +\begin{multline} +d(P,Q)|_{Stat.,Dependent}=\\ + \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ + \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\ + \overline{\rule{0pt}{2.5ex} + \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} + (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\ + \overline{\rule{0pt}{2.5ex} + \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]} +\end{multline} + + +\begin{lstlisting} +\begin{multline} +d(P,Q)|_{Stat.,Dependent}=\\ + \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ + \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\ + \overline{\rule{0pt}{2.5ex} + \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} + (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\ + \overline{\rule{0pt}{2.5ex} + \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]} +\end{multline} +\end{lstlisting} + + +Alternative: + +\begin{multline} +d(P,Q)|_{Stat.,Dependent}=\\ + \Big(\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ + \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+ \\ + \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} + (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\ + \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\Big)^{1/2} +\end{multline} + + +\begin{lstlisting} +\begin{multline} +d(P,Q)|_{Stat.,Dependent}=\\ + \left\{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ + \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+\right. \\ + \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} + (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\ + \left.\left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\right\}^{1/2} +\end{multline} +\end{lstlisting} + + + +\part{Lists, bibliography and index} +\bgroup +\lhead{}\rhead{} +\clearpage\phantomsection\addcontentsline{toc}{section}{List of Figures} +\listoffigures +\clearpage\phantomsection\addcontentsline{toc}{section}{List of Tables} +\listoftables +\clearpage\phantomsection\addcontentsline{toc}{section}{Bibliography} + +{\nocite{*} +\raggedright +\bibliography{Mathmode} +\bibliographystyle{plain} +} +\clearpage\addcontentsline{toc}{section}{Index} +{\let\BSL\textbackslash +\renewcommand\textbackslash{{\ttfamily\BSL}} +\printindex{} +} +\egroup + + +\appendix +\section*{Appendix} +\section{Filelist} +This document was build with + +\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth] +This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2007.3.18) 21 APR 2007 09:54 +\end{lstlisting} + +and with the following file and package versions: + + +\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth] + *File List* + article.cls 2005/09/16 v1.4f Standard LaTeX document class + size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option) +fixltx2e.sty 2006/03/24 v1.1n fixes to LaTeX + fontenc.sty + t1enc.def 2005/09/27 v1.99g Standard LaTeX file +inputenc.sty 2006/05/05 v1.1b Input encoding file + latin1.def 2006/05/05 v1.1b Input encoding file + ifpdf.sty 2006/02/20 v1.4 Provides the ifpdf switch (HO) + ifvtex.sty 2007/01/10 v1.2 Switches for detecting VTeX and its modes (HO) + comment.sty +graphicx.sty 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) + keyval.sty 1999/03/16 v1.13 key=value parser (DPC) +graphics.sty 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) + trig.sty 1999/03/16 v1.09 sin cos tan (DPC) +graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive + pdftex.def 2007/01/08 v0.04d Graphics/color for pdfTeX +varwidth.sty 2003/03/10 ver 0.9a; Variable-width minipages + array.sty 2005/08/23 v2.4b Tabular extension package (FMi) +delarray.sty 1994/03/14 v1.01 array delimiter package (DPC) +tabularx.sty 1999/01/07 v2.07 `tabularx' package (DPC) + amsmath.sty 2000/07/18 v2.13 AMS math features + amstext.sty 2000/06/29 v2.01 + amsgen.sty 1999/11/30 v2.0 + amsbsy.sty 1999/11/29 v1.2d + amsopn.sty 1999/12/14 v2.01 operator names + amssymb.sty 2002/01/22 v2.2d +amsfonts.sty 2001/10/25 v2.2f + bm.sty 2004/02/26 v1.1c Bold Symbol Support (DPC/FMi) + upgreek.sty 2003/02/12 v2.0 (WaS) + cancel.sty 2000/03/12 v2.1 Cancel math terms + amscd.sty 1999/11/29 v1.2d + accents.sty 2006/05/12 v1.3 Math Accent Tools + dsfont.sty 1995/08/01 v0.1 Double stroke roman fonts +multirow.sty +bigdelim.sty + framed.sty 2003/07/21 v 0.8a: framed or shaded text with page breaks +longtable.sty 2004/02/01 v4.11 Multi-page Table package (DPC) +varioref.sty 2006/05/13 v1.4p package for extended references (FMi) + xcolor.sty 2007/01/21 v2.11 LaTeX color extensions (UK) + color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive + makeidx.sty 2000/03/29 v1.0m Standard LaTeX package + url.sty 2005/06/27 ver 3.2 Verb mode for urls, etc. +setspace.sty 2000/12/01 6.7 Contributed and Supported LaTeX2e package + empheq.sty 2004/10/10 v2.11a Emphasizing equations (MH) + mhsetup.sty 2004/10/10 v1.0b programming setup (MH) +mathtools.sty 2004/10/10 v1.01a mathematical typesetting tools (MH) + calc.sty 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) +nicefrac.sty 1998/08/04 v0.9b Nice fractions + ifthen.sty 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) + exscale.sty 1997/06/16 v2.1g Standard LaTeX package exscale + relsize.sty 2003/07/04 ver 3.1 + xspace.sty 2006/05/08 v1.12 Space after command names (DPC,MH) + eucal.sty 2001/10/01 v2.2d Euler Script fonts +footmisc.sty 2005/03/17 v5.3d a miscellany of footnote facilities + esint.sty + esvect.sty +remreset.sty + cool.sty 2006/12/29 v1.35 COntent Oriented LaTeX +coollist.sty 2006/08/14 v1 COntent Oriented LaTeX Lists + coolstr.sty 2007/01/08 v2.1 COntent Oriented LaTeX Strings + forloop.sty 2006/09/18 v3.0 For Loops for LaTeX + bbm.sty 1999/03/15 V 1.2 provides fonts for set symbols - TH + xypic.sty 1999/02/16 Xy-pic version 3.7 + xy.sty +fancyhdr.sty +showexpl.sty 2007/02/03 v0.3h Typesetting example code (RN) +listings.sty 2004/10/17 1.3b (Carsten Heinz) +lstpatch.sty 2004/10/17 1.3b (Carsten Heinz) + lstmisc.sty 2004/09/07 1.3 (Carsten Heinz) +listings.cfg 2004/09/05 1.3 listings configuration + lstmisc.sty 2004/09/07 1.3 (Carsten Heinz) +showexpl.cfg 2005/06/30 v0.02 Definitions for the showexpl package (hv) +lstlang1.sty 2004/09/05 1.3 listings language file +lstlang2.sty 2004/09/05 1.3 listings language file +lstlang3.sty 2004/09/05 1.3 listings language file + lstmisc.sty 2004/09/07 1.3 (Carsten Heinz) +microtype.sty 2007/01/21 v2.0 Micro-typography with pdfTeX (RS) +microtype.cfg 2007/01/14 v2.0 microtype main configuration file (RS) +hyperref.sty 2007/02/07 v6.75r Hypertext links for LaTeX + pd1enc.def 2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO) +hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive +kvoptions.sty 2006/08/22 v2.4 Connects package keyval with LaTeX options (HO) + hpdftex.def 2007/02/07 v6.75r Hyperref driver for pdfTeX + hypcap.sty 2006/02/20 v1.5 Adjusting anchors of captions (HO) + babel.sty 2005/11/23 v3.8h The Babel package + english.ldf 2005/03/30 v3.3o English support from the babel system + braket.sty +supp-pdf.tex + mt-cmr.cfg 2005/11/07 v1.9 microtype config. file: Computer Modern Roman (RS) + nameref.sty 2006/12/27 v2.28 Cross-referencing by name of section +refcount.sty 2006/02/20 v3.0 Data extraction from references (HO) +Mathmode.out +Mathmode.tex + umsa.fd 2002/01/19 v2.2g AMS font definitions + mt-msa.cfg 2006/02/04 v1.1 microtype config. file: AMS symbols (a) (RS) + umsb.fd 2002/01/19 v2.2g AMS font definitions + mt-msb.cfg 2005/06/01 v1.0 microtype config. file: AMS symbols (b) (RS) + mt-eur.cfg 2006/07/31 v1.1 microtype config. file: AMS Euler Roman (RS) + uesint.fd + uesvect.fd + t1cmtt.fd 1999/05/25 v2.5h Standard LaTeX font definitions + omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions + t1cmss.fd 1999/05/25 v2.5h Standard LaTeX font definitions +Mathmode.bbl +Mathmode.ind + *********** +\end{lstlisting} diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.eps new file mode 100644 index 00000000000..b2a8de26859 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.eps @@ -0,0 +1,1462 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 3.00 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 275 11 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 3.00 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFill [0] def + /pdfStroke [0] def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% separation convention operators +/findcmykcustomcolor where { + pop +}{ + /findcmykcustomcolor { 5 array astore } def +} ifelse +/setcustomcolor where { + pop +}{ + /setcustomcolor { + exch + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval cvx + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace setcolor + } def +} ifelse +/customcolorimage where { + pop +}{ + /customcolorimage { + gsave + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace + 10 dict begin + /ImageType 1 def + /DataSource exch def + /ImageMatrix exch def + /BitsPerComponent exch def + /Height exch def + /Width exch def + /Decode [1 0] def + currentdict end + image + grestore + } def +} ifelse +% PDF color state +/sCol { + pdfLastStroke not { + pdfStroke aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastStroke true def /pdfLastFill false def + } if +} def +/fCol { + pdfLastFill not { + pdfFill aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastFill true def /pdfLastStroke false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16L3 { + 1 index /CIDFont resourcestatus { + pop pop 1 index /CIDFont findresource /CIDFontType known + } { + false + } ifelse + { + 0 eq { /Identity-H } { /Identity-V } ifelse + exch 1 array astore composefont pop + } { + pdfMakeFont16 + } ifelse +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { end grestore } def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% color operators +/g { dup 1 array astore /pdfFill exch def setgray + /pdfLastFill true def /pdfLastStroke false def } def +/G { dup 1 array astore /pdfStroke exch def setgray + /pdfLastStroke true def /pdfLastFill false def } def +/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor + /pdfLastFill true def /pdfLastStroke false def } def +/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor + /pdfLastStroke true def /pdfLastFill false def } def +/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor + /pdfLastFill true def /pdfLastStroke false def } def +/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor + /pdfLastStroke true def /pdfLastFill false def } def +/ck { 6 copy 6 array astore /pdfFill exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastFill true def /pdfLastStroke false def } def +/CK { 6 copy 6 array astore /pdfStroke exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastStroke true def /pdfLastFill false def } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImSep { + findcmykcustomcolor exch + dup /Width get /pdfImBuf1 exch string def + dup /Decode get aload pop 1 index sub /pdfImDecodeRange exch def + /pdfImDecodeLow exch def + begin Width Height BitsPerComponent ImageMatrix DataSource end + /pdfImData exch def + { pdfImData pdfImBuf1 readstring pop + 0 1 2 index length 1 sub { + 1 index exch 2 copy get + pdfImDecodeRange mul 255 div pdfImDecodeLow add round cvi + 255 exch sub put + } for } + 6 5 roll customcolorimage + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font JPKANY+SFTT1095 +%!FontType1-1.0: SFTT1095 0.3 +%%CreationDate: Wed Sep 12 2001 +% Copyright (c) 2001 Vladimir Volovich . +% See the file COPYING (GNU General Public License) for license conditions. +% Converted from METAFONT EC/TC and LH fonts: +% ectt1095, tctt1095, latt1095, lbtt1095, lctt1095, rxtt1095. +11 dict begin +/FontInfo 6 dict dup 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+!!!~> +%-EOD- +Q +q +[30 0 0 -120 3590.28 7489.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[4.8 0 0 -120 3620.28 7489.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -120 3620.28 7489.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 244.68 740.6] Tm +0 0 Td +/F13_0 5.97758 Tf +(1) 3.17409 Tj +9.16918 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 267.239 740.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(y) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 279.959 740.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(&) 5.23039 Tj +-77.3397 TJm +(=) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 298.558 740.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(x) 5.23039 Tj +-5.10942 TJm +Q +1 1 0.849609 rg +q +[4.8 0 0 -120 2507.88 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -120 2507.88 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +1 1 0.849609 rg +q +[30 0 0 -120 2511.48 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[1048.8 0 0 -120 2541.48 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[30 0 0 -120 3590.28 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[4.8 0 0 -120 3620.28 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -120 3620.28 7369.88] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 G +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 244.68 728.6] Tm +0 0 Td +/F13_0 5.97758 Tf +(2) 3.17409 Tj +9.16918 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 267.239 728.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(y) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 279.959 728.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(=) 5.23039 Tj +-77.3397 TJm +(&) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 298.558 728.6] Tm +0 0 Td +/F12_0 9.96264 Tf +(x) 5.23039 Tj +-5.10942 TJm +Q +1 1 0.849609 rg +q +[4.8 0 0 -120 2507.88 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -120 2507.88 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +1 1 0.849609 rg +q +[30 0 0 -120 2511.48 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[1048.8 0 0 -120 2541.48 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[30 0 0 -120 3590.28 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[4.8 0 0 -120 3620.28 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -120 3620.28 7251.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 G +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 244.68 716.72] Tm +0 0 Td +/F13_0 5.97758 Tf +(3) 3.17409 Tj +9.16918 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 267.239 716.72] Tm +0 0 Td +/F12_0 9.96264 Tf +(y) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 280.079 716.72] Tm +0 0 Td +/F12_0 9.96264 Tf +(=) 5.23039 Tj +-89.3769 TJm +({) 5.23039 Tj +-89.3769 TJm +(}) 5.23039 Tj +-89.3769 TJm +(&) 5.23039 Tj +-5.10942 TJm +Q +0 G +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 311.157 716.72] Tm +0 0 Td +/F12_0 9.96264 Tf +(x) 5.23039 Tj +-5.10942 TJm +Q +1 1 0.849609 rg +q +[1116 0 0 -34.8 2507.88 7131.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +0 g +q +[4.8 0 0 -34.8 2507.88 7131.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[34.8 0 0 -4.8 2509.08 7101.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[1048.8 0 0 -4.8 2541.48 7101.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[34.8 0 0 -4.8 3590.28 7101.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +q +[4.8 0 0 -34.8 3621.48 7131.08] cm +<< + /ImageType 1 + /Width 1 + /Height 1 + /ImageMatrix [1 0 0 -1 0 1] + /BitsPerComponent 1 + /Decode [0 1] + /DataSource currentfile + /ASCII85Decode filter + /RunLengthDecode filter +>> +pdfImM +!!!~> +%-EOD- +Q +Q +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font PATextEx +%%+ font PAMath-Italic +%%+ font SFTT1000 +%%+ font SFTT0800 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf new file mode 100644 index 00000000000..08194ee4508 Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.eps new file mode 100644 index 00000000000..b6ea7a3187c --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.eps @@ -0,0 +1,3421 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 3.01 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 362 158 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 3.