%\iffalse
%<paracol>%% Style file `paracol'.
%<man>%% LaTeX file 'paracol-man'.
%<*paracol|man>
%% Copyright (C) 2005-2018
%%   Hiroshi Nakashima (Kyoto University, deceased)
%% Copyright (C) 2024,2025
%%   Markus Kurtz
%% 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; either
%% version 1 of the License, or any later version.

%</paracol|man>
%<*dtx>
\ProvidesFile{paracol.dtx}
%</dtx>
%<*paracol>
\NeedsTeXFormat{LaTeX2e}[2018-04-01]
\DeclareRelease{1.35}{2018-12-31}{paracol-2018-12-31.sty}
\DeclareCurrentRelease{1.37}{2025-07-14}
\ProvidesPackage{paracol}[2025/07/14 1.37 typeset columns in parallel]
%</paracol>
%<man>\ProvidesFile{paracol-man.tex}
% \fi
% \ProvidesFile{paracol.dtx}[2025-07-14 1.37 docstrip source of paracol]
% \iffalse
%<*man>
\documentclass{ltxdoc}\normalmarginpar
\usepackage{color}
\usepackage{paracol}
\usepackage{newvbtm}
\DisableCrossrefs
\PageIndex
\RecordChanges
%</man>
%<man>\OnlyDescription
%<man>\def\ONLYDESCRIPTION{}
%<*man>
\textwidth210mm
\advance\textwidth-40mm \oddsidemargin20mm \advance\oddsidemargin-1in
\columnsep10mm
\marginparwidth20mm \advance\marginparwidth-\marginparsep
\marginparsep.5\marginparsep
\raggedbottom
\begin{document}
\DocInput{paracol.dtx}
\end{document}
%</man>
% \fi
% 
% 
% 
% \CodelineNumbered
% \makeatletter
% 
% \newcount\ChangeCount \ChangeCount10000
% \def\changes@#1#2#3{%
%   \global\advance\ChangeCount\@ne
%   \protected@edef\@tempa{\noexpand\glossary{#1\levelchar
%                                  \number\ChangeCount
%                                  \actualchar
%                                  \ifx\saved@macroname\@empty
%                                    \generalname
%                                  \else
%                                    \string\verb\quotechar*
%                                    \verbatimchar\saved@macroname
%                                    \verbatimchar
%                                  \fi
%                                  :\levelchar #3}}%
%   \@tempa\endgroup\@esphack}
% 
% \def\theglossary{\onecolumn \glossary@prologue
%	\GlossaryParms \let\item\@idxitem
%       \rightskip 1em plus 1fil
%       \parfillskip-1em
%       \ignorespaces}
% \def\endtheglossary{\relax}
% 
% 
% 
% \errorcontextlines10000
% \GetFileInfo{paracol.dtx}
% \setcounter{IndexColumns}{2}
% 
% \def\bottomfraction{.9}
% \def\cs#1{\texttt{\char\escapechar#1}}
% \def\Item{\vskip-\itemsep\vskip-\parsep\vskip0pt\nobreak\item}
%
% \def\nosv{\catcode`\|12\relax}
% \begingroup
% \nosv
% \gdef\Set#1#2{\{#1\,|\,#2\}}
% \gdef\Abs#1{|#1|}
% \gdef\Bar{|}
% \endgroup
% 
% \def\eqnarray{\stepcounter{equation}\let\@currentlabel=\theequation
% \global\@eqnswtrue
% \global\@eqcnt\z@\tabskip\@centering\let\\=\@eqncr
% $$\halign to \displaywidth\bgroup\hskip\@centering
%   $\displaystyle\tabskip\z@{##}$\@eqnsel&\global\@eqcnt\@ne
%   \hfil$\;{##}\;$\hfil
%   &\global\@eqcnt\tw@ $\displaystyle\tabskip\z@{##}$\hfil
%    \tabskip\@centering&\llap{##}\tabskip\z@\cr}
%
% \def\Meta#1{\penalty\@highpenalty
%	\hbox{{\tt\char`\{}{\it\meta{#1}}{\tt\char`\}}}}
% \def\opt#1{{\tt[}{\it\meta{#1}}{\tt]}}
% \def\optn#1{{\tt[#1]}}
%
% \let\latex@addmarginpar\@addmarginpar
% \let\latex@latex@warning@no@line\@latex@warning@no@line
% \def\@addmarginpar{\let\@latex@warning@no@line\@gobble
%	\latex@addmarginpar
%	\let\@latex@warning@no@line\latex@latex@warning@no@line}
% \let\@font@warning\@gobble
%
% \long\def\m@cro@#1#2{\endgroup \topsep\MacroTopsep \trivlist
%    \edef\saved@macroname{\string#2}
%   \def\makelabel##1{\llap{##1\hskip\@totalleftmargin}}
%   \if@inlabel
%     \let\@tempa\@empty \count@\macro@cnt
%     \loop \ifnum\count@>\z@
%       \edef\@tempa{\@tempa\hbox{\strut}}\advance\count@\m@ne \repeat
%     \edef\makelabel##1{\llap{\vtop to\baselineskip
%                                {\@tempa\hbox{##1}\vss}
%			       \hskip\@totalleftmargin}}
