path: root/macros/latex/contrib/constants/constants.dtx

% \iffalse meta-comment
%
% Copyright (C) 2008 by
% 	Antoine Lejay <Antoine dot Lejay at iecn dot u-nancy dot fr>
% 
% Based on ltxref.dtx of the Latex Kernel (Copyright the LaTeX 3 project).
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3c of this license or (at your option) any later
% version. The latest version of this license is in
%    http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of
% LaTeX version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained.'
%
% The current maintainer of this work is Antoine Lejay.
%
% This work consists of the source file constants.dtx
%                 and the derived files constants.ins,
%                                       constants.sty,
%                                       constants.pdf,
% \fi
% \iffalse
%<*driver>
\documentclass[a4paper]{ltxdoc}
\EnableCrossrefs
\CodelineIndex
\RecordChanges
%\OnlyDescription
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{fancyvrb}
%\usepackage[dvipdfm]{hyperref}
\usepackage{hyperref}
\usepackage{constants}
\hypersetup{
  pdftitle={The constants package},
  pdfauthor={Antoine Lejay}
}
\newcommand{\parenthezises}[1]{(\arabic{#1})}
\newconstantfamily{example1}{
	symbol=K,
	format=\parenthezises,
	reset={section}
}
\newcommand{\family}{$\langle$\textsl{family}$\rangle$}
\newcommand{\cstpage}{$\langle$\textsl{page}$\rangle$}
\newcommand{\cstlabel}{$\langle$\textsl{label}$\rangle$}
\newcommand{\cstnumber}{$\langle$\textsl{number}$\rangle$}

\begin{document}
  \DocInput{\jobname.dtx}
\PrintIndex
\PrintChanges
\end{document}
%</driver>
%
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%   Lower-case    \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
%   Digits        \0\1\2\3\4\5\6\7\8\9
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%\changes{1.0}{2008/03/25}{First released}
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%
% \title{\texttt{\filename},\\ a package for automatic numbering\\ of constants%
%  \thanks{This file describes version \fileversion, last revised
%    \filedate.}}
% \author{Antoine Lejay}
% \date{Released \filedate}
%
% \maketitle
%
% \begin{abstract}
% This set of macros aims to provide a way to number automatically
% constants in a mathematical proof
% with a system for labelling/referencing. In addition, 
% several families of constants (with different symbols) may be defined.
% \end{abstract}
%
%\begin{multicols}{2}
% \footnotesize
%  \tableofcontents
%\end{multicols}
% \section{Introduction}
%
% Some domains of mathematics such as the theory of (partial)
% differential equations heavily rely on inequalities, and many
% proofs are done by writing down a long sequence of inequalities
% involving constants that may change from line to line. 
% Thus, a standard redaction trick consists in starting a proof
% by the statement 
% \begin{quote}
% Let $C$ denotes a constants that varies 
% from line to line.
% \end{quote}
% However, it is sometimes necessary 
% to get more informations about the involved constants. 
% Thus, either one has to finds different symbols, to the risk of 
% introduce some confusions in the notations, or to labels the 
% constants. Of course, manual labelling is not that easy, 
% especially at the early stages of redaction.  
% 
% The aim of this package is then to provide an automatic
% way to incrementally label the constants with numbers.  
% In addition, it offers the possibility to 
% label the constants with a mechanism similar to 
% |\label| and |\ref|. Finally, it is possible to 
% define several families of constants with different 
% rules for printing. 
%
% \paragraph{Dependencies: } this package uses the |keyval| 
% package of the \emph{graphic bundle} (which is in every standard distribution). 
%
% \section{Basic usage}
%
% \DescribeMacro{\C}
% The most basic usage of this package consists in calling 
% the macro |\C| in math mode, that prints $C_1$ for the first time, $C_2$
% for the second time, ...
%
% \DescribeMacro{\Cl}
% The macro |\Cl| is similar to |\C| except that it takes
% a mandatory argument which is a label's name, for 
% example |\Cl{cst-1}|. The number of the constant which
% is then printed is recorded and written in the |.aux| file. 
% Note that |\label{cst-1}| does not interact with 
% and |\Cl{cst-1}|, that is 
% the labels for constants are treated in a specific way 
% and can be only accessed through the command |\Cr| below.
%
% \DescribeMacro{\Cr}
% The macro |\Cr| takes a mandatory argument which 
% shall be the name of a label defined by |\Cl|. 
% As for standard labels in \LaTeX, if |\Cr| calls 
% a label that have not yet been defined are, then 
% the result is replaced by ``\textrm{C\textsuperscript{st}\textbf{??}}''.