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font FFXXTL+SFBX1000 +%!FontType1-1.0: SFBX1000 0.3 +%%CreationDate: Wed Sep 12 2001 +% Copyright (c) 2001 Vladimir Volovich . +% See the file COPYING (GNU General Public License) for license conditions. +% Converted from METAFONT EC/TC and LH fonts: +% ecbx1000, tcbx1000, labx1000, lbbx1000, lcbx1000, rxbx1000. +11 dict begin +/FontInfo 6 dict dup begin +/version (0.3) def +/FullName (Computer Modern Bold Extended) def +/FamilyName (Computer Modern) def +/ItalicAngle 0 def +/isFixedPitch false def +/Weight (Bold) def +end readonly def +/FontName /FFXXTL+SFBX1000 def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] def +/FontBBox{-229 -316 1737 939}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6b55c6e47ad7a9a958a6e22e00fdd4d6492d53addc90ecd778346c06747 +57609fe8907dfffed75e2cf963a64c7f72488f4a02372be681e9bbf09a9ce5a9 +3894f6358c244fcd46c148f1eb60de2137e6d3079d6ae03b3724f7d7bba47bc4 +41c27fffdff9fb7b7738a8d88c27573a53e244723e07c995948ded2516b6044e +aded62c496a56bc14483d307884467ade985655a4712dd06ed00811f9a05bf9f 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font OTWDMF+CMSY10 +%!PS-AdobeFont-1.1: CMSY10 001.100 +%%CreationDate: 1997 Aug 23 16:21:30 +% Copyright (C) 1997 Y&Y, Inc. All Rights Reserved. +% Notice: This font is not in the public domain +% Notice: Computer Modern fonts were designed by Donald E. Knuth +11 dict begin +/FontInfo 9 dict dup begin +/version (001.100) readonly def +/Notice (Copyright (c) 1996 Y&Y, Inc. All Right Reserved. http://www.YandY.com) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /OTWDMF+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf17efb0ffe6c69feba838a0db1152abbd11c 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/propersubset/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/proportional + /.notdef/infinity/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/emptyset/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/braceleft/braceright + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/backslash/.notdef + /.notdef/.notdef/nabla/.notdef/.notdef/.notdef/.notdef/.notdef + 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font SUYTYO+CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /SUYTYO+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf7158f1163bc1f3352e22a1452e73feca8a4 +87100fb1ffc4c8af409b2067537220e605da0852ca49839e1386af9d7a1a455f 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font NMLNQC+CMMI7 +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /NMLNQC+CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{0 -250 1171 750}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa0529731c99a784ccbe85b4993b2eebde +3b12d472b7cf54651ef21185116a69ab1096ed4bad2f646635e019b6417cc77b +532f85d811c70d1429a19a5307ef63eb5c5e02c89fc6c20f6d9d89e7d91fe470 +b72befda23f5df76be05af4ce93137a219ed8a04a9d7d6fdf37e6b7fcde0d90b +986423e5960a5d9fbb4c956556e8df90cbfaec476fa36fd9a5c8175c9af513fe +d919c2ddd26bdc0d99398b9f4d03d77639df1232a4d6233a9caf69b151dfd33f +c0962eac6e3ebfb8ad256a3c654eaaf9a50c51bc6fa90b61b60401c235afab7b 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font CIQOPK+CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CIQOPK+CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cabb9ffc6cc3f1e9ae32f234eb60fe7d +e34995b1acff52428ea20c8ed4fd73e3935cebd40e0ead70c0887a451e1b1ac8 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font LHFDRN+CMEX10 +%!PS-AdobeFont-1.1: CMEX10 001.101 +%%CreationDate: 1992 Jul 23 21:22:48 +%%RevisionDate: 1997 Feb 16 10:50:33 +% Copyright (C) 1992, 1997 Y&Y, Inc. All Rights Reserved. +% Please note: This font is NOT in the public domain. +11 dict begin +/FontInfo 9 dict dup begin +/version (001.101) readonly def +/Notice (Copyright (c) 1992, 1997 Y&Y, Inc. All Right Reserved. (508) 371-3286) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /LHFDRN+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cac6a7beb5d02276e511ffaf2ae11910 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font XYLJKN+MSBM10 +%!PS-AdobeFont-1.1: MSBM10 2.1 +%%CreationDate: 1993 Sep 17 11:10:37 +% Math Symbol fonts were designed by the American Mathematical Society. +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /XYLJKN+MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cabb9ffc6a66a4000a13d5f68bff326d +1d432b0d064b56c598f4338c319309181d78e1629a31eca5dd8536379b03c383 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begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% 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forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font XMOXBA+CMEX10 +%!PS-AdobeFont-1.1: CMEX10 001.101 +%%CreationDate: 1992 Jul 23 21:22:48 +%%RevisionDate: 1997 Feb 16 10:50:33 +% Copyright (C) 1992, 1997 Y&Y, Inc. All Rights Reserved. +% Please note: This font is NOT in the public domain. +11 dict begin +/FontInfo 9 dict dup begin +/version (001.101) readonly def +/Notice (Copyright (c) 1992, 1997 Y&Y, Inc. All Right Reserved. (508) 371-3286) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /XMOXBA+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 90 /integraldisplay put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cac6a7beb5d02276e511ffaf2ae11910 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font RNVVIF+HFBRBS10 +%!PS-AdobeFont-1.0: HFBRBS10 0.6 +%%Title: HFBRBS10 +%%CreationDate: Fri Nov 22 09:28:55 2002 +%%Creator: Harald Harders +%%DocumentSuppliedResources: font HFBRBS10 +% Part of the hfbright font family by Harald Harders, h.harders@tu-bs.de +% Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) +%%EndComments +FontDirectory/HFBRBS10 known{/HFBRBS10 findfont dup/UniqueID known{dup +/UniqueID get 4214399 eq exch/FontType get 1 eq and}{pop false}ifelse +{save true}{false}ifelse}{false}ifelse +11 dict begin +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def +/FontName /RNVVIF+HFBRBS10 def +/FontBBox [-56 -406 2344 933 ]readonly def +/UniqueID 4214399 def +/PaintType 0 def +/FontInfo 9 dict dup begin +/version (0.6) readonly def +/Notice (Part of the hfbright font family by Harald Harders, h.harders@tu-bs.de) readonly def +/FullName (Computer Modern Bright MSB Symbols) readonly def +/FamilyName (Computer Modern Bright) readonly def +/Weight (Regular) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +dup 102 /Omegainv put +dup 103 /eth put +dup 123 /kappa put +dup 125 /planckover2pi put +dup 126 /planckover2pi1 put +dup 127 /epsiloninv put +readonly def +currentdict end +currentfile eexec +d9d66f633b846ab284bcf8b0411b772de5ce33c33655f6ff751f340a8d6c01e3 +2e02c24e186ba91b34a1f538959d4450cb683eae5b034d030186901b458d3777 +6b3942bd2e07121385120248891aec2eb33c4e3a0cf00828d0f130c31a918c18 +979fe94379c648ef21abf659253e43cd1253866f157f1df85ae7e8714f061b1e +aba3ad094fe8d6293916fa82ee4f486c7e513a06d4c9be44306a8287970b4abf +b6d1f9274a5a0bb6ecf713adbd1260d5d6c4420d357fd486470a74b2f0621b59 +a9373abecdbf32fa68ac06351eb3a0c389a3d2b08c29f4c9fdb187846925f2b5 +2ab2bd00094110ed80b925cd1b8de5bccafd429659e757f19bfc97255048f010 +155b9a168cb062357f42ea653df22bcb75fb5e21dfad47ab81ef8c322521324b +faa4e0bf6ad114496e2d3498d037d1a04e3ac87c4da09a27c1179328a0591de3 +d956eee44931f136d19484f135dfb754f3520d8cad87a1dafda8816f31384d50 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TJm +(\012) 7.55195 Tj +209.391 505.415 Td +/F17_0 9.963 Tf +(f) 7.55195 Tj +216.946 505.415 Td +/F13_0 9.963 Tf +(P\010) 14.1076 Tj +-1 TJm +(\005\004QRSTUVW) 64.7994 Tj +1 TJm +(XY) 13.4501 Tj +-27 TJm +(\007) 8.13977 Tj +1 TJm +(\011Z) 14.536 Tj +60.08 492.962 Td +/F11_0 9.963 Tf +(a) 4.9018 Tj +-17 TJm +(\013b) 11.9257 Tj +-23 TJm +(\014) 5.75861 Tj +-51 TJm +(c) 4.65272 Tj +-88 TJm +(@) 5.14091 Tj +-59 TJm +(d) 5.15087 Tj +-96 TJm +(\016) 4.49331 Tj +-36 TJm +(e) 4.65272 Tj +-65 TJm +(\017"f) 12.2445 Tj +-220 TJm +(\020) 4.64276 Tj +-49 TJm +(\030) 4.64276 Tj +-19 TJm +(g) 5.15087 Tj +-49 TJm +(\015) 5.36009 Tj +-58 TJm +(h) 5.15087 Tj +152.471 492.962 Td +/F17_0 9.963 Tf +(~}) 10.3017 Tj +163.018 492.962 Td +/F11_0 9.963 Tf +(\023i) 6.08739 Tj +-101 TJm +({) 2.24168 Tj +-49 TJm +(j) 2.5306 Tj +-96 TJm +(|) 2.5306 Tj +-49 TJm +(k) 4.85198 Tj +-89 TJm +(\024) 6.17706 Tj +191.262 492.962 Td +/F17_0 9.963 Tf +({) 6.9741 Tj +199.178 492.962 Td +/F11_0 9.963 Tf +(l) 2.24168 Tj +-96 TJm +(`\025m) 18.2323 Tj +-26 TJm +(n) 5.15087 Tj +-25 TJm +(\021) 5.38002 Tj +-33 TJm +(\022) 4.56305 Tj +-30 TJm +(#o) 11.7065 Tj +-70 TJm +(\033) 5.79847 Tj +-33 TJm +(&) 3.85568 Tj +-72 TJm +(\036') 12.7726 Tj +1 TJm +(}) 6.53573 Tj +-1 TJm +(p) 5.15087 Tj +-32 TJm +(\032%q) 15.2135 Tj +-49 TJm +(r) 3.4472 Tj +-114 TJm +(s) 4.00513 Tj +-84 TJm +(t) 3.77598 Tj +-77 TJm +(\034) 4.85198 Tj +-103 TJm +(\031) 6.12725 Tj +-33 TJm +(u) 5.15087 Tj +-48 TJm +(\026\027) 11.318 Tj +-63 TJm +(v) 4.56305 Tj +-115 TJm +(\035) 5.83832 Tj +-34 TJm +(w) 6.8944 Tj +-114 TJm +(!) 6.52577 Tj +-34 TJm +($) 8.7774 Tj +60.08 480.508 Td +(x) 4.56305 Tj +-98 TJm +(\037y) 11.1984 Tj +-115 TJm +( ) 7.00399 Tj +-34 TJm +(z) 4.48335 Tj +90.777 480.508 Td +/F12_0 9.963 Tf +(1) 9.963 Tj +-278 TJm +(/) 7.75121 Tj +-277 TJm +(;) 4.9815 Tj +119.004 480.508 Td +/F17_0 9.963 Tf +(?) 7.75121 Tj +126.753 480.508 Td +/F13_0 9.963 Tf +(d) 5.15087 Tj +131.9 480.508 Td +/F17_0 9.963 Tf +(g) 5.80843 Tj +-278 TJm +() 4.24424 Tj +[1 0 0 1 417.4 465.066] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 158.157 l +S +Q +[1 0 0 1 -360.707 -0.398] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +361.105 0.199 l +S +Q +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font IUCDYU+SFBBX10 +%%+ font XJHAZI+SFBMR10 +%%+ font AIHXYM+HFBRMI10 +%%+ font PJEMQP+HFBRSY10 +%%+ font IKIRHD+HFBR10 +%%+ font SJEGFZ+HFBRMI8 +%%+ font UWAHAL+HFBR8 +%%+ font XMOXBA+CMEX10 +%%+ font RNVVIF+HFBRBS10 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf new file mode 100644 index 00000000000..ea5117d91a7 Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.eps new file mode 100644 index 00000000000..2c35d1793f2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.eps @@ -0,0 +1,2856 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 2.02pl1 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 390 189 +%%HiResBoundingBox: 0 0 389.54 188.63 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 2.02pl1 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 14 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFill [0] def + /pdfStroke [0] def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def +} def +/pdfEndPage { end } def +% separation convention operators +/findcmykcustomcolor where { + pop +}{ + /findcmykcustomcolor { 5 array astore } def +} ifelse +/setcustomcolor where { + pop +}{ + /setcustomcolor { + exch + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval cvx + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace setcolor + } def +} ifelse +/customcolorimage where { + pop +}{ + /customcolorimage { + gsave + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace + 10 dict begin + /ImageType 1 def + /DataSource exch def + /ImageMatrix exch def + /BitsPerComponent exch def + /Height exch def + /Width exch def + /Decode [1 0] def + currentdict end + image + grestore + } def +} ifelse +% PDF color state +/sCol { + pdfLastStroke not { + pdfStroke aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastStroke true def /pdfLastFill false def + } if +} def +/fCol { + pdfLastFill not { + pdfFill aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastFill true def /pdfLastStroke false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16L3 { + 1 index /CIDFont resourcestatus { + pop pop 1 index /CIDFont findresource /CIDFontType known + } { + false + } ifelse + { + 0 eq { /Identity-H } { /Identity-V } ifelse + exch 1 array astore composefont pop + } { + pdfMakeFont16 + } ifelse +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { end grestore } def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% color operators +/g { dup 1 array astore /pdfFill exch def setgray + /pdfLastFill true def /pdfLastStroke false def } def +/G { dup 1 array astore /pdfStroke exch def setgray + /pdfLastStroke true def /pdfLastFill false def } def +/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor + /pdfLastFill true def /pdfLastStroke false def } def +/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor + /pdfLastStroke true def /pdfLastFill false def } def +/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor + /pdfLastFill true def /pdfLastStroke false def } def +/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor + /pdfLastStroke true def /pdfLastFill false def } def +/ck { 6 copy 6 array astore /pdfFill exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastFill true def /pdfLastStroke false def } def +/CK { 6 copy 6 array astore /pdfStroke exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastStroke true def /pdfLastFill false def } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/awcp { % awidthcharpath + exch { + 1 string dup 0 3 index put 2 index charpath + 3 index 3 index rmoveto + 4 index eq { 5 index 5 index rmoveto } if + } forall + 6 {pop} repeat +} def +/Tj { fCol + 0 pdfTextRise pdfTextMat dtransform rmoveto + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 8 6 roll moveto + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/Tj16 { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse + 0 pdfTextRise pdfTextMat dtransform rmoveto + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll awidthshow + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse + 0 pdfTextRise pdfTextMat dtransform rmoveto + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll awidthshow + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +% Level 1 image operators +/pdfIm1 { + /pdfImBuf1 4 index string def + { currentfile pdfImBuf1 readhexstring pop } image +} def +/pdfIm1Sep { + /pdfImBuf1 4 index string def + /pdfImBuf2 4 index string def + /pdfImBuf3 4 index string def + /pdfImBuf4 4 index string def + { currentfile pdfImBuf1 readhexstring pop } + { currentfile pdfImBuf2 readhexstring pop } + { currentfile pdfImBuf3 readhexstring pop } + { currentfile pdfImBuf4 readhexstring pop } + true 4 colorimage +} def +/pdfImM1 { + /pdfImBuf1 4 index 7 add 8 idiv string def + { currentfile pdfImBuf1 readhexstring pop } imagemask +} def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImSep { + findcmykcustomcolor exch + dup /Width get /pdfImBuf1 exch string def + dup /Decode get aload pop 1 index sub /pdfImDecodeRange exch def + /pdfImDecodeLow exch def + begin Width Height BitsPerComponent ImageMatrix DataSource end + /pdfImData exch def + { pdfImData pdfImBuf1 readstring pop + 0 1 2 index length 1 sub { + 1 index exch 2 copy get + pdfImDecodeRange mul 255 div pdfImDecodeLow add round cvi + 255 exch sub put + } for } + 6 5 roll customcolorimage + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font FGXNEI+CMEX10 +%!FontType1-1.0: FGXNEI+CMEX10 +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /FGXNEI+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [7 63776 659 40] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 50 /bracketlefttp put +dup 54 /bracketleftex put +dup 52 /bracketleftbt put +dup 51 /bracketrighttp put +dup 55 /bracketrightex put +dup 53 /bracketrightbt put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font TPVOAW+CMSY8 +%!FontType1-1.0: TPVOAW+CMSY8 +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY8) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /TPVOAW+CMSY8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [0 -7 669 507] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 2 /multiply put +dup 163 /multiply put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B +1A564DFCECB963478373C69F52172F071E0AA6082A3E10D9E1CE02D4556639B7 +6E51CEE5CA47176526577DCAD330986D3F10AF7B211765AF9751A064CB337B01 +56656DD95332590218B3675BDDD91DCA09CDF3C789636C6F792A396FE19645F2 +1B1867D6097F650D34C6B6C3368CE921E515344B1C5452C05252140DA29D404D +3D9CBCDAAE6E43FC6B07AFDED6F57C12B99B761D8478A484C6F4ED0B5834E6F6 +C5FACF0E1A4FF757DE8243E5C0867762774E4AFE53A5BC752BD9928AF5B1ED93 +2F821C28A58D73D8B25D28EF81264AD72C8384F071641662407585DFE3D8EBC3 +05E90AA9C7B65693A9F0137ABC75FF52261E44706141D8F4DCEE95280258B738 +0BAD7C4B16EF1AECBFA39D4A641E9D57D106E3B4C37C6DFC84306738A5F85172 +FC741BD63E8251B1FD74959DA4C9133CA03CFC169D4A888F08CEF635FC475554 +5639E768433BE8D7696E8C195F0609D5C887FB23BCA89D22ADC436596CAE59F9 +955606E6DD2456AEE72362219CF02BB28392AC5886EF4B73E2021EAB12E80549 +54E430E18066BC14D4941556BEBF7BD4AA09E10A0600823635C62F5FA09EB524 +32CBB82618413DD42038FF29DFCC4AA2EF733EB579F55C616789C4B03D5C8A98 +1352CBE43BDCA55A8FEC03EA950472507E5854B11B6CB96E4A16 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndResource +/F28_0 /TPVOAW+CMSY8 1 1 +[ /.notdef/.notdef/multiply/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/multiply/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font EIXNXU+CMSY10 +%!FontType1-1.0: EIXNXU+CMSY10 +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /EIXNXU+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [0 0 694 270] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 161 /minus put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B +1A564DFCECB963478373C69F52172F071E0AA6082A3E10D9E1CE02D4556639B7 +6E51CEE5CA47176526577DCAD58DEADE9FDD8D1161040A11504872D56EDB3D8A +754DA50DF613433572E45F990F01381BC7E8141871C01DE3E731162DE2206649 +4D782ACD8AA055EAE84DD0DEB16C09CFA1774FA78BCB61839501922FF62F7037 +3E6C1F5DBDD3567A54F189008B0F5225798FB59F3FD46468BD1CF510B02F535E +3EA7FFE2583BAE928445D43359B4A7C4BF027456BA45D781AB71B5A7DD87F16D +E8E2A0E5C3E7175363255A9FC1B2C1734066515DA9C0C9C3AB23EBAFC56EF014 +FD1CAE59E9643B8D659ED91F7E5D38225A489707A6406BB8FAB4AC592D8F7849 +6D1EE5D02F37964D389F52A9D6F6088DBA3E88BDA46B006DEB21A55DBFA37D2F +174498304AD593651746AD2A9F1C026F612184F0436B032B1C581A0735F9D473 +890E6E7D72F5B429717EA8E1654A07A9B576258F9DFDE14EAFF935DFECADEAC8 +35035CA459C4BDC9577484FF36EA4BE997A020DD0AD3DCE87894C773CFE10D88 +CD91683874A6FAB9D28597DB2E32D200C3D8 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndResource +/F25_0 /EIXNXU+CMSY10 1 1 +[ /minus/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/minus/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font OLGOPF+CMR12 +%!FontType1-1.0: OLGOPF+CMR12 +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR12) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /OLGOPF+CMR12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [41 -251 448 750] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 40 /parenleft put +dup 41 /parenright put +readonly def +currentdict end +currentfile eexec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cleartomark +%%EndResource +/F22_0 /OLGOPF+CMR12 1 1 +[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /parenleft/parenright/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /zero/one/two/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font DIRGWX+CMR8 +%!FontType1-1.0: DIRGWX+CMR8 +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR8) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /DIRGWX+CMR8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [30 -21 500 675] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B 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All Rights Reserved) readonly def +/FullName (CMMI8) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /JGBJQA+CMMI8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [57 -193 533 694] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 107 /k put +dup 59 /comma put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B +1A564DFCECB963478373C69F52172F071E0AA6082A3E10D9E1CE02D4556639B7 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+29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +2104 1029 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 107.285] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +1 g +2820 1029 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 314.789 107.285] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +162 885 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 92.84] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +673 885 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 72.298 92.84] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.745 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3685 -1.79102 Td +(;) 2.34321 Tj +13.7116 -1.79102 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.9358 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.279 -1.79102 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.033 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5759 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2127 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1658 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +1389 885 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.816 92.84] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77717 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79102 Td +(;) 2.34321 Tj +13.7438 -1.79102 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.968 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3112 -1.79102 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +2104 885 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 92.84] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79102 Td +(;) 2.34321 Tj +13.7438 -1.79102 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.9679 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79102 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +1 g +2820 885 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 314.789 92.84] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +162 741 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 78.395] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +673 741 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 72.298 78.395] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.745 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3685 -1.79102 Td +(;) 2.34321 Tj +13.7116 -1.79102 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.9358 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.279 -1.79102 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.033 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5759 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2127 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1658 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +1389 741 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.816 78.395] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77717 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79102 Td +(;) 2.34321 Tj +13.7438 -1.79102 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.968 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3112 -1.79102 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +2104 741 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 78.395] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79102 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79102 Td +(;) 2.34321 Tj +13.7438 -1.79102 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.9679 -1.79102 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79102 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +1 g +2820 741 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 314.789 78.395] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +162 596 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 63.95] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.8 0.8 0.498 rg +673 596 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 72.298 63.95] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.745 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3685 -1.79099 Td +(;) 2.34321 Tj +13.7116 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.9358 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.279 -1.79099 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.033 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5759 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2127 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1658 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +1389 596 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.816 63.95] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77717 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.968 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3112 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +0.953 g +2104 596 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 63.95] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(1\)) 10.389 Tj +Q +1 g +2820 596 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 314.789 63.95] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +162 452 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 49.505] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +673 452 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 100.162 49.505] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +1389 452 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.844 49.505] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.74895 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3724 -1.79099 Td +(;) 2.34321 Tj +13.7156 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +17.9397 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.2829 -1.79099 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.0369 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5799 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2257 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1698 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2104 452 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 49.505] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2820 452 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 286.916 49.505] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +1 g +162 307 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 35.051] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +673 307 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 100.162 35.051] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +1389 307 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.844 35.051] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.74895 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3724 -1.79099 Td +(;) 2.34321 Tj +13.7156 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.9397 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.2829 -1.79099 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.0369 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5799 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2257 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1698 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2104 307 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 35.051] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2820 307 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 286.916 35.051] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +1 g +162 163 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 20.606] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +673 163 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 100.162 20.606] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +1389 163 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.844 20.606] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.74895 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3724 -1.79099 Td +(;) 2.34321 Tj +13.7156 -1.79099 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.9397 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.2829 -1.79099 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.0369 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5799 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2257 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1698 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2104 163 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 20.606] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2820 163 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 286.916 20.606] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(3) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +1 g +162 18 510.93 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 38.849 6.16099] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +1 g +673 18 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 100.162 6.16099] Tm +0 0 Td +/F22_0 11.9551 Tf +(0) 5.84604 Tj +Q +0.953 g +1389 18 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 143.844 6.16099] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.74895 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.3724 -1.79099 Td +(;) 2.34321 Tj +13.7156 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.9397 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.2829 -1.79099 Td +/F19_0 7.97011 Tf +(0) 4.22416 Tj +25.0369 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.5799 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2257 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.1698 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2104 18 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 215.366 6.16099] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(1) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +Q +0.953 g +2820 18 715.59 144.54 re +f +0 g +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 286.916 6.16099] Tm +0 0 Td +/F13_0 11.9551 Tf +(h) 6.73072 Tj +6.77715 -1.79099 Td +/F16_0 7.97011 Tf +(k) 4.40747 Tj +11.4006 -1.79099 Td +(;) 2.34321 Tj +13.7438 -1.79099 Td +/F19_0 7.97011 Tf +(4) 4.22416 Tj +17.9679 -1.79099 Td +/F16_0 7.97011 Tf +(;) 2.34321 Tj +20.3111 -1.79099 Td +/F19_0 7.97011 Tf +(2) 4.22416 Tj +25.0652 0 Td +/F22_0 11.9551 Tf +(\() 4.54294 Tj +29.6081 0 Td +/F13_0 11.9551 Tf +(n) 6.98178 Tj +39.2539 0 Td +/F25_0 11.9551 Tf +(\241) 9.28911 Tj +51.198 0 Td +/F22_0 11.9551 Tf +(2\)) 10.389 Tj +68.5981 168.624 Td +/F10_0 9.96264 Tf +(3) 6.63512 Tj +68.5981 151.083 Td +(7) 6.63512 Tj +68.5981 145.107 Td +(7) 6.63512 Tj +68.5981 139.131 Td +(7) 6.63512 Tj +68.5981 133.155 Td +(7) 6.63512 Tj +68.5981 127.179 Td +(7) 6.63512 Tj +68.5981 121.194 Td +(7) 6.63512 Tj +68.5981 115.218 Td +(7) 6.63512 Tj +68.5981 109.242 Td +(7) 6.63512 Tj +68.5981 103.266 Td +(7) 6.63512 Tj +68.5981 97.2901 Td +(7) 6.63512 Tj +68.5981 91.3141 Td +(7) 6.63512 Tj +68.5981 85.3291 Td +(7) 6.63512 Tj +68.5981 79.3531 Td +(7) 6.63512 Tj +68.5981 73.3771 Td +(7) 6.63512 Tj +68.5981 67.4011 Td +(7) 6.63512 Tj +68.5981 61.4251 Td +(7) 6.63512 Tj +68.5981 55.4401 Td +(7) 6.63512 Tj +68.5981 49.4641 Td +(7) 6.63512 Tj +68.5981 43.4881 Td +(7) 6.63512 Tj +68.5981 37.5121 Td +(7) 6.63512 Tj +68.5981 31.5361 Td +(7) 6.63512 Tj +68.5981 25.5601 Td +(7) 6.63512 Tj +68.5981 19.5751 Td +(7) 6.63512 Tj +68.5981 13.2031 Td +(5) 6.63512 Tj +75.2401 -4.83294 Td +/F19_0 7.97011 Tf +(12) 8.44832 Tj +83.6884 -4.83294 Td +/F28_0 7.97011 Tf +(\243) 6.58331 Tj +90.2717 -4.83294 Td +/F19_0 7.97011 Tf +(5) 4.22416 Tj +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font FGXNEI+CMEX10 +%%+ font TPVOAW+CMSY8 +%%+ font EIXNXU+CMSY10 +%%+ font OLGOPF+CMR12 +%%+ font DIRGWX+CMR8 +%%+ font JGBJQA+CMMI8 +%%+ font TSAJCV+CMMI12 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf new file mode 100644 index 00000000000..5cfbbb8bb50 Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.eps new file mode 100644 index 00000000000..b56e6f87488 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.eps @@ -0,0 +1,1279 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 2.01 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 477 68 +%%HiResBoundingBox: 0 0 476.22 67.27 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 2.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 14 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFill [0] def + /pdfStroke [0] def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def +} def +/pdfEndPage { end } def +% separation convention operators +/findcmykcustomcolor where { + pop +}{ + /findcmykcustomcolor { 5 array astore } def +} ifelse +/setcustomcolor where { + pop +}{ + /setcustomcolor { + exch + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval cvx + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace setcolor + } def +} ifelse +/customcolorimage where { + pop +}{ + /customcolorimage { + gsave + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval cvx + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace + 10 dict begin + /ImageType 1 def + /DataSource exch def + /ImageMatrix exch def + /BitsPerComponent exch def + /Height exch def + /Width exch def + /Decode [1 0] def + currentdict end + image + grestore + } def +} ifelse +% PDF color state +/sCol { + pdfLastStroke not { + pdfStroke aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastStroke true def /pdfLastFill false def + } if +} def +/fCol { + pdfLastFill not { + pdfFill aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastFill true def /pdfLastStroke false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16L3 { + 1 index /CIDFont resourcestatus { + pop pop 1 index /CIDFont findresource /CIDFontType known + } { + false + } ifelse + { + 0 eq { /Identity-H } { /Identity-V } ifelse + exch 1 array astore composefont pop + } { + pdfMakeFont16 + } ifelse +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { end grestore } def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% color operators +/g { dup 1 array astore /pdfFill exch def setgray + /pdfLastFill true def /pdfLastStroke false def } def +/G { dup 1 array astore /pdfStroke exch def setgray + /pdfLastStroke true def /pdfLastFill false def } def +/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor + /pdfLastFill true def /pdfLastStroke false def } def +/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor + /pdfLastStroke true def /pdfLastFill false def } def +/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor + /pdfLastFill true def /pdfLastStroke false def } def +/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor + /pdfLastStroke true def /pdfLastFill false def } def +/ck { 6 copy 6 array astore /pdfFill exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastFill true def /pdfLastStroke false def } def +/CK { 6 copy 6 array astore /pdfStroke exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastStroke true def /pdfLastFill false def } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/awcp { % awidthcharpath + exch { + 1 string dup 0 3 index put 2 index charpath + 3 index 3 index rmoveto + 4 index eq { 5 index 5 index rmoveto } if + } forall + 6 {pop} repeat +} def +/Tj { fCol + 0 pdfTextRise pdfTextMat dtransform rmoveto + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 8 6 roll moveto + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/Tj16 { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse + 0 pdfTextRise pdfTextMat dtransform rmoveto + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll awidthshow + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse + 0 pdfTextRise pdfTextMat dtransform rmoveto + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll awidthshow + 0 pdfTextRise neg pdfTextMat dtransform rmoveto } def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +% Level 1 image operators +/pdfIm1 { + /pdfImBuf1 4 index string def + { currentfile pdfImBuf1 readhexstring pop } image +} def +/pdfIm1Sep { + /pdfImBuf1 4 index string def + /pdfImBuf2 4 index string def + /pdfImBuf3 4 index string def + /pdfImBuf4 4 index string def + { currentfile pdfImBuf1 readhexstring pop } + { currentfile pdfImBuf2 readhexstring pop } + { currentfile pdfImBuf3 readhexstring pop } + { currentfile pdfImBuf4 readhexstring pop } + true 4 colorimage +} def +/pdfImM1 { + /pdfImBuf1 4 index 7 add 8 idiv string def + { currentfile pdfImBuf1 readhexstring pop } imagemask +} def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImSep { + findcmykcustomcolor exch + dup /Width get /pdfImBuf1 exch string def + begin Width Height BitsPerComponent ImageMatrix DataSource end + /pdfImData exch def + { pdfImData pdfImBuf1 readstring pop + 0 1 2 index length 1 sub { + 1 index exch 2 copy get 255 exch sub put + } for } + 6 5 roll customcolorimage + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font VWGKMN+CMMI12~1b +%!FontType1-1.0: VWGKMN+CMMI12~1b +11 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI12) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /VWGKMN+CMMI12~1b def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [-30 -250 1026 750] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 110 /n put +dup 105 /i put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B +1A564DFCECB963478373C69F52172F071E0AA6082A3E10D9E1CE02D4556639B7 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All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /VTBQKO+CMSY10~18 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [-29 -960 1116 775] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 161 /minus put +dup 112 /radical put +dup 188 /approxequal put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B +1A564DFCECB963478373C69F52172F071E0AA6082A3E10D9E1CE02D4556639B7 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All Rights Reserved) readonly def +/FullName (CMR17) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /GMDPHN+CMR17~15 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [-33 -250 945 749] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 99 /c put +dup 111 /o put +dup 115 /s put +dup 49 /one put +dup 50 /two put +dup 40 /parenleft put +dup 41 /parenright put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B 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All Rights Reserved) readonly def +/FullName (CMMI12) readonly def +/FamilyName (Computer Modern) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /HKDPOA+CMMI12 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [-30 -250 1026 750] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 110 /n put +dup 100 /d put +dup 102 /f put +dup 105 /i put +dup 120 /x put +dup 188 /pi put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 +1985C79DC71C47E26F9F0F042B2CDEE97B679358059256FB93D662D43C7ECB5B 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Tj +104.033 18.54 Td +/F25_0 24.7871 Tf +(\274) 19.2596 Tj +131.416 35.307 Td +/F19_0 24.7871 Tf +(\274) 13.7568 Tj +Q +2306 270 146.61 4.0498 re +f +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 230.715 3.97798] Tm +0 0 Td +/F19_0 24.7871 Tf +(n) 14.4757 Tj +29.484 33.156 Td +/F28_0 20.6626 Tf +(n) 12.067 Tj +28.332 30.168 Td +/F10_0 9.96264 Tf +(X) 14.3861 Tj +19.899 0.01801 Td +/F28_0 20.6626 Tf +(i) 6.90131 Tj +26.8003 0.01801 Td +/F13_0 20.6626 Tf +(=1) 24.3199 Tj +55.287 17.001 Td +/F19_0 24.7871 Tf +(f) 11.9474 Tj +74.025 49.698 Td +/F10_0 9.96264 Tf +(0) 8.71731 Tj +74.025 32.166 Td +(B) 8.71731 Tj +74.025 26.181 Td +(B) 8.71731 Tj +74.025 20.205 Td +(B) 8.71731 Tj +74.025 13.833 Td +(@) 8.71731 Tj +82.737 17.001 Td +/F22_0 24.7871 Tf +(cos) 30.3146 Tj +117.216 49.698 Td +/F10_0 9.96264 Tf +(0) 8.71731 Tj +117.216 32.166 Td +(B) 8.71731 Tj +117.216 26.181 Td +(B) 8.71731 Tj +117.216 20.205 Td +(B) 8.71731 Tj +117.216 13.833 Td +(@) 8.71731 Tj +127.134 33.768 Td +/F22_0 24.7871 Tf +(2) 11.3525 Tj +138.486 33.768 Td +/F19_0 24.7871 Tf +(i) 8.27889 Tj +152.273 33.768 Td +/F25_0 24.7871 Tf +(\241) 19.2596 Tj +177.041 33.768 Td +/F22_0 