%     \advance \macro@cnt \@ne
%   \else  \macro@cnt\@ne  \fi
%   \edef\@tempa{\noexpand\item[
%      #1
%        \noexpand\PrintMacroName
%      \else
%        \noexpand\PrintEnvName
%      \fi
%      {\string#2}]}
%   \@tempa
%   \global\advance\c@CodelineNo\@ne
%    #1
%       \SpecialMainMacroIndex{#2}\nobreak
%       \DoNotIndex{#2}
%    \else
%       \SpecialMainEnvIndex{#2}\nobreak
%    \fi
%   \global\advance\c@CodelineNo\m@ne
%   \ignorespaces}
% 
% \def\dummymacro{\topsep\MacroTopsep \trivlist \item[]}
% \let\enddummymacro\endtrivlist
% 
% \def\DescribeOpt{\leavevmode\@bsphack\begingroup\MakePrivateLetters
%   \Describe@Opt}
% \def\Describe@Opt#1{\endgroup \Describe@pt{#1}}
% \def\Describe@pt#1#2{
%               \marginpar{\raggedleft\PrintDescribeMacro{#1}}
% 		\SpecialOptUsageIndex{#1}{#2}}
% 
% \def\Midx{\begingroup
% 	\let\Index\MainIndex
%	\let\CodeIndex\CodeMainIndex
%	\let\ArgedCodeIndex\ArgedCodeMainIndex
%	\let\MathIndex\MathMainIndex
%	\let\SpecialIndex\SpecialMainMacroIndex
% 	\MIDX}
% \def\MIDX#1{#1\endgroup}
% \def\Uidx{\begingroup
% 	\let\Index\UsageIndex
%	\let\CodeIndex\CodeUsageIndex
%	\let\ArgedCodeIndex\ArgedCodeUsageIndex
%	\let\MathIndex\MathUsageIndex
%	\let\SpecialIndex\SpecialMacroIndex
% 	\UIDX}
% \def\UIDX#1{#1\endgroup}
% 
% \def\Index{\@Index{}}
% \def\MainIndex{\@Index{\encapchar main}}
% \def\UsageIndex{\@Index{\encapchar usage}}
% \def\@Index#1{\@ifnextchar[]
%	{\@IndexWithActualChar{#1}}{\@IndexPlain{#1}}}
% \def\@IndexPlain#1#2{\special@index{#2#1}\ignorespaces}
% \def\@IndexWithActualChar#1[#2]#3{\special@index{#3\actualchar#2#1}
%	\ignorespaces}
% \let\LaTeX@theindex\theindex
% \def\theindex{\LaTeX@theindex \hbadness\@M}
% 
% \def\CodeMainIndex{\Code@Index{\encapchar main}}
% \def\CodeUsageIndex{\Code@Index{\encapchar usage}}
% \def\CodeIndex{\Code@Index{}}
% \def\Code@Index{\S@nitizedIndex\IndexVerb@timed}
% 
% \def\ArgedCodeMainIndex{\Arged@Code@Index{\encapchar main}}
% \def\ArgedCodeUsageIndex{\Arged@Code@Index{\encapchar usage}}
% \def\ArgedCodeIndex{\Arged@Code@Index{}}
% \def\Arged@Code@Index{\S@nitizedArgedIndex\IndexVerb@timed}
% 
% \def\MathMainIndex{\Math@Index{\encapchar main}}
% \def\MathUsageIndex{\Math@Index{\encapchar usage}}
% \def\MathIndex{\Math@Index{}}
% \def\Math@Index{\S@nitizedIndex\IndexM@thed}
% 
% \def\S@nitizedIndex#1#2{\@bsphack
%	\begingroup \@sanitize \S@nitized@Index{#1}{#2}}
% \def\S@nitized@Index#1#2#3{\endgroup
% 	\special@index{#1{#3}#2}\@esphack\ignorespaces}
% \def\S@nitizedArgedIndex#1#2{\@bsphack
%	\begingroup \@sanitize \S@nitized@rgedIndex{#1}{#2}}
% \def\S@nitizedNonArgedIndex#1#2{\@bsphack
%	\begingroup \@sanitize \S@nitizedNon@rgedIndex{#1}{#2}}
% \def\S@nitized@rgedIndex#1#2#3{\endgroup
%	\ArgedIndexMainAndSub{#1}{#2}{#3}}
% \def\S@nitizedNon@rgedIndex#1#2#3{\endgroup
% 	\special@index{#1{#3}#2}
%	\ArgedIndexSub{#1}{#2}{#3}}
% \def\S@nitized@rgedIndex#1#2#3{\endgroup
%	\ArgedIndexMainAndSub{#1}{#2}{#3}}
% \def\S@nitizedNon@rgedIndex#1#2#3{\endgroup
% 	\special@index{#1{#3}#2}
%	\ArgedIndexSub{#1}{#2}{#3}}
% \def\ArgedIndexMainAndSub#1#2#3#4{\ArgedIndexMain{#1}{#2}{#3}{#4}
%	\ArgedIndexSub{#1}{#2}{#3}{#4}}
% \def\ArgedIndexMain#1#2#3#4{\begingroup
%	\def\@tempa{\@rgedIndexMain{#1}{#2}{#3}}
%	\def\e{}\edef\@tempb{{#4}}
%	\expandafter\@tempa\@tempb
%	\endgroup}
% \def\@rgedIndexMain#1#2#3#4{\special@index{#1{#3} (#4)#2}}
% \def\ArgedIndexSub#1#2#3#4{\begingroup
%	\def\@tempa{\@rgedIndexSub{#1}{#2}{#3}}
%	\def\e{e}\edef\@tempb{{#4}}
%	\expandafter\@tempa\@tempb
%	\endgroup}
% \def\@rgedIndexSub#1#2#3#4{\special@index{#4s:\levelchar#1{#3}#2}}
% 
% \def\IndexBr@cedWith#1#2{#2\actualchar#1{#2}}
% \def\IndexVerb@timed#1{#1\actualchar\string\verb\quotechar*\verbatimchar
% 	#1\verbatimchar}
% \def\IndexM@thed#1{#1\actualchar\doll@rm@rk#1\doll@rm@rk}
% 
% \def\env#1{\texttt{#1}\EnvIndex{#1}}