% A message is written at the end of the compilation to indicate 
% the need of a second compilation to get all the references right.
% 
% \DescribeMacro{\pagerefconstant}
% This macros takes the label of a constant as a mandatory
% argument and returns the page were the constant is. 
%
% \DescribeMacro{\resetconstant}
% This macros resets the counter of constants, so that the 
% next call to |\C| will print again $C_1$.
%
% \section{Family of constants}
% 
% What if one whishes to use two families of 
% constants $\C[example1]$, $\C[example1]$, ... and $\C$, $\C$, ...
% in the same document, and that the $K_{(i)}$'s are reseted
% at each new section? A possibility consists then in defining 
% a new family of constant using the following code in the preamble.
% \begin{verbatim}
%\newcommand{\parenthezises}[1]{(\arabic{#1})}
%\newconstantfamily{example1}{
%	symbol=K,
%	format=\parenthezises,
%	reset={section}
%}
% \end{verbatim}
%
% \subsection{Defining a family}
%
% \DescribeMacro{\newconstantfamily} 
% The macro |\newconstantfamily| allows one to define a new 
% family of constants. Its first argument is the name of the 
% family, while the second argument uses the key-value principle. 
% 
% The key |symbol| is for the symbol that is used. 
% The key |format| shall takes as argument a command
% with one argument that can be applied to a counter
% (such as |\alph|, |\roman|, ...), or any user-defined command 
% such a |\parenthezises| above.
% The key |reset| takes the name of a counter and thus 
% the counter for this family of constants is reseted
% each time the corresponding counter is stepped by one.
% Note that several |reset| key may be used (technically, 
% it adds the name of the counter to a list of counters to be reseted
% each time a given counter is stepped).
% Here, possible names are |section|, |subsection|, |equation|, ...
%
% By default, there is one family which is defined, whose
% name is |normal|.
%
% If a key is missing, then the corresponding standard values are used
% (that is |symbol=C|, |format=\arabic| and no |reset| key).
%
% \DescribeMacro{\renewconstantfamily}
% If |\newconstantfamily| is called upon a family name that 
% has been already defined, then the compilers stops and 
% returns an error message. The |\renewconstantfamily| 
% (still to be used in the preamble) 
% allows one to override the behavior of a family
% without getting an arror message. Using |normal| as 
% a family name, one can get replace the standard behavior
% of |\C|.
% 
% \subsection{Using a family}
%
% \DescribeMacro{\C}
% \DescribeMacro{\Cl}
% \DescribeMacro{\Cr}
% \DescribeMacro{\pagerefconstant}
% Using a family is simple: it is sufficient to 
% call |\C| and |\Cl| with an optional argument
% which is the family name (if the name is incorrect,
% an error message is printed), that is 
% |\C[example1]| and |\Cl[example1]{cst-2}|
% to get $\C[example1]$ and~$\Cl[example1]{cst-2}$.
% For |\Cr|, there is no need to call the family,
% as it is stored with the family name. Thus, 
% |\Cr{cst-2}| will print $\Cr{cst-2}$. The macro
% |\pagerefconstant| also do not need any reference
% to a family name.
%
% \DescribeMacro{\resetconstant}
% The command |\resetconstant| also accepts the family 
% name as an optional argument.
% 
%
% \iffalse
%<*package>
% \fi
% \section{The code}
% \label{sec-1}
%
% The mechanism of labelling constants is similar 
% to the mechanism used by the standard \LaTeX\ 
% |\label| and |\ref| mechanism (see the files |source2e.pdf|, 
% |latex.ltx| and |ltxref.dtx|), excepted that 
% the family of the constant is taken into 
% account.
% 
% This works the following way:
% \begin{enumerate}
% \item The |aux| file is read first. If a line of type 
% \begin{quote}
% |\newlabelconstant{|\cstlabel|}{{|\cstnumber|}{|\cstpage|}{|\family|}}|
% \end{quote}
% is found, then a new macro |\cstr@|\cstlabel\ is created. This 
% macro shall expand into 
% \begin{quote}
% |{{|\cstnumber|}{|\cstpage|}{|\family|}}|
% \end{quote}
% where \cstnumber\ is the number of the constant, 
% \cstpage\ is the page were it appears and \family\ is its family name.
% 
% \item When a reference \cstlabel\ to a constant is found (call
% of |\Cr{|\cstlabel|}|), then 
% \TeX\ determines if |\cstr@|\cstlabel\ is already defined. 
% If not, then it prints a symbol for unknown constants and send 
% a warning message. 
%
% \item When a label to a constant is defined (call of 
% |\Cr[\family]{|\cstlabel|}|), then \TeX\ writes into the 
% |aux| file the corresponding |\newlabelconstant| line.