24.7871 Tf +(1) 11.3525 Tj +Q +3578 270 613.17 4.0498 re +f +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +[1 0 0 1 375.579 3.97798] Tm +0 0 Td +/F22_0 24.7871 Tf +(2) 11.3525 Tj +11.3525 0 Td +/F19_0 24.7871 Tf +(n) 14.4757 Tj +44.7751 49.698 Td +/F10_0 9.96264 Tf +(1) 8.71731 Tj +44.7751 32.166 Td +(C) 8.71731 Tj +44.7751 26.181 Td +(C) 8.71731 Tj +44.7751 20.205 Td +(C) 8.71731 Tj +44.7751 13.833 Td +(A) 8.71731 Tj +53.4961 49.698 Td +(1) 8.71731 Tj +53.4961 32.166 Td +(C) 8.71731 Tj +53.4961 26.181 Td +(C) 8.71731 Tj +53.4961 20.205 Td +(C) 8.71731 Tj +53.4961 13.833 Td +(A) 8.71731 Tj +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font VWGKMN+CMMI12~1b +%%+ font VTBQKO+CMSY10~18 +%%+ font GMDPHN+CMR17~15 +%%+ font HKDPOA+CMMI12 +%%+ font QPMPZX+CMSY10 +%%+ 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exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFill [0] def + /pdfStroke [0] def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% separation convention operators +/findcmykcustomcolor where { + pop +}{ + /findcmykcustomcolor { 5 array astore } def +} ifelse +/setcustomcolor where { + pop +}{ + /setcustomcolor { + exch + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval cvx + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace setcolor + } def +} ifelse +/customcolorimage where { + pop +}{ + /customcolorimage { + gsave + [ exch /Separation exch dup 4 get exch /DeviceCMYK exch + 0 4 getinterval + [ exch /dup load exch { mul exch dup } /forall load + /pop load dup ] cvx + ] setcolorspace + 10 dict begin + /ImageType 1 def + /DataSource exch def + /ImageMatrix exch def + /BitsPerComponent exch def + /Height exch def + /Width exch def + /Decode [1 0] def + currentdict end + image + grestore + } def +} ifelse +% PDF color state +/sCol { + pdfLastStroke not { + pdfStroke aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastStroke true def /pdfLastFill false def + } if +} def +/fCol { + pdfLastFill not { + pdfFill aload length + dup 1 eq { + pop setgray + }{ + dup 3 eq { + pop setrgbcolor + }{ + 4 eq { + setcmykcolor + }{ + findcmykcustomcolor exch setcustomcolor + } ifelse + } ifelse + } ifelse + /pdfLastFill true def /pdfLastStroke false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16L3 { + 1 index /CIDFont resourcestatus { + pop pop 1 index /CIDFont findresource /CIDFontType known + } { + false + } ifelse + { + 0 eq { /Identity-H } { /Identity-V } ifelse + exch 1 array astore composefont pop + } { + pdfMakeFont16 + } ifelse +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { end grestore } def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% color operators +/g { dup 1 array astore /pdfFill exch def setgray + /pdfLastFill true def /pdfLastStroke false def } def +/G { dup 1 array astore /pdfStroke exch def setgray + /pdfLastStroke true def /pdfLastFill false def } def +/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor + /pdfLastFill true def /pdfLastStroke false def } def +/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor + /pdfLastStroke true def /pdfLastFill false def } def +/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor + /pdfLastFill true def /pdfLastStroke false def } def +/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor + /pdfLastStroke true def /pdfLastFill false def } def +/ck { 6 copy 6 array astore /pdfFill exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastFill true def /pdfLastStroke false def } def +/CK { 6 copy 6 array astore /pdfStroke exch def + findcmykcustomcolor exch setcustomcolor + /pdfLastStroke true def /pdfLastFill false def } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImSep { + findcmykcustomcolor exch + dup /Width get /pdfImBuf1 exch string def + dup /Decode get aload pop 1 index sub /pdfImDecodeRange exch def + /pdfImDecodeLow exch def + begin Width Height BitsPerComponent ImageMatrix DataSource end + /pdfImData exch def + { pdfImData pdfImBuf1 readstring pop + 0 1 2 index length 1 sub { + 1 index exch 2 copy get + pdfImDecodeRange mul 255 div pdfImDecodeLow add round cvi + 255 exch sub put + } for } + 6 5 roll customcolorimage + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font PGQRTT+SFTT1095 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/oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/germandbls] +pdfMakeFont +%%BeginResource: font HVKGPJ+URWPalladioL-Roma +%!PS-AdobeFont-1.0: URWPalladioL-Roma 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Roman) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Roman) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /HVKGPJ+URWPalladioL-Roma def +/PaintType 0 def +/WMode 0 def +/FontBBox {-166 -283 1021 943} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /YVFMIW+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /angbracketrightbig put +dup 12 /vextendsingle put +dup 13 /vextenddouble put +dup 49 /parenrighttp put +dup 50 /bracketlefttp put +dup 51 /bracketrighttp put +dup 65 /parenrightbt put +dup 66 /parenleftex put +dup 67 /parenrightex put +dup 97 /coproductdisplay put +dup 98 /hatwide put +dup 99 /hatwider put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font JHSYYF+PAMathSyA +%!PS-AdobeFont-1.0: PAMathSyA 001.005 +%%CreationDate: Wed Oct 08 17:22:46 2003 +%%VMusage: 120000 150000 +11 dict begin +/FontInfo 14 dict dup begin +/version (001.005) readonly def +/Notice (Copyright (c) 2000-2003 MicroPress, Inc. All rights reserved.) readonly def +/FullName (PAMathSyA) readonly def +/FamilyName (PAMathSyA) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +/Weight (Normal) readonly def +end readonly def +/FontName /JHSYYF+PAMathSyA def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 11 /harpoonrightleft put +dup 12 /squareminus put +dup 13 /forces put +dup 49 /equalorgreater put +dup 50 /equalorprecedes put +dup 51 /equalorfollows put +dup 65 /squareoriginal put +dup 66 /triangleright put +dup 67 /triangleleft put +dup 97 /frown put +dup 98 /subsetdbl put +dup 99 /supersetdbl put +readonly def +/PaintType 0 def +/FontType 1 def +/FontMatrix [ 0.00100 0 0 0.00100 0 0 ] readonly def +/FontBBox { 1 -398 1228 922 } readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bcf7c3c3333173232e3fdbff43949 +1db866c39088c203dc22fdc758584860ec7bb67fda28cc6208249060e18fab32 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+0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndResource +/F16_0 /OUTYJC+PAMathSyB 1 1 +[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/notgreaterorslnteql/lessnotequal/greaternotequal/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/notforces/notsatisfies/notforcesextra/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/A/B/C/.notdef/.notdef/.notdef/.notdef + 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+ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font XFAPVH+URWPalladioL-Bold +%!PS-AdobeFont-1.0: URWPalladioL-Bold 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Bold) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /XFAPVH+URWPalladioL-Bold def +/PaintType 0 def +/WMode 0 def +/FontBBox {-152 -301 1000 935} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply + /Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls + /agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla + /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis + /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide + /oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +pdfMakeFont +%%BeginResource: font QBRTMK+PATextEx-Bold +%!PS-AdobeFont-1.0: PATextEx-Bold 001.001 +%%CreationDate: Thu Jun 19 16:25:18 2003 +%%VMusage: 120000 150000 +11 dict begin +/FontInfo 14 dict dup begin +/version (001.001) readonly def +/Notice (Copyright (c) MicroPress Inc., 2001, 2003. All rights reserved.) readonly def +/FullName (PATextEx Bold) readonly def +/FamilyName (PATextEx) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +/Weight (Bold) readonly def +end readonly def +/FontName /QBRTMK+PATextEx-Bold def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 19 /ff put +readonly def +/PaintType 0 def +/FontType 1 def +/FontMatrix [ 0.00100 0 0 0.00100 0 0 ] readonly def +/FontBBox { -4 -266 1170 924 } readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bcf7c3c3333173232e3fdbff43949 +1db866c39088c203dc22fdc758584860ec7bb67fda28cc6208249060e18fab32 +204779b5c03c0493bbbbc95cf02692cc4deaa8d2ea90b5c2e64374e92bcb8501 +429b8fae4a76c0c6b76d6ff7cf9a7d5edfbca0e959541c59bd05b7de43d25d53 +fc3dda6ef0c2743978a6d03e19cced4a11f2ea4bcc3110be8b8d9e2772361969 +c19258efafdc276cb1ade9208a941a36d18f9fb1c33def76aa315ddb05770ecd 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font YIQOKH+URWPalladioL-Ital +%!PS-AdobeFont-1.0: URWPalladioL-Ital 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Italic) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Regular) readonly def +/ItalicAngle -9.5 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /YIQOKH+URWPalladioL-Ital def +/PaintType 0 def +/WMode 0 def +/FontBBox {-170 -305 1010 941} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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Tj +1 TJm +(t) 4.70715 Tj +[1 0 0 1 285.439 543.845] cm +0 g +0 G +[1 0 0 1 -285.439 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +285.439 543.845 Td +/F21_0 8.966 Tf +({123) 18.8286 Tj +[1 0 0 1 304.264 543.845] cm +0 g +0 G +[1 0 0 1 -304.264 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +304.264 543.845 Td +/F21_0 8.966 Tf +(abcAB) 23.5358 Tj +1 TJm +(C) 4.70715 Tj +[1 0 0 1 332.501 543.845] cm +0 g +0 G +[1 0 0 1 -332.501 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +332.501 543.845 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 337.207 543.845] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -337.207 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +337.207 543.845 Td +/F21_0 8.966 Tf +(alpha) 23.5358 Tj +[1 0 0 1 360.738 543.845] cm +0 g +0 G +[1 0 0 1 -360.738 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +360.738 543.845 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 365.445 543.845] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -365.445 -543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +365.445 543.845 Td +/F21_0 8.966 Tf +(beta) 18.8286 Tj +[1 0 0 1 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-543.845] cm +[1 0 0 1 0 0] Tm +0 0 Td +459.568 543.845 Td +/F21_0 8.966 Tf +(\)) 4.70715 Tj +[1 0 0 1 244.402 532.886] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +0 g +0 G +[1 0 0 1 -0.399 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 228.694 10.959 re +f +[1 0 0 1 228.693 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.398 3.288] cm +0 g +0 G +[1 0 0 1 -0.398 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 -479.472 -529.598] cm +[1 0 0 1 0 0] Tm +0 0 Td 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-3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +0 g +0 G +[1 0 0 1 -0.399 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 228.694 10.959 re +f +[1 0 0 1 228.693 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.398 3.288] cm +0 g +0 G +[1 0 0 1 -0.398 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 -479.472 -496.722] cm +[1 0 0 1 0 0] Tm +0 0 Td +243.007 500.01 Td +/F10_0 5.978 Tf +(5) 2.989 Tj +247.79 500.01 Td +/F21_0 8.966 Tf +($\\) 9.4143 Tj +[1 0 0 1 257.202 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -257.202 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +257.202 500.01 Td +/F21_0 8.966 Tf +(maths) 23.5358 Tj +1 TJm +(f) 4.70715 Tj +[1 0 0 1 285.439 500.01] cm +0 g +0 G +[1 0 0 1 -285.439 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +285.439 500.01 Td +/F21_0 8.966 Tf +({123) 18.8286 Tj +[1 0 0 1 304.264 500.01] cm +0 g +0 G +[1 0 0 1 -304.264 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +304.264 500.01 Td +/F21_0 8.966 Tf +(abcAB) 23.5358 Tj +1 TJm +(C) 4.70715 Tj +[1 0 0 1 332.501 500.01] cm +0 g +0 G +[1 0 0 1 -332.501 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +332.501 500.01 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 337.207 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -337.207 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +337.207 500.01 Td +/F21_0 8.966 Tf +(alpha) 23.5358 Tj +[1 0 0 1 360.738 500.01] cm +0 g +0 G +[1 0 0 1 -360.738 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +360.738 500.01 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 365.445 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -365.445 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +365.445 500.01 Td +/F21_0 8.966 Tf +(beta) 18.8286 Tj +[1 0 0 1 384.269 500.01] cm +0 g +0 G +[1 0 0 1 -384.269 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +384.269 500.01 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 388.976 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -388.976 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +388.976 500.01 Td +/F21_0 8.966 Tf +(gamma) 23.5358 Tj +[1 0 0 1 412.507 500.01] cm +0 g +0 G +[1 0 0 1 -412.507 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +417.213 500.01 Td +/F21_0 8.966 Tf +(\(\\) 9.4143 Tj +[1 0 0 1 426.625 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -426.625 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +426.625 500.01 Td +/F21_0 8.966 Tf +(the) 14.1215 Tj +[1 0 0 1 440.744 500.01] cm +0 g +0 G +[1 0 0 1 -440.744 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +440.744 500.01 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 445.45 500.01] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -445.45 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +445.45 500.01 Td +/F21_0 8.966 Tf +(fam) 14.1215 Tj +[1 0 0 1 459.568 500.01] cm +0 g +0 G +[1 0 0 1 -459.568 -500.01] cm +[1 0 0 1 0 0] Tm +0 0 Td +459.568 500.01 Td +/F21_0 8.966 Tf +(\)) 4.70715 Tj +[1 0 0 1 244.402 489.051] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +0 g +0 G +[1 0 0 1 -0.399 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 228.694 10.959 re +f +[1 0 0 1 228.693 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.398 3.288] cm +0 g +0 G +[1 0 0 1 -0.398 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 -479.472 -485.763] cm +[1 0 0 1 0 0] Tm +0 0 Td +257.752 489.051 Td +/F21_0 8.966 Tf +(}$\\\\[) 23.5358 Tj +1 TJm +(5) 4.70715 Tj +[1 0 0 1 285.989 489.051] cm +0 g +0 G +[1 0 0 1 -285.989 -489.051] cm +[1 0 0 1 0 0] Tm +0 0 Td +285.989 489.051 Td +/F21_0 8.966 Tf +(pt) 9.4143 Tj +[1 0 0 1 295.402 489.051] cm +0 g +0 G +[1 0 0 1 -295.402 -489.051] cm +[1 0 0 1 0 0] Tm +0 0 Td +295.402 489.051 Td +/F21_0 8.966 Tf +(]) 4.70715 Tj +[1 0 0 1 244.402 478.092] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +0 g +0 G +[1 0 0 1 -0.399 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 228.694 10.959 re +f +[1 0 0 1 228.693 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.398 3.288] cm +0 g +0 G +[1 0 0 1 -0.398 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 -479.472 -474.804] cm +[1 0 0 1 0 0] Tm +0 0 Td +243.007 478.092 Td +/F10_0 5.978 Tf +(6) 2.989 Tj +247.79 478.092 Td +/F21_0 8.966 Tf +($\\) 9.4143 Tj +[1 0 0 1 257.202 478.092] cm +0 g +0 G +[1 0 0 1 -257.202 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +257.202 478.092 Td +/F21_0 8.966 Tf +(mathn) 23.5358 Tj +1 TJm +(ormal) 23.5358 Tj +[1 0 0 1 304.264 478.092] cm +0 g +0 G +[1 0 0 1 -304.264 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +304.264 478.092 Td +/F21_0 8.966 Tf +({123) 18.8286 Tj +[1 0 0 1 323.089 478.092] cm +0 g +0 G +[1 0 0 1 -323.089 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +323.089 478.092 Td +/F21_0 8.966 Tf +(abcAB) 23.5358 Tj +1 TJm +(C) 4.70715 Tj +[1 0 0 1 351.326 478.092] cm +0 g +0 G +[1 0 0 1 -351.326 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +351.326 478.092 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 356.032 478.092] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -356.032 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +356.032 478.092 Td +/F21_0 8.966 Tf +(alpha) 23.5358 Tj +[1 0 0 1 379.563 478.092] cm +0 g +0 G +[1 0 0 1 -379.563 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +379.563 478.092 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 384.269 478.092] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -384.269 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +384.269 478.092 Td +/F21_0 8.966 Tf +(beta) 18.8286 Tj +[1 0 0 1 403.094 478.092] cm +0 g +0 G +[1 0 0 1 -403.094 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +403.094 478.092 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 407.8 478.092] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -407.8 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +407.8 478.092 Td +/F21_0 8.966 Tf +(gamma) 23.5358 Tj +[1 0 0 1 431.331 478.092] cm +0 g +0 G +[1 0 0 1 -431.331 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +436.037 478.092 Td +/F21_0 8.966 Tf +(\(\\) 9.4143 Tj +[1 0 0 1 445.45 478.092] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -445.45 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +445.45 478.092 Td +/F21_0 8.966 Tf +(the) 14.1215 Tj +[1 0 0 1 459.568 478.092] cm +0 g +0 G +[1 0 0 1 -459.568 -478.092] cm +[1 0 0 1 0 0] Tm +0 0 Td +459.568 478.092 Td +/F21_0 8.966 Tf +(\\) 4.70715 Tj +[1 0 0 1 244.402 467.133] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +0 g +0 G +[1 0 0 1 -0.399 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.399 3.288] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 228.694 10.959 re +f +[1 0 0 1 228.693 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +0 0 2.989 10.959 re +f +[1 0 0 1 2.989 3.288] cm +0 g +0 G +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 0 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 0.398 3.288] cm +0 g +0 G +[1 0 0 1 -0.398 -3.288] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 10.959 l +S +Q +[1 0 0 1 -221.72 3.288] cm +0 0 1 rg +0 0 1 RG +[1 0 0 1 -257.752 -467.133] cm +[1 0 0 1 0 0] Tm +0 0 Td +257.752 467.133 Td +/F21_0 8.966 Tf +(fam) 14.1215 Tj +[1 0 0 1 271.871 467.133] cm +0 g +0 G +[1 0 0 1 -271.871 -467.133] cm +[1 0 0 1 0 0] Tm +0 0 Td +271.871 467.133 Td +/F21_0 8.966 Tf +(\)}$) 14.1215 Tj +[1 0 0 1 244.402 460.458] cm +1 1 0.85 rg +1 1 0.85 RG +0 0 235.468 3.387 re +f +[1 0 0 1 235.468 0] cm +0 g +0 G +[1 0 0 1 -232.08 0] cm +1 1 0.85 rg +1 1 0.85 RG +[1 0 0 1 228.693 0] cm +0 g +0 G +[1 0 0 1 -232.081 0] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 3.387 l +S +Q +q +[] 0 d +0 J +0.398 w +0 0.199 m +3.387 0.199 l +S +Q +[1 0 0 1 3.388 0] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +228.694 0.199 l +S +Q +[1 0 0 1 228.693 0] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +3.387 0.199 l +S +Q +[1 0 0 1 2.989 0] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 3.387 l +S +Q +[1 0 0 1 -231.682 3.387] cm +0 g +0 G +[1 0 0 1 -9.413 -3.387] cm +0 g +0 G +[1 0 0 1 -120.549 -368.825] cm +0 g +0 G +[1 0 0 1 358.655 0] cm +0 g +0 G +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font PGQRTT+SFTT1095 +%%+ font HVKGPJ+URWPalladioL-Roma +%%+ font XEDWYH+PAMath-Italic +%%+ font RFLDOC+PATextEx +%%+ font PRHKDE+PAMathSy +%%+ font YVFMIW+CMEX10 +%%+ font JHSYYF+PAMathSyA +%%+ font OUTYJC+PAMathSyB +%%+ font XFAPVH+URWPalladioL-Bold +%%+ font QBRTMK+PATextEx-Bold +%%+ font YIQOKH+URWPalladioL-Ital +%%+ font WJYWHM+CMTT10 +%%+ font SHXCWH+SFTT0900 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/family.