% \def\EnvIndex#1{\ArgedCodeIndex{#1}{environment}}
% \def\counter#1{\texttt{#1}\CounterIndex{#1}}
% \def\CounterIndex#1{\ArgedCodeIndex{#1}{counter}}
% 
% \begingroup
% \catcode`\_12 \catcode`\$12
% \gdef\TheUnderScore{_}
% \gdef\doll@rm@rk{$}
% \endgroup
% 
% \long\def\Special@Index#1#2{\@bsphack
%	\RemoveAtFromCS{#2}
% 	\protected@edef\@tempa{\RAFCtempa
%		\actualchar \string\verb
% 		\quotechar*\verbatimchar\string#2\verbatimchar}
% 		\expandafter\special@index\expandafter{\@tempa#1}
%	\@esphack}
% \def\SpecialIndex{\Special@Index{}}
% \def\SpecialMainMacroIndex{\Special@Index{\encapchar main}}
% \def\SpecialMacroIndex{\Special@Index{\encapchar usage}}
% \def\SpecialArrayIndex#1{\Special@Index{${\cdot}#1$}}
% \def\SpecialArrayMainIndex#1{\Special@Index{${\cdot}#1$\encapchar main}}
% \def\SpecialArrayUsageIndex#1{\Special@Index{${\cdot}#1$\encapchar usage}}
% 
% \def\Macro{\begingroup \@sanitize \iMacro}
% \def\iMacro#1{\endgroup
%	\def\SpecialMainMacroIndex##1{\SWiIndex{##1}{\encapchar main}}
%	\macro{#1}}
% \let\endMacro\endmacro
% 
% \def\SpecialWeirdIndex{\@bsphack \begingroup \@sanitize \SWIndex{}}
% \def\SWIndex#1#2{\endgroup \SWiIndex{#2}{#1}}
% \def\SWiIndex#1#2{%
%	\protected@edef\@tempa{#1\actualchar \string\verb
%		\quotechar*\verbatimchar#1\verbatimchar}
%		\expandafter\special@index\expandafter{\@tempa#2}
% 	\@esphack}
% 
% \let\RAFCempty\@empty
% \let\RAFCgobble\@gobble
% \edef\RAFCIfPrefix{\expandafter\string\csname if\endcsname}
% \edef\RAFCIfPrefix{\expandafter\RAFCgobble\RAFCIfPrefix}
% \makeatother
% \long\def\RemoveAtFromCS#1{
% 	\edef\RAFCtempa{\expandafter\RAFCgobble\string#1}
% 	\edef\RAFCtempa{\expandafter\string\csname\RAFCtempa\endcsname}
%	\expandafter\iRemoveAtFromCS\RAFCtempa@\NIL}
% \def\iRemoveAtFromCS#1#2@#3\NIL{\def\RAFCtempb{#3}
% 	\ifx\RAFCtempb\RAFCempty \def\RAFCtempa{#2}\let\next\relax
%	\else \def\RAFCtempa{ #2@}\def\next{\iiRemoveAtFromCS#3\NIL}
% 	\def\RAFCtempb{#2}
%	\ifx\RAFCtempb\RAFCempty
% 	\else\ifx\RAFCtempb\RAFCIfPrefix
%	\else\ifx\RAFCtempb\CommonCSPrefix
%	\else\ifx\RAFCtempb\CommonIfPrefix
%	\else \def\RAFCtempa{}\def\next{\xRemoveAtFromCS#2@#3\NIL}
% 	\fi\fi\fi\fi\fi
%	\next}
% \def\iiRemoveAtFromCS#1{\ifx#1@\edef\RAFCtempa{\RAFCtempa@}
%	\let\next\iiRemoveAtFromCS
%	\else \def\next{\xRemoveAtFromCS#1}\fi
% 	\next}
% \def\xRemoveAtFromCS#1@\NIL{\edef\RAFCtempa{#1\RAFCtempa}}
% \makeatletter
% 
% \begingroup
% \makeatother
% \gdef\TheAtMark{@}
% \catcode`\@\active
% \gdef\!{\begingroup \catcode`\@\active \IndexedVerb}
% \gdef\IndexedVerb#1!{\def@{\TheAtMark \penalty\exhyphenpenalty}
% 	\def~{\badbreak}
% 	\rm\texttt{\string#1}\let@\TheAtMark \def~{}
% 	\edef\RAFCTempa{\expandafter\RAFCgobble\string#1}
%	\expandafter\SpecialIndex\csname\RAFCTempa\endcsname \endgroup}
% \endgroup
% \let\Tie~
% \let\~\allowbreak
% 
% \def\CSIndex#1{\expandafter\def\expandafter\@tempa\expandafter{\csname
% 	#1\endcsname}
% 	\edef\@tempb{\expandafter\string\@tempa}
%	\texttt{\@tempb}
% 	\expandafter\SpecialIndex\@tempa}
% \def\CSINDEX#1{\expandafter\def\expandafter\@tempa\expandafter{\csname
% 	#1\endcsname}
% 	\expandafter\SpecialIndex\@tempa}
% 
% \begingroup
% \gdef\@sverbcat{\catcode`\@\active\catcode`\#\active}
% \catcode`\@\active \gdef@{\char`\@\penalty\exhyphenpenalty}
% \catcode`\#\active \gdef#{\penalty\exhyphenpenalty}
% \endgroup
% \let\latex@sverb\@sverb
% \def\@sverb{\@sverbcat\latex@sverb}
% 
% \def\Paracol{\textsf{paracol}}
% \let\LB[\let\RB]\let\LP(\let\RP)
% \def\LBRP#1#2{\LB#1,#2\RP}
% \def\In{\in\LBRP}
% \let\Sec\S
% \def\secref{\Sec\ref}
% \let\<\langle \let\>\rangle
% \let\ARG\arg
% \def\arg#1{\<\mathit{#1}\>}
% \def\Arg#1{\texttt{\char`\{}#1\texttt{\char`\}}}
% \def\ARg#1{\texttt{\char`\{}\textit{#1}\texttt{\char`\}}}
% \def\Oarg#1{\texttt{[\textit{#1}]}}
% \def\Sub#1{{\hbox to0pt{\hss$\scriptstyle #1$\hss}}}
% \def\PT{\,{\rm pt}}
% 