%
% \item At the end of the document, the |aux| file is read 
% once to determined wether or not there the source file has 
% to be compiled or not.
% \end{enumerate}
%
%
% \subsection{Initialization}
%
% The initializaton call the package |keyval|. 
%
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{constants}%
  [2008/03/25 v.1 Labeling and numbering constants]
\PackageInfo{constants}
  {This package aims to label et number constants in a mathematical proof.}
\RequirePackage{keyval}
%    \end{macrocode}
%
% \subsection{Macros associated to constants}
%
% When a family \family\ of constants is defined, several macros are
% created, that are |\cst@family@|\family, to check the existence
% of a family, |\cst@format@|\family, that takes a counter name as argument, 
% and |\cst@symbol@|\family, that expand into the symbol of the constant.
% In addition, a counter |cst@counter@|\family\ is created. 
% 
% \subsection{Macros for testing existence of families}
%
% \DescribeMacro{\@if@constant@exists}
% When a new family \family\ is defined, a macro 
% |\cst@family@|\family\ is defined, that expands to nothing.
%
%    \begin{macrocode}
\def\@if@constant@exists#1#2#3{\@ifundefined{cst@family@#1}{#3}{#2}}
%    \end{macrocode}
%
% \subsection{The family of constants \emph{normal}}
%
% The normal family is the family by default. The corresponding 
% macros are then defined.
%
%    \begin{macrocode}
\global\@namedef{cst@family@normal}{}
\newcounter{cst@counter@normal}
\def\cst@format@normal#1{\arabic{#1}}
\def\cst@symbol@normal{C}
%    \end{macrocode}
%
% \subsection{Definition of families}
%
% \DescribeMacro{\newconstantfamily}
% The macro |\newconstantfamily| defines the macros and counter
% associated to a family.
%    \begin{macrocode}
\newcommand{\newconstantfamily}[2]{
\@if@constant@exists{#1}{%
	\PackageError{constants}{The family of constants '#1' already exists}{%
Use \protect\renewconstantfamily\space to override}}%
{%
\expandafter\def\csname cst@family@#1\endcsname{}
\expandafter\def\csname cst@format@#1\endcsname{\cst@format@normal}
\expandafter\def\csname cst@symbol@#1\endcsname{\cst@symbol@normal}
\expandafter\newcounter{cst@counter@#1}
\define@key{constants}{format}%
{\expandafter\def\csname cst@format@#1\endcsname{##1}}
\define@key{constants}{symbol}%
{\expandafter\def\csname cst@symbol@#1\endcsname{##1}}
\define@key{constants}{reset}{\@addtoreset{cst@counter@#1}{##1}}
\setkeys{constants}{#2}
}}
%    \end{macrocode}
%
% \DescribeMacro{\renewconstantfamily}
% The |\renewconstantfamily| also redefines the macros associated to 
% constants, but does not re-create the counter. 
%
%    \begin{macrocode}
\newcommand{\renewconstantfamily}[2]{
\@if@constant@exists{#1}{
\define@key{constants}{format}{%
\expandafter\def\csname cst@format@#1\endcsname{##1}}
\define@key{constants}{symbol}{%
\expandafter\def\csname cst@symbol@#1\endcsname{##1}}
\define@key{constants}{reset}{\@addtoreset{cst@counter@#1}{##1}}
\setkeys{constants}{#2}
}{%
	\PackageError{constants}{The family of constants '#1' already exists}{%
Use \protect\renewconstantfamily\space to override}}%
}
%    \end{macrocode}
%
% The macros |\newconstantfamily| and |\renewconstantfamily|
% can only be called in the preamble.
%
%    \begin{macrocode}
\@onlypreamble\newconstantfamily
\@onlypreamble\renewconstantfamily
%    \end{macrocode}
%
% \subsection{Reading constants informations}
% 
% The following macros aims to read the informations
% from the macro |\cstr@|\cstlabel\ (See Section~\ref{sec-1}).
%
% When constants informations are read from the |aux| file, 
% the format, deduced from the family name \family, 
% is put in |\cst@tmp@format| and the symbol is put
% in |\cst@tmp@symbol|. By default, these macros expand into 
% |\cst@undefined@format| and |\cst@undefined@symbol|.
%    \begin{macrocode}
\def\G@refundefinedconstanttrue{%
  \gdef\@refundefinedconstant{%
    \@latex@warning@no@line{%
There were undefined references to constants}}}
\let\@refundefinedconstant\relax
\def\cst@tmp@format{cst@undefined@format}
\def\cst@tmp@symbol{cst@undefined@symbol}
%    \end{macrocode}
%
% \DescribeMacro{\@firstofthree}
% \DescribeMacro{\@secondofthree}
% \DescribeMacro{\@thirdofthree}
% These macros return respectively their first, second and third argument.