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/family.pdf new file mode 100644 index 00000000000..4e0c6192d4c Binary files /dev/null and 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/pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font MSAM10 +%!FontType1-1.0: MSAM10 +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition 0 def +/UnderlineThickness 0 def +end readonly def +/FontName /MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [-55 -303 703 803] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /notforces put +dup 50 /notsatisfies put +dup 51 /notforcesextra put +dup 52 /nottriangeqlright put +dup 53 /nottriangeqlleft put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 97 /Gmir put +readonly def +currentdict end +currentfile eexec +5AA4F71255501637F1A431BAB555283D093E1B588B45B0281559110D21315C62 +BD638C6B34BA54AA75227715D9947EBCD51A104CAEA657499E94138F5645BF68 +368BB1B1EC8E4776F067FFF2CE9B89FB7E63A7DB304498C1036D399C47A4CB79 +BD517EDB02BEB90195FD7DDAF3E839BCE2DB156D9337DBB2305A465B3E0FFB97 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/agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla + /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis + /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide + /oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +pdfMakeFont +%%BeginResource: font LuxiMono +%!FontType1-1.0: LuxiMono +12 dict begin +/FontInfo 10 dict dup begin +/Notice (Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def +/Copyright (Copyright Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def +/FullName (Luxi Mono Regular) readonly def +/FamilyName (Luxi Mono) readonly def +/isFixedPitch true def +/ItalicAngle 0 def +/UnderlinePosition 0 def +/UnderlineThickness 0 def +end readonly def +/FontName /LuxiMono def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/FontBBox [0 -193 588 784] readonly def +/StrokeWidth 0 def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 36 /dollar put +dup 38 /ampersand put +dup 43 /plus put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 61 /equal put +dup 62 /greater put +dup 64 /at put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 92 /backslash put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 105 /i put +dup 108 /l put +dup 109 /m put +dup 112 /p put +dup 115 /s put +dup 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254.152 29.8906 109.59 re +f +79.3594 254.152 3420.77 109.59 re +f +3500.13 254.152 29.8906 109.59 re +f +/DeviceRGB {} CS +[1 1 0.800766] SC +3532 254.152 m +3532 363.742 l +S +/DeviceGray {} CS +[0] SC +3532 254.152 m +3532 363.742 l +S +/DeviceGray {} cs +[0] sc +q +[10 0 0 10 0 0] cm +[1 0 0 1 0 0] Tm +0 0 Td +0.000299215 Tc +[1 0 0 1 0.184766 28.7031] Tm +0 0 Td +/F10_0 4.981 Tf +(5) 2.76944 Tj +0.000203133 Tc +7.75117 0 Td +/F12_0 8.07 Tf +($\\) 9.684 Tj +17.434 0 Td +/F14_0 8.07 Tf +(mathsf) 29.052 Tj +0.000203301 Tc +46.4852 0 Td +/F12_0 8.07 Tf +({12345abcdeABCDE\\) 82.314 Tj +0.000202942 Tc +128.796 0 Td +/F14_0 8.07 Tf +(alpha) 24.21 Tj +0.000203133 Tc +153.005 0 Td +/F12_0 8.07 Tf +(\\) 4.842 Tj +157.847 0 Td +/F14_0 8.07 Tf +(beta) 19.368 Tj +177.214 0 Td +/F12_0 8.07 Tf +(\\) 4.842 Tj +0.000202942 Tc +182.056 0 Td +/F14_0 8.07 Tf +(gamma) 24.21 Tj +0.000203133 Tc +206.265 0 Td +/F12_0 8.07 Tf +(\\) 4.842 Tj +0.000202942 Tc +211.107 0 Td +/F14_0 8.07 Tf +(delta) 24.21 Tj 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diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf new file mode 100644 index 00000000000..eb52309ebcd Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.eps new file mode 100644 index 00000000000..ea22fc55133 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.eps @@ -0,0 +1,4024 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 3.01 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 362 158 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 3.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font WBJEOI+LMRoman10-Bold +%!PS-AdobeFont-1.0: LMRoman10-Bold 0.99.3 +%%CreationDate: 28th September (Friday), 2005 +% Generated by MetaType1 (a MetaPost-based engine) +% Supported by DANTE eV, GUST, GUTenberg, NTG, and TUG. METATYPE1/Type 1 version by B. Jackowski & J. M. Nowacki from GUST (http://www.gust.org.pl). +% Copyright 2003--2005 TeX USERS GROUPS. +% This work is released under the GUST Font Source License. +% For the most recent version of this license see +% http://www.gust.org.pl/fonts/licenses/GUST-FONT-SOURCE-LICENSE.txt or +% http://tug.org/fonts/licenses/GUST-FONT-SOURCE-LICENSE.txt +% This work has the LPPL maintenance status "maintained". +% The Current Maintainer of this work is Bogus\l{}aw Jackowski and Janusz M. Nowacki. +% This work consists of the files listed in the MANIFEST.txt file. +% ADL: 806 194 0 +%%EndComments +FontDirectory/LMRoman10-Bold known{/LMRoman10-Bold findfont dup/UniqueID known{dup +/UniqueID get 0 eq exch/FontType get 1 eq and}{pop false}ifelse +{save true}{false}ifelse}{false}ifelse +17 dict begin +/FontInfo 9 dict dup begin +/version(0.99.3)readonly def +/Notice(Supported by DANTE eV, GUST, GUTenberg, NTG, and TUG. METATYPE1/Type 1 version by B. Jackowski & J. 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All Rights Reserved. +% Notice: This font is not in the public domain +% Notice: Computer Modern fonts were designed by Donald E. Knuth +11 dict begin +/FontInfo 9 dict dup begin +/version (001.100) readonly def +/Notice (Copyright (c) 1996 Y&Y, Inc. All Right Reserved. http://www.YandY.com) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /BSVUWA+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 26 /propersubset put +dup 47 /proportional put +dup 49 /infinity put +dup 59 /emptyset put +dup 102 /braceleft put +dup 103 /braceright put +dup 110 /backslash put +dup 114 /nabla put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f 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+0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndResource +/F12_0 /BSVUWA+CMSY10 1 1 +[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/propersubset/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/proportional + /.notdef/infinity/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/emptyset/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/braceleft/braceright + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/backslash/.notdef + /.notdef/.notdef/nabla/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font GWPATD+CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /GWPATD+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /Gamma put +dup 1 /Delta put +dup 2 /Theta put +dup 3 /Lambda put +dup 4 /Xi put +dup 5 /Pi put +dup 6 /Sigma put +dup 7 /Upsilon put +dup 8 /Phi put +dup 9 /Psi put +dup 10 /Omega put +dup 40 /parenleft put +dup 41 /parenright put +dup 49 /one put +dup 50 /two put +dup 61 /equal put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 100 /d put +dup 101 /e put +dup 105 /i put +dup 115 /s put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf7158f1163bc1f3352e22a1452e73feca8a4 +87100fb1ffc4c8af409b2067537220e605da0852ca49839e1386af9d7a1a455f +d1f017ce45884d76ef2cb9bc5821fd25365ddea6e45f332b5f68a44ad8a530f0 +92a36fac8d27f9087afeea2096f839a2bc4b937f24e080ef7c0f9374a18d565c +295a05210db96a23175ac59a9bd0147a310ef49c551a417e0a22703f94ff7b75 +409a5d417da6730a69e310fa6a4229fc7e4f620b0fc4c63c50e99e179eb51e4c 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /JVFEHB+CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 61 /equal put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cabb9ffc6cc3f1e9ae32f234eb60fe7d +e34995b1acff52428ea20c8ed4fd73e3935cebd40e0ead70c0887a451e1b1ac8 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font WWXADO+CMEX10 +%!PS-AdobeFont-1.1: CMEX10 001.101 +%%CreationDate: 1992 Jul 23 21:22:48 +%%RevisionDate: 1997 Feb 16 10:50:33 +% Copyright (C) 1992, 1997 Y&Y, Inc. All Rights Reserved. +% Please note: This font is NOT in the public domain. +11 dict begin +/FontInfo 9 dict dup begin +/version (001.101) readonly def +/Notice (Copyright (c) 1992, 1997 Y&Y, Inc. All Right Reserved. (508) 371-3286) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /WWXADO+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 90 /integraldisplay put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cac6a7beb5d02276e511ffaf2ae11910 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font NMAKYG+MSBM10 +%!PS-AdobeFont-1.1: MSBM10 2.1 +%%CreationDate: 1993 Sep 17 11:10:37 +% Math Symbol fonts were designed by the American Mathematical Society. +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /NMAKYG+MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +dup 102 /Omegainv put +dup 103 /eth put +dup 123 /kappa put +dup 125 /planckover2pi put +dup 126 /planckover2pi1 put +dup 127 /epsiloninv put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 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+%%BeginResource: procset xpdf 3.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: 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All Rights Reserved. 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All Rights Reserved. U.S. Patents D338,907; D337,604.Minion is either a registered trademark or a trademark of Adobe Systems Incorporated in the United States and/or other countries.) readonly def +/FullName (Minion Pro Italic) readonly def +/FamilyName (Minion Pro) readonly def +/Weight (Regular) readonly def +/isFixedPitch false def +/ItalicAngle -12 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/StrokeWidth 0 def +/FontBBox {-201 -360 1684 1002} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc4458babd05d76517d9c24fed216be906 +1643b22aabea637bffcb75ff65a91279495b00b8b92cfb39c8899c3818357033 +2bbd344cbb263d4250a46e5b09e712d88275731e98c996c69406e43e9dbefdd7 +161a841ee17304d49501f13d3ad3cfb00da1700ead2364c31908f18b9f3643ea +e9514021b52ffc8eea03d195015d30e3bb12c272a254955f88a4dcd045432cdb 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+%!PS-AdobeFont-1.0: MinionPro-It 002.000 +9 dict begin +/FontName /PVZOFV+MinionPro-It def +/FontInfo 9 dict dup begin +/version (002.000) readonly def +/Notice (Copyright 2000, 2002, 2004 Adobe Systems Incorporated. All Rights Reserved. U.S. Patents D338,907; D337,604.Minion is either a registered trademark or a trademark of Adobe Systems Incorporated in the United States and/or other countries.) readonly def +/FullName (Minion Pro Italic) readonly def +/FamilyName (Minion Pro) readonly def +/Weight (Regular) readonly def +/isFixedPitch false def +/ItalicAngle -12 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/StrokeWidth 0 def +/FontBBox {-201 -360 1684 1002} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc4458babd05d76517d9c24fed216be906 +1643b22aabea637bffcb75ff65a91279495b00b8b92cfb39c8899c3818357033 +2bbd344cbb263d4250a46e5b09e712d88275731e98c996c69406e43e9dbefdd7 +161a841ee17304d49501f13d3ad3cfb00da1700ead2364c31908f18b9f3643ea +e9514021b52ffc8eea03d195015d30e3bb12c272a254955f88a4dcd045432cdb 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All Rights Reserved. U.S. Patents D338,907; D337,604.Minion is either a registered trademark or a trademark of Adobe Systems Incorporated in the United States and/or other countries.) readonly def +/FullName (Minion Pro Italic) readonly def +/FamilyName (Minion Pro) readonly def +/Weight (Regular) readonly def +/isFixedPitch false def +/ItalicAngle -14.2906 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.00075 0 3e-05 0.001 0 0 ] readonly def +/StrokeWidth 0 def +/FontBBox {-201 -360 1684 1002} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc4458babd05d76517d9c24fed216be906 +1643b22aabea637bffcb75ff65a91279495b00b8b92cfb39c8899c3818357033 +2bbd344cbb263d4250a46e5b09e712d88275731e98c996c69406e43e9dbefdd7 +161a841ee17304d49501f13d3ad3cfb00da1700ead2364c31908f18b9f3643ea +e9514021b52ffc8eea03d195015d30e3bb12c272a254955f88a4dcd045432cdb 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U.S. Patent D371,799.Minion is either a registered trademark or a trademark of Adobe Systems Incorporated in the United States and/or other countries.) readonly def +/FullName (Minion Pro Regular) readonly def +/FamilyName (Minion Pro) readonly def +/Weight (Regular) readonly def +/isFixedPitch false def +/ItalicAngle 0 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/StrokeWidth 0 def +/FontBBox {-290 -360 1684 989} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc4458babd05d76517d9c24fed216be906 +1643b22aabea637bffcb75ff65a91279495b00b8b92cfb39c8899c3818357033 +2bbd344cbb263d4250a46e5b09e712d88275731e98c996c69406e43e9dbefdd7 +161a841ee17304d49501f13d3ad3cfb00da1700ead2364c31908f18b9f3643ea +e9514021b52ffc8eea03d195015d30e3bb12c272a254955f88a4dcd045432cdb 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font JKFWAW+MinionPro-ItLCDFJ +%!PS-AdobeFont-1.0: MinionPro-ItLCDFJ 002.000 +9 dict begin +/FontName /JKFWAW+MinionPro-ItLCDFJ def +/FontInfo 9 dict dup begin +/version (002.000) readonly def +/Notice (Copyright 2000, 2002, 2004 Adobe Systems Incorporated. All Rights Reserved. U.S. Patents D338,907; D337,604.Minion is either a registered trademark or a trademark of Adobe Systems Incorporated in the United States and/or other countries.) readonly def +/FullName (Minion Pro Italic) readonly def +/FamilyName (Minion Pro) readonly def +/Weight (Regular) readonly def +/isFixedPitch false def +/ItalicAngle -12 def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 106 /uni0237 put +readonly def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/StrokeWidth 0 def +/FontBBox {-201 -360 1684 1002} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc4458babd05d76517d9c24fed216be906 +1643b22aabea637bffcb75ff65a91279495b00b8b92cfb39c8899c3818357033 +2bbd344cbb263d4250a46e5b09e712d88275731e98c996c69406e43e9dbefdd7 +161a841ee17304d49501f13d3ad3cfb00da1700ead2364c31908f18b9f3643ea 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All rights reserved. +%%BeginResource: procset GS_epswrite_2_0_1001 +/GS_epswrite_2_0_1001 80 dict dup begin +/PageSize 2 array def/setpagesize{ PageSize aload pop 3 index eq exch +4 index eq and{ pop pop pop}{ PageSize dup 1 +5 -1 roll put 0 4 -1 roll put dup null eq {false} {dup where} ifelse{ exch get exec} +{ pop/setpagedevice where +{ pop 1 dict dup /PageSize PageSize put setpagedevice} +{ /setpage where{ pop PageSize aload pop pageparams 3 {exch pop} repeat +setpage}if}ifelse}ifelse}ifelse} bind def +/!{bind def}bind def/#{load def}!/N/counttomark # +/rG{3{3 -1 roll 255 div}repeat setrgbcolor}!/G{255 div setgray}!/K{0 G}! +/r6{dup 3 -1 roll rG}!/r5{dup 3 1 roll rG}!/r3{dup rG}! +/w/setlinewidth #/J/setlinecap # +/j/setlinejoin #/M/setmiterlimit #/d/setdash #/i/setflat # +/m/moveto #/l/lineto #/c/rcurveto # +/p{N 2 idiv{N -2 roll rlineto}repeat}! +/P{N 0 gt{N -2 roll moveto p}if}! +/h{p closepath}!/H{P closepath}! +/lx{0 rlineto}!/ly{0 exch rlineto}!/v{0 0 6 2 roll c}!/y{2 copy c}! +/re{4 -2 roll m exch dup lx exch ly neg lx h}! +/^{3 index neg 3 index neg}! +/f{P fill}!/f*{P eofill}!/s{H stroke}!/S{P stroke}! +/q/gsave #/Q/grestore #/rf{re fill}! +/Y{P clip newpath}!/Y*{P eoclip newpath}!/rY{re Y}! +/|={pop exch 4 1 roll 1 array astore cvx 3 array astore cvx exch 1 index def exec}! +/|{exch string readstring |=}! +/+{dup type/nametype eq{2 index 7 add -3 bitshift 2 index mul}if}! +/@/currentfile #/${+ @ |}! +/B{{2 copy string{readstring pop}aload pop 4 array astore cvx +3 1 roll}repeat pop pop true}! +/Ix{[1 0 0 1 11 -2 roll exch neg exch neg]exch}! +/,{true exch Ix imagemask}!/If{false exch Ix imagemask}!/I{exch Ix image}! +/Ic{exch Ix false 3 colorimage}! +/F{/Columns counttomark 3 add -2 roll/Rows exch/K -1/BlackIs1 true>> +/CCITTFaxDecode filter}!/FX{<Ks8W-!rHeMDdf9/N +lg(aW]e +, +1110 7011 35 82 /6E +$C +4rKbRBS-J(gAh3Qs8W-!s8W-!s8W,b=n'a^GW[#X%gS0qnt!W-TA=qgm6_3~> +, +1151 7010 48 56 /3I +$C +22$Q(`F/uW3Y%]AF?k^E":a;okrtT4hOdNmo\];pKhS3oG +, +1225 7011 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b/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.eps new file mode 100644 index 00000000000..ca581ae8cb3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.eps @@ -0,0 +1,3471 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 3.01 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 362 160 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 3.