% \def\Sloppy#1{\tolerance#1\hbadness#1\relax}
% \let\endSloppy\par
% \def\Hfuzz#1{\hfuzz#1\relax}
% \let\endHfuzz\par
% \def\KeepSpace#1{\par \vskip-\lastskip \vskip#1\baselineskip \allowbreak
%   \vskip-#1\baselineskip\nobreak}
% 
% 
% 
% \edef\CommonCSPrefix{\expandafter\RAFCgobble\string\pcol}
% \edef\CommonIfPrefix{\expandafter\RAFCgobble\string\ifpcol}
% 
% \def\beginenv#1{\CSIndex{begin}\allowbreak
% 	\texttt{\char`{#1\char`}}\EnvIndex{#1}}
% \def\beginparacol{\beginenv{paracol}}
% 
% \def\bgext{extension\Index{extension of background painting region}}
% \def\bginfext{infinite extension
%     \Index{infinite extension of background painting region}}
% \def\bgpaint{background painting\Index{background painting}}
% \def\bground{background\Index{background painting}}
% \def\bpage{base page\Index{base page}}
% \def\colorctext{color context\Index{color context}}
% \def\colorstack{color stack\Index{color stack}}
% \def\cctext{column-context\Index{column-context}}
% \def\colpage{column-page\Index{column-page}}
% \def\colpream{column preamble\Index{column preamble}}
% \def\Colpream{preamble\Index{column preamble}}
% \def\cscan{column-scan\Index{column-scan}}
% \def\csepgap{column-separating gap\Index{column-separating rule}}
% \def\cseprule{column-separating rule\Index{column-separating rule}}
% \def\cswap{column-swapping\Index{column-swapping}}
% \def\cswitch{column-switching\Index{column-switching}}
% \def\csenv{column-switching environment\Index{column-switching environment}}
% \def\cwise{column-wise\Index{column-wise stuff}}
% \def\csync{counter synchronization\Index{counter synchronization}}
% \def\ccolpage{current column-page\Index{current column-page}}
% \def\Endparacol{\CSIndex{end}\allowbreak
% 	\texttt{\char`\{paracol\char`\}}\EnvIndex{paracol}}
% \def\elocal{environment-local\Index{environment-local}}
% \def\exsync{explicit synchronization\Index{explicit synchronization}}
% \def\fcolumn{float column\Index{float column}}
% \def\fpage{float page\Index{float page}}
% \def\gcounter{global counter\Index{global counter}}
% \def\imsync{implicit synchronization\Index{implicit synchronization}}
% \def\lpage{last page\Index{last page}}
% \def\lcommand{local command\Index{local command}}
% \def\lcolumn{leading column\Index{leading column}}
% \def\lcolpage{leading column-page\Index{leading column-page}}
% \def\lcounter{local counter\Index{local counter}}
% \def\lrep{local representation\Index{local representation}}
% \def\Mcfnote{column-wise footnote\Index{column-wise footnote}}
% \def\mcfnote{column-wise\Index{column-wise footnote}}
% \def\Mgfnote{merged footnote\Index{merged footnote}}
% \def\mgfnote{merged\Index{merged footnote}}
% \def\mctext{spanning text\Index{spanning text}}
% \def\mirror{mirror\Index{mirrored background painting}}
% \def\mvlfloat{MVL-float\Index{MVL-float}}
% \def\npaired{non-paired\Index{non-paired parallel-paging}}
% \def\paired{paired\Index{paired parallel-paging}}
% \def\parapag{parallel-pag\Index{parallel-paging}}
% \def\pctext{page context\Index{page context}}
% \def\pfcheck{pre-flushing column height check
%	\Index{pre-flushing column height check}}
% \def\Postenv{post-environment\Index{post-environment stuff}}
% \def\postenv{post-environment stuff\Index{post-environment stuff}}
% \def\Preenv{pre-environment\Index{pre-environment stuff}}
% \def\preenv{pre-environment stuff\Index{pre-environment stuff}}
% \def\prespan{pre-spanning-text stuff\Index{pre-spanning-text stuff}}
% \def\prim{page rim\Index{page rim}}
% \def\pwise{page-wise\Index{page-wise stuff}}
% \def\pwstuff{page-wise stuff\Index{page-wise stuff}}
% \def\Scfnote{page-wise footnote\Index{page-wise footnote}}
% \def\scfnote{page-wise\Index{page-wise footnote}}
% \def\spanning{spanning stuff\Index{spanning stuff}}
% \def\sptext{spanning text\Index{spanning text}}
% \def\spage{starting page\Index{starting page}}