%    \begin{macrocode}
\long\def\@firstofthree#1#2#3{#1}
\long\def\@secondofthree#1#2#3{#2}
\long\def\@thirdofthree#1#2#3{#3}
%    \end{macrocode}
%
% If a reference to a macro is not defined, then 
% the counter value is not expanded, while a 
% symbol ``\textrm{C\textsuperscript{st}\textbf{??}}'' is returned.
%    \begin{macrocode}
\def\cst@undefined@format#1{}
\def\cst@undefined@symbol{%
\nfss@text{\reset@font\textrm{C\textsuperscript{st}\textbf{??}}}}
%    \end{macrocode}
%
% \DescribeMacro{\@setrefconstant}
% This macro expands into one of the arguments of the constant. 
% The argument |#1| shall be of type |cstr@|\cstlabel, 
% the argument |#2| shall then be |\@firstofthree|, 
% |\@secondofthree| and |\@thirdofthree|. The third argument 
% |#3| expands into |{{|\cstnumber|}{|\cstpage|}{|\family|}}|.
% If |cstr@|\cstlabel\ is not defined, then the package send
% a warning and the macro expands to ``\textbf{??}''.
%    \begin{macrocode}
\def\@setrefconstant#1#2#3{%
  \ifx#1\relax
   \protect\G@refundefinedconstanttrue
   \nfss@text{\reset@font\bfseries ??}%
   \@latex@warning{Reference to constant `#3' on page \thepage \space
             undefined}%
  \else
   \expandafter#2#1\null
  \fi}
%    \end{macrocode}
%
% \DescribeMacro{\@setfamconstant}
% This macro is similar to |\@setrefconstant| but 
% initializes |\cst@tmp@format| and |\cst@tmp@symbol|
% to |\cst@format@|\family\ and |\cst@fsymbol@|\family.
%    \begin{macrocode}
\def\@setfamconstant#1#2#3{%
\ifx#1\relax%
	\def\cst@tmp@format{cst@undefined@format}\null
	\def\cst@tmp@symbol{cst@undefined@symbol}\null
\else% 
	\def\cst@tmp@format{cst@format@\expandafter#2#1}\null
	\def\cst@tmp@symbol{cst@symbol@\expandafter#2#1}\null
\fi}
%    \end{macrocode}
%
% \DescribeMacro{\@setcounterconstant}
% This macro is similar to |\@setrefconstant| but 
% set the temporary counter |cst@tmp@counter| to 
% the value of \cstnumber.
%    \begin{macrocode}
\newcounter{cst@tmp@counter}
\def\@setcounterconstant#1#2#3{%
  \ifx#1\relax
   \protect\G@refundefinedconstanttrue
   \@latex@warning{Reference to constant `#3' on page \thepage \space
             undefined}%
  \else
   	\setcounter{cst@tmp@counter}{\expandafter#2#1}\null
\fi}
%    \end{macrocode}
%
% \DescribeMacro{\refconstant}
% \DescribeMacro{\familyconstant}
% \DescribeMacro{\counterconstant}
% These macros are used to call |\@setrefconstant|, |\@setfamconstant|
% and |\@setcounterconstant|.
%    \begin{macrocode}
\def\refconstant#1{%
\expandafter\@setrefconstant\csname cstr@#1\endcsname\@firstofthree{#1}}
\def\familyconstant#1{%
\expandafter\@setfamconstant\csname cstr@#1\endcsname\@thirdofthree{#1}}
\def\counterconstant#1{%
\expandafter\@setcounterconstant%
\csname cstr@#1\endcsname\@firstofthree{#1}}
%    \end{macrocode}
%
% \subsection{Calling constants}
%
% \DescribeMacro{\Cr}
% The macro is used to call a referenced constant.
% Using |\counterconstant| and |\familyconstant|, 
% the macros |\cst@tmp@symbols|, |\cst@tmp@format| 
% and the counter |cst@tmp@counter| have been properly initialized.
%    \begin{macrocode}
\newcommand{\Cr}[1]{%
\counterconstant{#1}%
\familyconstant{#1}%
{\@nameuse{\cst@tmp@symbol}}_{\@nameuse{\cst@tmp@format}{cst@tmp@counter}}}
%    \end{macrocode}
%
% \DescribeMacro{\C}
% This macro checks the existence of a family of constants
% and then expand to the symbol with the value of the counter.