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font WNBODM+URWPalladioL-Bold +%!PS-AdobeFont-1.0: URWPalladioL-Bold 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Bold) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /WNBODM+URWPalladioL-Bold def +/PaintType 0 def +/WMode 0 def +/FontBBox {-152 -301 1000 935} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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/dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron + /degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered + /cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown + /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla + /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis + /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply + /Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls + /agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla + /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis + /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide + /oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +pdfMakeFont +%%BeginResource: font IRCLTK+URWPalladioL-Roma +%!PS-AdobeFont-1.0: URWPalladioL-Roma 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Roman) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Roman) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /IRCLTK+URWPalladioL-Roma def +/PaintType 0 def +/WMode 0 def +/FontBBox {-166 -283 1021 943} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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TJm +(punktierten) 52.0069 Tj +-314 TJm +(Kr) 11.1685 Tj +5 TJm +(eisscheibe) 44.2955 Tj +363.521 608.28 Td +/F11_0 9.963 Tf +(D) 8.19955 Tj +371.969 608.28 Td +/F12_0 9.963 Tf +(nf) 9.76374 Tj +381.733 608.28 Td +/F11_0 9.963 Tf +(a) 5.68887 Tj +387.421 608.28 Td +/F12_0 9.963 Tf +(g) 4.78224 Tj +395.332 608.28 Td +/F10_0 9.963 Tf +(ana-) 19.0791 Tj +60.08 596.324 Td +(lytische) 33.8045 Tj +-291 TJm +(Funktion) 40.2704 Tj +139.951 596.324 Td +/F11_0 9.963 Tf +(f) 5.16083 Tj +148.997 596.324 Td +/F10_0 9.963 Tf +(de\002niert) 37.5406 Tj +-291 TJm +(man) 19.5773 Tj +-291 TJm +(das) 15.2932 Tj +-291 TJm +(Residuum) 45.4512 Tj +-291 TJm +(im) 11.6966 Tj +-290 TJm +(Punkt) 26.6112 Tj +322.556 596.324 Td +/F11_0 9.963 Tf +(a) 5.68887 Tj +331.144 596.324 Td +/F10_0 9.963 Tf +(als) 12.105 Tj +164.834 568.678 Td +(Res) 15.6519 Tj +166.655 562.486 Td +/F11_0 6.974 Tf +(z) 3.80083 Tj +170.455 562.486 Td +/F13_0 6.974 Tf +(=) 4.22624 Tj +174.682 562.486 Td +/F11_0 6.974 Tf +(a) 3.98215 Tj +180.485 568.678 Td +/F11_0 9.963 Tf +(f) 5.16083 Tj +186.632 568.678 Td +/F13_0 9.963 Tf +(\() 3.9852 Tj +190.617 568.678 Td +/F11_0 9.963 Tf +(z) 5.42984 Tj +196.046 568.678 Td +/F13_0 9.963 Tf +(\)) 3.9852 Tj +-278 TJm +(=) 6.03758 Tj +211.604 568.678 Td +/F10_0 9.963 Tf +(Res) 15.6519 Tj +217.438 562.486 Td +/F11_0 6.974 Tf +(a) 3.98215 Tj +227.255 568.678 Td +/F11_0 9.963 Tf +(f) 5.16083 Tj +236.169 568.678 Td +/F13_0 9.963 Tf +(=) 6.03758 Tj +251.345 575.423 Td +/F10_0 9.963 Tf +(1) 4.9815 Tj +[1 0 0 1 246.169 570.89] cm +q +[] 0 d +0 J +0.558 w +0 0.279 m +15.332 0.279 l +S +Q +[1 0 0 1 -246.169 -570.89] cm +[1 0 0 1 0 0] Tm +0 0 Td +246.169 561.844 Td +/F10_0 9.963 Tf +(2) 4.9815 Tj +251.151 561.844 Td +/F11_0 9.963 Tf +(\031) 6.65528 Tj +258.603 561.844 Td +/F10_0 9.963 Tf +(i) 2.89923 Tj +264.358 582.546 Td +/F14_0 9.963 Tf +(Z) 5.83832 Tj +264.731 553.246 Td +/F11_0 6.974 Tf +(C) 4.98641 Tj +272.852 568.678 Td +/F11_0 9.963 Tf +(f) 5.16083 Tj +278.999 568.678 Td +/F13_0 9.963 Tf +(\() 3.9852 Tj +282.984 568.678 Td +/F11_0 9.963 Tf +(z) 5.42984 Tj +288.414 568.678 Td +/F13_0 9.963 Tf +(\)) 3.9852 Tj +294.059 568.678 Td +/F11_0 9.963 Tf +(d) 5.86821 Tj +-15 TJm +(z) 5.42984 Tj +-167 TJm +(;) 2.49075 Tj +60.08 533.834 Td +/F10_0 9.963 Tf +(w) 8.30914 Tj +40 TJm +(obei) 18.6208 Tj +90.258 533.834 Td +/F11_0 9.963 Tf +(C) 7.12355 Tj +101.485 533.834 Td +/F12_0 9.963 Tf +(\032) 6.03758 Tj +111.476 533.834 Td +/F11_0 9.963 Tf +(D) 8.19955 Tj +119.925 533.834 Td +/F12_0 9.963 Tf +(nf) 9.76374 Tj +129.688 533.834 Td +/F11_0 9.963 Tf +(a) 5.68887 Tj +135.377 533.834 Td +/F12_0 9.963 Tf +(g) 4.78224 Tj +143.806 533.834 Td +/F10_0 9.963 Tf +(ein) 13.47 Tj +-366 TJm +(geschlossener) 60.8241 Tj +-366 TJm +(W) 9.963 Tj +92 TJm +(eg) 10.3117 Tj +-366 TJm +(mit) 14.9445 Tj +266.986 533.834 Td +/F11_0 9.963 Tf +(n) 5.87817 Tj +272.864 533.834 Td +/F13_0 9.963 Tf +(\() 3.9852 Tj +276.849 533.834 Td +/F11_0 9.963 Tf +(C) 7.12355 Tj +35 TJm +(;) 2.49075 Tj +-167 TJm +(a) 5.68887 Tj +293.464 533.834 Td +/F13_0 9.963 Tf +(\)) 3.9852 Tj +-397 TJm +(=) 6.03758 Tj +311.395 533.834 Td +/F10_0 9.963 Tf +(1) 4.9815 Tj +-366 TJm +(ist) 10.3715 Tj +-366 TJm +(\(z.B.) 19.3681 Tj +-366 TJm +(ein) 13.47 Tj +-366 TJm +(entgegen) 40.2406 Tj +60.08 521.879 Td +(dem) 19.657 Tj +-291 TJm +(Uhrzeigersinn) 63.1056 Tj +-291 TJm +(dur) 16.0305 Tj +10 TJm +(chlaufener) 46.7065 Tj +-290 TJm +(Kr) 11.1685 Tj +5 TJm +(eis\).) 17.7043 Tj +60.08 503.946 Td +(A) 7.75121 Tj +67.831 503.946 Td +/F11_0 9.963 Tf +(\003\001) 15.3231 Tj +83.154 503.946 Td +/F12_0 9.963 Tf +(r) 7.75121 Tj +90.905 503.946 Td +/F10_0 9.963 Tf +(BCD) 20.8625 Tj +111.766 503.946 Td +/F11_0 9.963 Tf +(\006) 7.34273 Tj +119.258 503.946 Td +/F10_0 9.963 Tf +(EF) 11.6268 Tj +130.885 503.946 Td +/F11_0 9.963 Tf +(\000) 5.61913 Tj +137.649 503.946 Td +/F10_0 9.963 Tf +(GHIJKLMNO) 61.4219 Tj +199.069 503.946 Td +/F11_0 9.963 Tf +(\002) 8.0501 Tj +-30 TJm +(\012) 8.29918 Tj +215.866 503.946 Td +/F15_0 9.963 Tf +(f) 8.07003 Tj +223.936 503.946 Td +/F10_0 9.963 Tf +(P) 6.01765 Tj +229.953 503.946 Td +/F11_0 9.963 Tf +(\010) 8.66781 Tj +-15 TJm +(\005) 9.06633 Tj +-67 TJm +(\004) 7.47225 Tj +256.374 503.946 Td +/F10_0 9.963 Tf +(QRSTUVWXY) 64.0222 Tj +320.394 503.946 Td +/F11_0 9.963 Tf +(\007) 6.10732 Tj +-110 TJm +(\011) 7.9704 Tj +336.444 503.946 Td +/F10_0 9.963 Tf +(Z) 6.64532 Tj +60.08 491.991 Td +/F11_0 9.963 Tf +(a\013b) 16.5087 Tj +-15 TJm +(\014) 5.32024 Tj +-15 TJm +(c) 4.61287 Tj +-15 TJm +(@d) 11.298 Tj +-15 TJm +(\016) 5.48961 Tj +-30 TJm +(e) 4.9018 Tj +-15 TJm +(\017) 4.75235 Tj +-15 TJm +(") 4.57302 Tj +-15 TJm +(f) 5.16083 Tj +-99 TJm +(\020) 4.45346 Tj +-15 TJm +(\030) 4.12468 Tj +-30 TJm +(g) 5.47965 Tj +-60 TJm +(\015) 4.38372 Tj +-97 TJm +(h\200) 11.577 Tj +157.056 491.991 Td +/F15_0 9.963 Tf +(}) 5.18076 Tj +162.237 491.991 Td +/F11_0 9.963 Tf +(\023i{j) 12.3143 Tj +-71 TJm +(|) 3.41731 Tj +-15 TJm +(k) 5.48961 Tj +-30 TJm +(\024) 5.79847 Tj +190.411 491.991 Td +/F15_0 9.963 Tf +({) 4.78224 Tj +195.193 491.991 Td +/F11_0 9.963 Tf +(l) 2.82949 Tj +-15 TJm +(`) 4.9018 Tj +-51 TJm +(\025mn\021) 25.6149 Tj +-15 TJm +(\022) 5.31028 Tj +-30 TJm +(#) 6.32651 Tj +-15 TJm +(o\033) 11.1486 Tj +-64 TJm +(&\036) 10.9493 Tj +-15 TJm +('}p) 17.9533 Tj +-15 TJm +(\032) 5.38998 Tj +-15 TJm +(%q) 10.3914 Tj +-15 TJm +(r) 4.14461 Tj +-64 TJm +(st\034) 12.7726 Tj +-92 TJm +(\031) 6.65528 Tj +-80 TJm +(u\026\027) 17.0666 Tj +-30 TJm +(v) 5.69884 Tj +-24 TJm +(\035) 5.76858 Tj +-15 TJm +(w) 8.24936 Tj +-25 TJm +(!) 7.57188 Tj +-15 TJm +($) 8.31911 Tj +60.08 480.036 Td +(x) 5.80843 Tj +-15 TJm +(\037y) 11.9855 Tj +-30 TJm +( ) 6.18702 Tj +-60 TJm +(z) 5.42984 Tj +90.536 480.036 Td +/F12_0 9.963 Tf +(1) 9.36522 Tj +-278 TJm +(/) 6.03758 Tj +-277 TJm +(;) 4.9815 Tj +116.454 480.036 Td +/F15_0 9.963 Tf +(?) 7.59181 Tj +124.046 480.036 Td +/F10_0 9.963 Tf +(d) 6.08739 Tj +130.133 480.036 Td +/F15_0 9.963 Tf +(g) 5.4398 Tj +-278 TJm +() 4.05494 Tj +[1 0 0 1 417.4 465.092] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 158.132 l +S +Q +[1 0 0 1 -360.707 -0.399] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +361.105 0.199 l +S +Q +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font WNBODM+URWPalladioL-Bold +%%+ font IRCLTK+URWPalladioL-Roma +%%+ font WCLMIU+PAMath-Italic +%%+ font YTECJL+PAMathSy +%%+ font QZSBFC+PATextEx +%%+ font FXKYDG+PAMathEx +%%+ font FBDVFO+PAMathSyB +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf new file mode 100644 index 00000000000..3f9fc5e13e8 Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.eps new file mode 100644 index 00000000000..260af71a940 --- /dev/null +++ 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/pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font RDHBEY+URWPalladioL-Bold +%!PS-AdobeFont-1.0: URWPalladioL-Bold 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Bold) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /RDHBEY+URWPalladioL-Bold def +/PaintType 0 def +/WMode 0 def +/FontBBox {-152 -301 1000 935} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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WCJEMY+TeXPalladioL-BoldOsF +%!PS-AdobeFont-1.0: TeXPalladioL-BoldOsF 1.002 +%%DocumentSuppliedResources: font TeXPalladioL-BoldOsF +%%Title: TeXPalladioL-BoldOsF +%%Version: 1.002 +%%CreationDate: Sun Feb 13 11:54:33 2005 +%%Creator: Ralf Stubner +%Copyright: Copyright (URW)++,Copyright 1999 by (URW)++ Design & +%Copyright: Development, Copyright 2004, 2005 Ralf Stubner. See the +%Copyright: file COPYING (GNU General Public License) for license +%Copyright: conditions. As a special exception, permission is granted +%Copyright: to include this font program in a Postscript or PDF file +%Copyright: that consists of a document that contains text to be +%Copyright: displayed or printed using this font, regardless of the +%Copyright: conditions or license applying to the document itself. +% Generated by FontForge 20050203 (http://fontforge.sf.net/) +%%EndComments +10 dict begin +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def +/FontName /WCJEMY+TeXPalladioL-BoldOsF def +/FontBBox {-152 -301 988 935 }readonly def +/PaintType 0 def +/FontInfo 9 dict dup begin +/version (1.002) readonly def +/Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & Development, Copyright 2004, 2005 Ralf Stubner. See the file COPYING \050GNU General Public License\051 for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/FullName (TeX Palladio L Bold Old Style Figures) readonly def +/FamilyName (TeX Palladio L) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846ab284bcf8b0411b772de5ce32340dc6f28af40857e4451976e7 +5182433cf9f333a38bd841c0d4e68bf9e012eb32a8ffb76b5816306b5edf7c99 +8b3a16d9b4bc056662e32c7cd0123dfaeb734c7532e64bbfbf5a60336e646716 +efb852c877f440d329172c71f1e5d59ce9473c26b8aef7ad68ef0727b6ec2e0c +02ce8d8b07183838330c0284bd419cbdae42b141d3d4be492473f240ceed931d +46e9f999c5cb3235e2c6daaa2c0169e1991beaea0d704bf49cea3e98e8c2361a 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/p/q/r/s/t/u/v/w + /x/y/z/braceleft/bar/braceright/asciitilde/.notdef + /Euro/integral/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl + /circumflex/perthousand/Scaron/guilsinglleft/OE/Omega/radical/approxequal + /.notdef/.notdef/.notdef/quotedblleft/quotedblright/bullet/endash/emdash + /tilde/trademark/scaron/guilsinglright/oe/Delta/lozenge/Ydieresis + /.notdef/exclamdown/cent/sterling/currency/yen/brokenbar/section + /dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron + /degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered + /cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown + /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla + /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis + /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply + /Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls + /agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla + /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis + /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide + /oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis] +pdfMakeFont +%%BeginResource: font LPWDJH+URWPalladioL-Roma +%!PS-AdobeFont-1.0: URWPalladioL-Roma 1.05 +%%CreationDate: Wed Dec 22 1999 +% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development +% (URW)++,Copyright 1999 by (URW)++ Design & Development +% See the file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Roman) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Roman) readonly def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /LPWDJH+URWPalladioL-Roma def +/PaintType 0 def +/WMode 0 def +/FontBBox {-166 -283 1021 943} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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file COPYING (GNU General Public License) for license conditions. +% As a special exception, permission is granted to include this font +% program in a Postscript or PDF file that consists of a document that +% contains text to be displayed or printed using this font, regardless +% of the conditions or license applying to the document itself. +12 dict begin +/FontInfo 10 dict dup begin +/version (1.05) readonly def +/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def +/FullName (URW Palladio L Italic) readonly def +/FamilyName (URW Palladio L) readonly def +/Weight (Regular) readonly def +/ItalicAngle -9.5 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /KCTDDW+URWPalladioL-Ital def +/PaintType 0 def +/WMode 0 def +/FontBBox {-170 -305 1010 941} readonly def +/FontType 1 def +/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def +/Encoding StandardEncoding def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bc2c03103c68570a7b354a4a280ae 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All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /IKYUXS+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 40 /parenleft put +dup 41 /parenright put +dup 61 /equal put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf7158f1163bc1f3352e22a1452e73feca8a4 +87100fb1ffc4c8af409b2067537220e605da0852ca49839e1386af9d7a1a455f 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font FXRJVR+PazoMath-Italic +%!PS-AdobeFont-1.0: PazoMath-Italic 001.003 +%%CreationDate: Fri May 17 11:17:28 2002 +%%VMusage: 120000 150000 +11 dict begin +/FontInfo 14 dict dup begin +/version (001.003) readonly def +/Copyright ((c) Diego Puga, 2000, 2002.) readonly def +/Notice (Copyright (c) Diego Puga, 2000, 2002. Distributed under the GNU General Public License (http://www.gnu.org/copyleft/gpl.txt). As a special exception, permission is granted to include this font program in a PostScript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/FullName (Pazo Math Italic) readonly def +/FamilyName (PazoMath) readonly def +/ItalicAngle -9.50 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +/Weight (Regular) readonly def +end readonly def +/FontName /FXRJVR+PazoMath-Italic def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 35 /epsilon put +dup 36 /rho1 put +dup 74 /theta1 put +dup 86 /sigma1 put +dup 97 /alpha put +dup 98 /beta put +dup 99 /chi put +dup 100 /delta put +dup 101 /epsilon1 put +dup 102 /phi put +dup 103 /gamma put +dup 104 /eta put +dup 105 /iota put +dup 106 /phi1 put +dup 107 /kappa put +dup 108 /lambda put +dup 109 /mu put +dup 110 /nu put +dup 112 /pi put +dup 113 /theta put +dup 114 /rho put +dup 115 /sigma put +dup 116 /tau put +dup 117 /upsilon put +dup 118 /pi1 put +dup 119 /omega put +dup 120 /xi put +dup 121 /psi put +dup 122 /zeta put +dup 182 /partialdiff put +dup 226 /dotlessj put +readonly def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.00100 0 0 0.00100 0 0] readonly def +/FontBBox {-70 -277 902 733} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bcf7c3c3333173232e3fdbff43949 +1db866c39088c203dc22fdc758584860ec7bb67fda28cc6208249060e18fab32 +204779b5c03c0493bbbbc95cf02692cc4deaa8d2ea90b5c2e64374e92bcb8501 +429b8fae4a76c0c6b76d6ff7cf9a7d5edfbca0e959541c59bd05b7de43d25d53 +fc3dda6ef0c2743978a6d03e19cced4a11f2ea4bcc3110be8b8d9e2772361969 +c19258efafdc276cb1ade9208a941a36d18f9fb1c33def76aa315ddb0a7f85c4 +9167e58a181840ec46cc379eaae07071fbd381c7edf50327298ff86a6a4f6812 +2553c2caf67371991cb73dd3f08a7be3d12e5d0b885aa74f37d1940eee91e918 +45d5847cdbaab475b142774c14c38d20d16027aab426cfc43043b69e67862958 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/theta1/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/sigma1/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/alpha/beta/chi/delta/epsilon1/phi/gamma + /eta/iota/phi1/kappa/lambda/mu/nu/.notdef + /pi/theta/rho/sigma/tau/upsilon/pi1/omega + /xi/psi/zeta/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/partialdiff/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/dotlessj/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font XGWJPW+CMEX10 +%!PS-AdobeFont-1.1: CMEX10 001.101 +%%CreationDate: 1992 Jul 23 21:22:48 +%%RevisionDate: 1997 Feb 16 10:50:33 +% Copyright (C) 1992, 1997 Y&Y, Inc. All Rights Reserved. +% Please note: This font is NOT in the public domain. +11 dict begin +/FontInfo 9 dict dup begin +/version (001.101) readonly def +/Notice (Copyright (c) 1992, 1997 Y&Y, Inc. All Right Reserved. (508) 371-3286) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +end readonly def +/FontName /XGWJPW+CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 90 /integraldisplay put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cac6a7beb5d02276e511ffaf2ae11910 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+0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndResource +/F16_0 /XGWJPW+CMEX10 1 1 +[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/integraldisplay/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font DHNCBQ+PazoMath +%!PS-AdobeFont-1.0: PazoMath 001.003 +%%CreationDate: Fri May 17 11:17:28 2002 +%%VMusage: 120000 150000 +11 dict begin +/FontInfo 14 dict dup begin +/version (001.003) readonly def +/Copyright ((c) Diego Puga, 2000, 2002.) readonly def +/Notice (Copyright (c) Diego Puga, 2000, 2002. Distributed under the GNU General Public License (http://www.gnu.org/copyleft/gpl.txt). As a special exception, permission is granted to include this font program in a PostScript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def +/FullName (Pazo Math) readonly def +/FamilyName (PazoMath) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +/UnderlinePosition -100 def +/UnderlineThickness 50 def +/Weight (Regular) readonly def +end readonly def +/FontName /DHNCBQ+PazoMath def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 68 /Delta put +dup 70 /Phi put +dup 71 /Gamma put +dup 76 /Lambda put +dup 80 /Pi put +dup 81 /Theta put +dup 83 /Sigma put +dup 85 /Upsilon put +dup 87 /Omega put +dup 88 /Xi put +dup 89 /Psi put +dup 165 /infinity put +dup 181 /proportional put +dup 198 /emptyset put +readonly def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.00100 0 0 0.00100 0 0] readonly def +/FontBBox {-40 -283 878 946} readonly def +currentdict end +currentfile eexec +d9d66f633b846a989b9974b0179fc6cc445bcf7c3c3333173232e3fdbff43949 +1db866c39088c203dc22fdc758584860ec7bb67fda28cc6208249060e18fab32 +204779b5c03c0493bbbbc95cf02692cc4deaa8d2ea90b5c2e64374e92bcb8501 +429b8fae4a76c0c6b76d6ff7cf9a7d5edfbca0e959541c59bd05b7de43d25d53 +fc3dda6ef0c2743978a6d03e19cced4a11f2ea4bcc3110be8b8d9e2772361969 +c19258efafdc276cb1ade9208a941a36d18f9fb1c33def76aa315dd8f6fc13f6 +956df14f0bc043fc51433ef506a869d4dc4f4cc8551813bd4fb32a549aca63e0 +54d96d2899df1c91c0df800be3ba3183ed98550a1b6e8341018e5958d6fe55d9 +31f13205a8d7e8e8d272d572fa455e4f79a422e23bf4446dd2e07b074f30d20b +7b327fc652bf42ca69b3af4eb4edcc4dc3fdd9f6e97566fb964cb4941b14186f +90acf11eb96ef5dbe23ee591471c6cbb1e5febed31b6233cf057945c928eef4a +ba00c461e2bd02e6845fabf2469862c1868ac67e9820944df750735283ee93db +c5ac907f4db0e3ffaa4879f572b8a31e142821042905bce7cdd20581b4566def +6c7308188ca240dd953378ae17c8f146670b99ce786c72d24d538a986424ac14 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /NAVYDG+MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +dup 102 /Omegainv put +dup 103 /eth put +dup 123 /kappa put +dup 125 /planckover2pi put +dup 127 /epsiloninv put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf5b8cabb9ffc6a66a4000a13d5f68bff326d 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /DLHQZN+CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 96 /lscript put +dup 125 /weierstrass put +readonly def +/FontBBox{-32 -250 1048 750}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa0529731c99a784ccbe85b4993b2eebde +3b12d472b7cf54651ef21185116a69ab1096ed4bad2f646635e019b6417cc77b +532f85d811c70d1429a19a5307ef63eb5c5e02c89fc6c20f6d9d89e7d91fe470 +b72befda23f5df76be05af4ce93137a219ed8a04a9d7d6fdf37e6b7fcde0d90b +986423e5960a5d9fbb4c956556e8df90cbfaec476fa36fd9a5c8175c9af513fe +d919c2ddd26bdc0d99398b9f4d03d5993dfc0930297866e1cd0a319b6b1fd958 +9e394a533a081c36d456a09920001a3d2199583eb9b84b4dee08e3d12939e321 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/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%EndSetup +pdfStartPage +[] 0 d +1 i +0 j +0 J +10 M +1 w +/DeviceGray {} cs +[0] sc +/DeviceGray {} CS +[0] SC +false op +false OP +0 0 362 159 re +W +q +q +[1 0 0 1 0 0] cm +q +[1 0 0 1 0 0] cm +0 0 362 159 re +W +q +[1 0 0 1 -56 -465] cm +q +[1 0 0 1 0 0] cm +0 0 481.89 680.315 re +W +[1 0 0 1 56.693 623.224] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +361.105 0.199 l +S +Q +[1 0 0 1 0 -157.478] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 157.478 l +S +Q +[1 0 0 1 -56.693 -465.746] cm +[1 0 0 1 0 0] Tm +0 0 Td +60.08 608.28 Td +/F9_0 9.963 Tf +(Theorem) 40.9679 Tj +104.113 608.28 Td +/F10_0 9.963 Tf +(1) 4.9815 Tj +112.16 608.28 Td +/F9_0 9.963 Tf +(\(Residuum\).) 