% \def\sync{synchroniz\Index{synchronize}}
% \def\tpage{top page\Index{top page}}
% 
% \def\vb{\Index[$\kappa_c(\beta)$]{-k_c(-b)}\beta}
% \def\pd{\Index[$\kappa_c(\delta)$]{-k_c(-d)}\delta}
% \def\Celt{\Index[$\gamma_0^c$]{-c^c_0}\gamma_0}
% \def\Celtshadow{\Index[$\hat\gamma_0^c$]{-c^xc_0}\hat\gamma_0}
% \def\celt{\Index[$\gamma_i$]{-c^a_i}\gamma}
% \def\celtpop{\Index[$\gamma_i^-$]{-c^m_i}\gamma^-}
% \def\celtshadow{\Index[$\hat\gamma_i$]{-c^x_i}\hat\gamma}
% \def\mcelt{\Index[$\gamma_{i,m}$]{-c^a_i,m}\gamma}
% \def\mceltpop{\Index[$\gamma_{i,m}^-$]{-c^m_i,m}\gamma^-}
% \def\cst{\Index[$\string\mathit{\Gamma}$]{-C^a}\mathit{\Gamma}}
% \def\CST{\Index[$\string\mathit{\Gamma}^c$]{-C^c}\mathit{\Gamma}}
% \def\CSTraw{\Index[$\string\mathit{\Gamma}^c_r$]{-C^c_r}\mathit{\Gamma}_r}
% \def\cstraw{\Index[$\string\mathit{\Gamma}_r$]{-C^a_r}\mathit{\Gamma}_r}
% \def\csts{\Index[$\string\mathit{\Gamma}_s$]{-C_s}\mathit{\Gamma}_s}
% \def\CSTshadow{\Index[$\hat\string\mathit{\Gamma}^c$]{-C^xc}
%   \hat\mathit{\Gamma}}
% \def\cstshadow{\Index[$\hat\string\mathit{\Gamma}$]{-C^x}\hat\mathit{\Gamma}}
% \def\ep{\Index[$\kappa_c(\varepsilon)$]{-k_c(-e)}\varepsilon}
% \def\clist{\Index[$\zeta(\theta)$]{-f(-j)}\zeta}
% \def\fh{\Index[$\kappa_c(\eta)$]{-k_c(-h)}\eta}
% \def\CC{\Index[$\string\mathit{\Theta}$]{-J}\mathit{\Theta}}
% \def\Cc{\Index[$\string\mathit{\Theta}_c$]{-J_c}\mathit{\Theta}}
% \def\CG{\Index[$\string\mathit{\Theta}^g$]{-J^g}\mathit{\Theta}^g}
% \def\cg{\Index[$\theta^g$]{-j^g}\theta^g}
% \def\CTL{\Index[$\string\mathit{\Theta}^l$]{-J^l}\mathit{\Theta}^l}
% \def\cl{\Index[$\theta^l$]{-j^l}\theta^l}
% \def\cc{\Index[$\kappa_c$]{-k_c}\kappa}
% \def\bl{\Index[$\kappa_c(\lambda_b)$]{-k_c(-l_b)}\lambda_b}
% \def\dl{\Index[$\kappa_c(\lambda_d)$]{-k_c(-l_d)}\lambda_d}
% \def\ml{\Index[$\kappa_c(\lambda_m)$]{-k_c(-l_m)}\lambda_m}
% \def\tl{\Index[$\kappa_c(\lambda_t)$]{-k_c(-l_t)}\lambda_t}
% \def\lrm{\Index[$\mu$]{-m}\mu}
% \def\bn{\Index[$\kappa_c(\nu_b)$]{-k_c(-n_b)}\nu_b}
% \def\cn{\Index[$\kappa_c(\nu_c)$]{-k_c(-n_c)}\nu_c}
% \def\tn{\Index[$\kappa_c(\nu_t)$]{-k_c(-n_t)}\nu_t}
% \def\tf{\Index[$\kappa_c(\xi)$]{-k_c(-o)}\xi}
% \def\PP{\Index[$\string\mathit{\Pi}$]{-P}\mathit{\Pi}}
% \def\PPP{\Index[$\string\mathit{\Pi}^+$]{-P+}\mathit{\Pi}^+}
% \def\pp{\Index[$\pi(p)$]{-p(p)}\pi}
% \def\br{\Index[$\kappa_c(\rho_b)$]{-k_c(-r_b)}\rho_b}
% \def\tr{\Index[$\kappa_c(\rho_t)$]{-k_c(-r_t)}\rho_t}
% \def\sw{\Index[$\kappa_c(\sigma)$]{-k_c(-s)}\sigma}
% \def\ft{\Index[$\kappa_c(\tau)$]{-k_c(-t)}\tau}
% \def\df{\Index[$\string\mathit{\Phi}$]{-U}\mathit{\Phi}}
% 
% \def\bf{\Index[$b_f$]{b_f}b_f}
% \def\bgc{\Index[$B_a$]{B_a}B}
% \def\bge{\Index[$e_a(d^\pm)$]{e_a(d^+)}e}
% \def\bgr{\Index[$R_a$]{R_a}R}
% \def\C{\Index[$C$]{C}C}
% \def\Cfrom{\Index[$C^0$]{C0^0}{C^0}}
% \def\CBfrom{\Index[$C_b^0$]{C0_b^0}{C_b^0}}
% \def\CBto{\Index[$C_b^1$]{C0_b^1}{C_b^1}}
% \def\CL{\Index[$C_L$]{C0_L}C_L}
% \def\Cto{\Index[$C^1$]{C0^1}{C^1}}
% \def\cmax{\Index[$c_{\max}$]{c0_max}c_{\max}}
% \def\dc{\Index[$d_c$]{d_c}d_c}
% \def\DP{\Index[$D_P$]{D_P}D_P}
% \def\DT{\Index[$D_T$]{D_T}D_T}
% \def\false{\Index[$\string\mathit{false}$]{false}\mathit{false}}
% \def\Fc{\Index[$F_c(X)$]{F0_c}F_c}
% \def\fc{\Index[$f_c(x)$]{f0_c}f_c}
% \def\gap{\Index[$g_c$]{g_c}g}
% \def\HB{\Index[$H_B$]{H_B}H_B}
% \def\HM{\Index[$H_M$]{H_M}H_M}
% \def\HN{\Index[$H_N$]{H_N}H_N}
% \def\HP{\Index[$H_P$]{H_P}H_P}
% \def\HR{\Index[$H_R$]{H_R}H_R}
% \def\HS{\Index[$H_S$]{H_S}H_S}
% \def\HT{\Index[$H_T$]{H_T}H_T}
% \def\mplist{\Index[$I$]{I}I}
% \def\nf{\Index[$n_f$]{n_f}n_f}
% \def\npop{\Index[$n_{\rm pop}$]{n_pop}n_{\rm pop}}
% \def\mpar{\Index[$\mathit{mpar}(t_i,b_i)$]{mpar(t_i,b_i)}\mathit{mpar}}
% \def\mpb{\Index[$M_{\{L,R\}}^{\{l,r\}}$]{M0_{L,R}^{l,r}}M}
% \def\mpbout{\Index[${\string\cal{M}}$]{M1}{\cal M}}
% \def\mpboutz{\Index[${\string\cal{M}}_0$]{M1_0}{\cal M}_0}