%    \begin{macrocode}
\newcommand{\C}[1][normal]{%
\@if@constant@exists{#1}{%
\expandafter\refstepcounterconstant{cst@counter@#1}%
{\@nameuse{cst@symbol@#1}}_{\@nameuse{cst@format@#1}{cst@counter@#1}}}%
{\PackageError{constants}{Family for constants '#1' not defined}{
Check the name or use \protect\newconstantfamily}}%
}
%    \end{macrocode}
% \DescribeMacro{\Cl}
% This macro calls |\C| and then call |\labelconstant| to 
% add the constant label into the |aux| file.
%    \begin{macrocode}
\newcommand{\Cl}[2][normal]{\C[#1]\labelconstant{#2}{\string #1}}
%    \end{macrocode}
%
% \DescribeMacro{\pagerefconstant}
% This macro is similar to |refconstant| but returns the page number. 
%    \begin{macrocode}
\def\pagerefconstant#1{%
\expandafter\@setrefconstant\csname cstr@#1\endcsname
   \@secondofthree{#1}}
%    \end{macrocode}
%
% \DescribeMacro{\refstepcouterconstant}
% This macro is used to increment the number of the constants.
%    \begin{macrocode}
\def\refstepcounterconstant#1{\stepcounter{#1}%
    \protected@edef\@currentlabelconstant
       {\csname p@#1\endcsname\csname the#1\endcsname}%
}
%    \end{macrocode}
%
%
% \subsection{Writing informations in the \texttt{aux} file}
%
% \DescribeMacro{\@newl@belconstant}
% This macro checks the existence of |#1@#2| (here
% |cstr| is passed as argument |#1| and \cstlabel\ is passed as
% argument |#2|). If |#1@#2| has already been defined, then 
% it claims that the label already exists. 
% then it creates this macros that expands into |#3|, which 
% shall then expand into 
% \begin{quote}
% |{{|\cstnumber|}{|\cstpage|}{|\family|}}|
% \end{quote}
% This macro is called by |\newlabelconstant| and is 
% executed only when reading the |aux| file at the beginning
% of the page processing. In addition, it can only be called
% in the preamble.
%    \begin{macrocode}
\def\@newl@belconstant#1#2#3{{%
  \@ifundefined{#1@#2}%
    \relax
    {\gdef \@multiplelabelsconstant {%
       \@latex@warning@no@line{%
There were multiply-defined labels for constants}}%
     \@latex@warning@no@line{Label for constant `#2' multiply defined}}%
  \global\@namedef{#1@#2}{#3} 
}}
\def\@currentlabelconstant{}
\def\newlabelconstant{\@newl@belconstant{cstr}}
\@onlypreamble\@newl@belconstant
\let \@multiplelabelsconstant \relax
%    \end{macrocode}
%
% \DescribeMacro{\labelconstant}
% This macro is called when a new label is created and 
% writes the corresponding informations into the |aux| file. 
%    \begin{macrocode}
\def\labelconstant#1#2{\@bsphack
  \protected@write\@auxout{}%
	 {\string\newlabelconstant{#1}{{\@currentlabelconstant}{\thepage}{#2}}}%
  \@esphack}
%    \end{macrocode}
%
% The following codes corresponds to the final check to determine 
% if a supplementary compilation is needed.
%
%    \begin{macrocode}
\AtEndDocument{
\clearpage
\let\@newl@belconstant\@empty
\begingroup
     \if@filesw
       \immediate\closeout\@mainaux
       \let\@setckpt\@gobbletwo
       \let\@newl@belconstant\@testdef
       \let\@newl@bel\@testdef
       \@tempswafalse
       \makeatletter \input\jobname.aux
     \fi
	\@refundefinedconstant
     \if@filesw
       \ifx \@multiplelabelsconstant \relax
         \if@tempswa
           \@latex@warning@no@line{%
				Label(s) for constants may have changed.
               	Rerun to get cross-references right}%
         \fi
       \else
         \@multiplelabelsconstant
       \fi
     \fi
\endgroup
\deadcycles\z@\@@end
}
%    \end{macrocode}
%
% \subsection{Reseting constants}
%
% The macro |\resetconstant| set the counter |cst@counter@|\family\ to $0$.
% \DescribeMacro{\resetconstant}
%    \begin{macrocode}
\newcommand{\resetconstant}[1][normal]{%
\@if@constant@exists{#1}{%
	\setcounter{cst@counter@#1}{0}}{%
{\PackageError{constants}{Family for constants '#1' not defined}{%
Check the name or use \protect\newconstantfamily}}%
}}
%    \end{macrocode}
%
% \iffalse
%</package>
% \fi
% \Finale
\endinput