56.1614 Tj +172.416 608.28 Td +/F11_0 9.963 Tf +(F\374r) 15.4825 Tj +-308 TJm +(eine) 18.2423 Tj +-307 TJm +(in) 8.6977 Tj +-308 TJm +(einer) 22.1776 Tj +-308 TJm +(punktierten) 52.0069 Tj +-307 TJm +(Kr) 11.1685 Tj +5 TJm +(eisscheibe) 44.2955 Tj +363.151 608.28 Td +/F12_0 9.963 Tf +(D) 7.75121 Tj +371.251 608.28 Td +/F13_0 10.381 Tf +(n) 5.1905 Tj +-24 TJm +(f) 5.1905 Tj +382.279 608.28 Td +/F12_0 9.963 Tf +(a) 4.42357 Tj +386.951 608.28 Td +/F13_0 10.381 Tf +(g) 5.1905 Tj +395.332 608.28 Td +/F11_0 9.963 Tf +(ana-) 19.0791 Tj +60.08 596.324 Td +(lytische) 33.8045 Tj +-291 TJm +(Funktion) 40.2704 Tj +141.37 596.324 Td +/F12_0 9.963 Tf +(f) 2.76971 Tj +148.509 596.324 Td +/F11_0 9.963 Tf +(de\002niert) 37.5406 Tj +-291 TJm +(man) 19.5773 Tj +-291 TJm +(das) 15.2932 Tj +-291 TJm +(Residuum) 45.4512 Tj +-291 TJm +(i) 2.89923 Tj +1 TJm +(m) 8.79733 Tj +-291 TJm +(Punkt) 26.6112 Tj +322.342 596.324 Td +/F12_0 9.963 Tf +(a) 4.42357 Tj +329.789 596.324 Td +/F11_0 9.963 Tf +(als) 12.105 Tj +163.145 568.848 Td +(Res) 15.6519 Tj +164.296 562.711 Td +/F12_0 7.572 Tf +(z) 3.36197 Tj +167.847 562.711 Td +/F14_0 7.89 Tf +(=) 6.13842 Tj +174.283 562.711 Td +/F12_0 7.572 Tf +(a) 3.36197 Tj +180.216 568.848 Td +/F12_0 9.963 Tf +(f) 2.76971 Tj +184.58 568.848 Td +/F14_0 10.381 Tf +(\() 4.03821 Tj +188.854 568.848 Td +/F12_0 9.963 Tf +(z) 4.42357 Tj +193.526 568.848 Td +/F14_0 10.381 Tf +(\)) 4.03821 Tj +-289 TJm +(=) 8.07642 Tj +211.529 568.848 Td +/F11_0 9.963 Tf +(Res) 15.6519 Tj +217.73 562.711 Td +/F12_0 7.572 Tf +(a) 3.36197 Tj +228.6 568.848 Td +/F12_0 9.963 Tf +(f) 2.76971 Tj +235.731 568.848 Td +/F14_0 10.381 Tf +(=) 8.07642 Tj +252.964 575.592 Td +/F11_0 9.963 Tf +(1) 4.9815 Tj +[1 0 0 1 247.888 571.139] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +15.133 0.199 l +S +Q +[1 0 0 1 -247.888 -571.139] cm +[1 0 0 1 0 0] Tm +0 0 Td +247.888 562.013 Td +/F11_0 9.963 Tf +(2) 4.9815 Tj +252.994 562.013 Td +/F15_0 9.963 Tf +(p) 6.75491 Tj +260.122 562.013 Td +/F11_0 9.963 Tf +(i) 2.89923 Tj +266.001 581.301 Td +/F16_0 8.966 Tf +(Z) 4.9851 Tj +265.914 554.378 Td +/F12_0 7.572 Tf +(C) 5.05052 Tj +278.172 568.848 Td +/F12_0 9.963 Tf +(f) 2.76971 Tj +282.536 568.848 Td +/F14_0 10.381 Tf +(\() 4.03821 Tj +286.81 568.848 Td +/F12_0 9.963 Tf +(z) 4.42357 Tj +291.482 568.848 Td +/F14_0 10.381 Tf +(\)) 4.03821 Tj +297.417 568.848 Td +/F12_0 9.963 Tf +(d) 4.9815 Tj +-25 TJm +(z) 4.42357 Tj +308.855 568.848 Td +/F11_0 9.963 Tf +(,) 2.49075 Tj +60.08 534.488 Td +(w) 8.30914 Tj +40 TJm +(obei) 18.6208 Tj +90.049 534.488 Td +/F12_0 9.963 Tf +(C) 6.64532 Tj +100.531 534.488 Td +/F13_0 10.381 Tf +(\032) 8.07642 Tj +112.537 534.488 Td +/F12_0 9.963 Tf +(D) 7.75121 Tj +120.636 534.488 Td +/F13_0 10.381 Tf +(n) 5.1905 Tj +-24 TJm +(f) 5.1905 Tj +131.665 534.488 Td +/F12_0 9.963 Tf +(a) 4.42357 Tj +136.337 534.488 Td +/F13_0 10.381 Tf +(g) 5.1905 Tj +145.006 534.488 Td +/F11_0 9.963 Tf +(ein) 13.47 Tj +-336 TJm +(geschlossener) 60.8241 Tj +-337 TJm +(W) 9.963 Tj +92 TJm +(eg) 10.3117 Tj +-336 TJm +(mit) 14.9445 Tj +267.136 534.488 Td +/F12_0 9.963 Tf +(n) 5.53943 Tj +272.924 534.488 Td +/F14_0 10.381 Tf +(\() 4.03821 Tj +277.158 534.488 Td +/F12_0 9.963 Tf +(C) 6.64532 Tj +284.028 534.488 Td +/F11_0 9.963 Tf +(,) 2.49075 Tj +288.453 534.488 Td +/F12_0 9.963 Tf +(a) 4.42357 Tj +293.125 534.488 Td +/F14_0 10.381 Tf +(\)) 4.03821 Tj +-359 TJm +(=) 8.07642 Tj +312.57 534.488 Td +/F11_0 9.963 Tf +(1) 4.9815 Tj +-337 TJm +(is) 7.12355 Tj +1 TJm +(t) 3.24794 Tj +-337 TJm +(\(z.B.) 19.3681 Tj +-337 TJm +(ein) 13.47 Tj +-336 TJm +(entgegen) 40.2406 Tj +60.08 522.533 Td +(dem) 19.657 Tj +-291 TJm +(Uhrzeigersinn) 63.1056 Tj +-291 TJm +(dur) 16.0305 Tj +10 TJm +(chlaufener) 46.7065 Tj +-290 TJm +(Kr) 11.1685 Tj +5 TJm +(eis\).) 17.7043 Tj +60.08 504.6 Td +(A) 7.75121 Tj +67.956 504.6 Td +/F17_0 9.963 Tf +(L) 7.75121 Tj +-25 TJm +(D) 6.73499 Tj +82.939 504.6 Td +/F13_0 10.381 Tf +(r) 8.64737 Tj +91.711 504.6 Td +/F11_0 9.963 Tf +(BCD) 20.8625 Tj +112.698 504.6 Td +/F17_0 9.963 Tf +(S) 6.64532 Tj +119.467 504.6 Td +/F11_0 9.963 Tf +(EF) 11.6268 Tj +131.218 504.6 Td +/F17_0 9.963 Tf +(G) 5.53943 Tj +136.882 504.6 Td +/F11_0 9.963 Tf +(GHIJKLMNO) 61.4219 Tj +198.426 504.6 Td +/F17_0 9.963 Tf +(Q) 7.83092 Tj +-25 TJm +(W) 8.27925 Tj +214.909 504.6 Td +/F18_0 10.381 Tf +(f) 7.49508 Tj +222.407 504.6 Td +/F11_0 9.963 Tf +(P) 6.01765 Tj +228.549 504.6 Td +/F17_0 9.963 Tf +(F) 7.83092 Tj +-25 TJm +(P) 8.28922 Tj +-25 TJm +(X) 6.57558 Tj +251.866 504.6 Td +/F11_0 9.963 Tf +(QRSTUVWXY) 64.0222 Tj +316.01 504.6 Td +/F17_0 9.963 Tf +(U) 6.64532 Tj +-25 TJm +(Y) 7.50214 Tj +330.531 504.6 Td +/F11_0 9.963 Tf +(Z) 6.64532 Tj +60.354 492.645 Td +/F12_0 9.963 Tf +(a) 4.42357 Tj +65.027 492.645 Td +/F15_0 9.963 Tf +(a) 5.26046 Tj +70.536 492.645 Td +/F12_0 9.963 Tf +(b) 4.61287 Tj +75.647 492.645 Td +/F15_0 9.963 Tf +(b) 5.39995 Tj +81.296 492.645 Td +/F12_0 9.963 Tf +(c) 4.05494 Tj +85.599 492.645 Td +/F15_0 9.963 Tf +(\266) 4.85198 Tj +90.7 492.645 Td +/F12_0 9.963 Tf +(d) 4.9815 Tj +95.931 492.645 Td +/F15_0 9.963 Tf +(d) 4.56305 Tj +100.742 492.645 Td +/F12_0 9.963 Tf +(e) 3.87561 Tj +104.867 492.645 Td +/F15_0 9.963 Tf +(e) 4.64276 Tj +-25 TJm +(#) 3.74609 Tj +115.049 492.645 Td +/F12_0 9.963 Tf +(f) 2.76971 Tj +119.412 492.645 Td +/F15_0 9.963 Tf +(z) 4.42357 Tj +-75 TJm +(x) 4.42357 Tj +129.973 492.645 Td +/F12_0 9.963 Tf +(g) 4.9815 Tj +135.203 492.645 Td +/F15_0 9.963 Tf +(g) 6.08739 Tj +141.589 492.645 Td +/F12_0 9.963 Tf +(h) 4.9815 Tj +147.137 492.645 Td +/F11_0 9.963 Tf +(\257) 3.31768 Tj +146.866 492.645 Td +/F12_0 9.963 Tf +(h) 4.9815 Tj +151.972 492.645 Td +/F18_0 10.381 Tf +(}) 5.60574 Tj +157.705 492.645 Td +/F15_0 9.963 Tf +(i) 2.62027 Tj +160.504 492.645 Td +/F12_0 9.963 Tf +(i) 2.76971 Tj +-25 TJm +(\021) 2.76971 Tj +-60 TJm +(j) 2.76971 Tj +170.257 492.645 Td +/F15_0 9.963 Tf +(\342) 2.76971 Tj +173.276 492.645 Td +/F12_0 9.963 Tf +(k) 4.42357 Tj +177.899 492.645 Td +/F15_0 9.963 Tf +(k) 4.81213 Tj +183.084 492.645 Td +/F18_0 10.381 Tf +({) 6.92413 Tj +190.548 492.645 Td +/F12_0 9.963 Tf +(l) 2.76971 Tj +193.865 492.645 Td +/F19_0 10.381 Tf +(`) 4.32888 Tj +198.428 492.645 Td +/F15_0 9.963 Tf +(l) 6.02762 Tj +204.704 492.645 Td +/F12_0 9.963 Tf +(m) 7.75121 Tj +-25 TJm +(n) 5.53943 Tj +218.493 492.645 Td +/F15_0 9.963 Tf +(h) 5.19072 Tj +-55 TJm +(q) 4.42357 Tj +-55 TJm +(J) 5.44976 Tj +234.961 492.645 Td +/F12_0 9.963 Tf +(o) 4.42357 Tj +239.733 492.645 Td +/F15_0 9.963 Tf +(s) 5.60917 Tj +-30 TJm +(V) 4.64276 Tj +-25 TJm +(f) 5.86821 Tj +-75 TJm +(j) 5.86821 Tj +263.264 492.645 Td +/F19_0 10.381 Tf +(}) 6.60232 Tj +270.666 492.645 Td +/F12_0 9.963 Tf +(p) 4.9815 Tj +275.897 492.645 Td +/F15_0 9.963 Tf +(r) 4.9815 Tj +-25 TJm +($) 4.9815 Tj +286.357 492.645 Td +/F12_0 9.963 Tf +(q) 4.61287 Tj +-15 TJm +(r) 3.87561 Tj +-35 TJm +(s) 3.87561 Tj +-25 TJm +(t) 3.31768 Tj +303.035 492.645 Td +/F15_0 9.963 Tf +(t) 5.22061 Tj +-50 TJm +(p) 6.75491 Tj +316.006 492.645 Td +/F12_0 9.963 Tf +(u) 5.53943 Tj +321.794 492.645 Td +/F15_0 9.963 Tf +(m) 5.80843 Tj +-25 TJm +(n) 4.9815 Tj +333.081 492.645 Td +/F12_0 9.963 Tf +(v) 4.9815 Tj +338.312 492.645 Td +/F15_0 9.963 Tf +(u) 5.19072 Tj +343.751 492.645 Td +/F12_0 9.963 Tf +(w) 7.19329 Tj +351.193 492.645 Td +/F15_0 9.963 Tf +(w) 7.41247 Tj +-45 TJm +(v) 7.41247 Tj +60.374 480.69 Td +/F12_0 9.963 Tf +(x) 4.9815 Tj +65.704 480.69 Td +/F15_0 9.963 Tf +(c) 5.99773 Tj +71.951 480.69 Td +/F12_0 9.963 Tf +(y) 4.9815 Tj +77.181 480.69 Td +/F15_0 9.963 Tf +(y) 6.47595 Tj +83.906 480.69 Td +/F12_0 9.963 Tf +(z) 4.42357 Tj +88.578 480.69 Td +/F17_0 9.963 Tf +(\245) 8.49844 Tj +-303 TJm +(\265) 6.63536 Tj +-302 TJm +(\306) 7.44236 Tj +117.311 480.69 Td +/F18_0 10.381 Tf +(?) 8.07642 Tj +125.385 480.69 Td +/F11_0 9.963 Tf +(d) 6.08739 Tj +131.472 480.69 Td +/F18_0 10.381 Tf +(g) 5.77184 Tj +-266 TJm +() 4.45345 Tj +[1 0 0 1 417.4 465.746] cm +q +[] 0 d +0 J +0.398 w +0.199 0 m +0.199 157.478 l +S +Q +[1 0 0 1 -360.707 -0.399] cm +q +[] 0 d +0 J +0.398 w +0 0.199 m +361.105 0.199 l +S +Q +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font RDHBEY+URWPalladioL-Bold +%%+ font WCJEMY+TeXPalladioL-BoldOsF +%%+ font LPWDJH+URWPalladioL-Roma +%%+ font KCTDDW+URWPalladioL-Ital +%%+ font MCYFQY+CMSY10 +%%+ font IKYUXS+CMR10 +%%+ font FXRJVR+PazoMath-Italic +%%+ font XGWJPW+CMEX10 +%%+ font DHNCBQ+PazoMath +%%+ font NAVYDG+MSBM10 +%%+ font DLHQZN+CMMI10 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf new file mode 100644 index 00000000000..a9ec41a9245 Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.eps b/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.eps new file mode 100644 index 00000000000..d4ed69eef29 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.eps @@ -0,0 +1,8875 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: xpdf/pdftops 3.01 +%%LanguageLevel: 2 +%%BoundingBox: 0 0 360 287 +%%DocumentSuppliedResources: (atend) +%%EndComments +%%BeginProlog +%%BeginResource: procset xpdf 3.01 0 +/xpdf 75 dict def xpdf begin +% PDF special state +/pdfDictSize 15 def +/pdfSetup { + 3 1 roll 2 array astore + /setpagedevice where { + pop 3 dict begin + /PageSize exch def + /ImagingBBox null def + /Policies 1 dict dup begin /PageSize 3 def end def + { /Duplex true def } if + currentdict end setpagedevice + } { + pop pop + } ifelse +} def +/pdfStartPage { + pdfDictSize dict begin + /pdfFillCS [] def + /pdfFillXform {} def + /pdfStrokeCS [] def + /pdfStrokeXform {} def + /pdfFill [0] def + /pdfStroke [0] def + /pdfFillOP false def + /pdfStrokeOP false def + /pdfLastFill false def + /pdfLastStroke false def + /pdfTextMat [1 0 0 1 0 0] def + /pdfFontSize 0 def + /pdfCharSpacing 0 def + /pdfTextRender 0 def + /pdfTextRise 0 def + /pdfWordSpacing 0 def + /pdfHorizScaling 1 def + /pdfTextClipPath [] def +} def +/pdfEndPage { end } def +% PDF color state +/cs { /pdfFillXform exch def dup /pdfFillCS exch def + setcolorspace } def +/CS { /pdfStrokeXform exch def dup /pdfStrokeCS exch def + setcolorspace } def +/sc { pdfLastFill not { pdfFillCS setcolorspace } if + dup /pdfFill exch def aload pop pdfFillXform setcolor + /pdfLastFill true def /pdfLastStroke false def } def +/SC { pdfLastStroke not { pdfStrokeCS setcolorspace } if + dup /pdfStroke exch def aload pop pdfStrokeXform setcolor + /pdfLastStroke true def /pdfLastFill false def } def +/op { /pdfFillOP exch def + pdfLastFill { pdfFillOP setoverprint } if } def +/OP { /pdfStrokeOP exch def + pdfLastStroke { pdfStrokeOP setoverprint } if } def +/fCol { + pdfLastFill not { + pdfFillCS setcolorspace + pdfFill aload pop pdfFillXform setcolor + pdfFillOP setoverprint + /pdfLastFill true def /pdfLastStroke false def + } if +} def +/sCol { + pdfLastStroke not { + pdfStrokeCS setcolorspace + pdfStroke aload pop pdfStrokeXform setcolor + pdfStrokeOP setoverprint + /pdfLastStroke true def /pdfLastFill false def + } if +} def +% build a font +/pdfMakeFont { + 4 3 roll findfont + 4 2 roll matrix scale makefont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /Encoding exch def + currentdict + end + definefont pop +} def +/pdfMakeFont16 { + exch findfont + dup length dict begin + { 1 index /FID ne { def } { pop pop } ifelse } forall + /WMode exch def + currentdict + end + definefont pop +} def +% graphics state operators +/q { gsave pdfDictSize dict begin } def +/Q { + end grestore + /pdfLastFill where { + pop + pdfLastFill { + pdfFillOP setoverprint + } { + pdfStrokeOP setoverprint + } ifelse + } if +} def +/cm { concat } def +/d { setdash } def +/i { setflat } def +/j { setlinejoin } def +/J { setlinecap } def +/M { setmiterlimit } def +/w { setlinewidth } def +% path segment operators +/m { moveto } def +/l { lineto } def +/c { curveto } def +/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto + neg 0 rlineto closepath } def +/h { closepath } def +% path painting operators +/S { sCol stroke } def +/Sf { fCol stroke } def +/f { fCol fill } def +/f* { fCol eofill } def +% clipping operators +/W { clip newpath } def +/W* { eoclip newpath } def +% text state operators +/Tc { /pdfCharSpacing exch def } def +/Tf { dup /pdfFontSize exch def + dup pdfHorizScaling mul exch matrix scale + pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put + exch findfont exch makefont setfont } def +/Tr { /pdfTextRender exch def } def +/Ts { /pdfTextRise exch def } def +/Tw { /pdfWordSpacing exch def } def +/Tz { /pdfHorizScaling exch def } def +% text positioning operators +/Td { pdfTextMat transform moveto } def +/Tm { /pdfTextMat exch def } def +% text string operators +/cshow where { + pop + /cshow2 { + dup { + pop pop + 1 string dup 0 3 index put 3 index exec + } exch cshow + pop pop + } def +}{ + /cshow2 { + currentfont /FontType get 0 eq { + 0 2 2 index length 1 sub { + 2 copy get exch 1 add 2 index exch get + 2 copy exch 256 mul add + 2 string dup 0 6 5 roll put dup 1 5 4 roll put + 3 index exec + } for + } { + dup { + 1 string dup 0 3 index put 3 index exec + } forall + } ifelse + pop pop + } def +} ifelse +/awcp { + exch { + false charpath + 5 index 5 index rmoveto + 6 index eq { 7 index 7 index rmoveto } if + } exch cshow2 + 6 {pop} repeat +} def +/Tj { + fCol + 1 index stringwidth pdfTextMat idtransform pop + sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16 { + fCol + 2 index stringwidth pdfTextMat idtransform pop + sub exch div + pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing pdfHorizScaling mul add 0 + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj16V { + fCol + 2 index stringwidth pdfTextMat idtransform exch pop + sub exch div + 0 pdfWordSpacing pdfTextMat dtransform 32 + 4 3 roll pdfCharSpacing add 0 exch + pdfTextMat dtransform + 6 5 roll Tj1 +} def +/Tj1 { + 0 pdfTextRise pdfTextMat dtransform rmoveto + currentpoint 8 2 roll + pdfTextRender 1 and 0 eq { + 6 copy awidthshow + } if + pdfTextRender 3 and dup 1 eq exch 2 eq or { + 7 index 7 index moveto + 6 copy + currentfont /FontType get 3 eq { fCol } { sCol } ifelse + false awcp currentpoint stroke moveto + } if + pdfTextRender 4 and 0 ne { + 8 6 roll moveto + false awcp + /pdfTextClipPath [ pdfTextClipPath aload pop + {/moveto cvx} + {/lineto cvx} + {/curveto cvx} + {/closepath cvx} + pathforall ] def + currentpoint newpath moveto + } { + 8 {pop} repeat + } ifelse + 0 pdfTextRise neg pdfTextMat dtransform rmoveto +} def +/TJm { pdfFontSize 0.001 mul mul neg 0 + pdfTextMat dtransform rmoveto } def +/TJmV { pdfFontSize 0.001 mul mul neg 0 exch + pdfTextMat dtransform rmoveto } def +/Tclip { pdfTextClipPath cvx exec clip newpath + /pdfTextClipPath [] def } def +% Level 2 image operators +/pdfImBuf 100 string def +/pdfIm { + image + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImM { + fCol imagemask + { currentfile pdfImBuf readline + not { pop exit } if + (%-EOD-) eq { exit } if } loop +} def +/pdfImClip { + gsave + 0 2 4 index length 1 sub { + dup 4 index exch 2 copy + get 5 index div put + 1 add 3 index exch 2 copy + get 3 index div put + } for + pop pop rectclip +} def +/pdfImClipEnd { grestore } def +% shading operators +/colordelta { + false 0 1 3 index length 1 sub { + dup 4 index exch get 3 index 3 2 roll get sub abs 0.004 gt { + pop true + } if + } for + exch pop exch pop +} def +/funcCol { func n array astore } def +/funcSH { + dup 0 eq { + true + } { + dup 6 eq { + false + } { + 4 index 4 index funcCol dup + 6 index 4 index funcCol dup + 3 1 roll colordelta 3 1 roll + 5 index 5 index funcCol dup + 3 1 roll colordelta 3 1 roll + 6 index 8 index funcCol dup + 3 1 roll colordelta 3 1 roll + colordelta or or or + } ifelse + } ifelse + { + 1 add + 4 index 3 index add 0.5 mul exch 4 index 3 index add 0.5 mul exch + 6 index 6 index 4 index 4 index 4 index funcSH + 2 index 6 index 6 index 4 index 4 index funcSH + 6 index 2 index 4 index 6 index 4 index funcSH + 5 3 roll 3 2 roll funcSH pop pop + } { + pop 3 index 2 index add 0.5 mul 3 index 2 index add 0.5 mul + funcCol sc + dup 4 index exch mat transform m + 3 index 3 index mat transform l + 1 index 3 index mat transform l + mat transform l pop pop h f* + } ifelse +} def +/axialCol { + dup 0 lt { + pop t0 + } { + dup 1 gt { + pop t1 + } { + dt mul t0 add + } ifelse + } ifelse + func n array astore +} def +/axialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index axialCol 2 index axialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index axialSH + exch 3 2 roll axialSH + } { + pop 2 copy add 0.5 mul axialCol sc + exch dup dx mul x0 add exch dy mul y0 add + 3 2 roll dup dx mul x0 add exch dy mul y0 add + dx abs dy abs ge { + 2 copy yMin sub dy mul dx div add yMin m + yMax sub dy mul dx div add yMax l + 2 copy yMax sub dy mul dx div add yMax l + yMin sub dy mul dx div add yMin l + h f* + } { + exch 2 copy xMin sub dx mul dy div add xMin exch m + xMax sub dx mul dy div add xMax exch l + exch 2 copy xMax sub dx mul dy div add xMax exch l + xMin sub dx mul dy div add xMin exch l + h f* + } ifelse + } ifelse +} def +/radialCol { + dup t0 lt { + pop t0 + } { + dup t1 gt { + pop t1 + } if + } ifelse + func n array astore +} def +/radialSH { + dup 0 eq { + true + } { + dup 8 eq { + false + } { + 2 index dt mul t0 add radialCol + 2 index dt mul t0 add radialCol colordelta + } ifelse + } ifelse + { + 1 add 3 1 roll 2 copy add 0.5 mul + dup 4 3 roll exch 4 index radialSH + exch 3 2 roll radialSH + } { + pop 2 copy add 0.5 mul dt mul t0 add axialCol sc + exch dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h + dup dx mul x0 add exch dup dy mul y0 add exch dr mul r0 add + 0 360 arc h f* + } ifelse +} def +end +%%EndResource +%%EndProlog +%%BeginSetup +xpdf begin +%%BeginResource: font LLRYGB+SFBX1095 +%!FontType1-1.0: SFBX1095 0.3 +%%CreationDate: Wed Sep 12 2001 +% Copyright (c) 2001 Vladimir Volovich . +% See the file COPYING (GNU General Public License) for license conditions. +% Converted from METAFONT EC/TC and LH fonts: +% ecbx1095, tcbx1095, labx1095, lbbx1095, lcbx1095, rxbx1095. +11 dict begin +/FontInfo 6 dict dup begin +/version (0.3) def +/FullName (Computer Modern Bold Extended) def +/FamilyName (Computer Modern) def +/ItalicAngle 0 def +/isFixedPitch false def +/Weight (Bold) def +end readonly def +/FontName /LLRYGB+SFBX1095 def +/Encoding StandardEncoding def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] def +/FontBBox{-227 -316 1723 930}readonly def +currentdict end +currentfile eexec 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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/.notdef/A/B/C/D/E/F/G + /H/I/J/K/L/M/N/O + /P/Q/R/S/T/U/V/W + /X/Y/Z/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef] +pdfMakeFont +%%BeginResource: font ZCTGES+CMSS10 +%!PS-AdobeFont-1.1: CMSS10 1.0 +%%CreationDate: 1991 Aug 20 17:33:34 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSS10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /ZCTGES+CMSS10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o put +dup 112 /p put +dup 113 /q put +dup 114 /r put +dup 115 /s put +dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{-61 -250 999 759}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 +9098d5fee67660e69a7ab91b58f29a4d79e57022f783eb0fbbb6d4f4ec35014f +d2decba99459a4c59df0c6eba150284454e707dc2100c15b76b4c19b84363758 +469a6c558785b226332152109871a9883487dd7710949204ddcf837e6a8708b8 +2bdbf16fbc7512faa308a093fe5cf7158f1163bdceea888d07b439dbd4e8b4c9 +d198c03874b5e6f8fbf4922065a92bc3e66d05de53971cb1424510e892442858 +d69ce1f76e4da76c87c763a4b2fe36321e54b1328c9155b8ed6361855a151723 +3386aea3d042b8d89c8c0e9a33e5df3b466f7bb8c2c8a4ed4cdaff55fc6d3ee6 +0af2cebfc1ac3a6e6692f8bb81f82d86bae85016ad62fcb05467082c2e5ad348 +44d1439c2b59f65590e57ca0de481a7a34e79931b1513c4c30156170409a4bb8 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /DSCKSN+MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +currentdict end +currentfile eexec +d9d66f633b846a97b686a97e45a3d0aa052a014267b7904eb3c0d3bd0b83d891 +016ca6ca4b712adeb258faab9a130ee605e61f77fc1b738abc7c51cd46ef8171 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+%!PS-AdobeFont-1.1: CMTT10 1.00B +%%CreationDate: 1992 Apr 26 10:42:42 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /JUKYMP+CMTT10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /TIQNSQ+CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /GAGNKW+CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o 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All Rights Reserved) readonly def +/FullName (CMBX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /UQPOYB+CMBX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 71 /G put +dup 72 /H put +dup 73 /I put +dup 74 /J put +dup 75 /K put +dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put +dup 80 /P put +dup 81 /Q put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 86 /V put +dup 87 /W put +dup 88 /X put +dup 89 /Y put +dup 90 /Z put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 111 /o 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+<~!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!9%#64`(!!!Q-#CldS!"],0s8RTL!"],0s8RTL!"],0s8RTL~>] +0 +<< + /ImageType 1 + /Width 61 + /Height 61 + /ImageMatrix [61 0 0 -61 0 61] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a85 { +73.23 0 3 -2 70 62 setcachedevice +q +q +[66 0 0 64 3 -2] cm +[<~s8W-!n-B!n_#OH7s6p9ns1n[7s8VQns8Tk8s+'kE!'g5Y!.TOW!!!Pf!!%M!huE`^^]4@aJD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`Z~> +<~J,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW!!@`O!.TOW!!!+O!!%M!huE`ZJ,fS!JD^D-"+U@OIt6GW~> +<~!!@`O!.TOW!!!+O!!%M!huE`^J,fR6JD^D-#64`(5JZ1W!!`K(!'e9W!!!6(!!"+VhuE`f!!!!@i8=S8%KHJ/&)c@G!$2+?!"\SW!!!u=!!!8nhuEa>!!!!$ptu,PGQ7^D"8q'W!:Tsg!!3)W!!2!X!!!$!huEkpz5MuMPJ,fQL!$C,!56(Z`!!!9%!W2ot!!!!"s8VQgz!.Y$az!!!9'z~>] +0 +<< + /ImageType 1 + /Width 66 + /Height 64 + /ImageMatrix [66 0 0 -64 0 64] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a86 { +73.23 0 2 -1 71 62 setcachedevice +q +q +[68 0 0 63 2 -1] cm +[<~s8W-!huJ9,nGiOgs53m,s7$'gs8V!WJ,f!?rrMlp!"])0!WN/h!!!-!!!*%LhuE`Xp](;DJFEO=!Up'hIt2J +<~!!!!"rWBq92uipY!WE,8!&srY!!3*#^]8TZ!!!$!!8mirzrrCsWDu]k4z5JVLE^]4?7!'e7Y!Pe[8!!#7A3!6qr!!!!@i#DiLz+5e+@J,fQL!"\Q?#64`(!!!Q!%L2t6!!!!0p^Rf7z#P\f>z!!i9(%KHJ/!!!9%#9EjF!!!!$qu`Ghz"8i7kz!!3'$p](9o!!!'!!VcWp!!!!"rrMlp~> +<~z!<3)hz!!*$!n,NFg!!!$!JFEO=zIt6GWz!.VfBz!!#7"^]4?7!!!!`_8$$Nz5NBNZz!$C6Oz!!",$J,fQL!!!!@pOE5Dz&,-&(z!"])0z!!!9'z!!!!(rVuouz#Q=]'z!!E-!!!!!~>] +0 +<< + /ImageType 1 + /Width 68 + /Height 63 + /ImageMatrix [68 0 0 -63 0 63] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a87 { +98.49 0 2 -1 96 62 setcachedevice +q +q +[93 0 0 63 2 -1] cm +[<~s8W-!L]@DD!'gMYs8W-!L]@DD!'gMYs8W-!L]@DD!'gMY#Q=hp!'gA]!!iP>!WE2:!$Ct9!!*$!!WN29!"\Q!!!%HJ!<3)8!"\Q!!!%BH!<3)8!"\Q!!!"tY!<3&W!!i9!!!"tY!.TOW!!i9!!!$s +<~!$2%=!!0k8!$C,Y!$2%=!!0k8!$C,=!''uY!!0k8!$C\M!''uY!!C":!"\Q=!''uY!!@`O!"\Q?!-nNo!!@`O!"\Q/!-!F +<~!#tt=!!*$"_gi9e!&srY!!*$"_gi9e!&srY!!*$!k5Yb^!&srY!!*%Lk5Yb^!-eJD!!%M!k5Yb^!,qo +<~!!!Q!Du]lfK7Eq%!!!9!Du]lfLB%;S!!!9!Du]lfLB%;S!!!9!huEaA`rH)>!!!-!huEaAc2[hE!!!-!huEaAc2[hE!!!-"^]4?VmJm4e!!!-"^]4?VrVuou!!!'"^]4?Vqu?]s!!!'"^]4?Vqu?]s!!!'"J,fQ[qu?]s!!!$!J,fQ[p](9o!!!$!J,fQ[p](9o!!!$!!!!!(p](9o~>] +0 +<< + /ImageType 1 + /Width 93 + /Height 63 + /ImageMatrix [93 0 0 -63 0 63] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a88 { +78.28 0 2 0 76 62 setcachedevice +q +q +[73 0 0 62 2 0] cm +[<~s8W-!p]:Epp]1?os8Vips8Vios8W-!p]:Epp](?p^d#U75Q:]`!.Vd+!!",9!!!!`i#Vju&)[Ef!'fBP!!!O[!!!!@n-8pn%fcS0!"\i0J,gVj!!!!0p]J;3*WQ0?!!iE(^]6Is!!!!(rW1pWGQ7^D!!E3#huN6H!!!!"rrDNghuE`W!!3+MGQH_&zs+!'2^]4?7!!%Ma49pB:zJ&!*9z!!#7A%M&O>z+7Kd^z!!",1# +<~&,6D)z!!!Q-"7Q9jz#Q+Vlz!!!-#!T3qXz"9&;iz!!!'"!,qo +<~&,6B[z#Cm?["2Fm:!!!N0#Q+V] +0 +<< + /ImageType 1 + /Width 73 + /Height 62 + /ImageMatrix [73 0 0 -62 0 62] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a89 { +73.23 0 1 0 72 62 setcachedevice +q +q +[70 0 0 62 1 0] cm +[<~s8W-!n,OR1r;Zfss6p"1s8;oss8VQg+926@s+((K!!E8:!<7Ro!!!'!!!%MaGQ7^Dqu?_H^c2;o!;HNo5JTA]!!)Kg!'fB]!!!#W!!",!*WQ0@huEa!n.#Eu!Pe[8&+C)0!!C":!"\i0!!!+O!!!9!#CldZJ,fQSqu_HL#64`("8i8:!"T&0!!E3$^]4iE!!!'!!T3qt!!!!"rrCsW)uos=!<3&g!&srY!!*%LDub+_!!!"KJ9V'5~> +<~zJ&"#Dn,NFg!'e7Y!8mhW!!#7A*!+st!!!!@i#Dd5z+7KaB^]4?7!"\Q/"+U@O!!!Q)#7#bZ!!!!(p]h$(z#Q+[az!!E-$NW9%Z!!!-#!SdYT!!!!"rW1dSz!WN/pz!!*$!p](9o!!!$!J8bJgzIt2J +<~z5JV4] +0 +<< + /ImageType 1 + /Width 70 + /Height 62 + /ImageMatrix [70 0 0 -62 0 62] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +/a90 { +68.18 0 5 0 64 62 setcachedevice +q +q +[58 0 0 62 5 0] cm +[<~5QCc`s8W+L5QCc`s8W+L5QCc`s8W+L5QC3Q&,6A05Q1W_+7Kd@5PP3Y+7LDu]lf^c2;o!!!$!J9V%o!!!$!JFEO=!!!'"!:Tsg!!!-#~> +<~!T3qX!!!-#"2Fm:!!!9%"2Fm:!!!Q-#CldS!!!Q)#64`(!!",1%fcS0!!",1*WQ0?!!#7A)uos=!!%Ma49,?]!!%MaGQ7^D!!*%LGQ7^D!!3*"n,NFg!!3*#huE`W!!E3$huE`W!!iE(^]4DN!!iE,J,fVc!"\i0J,fVc!"\i8!!!&8!$C\?!!!&8!'fB_!!!&8!'fC(!!!,:!.VdD!!!,:!<7Ro!!!,:!<7T=!!!,:!WN/h!!!8>~> +<~"9&>Z!!!8>"9&D!!!O[&,ZZ_!!"*k&,6A0!!#66+7Kd@!!#66+7L] +0 +<< + /ImageType 1 + /Width 58 + /Height 62 + /ImageMatrix [58 0 0 -62 0 62] + /BitsPerComponent 1 + /Decode [1 0] + /DataSource { 2 copy get exch 1 add exch } +>> +imagemask +pop pop +Q +Q +} def +end +currentdict end +/T3_23_0 exch definefont pop +%%EndResource +/F23_0 /T3_23_0 1 1 +[ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef + /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright + /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash + /zero/one/two/three/four/five/six/seven + /eight/nine/colon/semicolon/less/equal/greater/question + /at/a65/a66/a67/a68/a69/a70/a71 + /a72/a73/a74/a75/a76/a77/a78/a79 + /a80/a81/a82/a83/a84/a85/a86/a87 + /a88/a89/a90/bracketleft/backslash/bracketright/asciicircum/underscore + /quoteleft/a/b/c/d/e/f/g + /h/i/j/k/l/m/n/o + /p/q/r/s/t/u/v/w + /x/y/z/braceleft/bar/braceright/asciitilde/.notdef + 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360 287 re +W +q +[1 0 0 1 -134 -429] cm +q +[1 0 0 1 0 0] cm +0 0 595.276 841.89 re +W +[1 0 0 1 0 0] Tm +0 0 Td +158.676 705.611 Td +/F9_0 10.9091 Tf +(Command) 55.907 Tj +q +[1 0 0 1 220.76 701.546] cm +[] 0 d +0 J +0.398 w +0 0 m +0 13.549 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 705.611 Td +/F9_0 10.9091 Tf +(T) 8.66728 Tj +95 TJm +(est) 15.4615 Tj +q +[1 0 0 1 152.698 701.347] cm +[] 0 d +0 J +0.398 w +0 0 m +322.787 0 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +158.676 691.663 Td +/F10_0 10.9091 Tf +(default) 32.8495 Tj +q +[1 0 0 1 220.76 674.049] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 691.663 Td +/F11_0 10.9091 Tf +(AB) 16.4564 Tj +-50 TJm +(C) 7.79673 Tj +-72 TJm +(D) 9.03164 Tj +-28 TJm +(E) 8.0531 Tj +-57 TJm +(F) 7.01564 Tj +-139 TJm +(GH) 17.6455 Tj +-81 TJm +(I) 4.79564 Tj +-79 TJm +(J) 6.0491 Tj +-96 TJm +(K) 9.2651 Tj +-71 TJm +(LM) 18.0077 Tj +-109 TJm +(N) 8.76546 Tj +-109 TJm +(O) 8.32146 Tj +-28 TJm +(P) 7.00364 Tj +-139 TJm 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0 1 220.76 633.402] cm +[] 0 d +0 J +0.398 w +0 0 m +0 13.549 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 637.466 Td +/F15_0 10.9091 Tf +(AB) 15.876 Tj +-30 TJm +(C) 5.74364 Tj +-59 TJm +(D) 8.41528 Tj +-28 TJm +(E) 5.75782 Tj +-89 TJm +(F) 7.84037 Tj +-99 TJm +(G) 6.48982 Tj +-60 TJm +(H) 9.21273 Tj +-9 TJm +(I) 5.94 Tj +-74 TJm +(J) 7.39419 Tj +-185 TJm +(K) 8.31273 Tj +-14 TJm +(LMN) 29.5757 Tj +-148 TJm +(O) 8.68473 Tj +-27 TJm +(P) 7.58837 Tj +-83 TJm +(Q) 8.90946 Tj +1 TJm +(RS) 15.852 Tj +-75 TJm +(T) 5.9411 Tj +-255 TJm +(U) 6.82691 Tj +-99 TJm +(V) 6.6851 Tj +-82 TJm +(W) 10.776 Tj +-82 TJm +(X) 7.78146 Tj +-147 TJm +(Y) 7.29055 Tj +-82 TJm +(Z) 7.90582 Tj +158.676 623.917 Td +/F12_0 10.9091 Tf +(\\mathsf) 39.4571 Tj +q +[1 0 0 1 220.76 606.303] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 623.917 Td +/F16_0 10.9091 Tf +(ABCDEF) 42.1211 Tj +28 TJm +(GHIJKLMNOPQRSTUVWXYZ) 143.788 Tj +226.937 610.368 Td +(ab) 10.8796 Tj +-28 TJm +(cdefghijklmnop) 68.6073 Tj +-27 TJm +(qrstuvwxyz) 50.4088 Tj +158.676 596.819 Td +/F12_0 10.9091 Tf +(\\mathbb) 39.4571 Tj +198.137 600.778 Td +/F17_0 7.9701 Tf +(a) 4.49832 Tj +q +[1 0 0 1 220.76 592.754] cm +[] 0 d +0 J +0.398 w +0 0 m +0 13.549 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 596.819 Td +/F18_0 10.9091 Tf +(ABCDEFGHIJKLMNOPQRSTUVWXYZ) 200.001 Tj +158.676 583.27 Td +/F12_0 10.9091 Tf +(\\mathtt) 39.4571 Tj +q +[1 0 0 1 220.76 565.656] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 583.27 Td +/F19_0 10.9091 Tf +(ABCDEFGHIJKLMNOPQRSTUVWXYZ) 148.909 Tj +226.937 569.72 Td +(abcdefghijklmnopqrstuvwxyz) 148.909 Tj +158.676 556.171 Td +/F12_0 10.9091 Tf +(\\mathit) 39.4571 Tj +q +[1 0 0 1 220.76 538.557] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 556.171 Td +/F20_0 10.9091 Tf +(ABCDEF) 46.3517 Tj +26 TJm +(GHIJKLMNOPQRSTUVWXYZ) 155.65 Tj +226.937 542.622 Td +(ab) 10.5938 Tj +51 TJm +(c) 5.01819 Tj +51 TJm +(defghijklmnop) 65.2375 Tj +51 TJm +(qr) 9.61855 Tj +1 TJm +(stuvwxyz) 41.0248 Tj +158.676 529.073 Td +/F12_0 10.9091 Tf +(\\mathrm) 39.4571 Tj +q +[1 0 0 1 220.76 511.459] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 529.073 Td +/F21_0 10.9091 Tf +(ABCDEF) 46.6669 Tj +28 TJm +(GHIJKLMNOPQRSTUVWXYZ) 156.744 Tj +226.937 515.524 Td +(ab) 11.5156 Tj +-28 TJm +(cdefghijklmnop) 72.4266 Tj +-27 TJm +(qrstuvwxyz) 54.6371 Tj +158.676 501.975 Td +/F12_0 10.9091 Tf +(\\mathbf) 39.4571 Tj +q +[1 0 0 1 220.76 484.361] cm +[] 0 d +0 J +0.398 w +0 0 m +0 27.098 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 501.975 Td +/F22_0 10.9091 Tf +(ABCDEF) 53.2266 Tj +32 TJm +(GHIJKLMNOPQRSTUVWXYZ) 181.303 Tj +226.937 488.425 Td +(ab) 13.068 Tj +-32 TJm +(cdefghijklmnop) 83.4612 Tj +-32 TJm +(qrstuvwxyz) 63.083 Tj +158.676 474.876 Td +/F12_0 10.9091 Tf +(\\mathds) 39.4571 Tj +198.137 478.835 Td +/F14_0 7.9701 Tf +(b) 3.93404 Tj +q +[1 0 0 1 220.76 470.811] cm +[] 0 d +0 J +0.398 w +0 0 m +0 13.549 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +226.937 474.876 Td +/F23_0 10.9091 Tf +(ABCDEFGHIJKLMNOPQRSTUV) 180.683 Tj +-14 TJm +(W) 11.8188 Tj +-14 TJm +(XY) 18.1812 Tj +-25 TJm +(Z) 8.18161 Tj +q +[1 0 0 1 134.765 463.638] cm +[] 0 d +0 J +0.398 w +0 0 m +143.46 0 l +S +Q +[1 0 0 1 0 0] Tm +0 0 Td +146.852 456.987 Td +/F24_0 5.9776 Tf +(a) 3.99842 Tj +[1.02 0 0 1 151.348 453.178] Tm +0 0 Td +/F25_0 8.9664 Tf +(Not) 15.0985 Tj +-387 TJm +(a) 4.60694 Tj +29 TJm +(v) 4.86248 Tj +57 TJm +(ailable) 26.1075 Tj +-387 TJm +(for) 11.026 Tj +-387 TJm +(lo) 7.16595 Tj +28 TJm +(w) 6.65397 Tj +29 TJm +(er) 7.70214 Tj +-387 TJm +(letters.) 27.7187 Tj +-602 TJm +(F) 6.01376 Tj +86 TJm +(or) 8.21053 Tj +-387 TJm +(mathcal) 32.2468 Tj +-387 TJm +(exists) 22.3712 Tj +-387 TJm +(a) 4.60694 Tj +-387 TJm +(non) 14.843 Tj +-387 TJm +(free) 14.6161 Tj +-387 TJm +(fon) 12.5404 Tj +29 TJm +(t) 3.58297 Tj +-387 TJm +(for) 11.026 Tj +-387 TJm +(lo) 7.16595 Tj +28 TJm +(w) 6.65397 Tj +29 TJm +(er) 7.70214 Tj +-387 TJm +(letters) 25.1597 Tj +[1 0 0 1 134.405 442.219] Tm +0 0 Td +/F25_0 8.9664 Tf +(\(h) 8.70099 Tj +28 TJm +(ttp://www.p) 51.6958 Tj +-28 TJm +(ctex.com\)) 39.1608 Tj +12.828 -7.438 Td +/F24_0 5.9776 Tf +(b) 3.61764 Tj +16.943 -11.247 Td +/F25_0 8.9664 Tf +(Needs) 23.8578 Tj +-343 TJm +(pac) 13.8199 Tj +29 TJm +(k) 4.86248 Tj +57 TJm +(age) 13.3124 Tj +78.169 -11.247 Td +/F26_0 8.9664 Tf +(dsfont) 28.2388 Tj +Q +Q +Q +Q +Q +showpage +%%PageTrailer +pdfEndPage +%%Trailer +end +%%DocumentSuppliedResources: +%%+ font LLRYGB+SFBX1095 +%%+ font IPEITT+SFRM1095 +%%+ font HEMJKC+CMMI10 +%%+ font XBBXVE+SFTT1095 +%%+ font PJIJGB+EUFM10 +%%+ font DMRFKN+SFTI0800 +%%+ font ZUJTBM+CMSY10 +%%+ font ZCTGES+CMSS10 +%%+ font LGXTPM+CMMI8 +%%+ font DSCKSN+MSBM10 +%%+ font JUKYMP+CMTT10 +%%+ font TIQNSQ+CMTI10 +%%+ font GAGNKW+CMR10 +%%+ font UQPOYB+CMBX10 +%%+ font T3_23_0 +%%+ font AZSCNZ+SFTI0600 +%%+ font ILSKEM+SFRM0900 +%%+ font EGTQXB+SFTT0900 +%%EOF diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf new file mode 100644 index 00000000000..c98539d9e0d Binary files /dev/null and b/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf differ diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/runLaTeX b/Master/texmf-dist/doc/latex/voss-mathmode/runLaTeX new file mode 100644 index 00000000000..3253d306df4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/runLaTeX @@ -0,0 +1,8 @@ +#!/bin/sh +latex Mathmode.ltx +latex Mathmode.ltx +bibtex Mathmode +makeindex -s Mathmode.ist Mathmode.idx +latex Mathmode.ltx +dvips Mathmode.dvi +ps2pdf Mathmode.ps diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/runPDFLaTeX b/Master/texmf-dist/doc/latex/voss-mathmode/runPDFLaTeX new file mode 100644 index 00000000000..e2528786e89 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/runPDFLaTeX @@ -0,0 +1,7 @@ +#!/bin/sh +pdflatex Mathmode.ltx +#pdflatex Mathmode.ltx +bibtex Mathmode +makeindex -s Mathmode.ist Mathmode.idx +pdflatex Mathmode.ltx +pdflatex Mathmode.ltx diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/runVTeX b/Master/texmf-dist/doc/latex/voss-mathmode/runVTeX new file mode 100644 index 00000000000..a104575bcc5 --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/runVTeX @@ -0,0 +1,6 @@ +#!/bin/sh +vlatex Mathmode.ltx +vlatex Mathmode.ltx +bibtex Mathmode +makeindex -s Mathmode.ist Mathmode.idx +vlatex Mathmode.ltx diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg b/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg new file mode 100644 index 00000000000..d80b1afecea --- /dev/null +++ b/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg @@ -0,0 +1,47 @@ +% config file for showexpl.sty +% +% Copyright Herbert Voss, 2005 +% Licence: LPPL. + +\ProvidesFile{showexpl.cfg} + [2005/06/30 v0.02 Definitions for the showexpl package (hv)] +% +\definecolor{hellgelb}{rgb}{1,1,0.85} +\definecolor{colKeys}{rgb}{0,0,1} +\definecolor{colIdentifier}{rgb}{0,0,0} +\definecolor{colComments}{rgb}{1,0,0} +\definecolor{colString}{rgb}{0,0.5,0} + +\lstset{% + preset=\centering,% + rframe={},% + language=[AlLaTeX]TeX,% + float=hbp,% + basicstyle=\footnotesize\ttfamily,% + identifierstyle=\color{colIdentifier},% + keywordstyle=\color{colKeys},% + stringstyle=\color{colString},% + commentstyle=\itshape\color{colComments},% +% columns=flexible,% +% columns=fullflexible,% + columns=fixed, + tabsize=4,% + frame=single,% + extendedchars=true,% + showspaces=false,% + showstringspaces=false,% + numbers=left,% + numberstyle=\tiny\ttfamily,% + breaklines=true,% + breakindent=10pt,% + backgroundcolor=\color{hellgelb},% + breakautoindent=true,% + captionpos=t,% + xleftmargin=1em,% + xrightmargin=\fboxsep,% + numbersep=1em,% +% xrightmargin=-1cm,% +% relwidth=0.5,% +% columnsep=10pt% +} +\renewcommand*\SX@Info{}% diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds index 5e3f767121d..01c3baaeb90 100755 --- a/Master/tlpkg/libexec/ctan2tds +++ b/Master/tlpkg/libexec/ctan2tds @@ -1615,6 +1615,7 @@ $standardtex='\.(.bx|cfg|sty|clo|ldf|cls|def|fd|cmap|4ht)$'; 'vaucanson-g', '\.(def|tex)|' . $standardtex, 'vertex', 'vertex\.tex|' . $standardtex, 'vhistory', '\.sty', # not hyperref.cfg + 'voss-mathmode','NULL', # doc 'vrb', 'vrb\.tex', 'vruler', '^..[^s].*\.sty', # not miscdoc.sty 'wasy2', 'wasyfont\.tex', @@ -2205,6 +2206,7 @@ $standardinsrunner="latex -interaction=nonstopmode"; 'seuthesis', => 'NULL', # doc 'tkz-tab', => 'NULL', # doc 'turnthepage', => 'NULL', # doc + 'voss-mathmode', => 'NULL', # doc ); $standardmakeindex='\.ist'; diff --git a/Master/tlpkg/tlpsrc/voss-mathmode.tlpsrc b/Master/tlpkg/tlpsrc/voss-mathmode.tlpsrc new file mode 100644 index 00000000000..e69de29bb2d -- cgit v1.2.3