% \def\pbase{\Index[$p_b$]{p0_b}p_b}
% \def\ptop{\Index[$p_t$]{p0_t}p_t}
% \def\page{\Index[$\string\mathit{page}(p)$]{page(p)}\mathit{page}}
% \def\S{\Index[$S_c$]{S_c}S}
% \def\SS{\Index[$S$]{S}S}
% \def\s{\Index[$s_c(p)$]{s_c(p)}s}
% \def\size{\Index[$\string\mathit{size}(x)$]{size}\mathit{size}}
% \def\Size{\Index[$\string\mathit{SIZE}(x)$]{SIZE}\mathit{SIZE}}
% \def\spt{\Index[$\mathit{span}(H_i,h_i)$]{span(H_i,h_i)}\mathit{span}}
% \def\T{\Index[$T$]{T}T}
% \def\true{\Index[$\string\mathit{true}$]{true}\mathit{true}}
% \def\val{\Index[$\string\mathit{val}_c(\theta)$]{val_c(j)}
% 	\mathit{val}}
% \def\Val{\Index[$\string\mathit{val}(\theta)$]{val(j)}
% 	\mathit{val}}
% \def\vc{\Index[$v_c(x)$]{v1_c}v_c}
% \def\VB{\Index[$V_B$]{V0_B}V_B}
% \def\VE{\Index[$V_E$]{V0_E}V_E}
% \def\VP{\Index[$V_P$]{V0_P}V_P}
% \def\VPP{\Index[$V'_P$]{V0_Px}V'_P}
% \def\VT{\Index[$V_T$]{V0_T}V_T}
% \def\w{\Index[$w_c$]{w1_c}w}
% \def\W{\Index[$W_c$]{W0_c}W}
% \def\WM{\Index[$W_M$]{W0_M}W_M}
% \def\WP{\Index[$W_P$]{W0_P}W_P}
% \def\WR{\Index[$W_R$]{W0_R}W_R}
% \def\WT{\Index[$W_T$]{W0_T}W_T}
% 
% 
%
% \def\bracepair{`{\tt\char`\{\char`\}'}}
% \@addtoreset{section}{part}
% \def\part#1{\refstepcounter{part}
%   \addcontentsline{toc}{part}{\thepart\hspace{1em}#1}
%   \vbox to\unitlength{\vfil\centerline{\Large\bfseries PART\ \thepart}\vfil
%     \centerline{\huge\bfseries#1}\vfil\vfil}}
% \def\Env#1#2{\!\begin!{\tt\char`\{\env{#1}\char`\}}#2\quad
%   $\mathit{body}$\quad\!\end!{\tt\char`\{\env{#1}\char`\}}}
% \def\ENV#1#2{\!\begin!{\tt\char`\{\Midx{\env{#1}}\char`\}}#2\quad
%   $\mathit{body}$\quad\!\end!{\tt\char`\{\env{#1}\char`\}}}
% \def\meta#1{\mbox{$\mathit{#1}$}}
% 
% \let\l@part\l@section
% \def\l@section{\@dottedtocline{1}{0pt}{1.5em}}
% 
% \newverbatim{Verbatim}{\topsep0pt\partopsep0pt\parsep0pt\parskip0pt\tt}{}{}{}
% \globalcounter{section}
% \globalcounter{figure}
% \globalcounter{table}
% \definethecounter{footnote}{1}{\textit{\arabic{footnote}}}
% \definethecounter{subsection}{1}{
%   \texttt{\arabic{section}.\arabic{subsection}}}
% \addcontentsonly{toc}{0}
%
% \def\Dotfill{\leavevmode\cleaders\hbox to.44em{\hss.\hss}\hfill\kern0pt}
% \def\Marginpar#1{\marginpar{\raggedright#1}}
% \def\Emph#1{{\bfseries#1}}
% \def\Hrule{\hbox to\linewidth{\hrulefill}}
% \def\\{\hfil\break\null\ignorespaces}
% 
% \let\AB\allowbreak
% \def\badbreak{\penalty50}
% \let\BB\badbreak
% 
% \hyphenation{col-umn col-umns}
%
% \let\EQ\relax \let\GT\relax \let\BAR\relax \let\NEQ\relax
% 
% 
% 
% \changes{v0.9}{2005/01/28}
%	{The style paracol is born. (2005/01/28)}
% \changes{v0.91}{2011/09/16}
%	{The style is included in CTAN with a very small
%	 modification. (2011/09/16) }
% \changes{v1.0}{2011/10/10}
%	{Add this document and fix the following problems on the author's
%	 30th wedding anniversary. (2011/10/10)}
% \changes{v1.1}{2012/05/11}
% 	{Add \cs{columnratio} and variable column width. (2012/05/11)}
% \changes{v1.2-1}{2013/05/11}
%	{Make \string\texttt{paracol} environment accept \cs{color} and add
%	 \cs{columncolor}. (2013/05/11)}
% \changes{v1.2-2}{2013/05/11}
%	{Add page-wise and merged footnote functions. (2013/05/11)}
% \changes{v1.2-3}{2013/05/11}
%	{Fix a problem in synchronization. (2013/05/11)}
% \changes{v1.2-4}{2013/05/11}
%	{Add column-swapping functions. (2013/05/11)}
% \changes{v1.2-5}{2013/05/11}
%	{Allow a \string\texttt{paracol} envrionment is enclosed in list-like
%	 environments. (2013/05/11)}
% \changes{v1.2-6}{2013/05/11}
%	{Add \cs{localcounter}. (2013/05/11)}
% \changes{v1.2-7}{2013/05/11}
%	{Bug fixes and minor revisions as follows. (2013/05/11)}
% \changes{v1.21}{2013/06/06}
%	{Fix the bug by which a column having empty column-pages followed by
%	 a synchronization point is lost or placed in a wrong
%	 page. (2013/06/06)} 
% \changes{v1.22}{2013/06/30}
%	{Fix the bug that \cs{color} and its relatives in a paragraph or
%	 around page top causes inconsistency of color context. (2013/06/30)}
% \changes{v1.23}{2013/07/08}
%	{Fix the problem that a colored text has a line break candidate at
%	 its end inappropriately. (2013/07/08)}
% \changes{v1.24}{2013/07/27}
%	{Fix the problem caused by the concealment of \cs{vadjust} in math
%	 group. (2013/07/27)}
% \changes{v1.3-1}{2013/09/17}
%	{Fix the known problem of the placement of page-crossing spanning
%	 texts. (2013/09/17)}
% \changes{v1.3-2}{2013/09/17}
%	{Introduce parallel-paging. (2013/09/17)}
% \changes{v1.3-3}{2013/09/17}
%	{Introduce column-separating rule drawing and background
%	 painting. (2013/09/17) }
% \changes{v1.3-4}{2013/09/17}
%	{Introduce API for column/gap width and marginal note position
%	 specification. (2013/09/17)}
% \changes{v1.3-5}{2013/09/17}
%	{Introduce \cs{thecolumn} and \cs{ensurevspace},
%	 \cs{footnotelayout}, \cs{twosided} and
%	 \cs{cleardoublepage}. (2013/09/17)}
% \changes{v1.3-6}{2013/09/17}
%	{Fix a few problems mainly related to synchronization and ordinary
%	 footnotes. (2013/09/17)} 
% \changes{v1.31}{2013/10/10}
%	{Add passing paramenters related sectioning commmands beyond
%	 \cs{end}\texttt{\char`\{paracol\char`\}} and fix misspells in
%	 error messages. (2013/10/10)}
% \changes{v1.32-1}{2015/10/10}
% 	{Add \cs{globalcounter*} to make all counters global. (2015/10/10)}
% \changes{v1.32-2}{2015/10/10}
% 	{Fix a memory leak in \cs{pcol@startcolumn}. (2015/10/10)}
% \changes{v1.32-3}{2015/10/10}
% 	{Fix a page-wise float problem. (2015/10/10)}
% \changes{v1.33-1}{2016/11/19}
% 	{Fix a marginal note problem. (2016/11/19)}
% \changes{v1.33-2}{2016/11/19}
% 	{Non-logical modifications to obey the coding convention, for
%	 clarification, etc.. (2016/11/19)}
% \changes{v1.34}{2018/05/07}
% 	{Fix a text coloring problem in non-breakable sequences of vertical
%	 items. (2018/05/07)}
% \changes{v1.35-1}{2018/12/31}
% 	{Fix a page break problem with a tall item in the very first line of
%	 the first column. (2018/12/31)}
% \changes{v1.35-2}{2018/12/31}
% 	{Fix a vertical space problem with \texttt{trivlist} immediately
%	 surrounding \texttt{paracol}. (2018/12/31)}
% \changes{v1.35-3}{2018/12/31}
% 	{Fix a bug in \cs{pcol@addmarginpar} and add emulation of
%	 \cs{marginnnote}. (2018/12/31)}
% \changes{v1.35-4}{2018/12/31}
% 	{Add \cs{belowfootnoteskip} for the additional space below the
%	 non-merged pre-environment footnotes. (2018/12/31)}
% \changes{v1.35-5}{2018/12/31}
% 	{Add \cs{definecolumnpreamble}. (2018/12/31)}
% \changes{v1.35-6}{2018/12/31}
% 	{Add error check if \texttt{paracol} environment is not in outer par
%	 mode and is with ordinary two-column typesetting. (2018/12/31)}
%
% 
% 
% \title{Package \textsf{paracol}:\\
% 	Yet Another Multi-Column Package to Typeset Columns in
% 	\textit{Parallel}}
% 
% \author{Hiroshi Nakashima (Kyoto University, deceased)\\Markus Kurtz (\url{https://codeberg.org/mgkurtz/paracol})}
% \date{version \fileversion: \filedate}
% \setbox0\vbox{\vskip\topskip\maketitle}\unitlength\ht0\copy0
% 
% \ifx\ONLYDESCRIPTION\undefined
% \tableofcontents
% \newpage \ifodd\c@page\else \hbox{}\newpage \fi
% \vbox to\unitlength{\unvbox0\vfil}
% \part{User's Manual}\label{part:man}
% \let\MidxSave\Midx \let\Midx\Uidx
% \else
% \addtocontents{toc}{\protect\label{toc}}
% \fi
% 
% \begin{abstract}
% This package provides a \LaTeX{} environment named |paracol| in which you
% may {\em switch} and {\em synchronize} columns by a command
% |\switchcolumn| and by internal environments |column|, |nthcolumn|,
% |leftcolumn| and |rightcolumn|.
% \ifx\ONLYDESCRIPTION\undefined\else
% See p.\Tie\pageref{toc} for the table of contents of this manual, see \href{https://mirrors.ctan.org/macros/latex/contrib/paracol/paracol.pdf}{paracol.pdf} for code documentation.
% \fi
% \end{abstract}
% 
% \tracingpages1 \tracingoutput1 \showboxdepth10000 \showboxbreadth10000
% \input{man.dtx}
% \tracingpages0 \tracingoutput0
% \newpage
% \input{ref.dtx}
% \newpage
% \input{pwfnote.dtx}
% \newpage
% \twosided
% \edef\OddSideMargin{\number\oddsidemargin}
% \advance\oddsidemargin1in
% \evensidemargin1.25\oddsidemargin \advance\evensidemargin-1in
% \oddsidemargin.75\oddsidemargin \advance\oddsidemargin-1in
% \input{ppts.dtx}
% \newpage
% \input{bgpaint.dtx}
% \newpage
% \twosided[]\oddsidemargin\OddSideMargin sp
% \resetbackgroundcolor \columnratio{}
% \input{probs.dtx}
% 
% \IndexPrologue{\newpage\section*{Index}
% Underlined number refers to the page where the specification of
% corresponding entry is described, while italicized number is for the page
% in which the usage of the entry is explained.}
% 
% \StopEventually{\ifx\ONLYDESCRIPTION\undefined\newpage\fi
% \section*{Acknowledgments}
% \addcontentsline{toc}{part}{\protect\numberline{}{Acknowledgments}}
% 
% The author thanks to Yacine Daddi Addoun who gave the author the
% motivation to write the style for his bilingual document.  He also thanks
% to the following people;
% 
% Robin Fairbairns who kindly invited the style to CTAN after the author's
% lazy six years failing to upload the style;
% 
% Joseph
% G.\ Rosenstein and Dieter K\"ohler who suggested the author adding the
% function of unbalanced column width incorporated in version 1.1;
% 
% Joaqu\'in Blas who motivated the author to challenge page-wise footnotes;
% 
% Olivier Vogel who pointed out the compatibility problem with coloring
% packages;
% 
% Heiner Richter who asked for the possibility of swapping unbalanced
% columns, revealed two bugs in version 1.22 related to coloring and
% float pages, showed the necessity of \!\coloredwordhyphenated!, and finally
% found the necessity of \!\globalcounter!|*|;
% 
% an anonymous user who reported a very rare-case but severe bug in the
% version~1.1 by which a page can be lost (whoops!);
% 
% Olivier Gerard who found another terrible bug fixed in version 1.21 but
% hidden in \textsf{paracol} for two years by which a column disappears or
% moves to a wrong page (another whoops!\@), suggested to implement
% \!\setcolumnwidth!, \!\marginparthreshold! and \!\thecolumn!  introduced
% in version 1.3, and kindly proofread this manual;
% 
% George Kamel who let the author know the coloring function newborn in
% version 1.2 had a bug fixed in version 1.22 to which he also made a great
% contribution testing many tentative versions with his own colored
% documents;
% 
% another anonymous user who pointed out version 1.22 had yet another
% coloring bug fixed in version 1.24;
% 
% Jean Druel who motivated the author to implement an advanced functionality
% parallel-paging;
% 
% Tilo Arens and other patient users who had wished \Paracol{} would have the
% capability of rule drawing in the gaps separating columns and painting
% backgrounds of columns and so on;
% 
% Michael Bolin who gave the author motivated examples showing the
% necessity of \!\ensurevspace!.
% 
% Tigran Aivazian who reported a memory leak problem fixed in version 1.32;
% 
% Marcus Zelezny and Touhami Mamouni who found an incompatibility with
% \LaTeX{} itself (2015/01/10 or later) and enlighten the author on the cause
% of the problem;
% 
% Manuel Kuehner who reported a bug in text coloring which had hidden
% for five years until the version 1.34 was released;
% 
% ZongXian Wang who found that the paracol misbehaves when an environment
% starts with an unusually tall item;
% 
% and Frank Mittelbach who pointed out bugs in \cs{marginpar} implementation
% and vertical spacing with \cs{trivlist}-like environments, and suggested
% new functionality with \cs{marginnote}, \cs{belowfootnoteskip} and
% \cs{definecolumnpreamble}.
% 
% For the implementation of the style file, the author referred to the base
% implementations of \cs{output} and othe many macros of \LaTeXe{} written
% by Leslie Lamport, Johannes Braams and other authors.  The author also
% referred to \textsf{color} written by David Carlisle and
% \textsf{marginnote} written by Markus Kohm to make the package working
% well with them.
%
% \ifx\ONLYDESCRIPTION\undefined\else
% \newpage\tableofcontents
% \fi
% 
% \PrintIndex}
% 
% \newpage
% \addtocounter{page}{2}
% \let\Midx\MidxSave
% \advance\oddsidemargin1in\evensidemargin\oddsidemargin
% \advance\textwidth-1in\columnwidth\textwidth
% \hsize\textwidth \linewidth\textwidth
% \part{Implementation}\label{part:impl}
% \input{impl.dtx}
% 
% \IndexPrologue{\newpage\section*{Index}
% \addcontentsline{toc}{part}{\protect\numberline{}{Index}}
% 
% Underlined number refers to the page where the implementation or the
% definition of the correspoinding entry is described, while italicized
% number is for the page in which the specificatoin or usage of the entry is
% explained.
% 
% To find a control sequence, remove prefixes \cs{@}, \cs{if@}, \cs{pcol@} and 
% \cs{ifpcol@} from its name if it has one of them.}
% \Finale
% \GlossaryPrologue{\newpage\section*{Revision History}
% \addcontentsline{toc}{part}{\protect\numberline{}{Revision History}}}
% \def\EQ{=} \def\GT{>} \def\BAR{|} \def\NEQ{\neq} \def\S{\Sec}
% \PrintChanges
\endinput
