% \iffalse meta-comment
% !TEX program  = pdfLaTeX

%<*internal>
\iffalse
%</internal>

%<*readme>
----------------------------------------------------------------------
`counterz' --- 2023/05/30 Version 1.1.0

Copyright (C) 2023 by Christopher McClain
E-mail: christopher.mcclain@mail.wvu.edu

Released under the LaTeX Project Public License v1.3c or later
See https://www.latex-project.org/lppl.txt
----------------------------------------------------------------------

The `counterz' package provides additional tools for manipulating
counters. The package facilitates the use of stealth prefixes for
counter names in order to help distinguish between counters from
multiple input files. The package also provides a means to generate
random counters and save such counter values for future typesetting.
%</readme>

%<*internal>
\fi
\def\nameofplainTeX{plain}
\ifx\fmtname\nameofplainTeX\else
  \expandafter\begingroup
\fi
%</internal>

%<*install>
\input docstrip.tex
\keepsilent
\askforoverwritefalse

\preamble
----------------------------------------------------------------------
`counterz' --- 2023/05/30 Version 1.1.0 Additional tools for counters
E-mail: christopher.mcclain@mail.wvu.edu
Released under the LaTeX Project Public License v1.3c or later
See https://www.latex-project.org/lppl.txt
----------------------------------------------------------------------

\endpreamble
\postamble

Copyright (C) 2023 by Christopher McClain

This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License (LPPL), either
version 1.3c of this license or (at your option) any later
version. The latest version of this license is in the file:

https://www.latex-project.org/lppl.txt

and version 1.3 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 Christopher McClain.

This work consists of the file  counterz.dtx
and the derived files           counterz.ins,
                                counterz.pdf and
                                counterz.sty.

\endpostamble

\usedir{tex/latex/counterz}
\generate{
  \file{\jobname.sty}{\from{\jobname.dtx}{package}}
}

%</install>
%<install>\endbatchfile

%<*internal>
\usedir{source/latex/counterz}
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  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
}
\nopreamble\nopostamble
\usedir{doc/latex/counterz}
\generate{
  \file{README.txt}{\from{\jobname.dtx}{readme}}
}
\ifx\fmtname\nameofplainTeX
  \expandafter\endbatchfile
\else
  \expandafter\endgroup
\fi
%</internal>

%<*package>
\NeedsTeXFormat{LaTeX2e}
%</package>

%<*driver>
\documentclass{ltxdoc}
\usepackage{\jobname}
\usepackage[numbered]{hypdoc}
\EnableCrossrefs
\DoNotIndex{\addtocounter,\Alph,\alph,\arabic,\begingroup,\boolfalse,\booltrue,
            \catcode,\endgroup,\fnsymbol,\gdef,\ifbool,\ifboolexpr,\ifnumequal,
            \ifnumgreater,\ifnumless,\immediate,\jobname,\newcommand,
            \newcounter,\newbool,\newwrite,\numexpr,\openout,\pdfuniformdeviate,
            \providecounter,\ProvidesPackage,\relax,\renewcommand,
            \RequirePackage,\Roman,\roman,\setcounter,\the,\unexpanded,\value,
            \whileboolexpr,\write,\@ifnextchar,\ifltxcounter,\InputIfFileExists,
            \m@k@gobbleendoptarg,\MessageBreak,\PackageError,\protect,\space,
            \typein,\@typein}
\CodelineIndex
\RecordChanges
\begin{document}
   \DocInput{\jobname.dtx}
\end{document}
%</driver>
%
% \fi
%
%\GetFileInfo{\jobname.sty}
%
%\title{^^A
%  The \textsf{counterz} package\thanks{^^A
%    This file describes version \fileversion, last revised \filedate.^^A
%  }^^A
%}
%\author{^^A
%  Christopher McClain\thanks{E-mail: christopher.mcclain@mail.wvu.edu}^^A
%}
%\date{Released \filedate}
%
%\maketitle
%
%\changes{v1.0.0}{2023/05/19}{First public release}
%\changes{v1.1.0}{2023/05/30}{New and revised commands and error reports}
%
%
%\begin{abstract}
% The \textsf{counterz} package provides additional tools for manipulating
% counters. The package facilitates the use of stealth prefixes for
% counter names in order to help distinguish between counters from
% multiple input files. The package also provides a means to generate
% random counters and save such counter values for future typesetting. 
%\end{abstract}
%
%\begin{multicols}{2}
%  \tableofcontents
%\end{multicols}
%
%\section{Introduction}
%
%\subsection{About}
%
% This project emerged from the author's frequent use of \LaTeX\ counters as
% traditional integer type variables when generating mathematics documents with
% random elements. While pdf\TeX\ primitives such as \cs{pdfuniformdeviate} may
% be used to generate random integers, these integer values will be randomized
% with every typesetting. The \textsf{counterz} package provides a way to save
% the values of counters. Another \textsf{.tex} file is created so that, if
% desired, it can be inputted upon a subsequent typesetting in order to
% initialize the counters with the previously generated values. A boolean
% variable and accompanying commands allow an author to toggle between reusing
% and rerandomizing counters.
%
% One of the consequences of preloading counter values in large projects with
% multiple source files is that one must take care to use distinct counter names
% throughout all of the different files. If the file \textsf{Main.tex} inputs
% \textsf{File1.tex} and \textsf{File2.tex}, and both input files define the
% counter \textit{mycounter}, then this could result in typesetting errors. One
% way to address this problem is to prefix every counter name with the file name
% or some other marker so that the counter names will actually be distinct. For
% example, \textit{File1mycounter} is distinct from \textit{File2mycounter}.
% Very long counter names, however, can make code difficult to read and hinder
% consistent application of this practice. The \textsf{counterz} package
% provides a way to stealthily define and recall such prefixes so that the
% shorter non-prefixed names can be used for the manipulation, recall, and
% typesetting of counters.
%
%\subsection{License}
%
% Copyright \copyright\ 2023 Christopher McClain. This software may be copied,
% distributed, and/or modified under the %terms of the
% \href{https://www.latex-project.org/lppl/}{LaTeX Project Public License},
% either version 1.3c of this license or any later version.
%
%\subsection{Installation}
%
% Run (pdf)\TeX{} on counterz.dtx to generate the file counterz.sty, and copy it
% to your local texmf directory. To generate both the package file counterz.sty
% and the documentation counterz.pdf, run (pdf)\LaTeX{} on counterz.dtx.
% Typesetting the documentation requires the package \textsf{hypdoc} which is
% included in \TeX\ distributions and at \href{http://www.ctan.org}
% {The Comprehensive TeX Archive Network}.
%
%\section{User Guide}
%
% To use this package, include the following line in the preamble of your
% document:
%
%\begin{verbatim}
%\usepackage{counterz}
%\end{verbatim}
%
% \noindent
% The package \textsf{counterz} loads the packages \textsf{etoolbox} and
% \textsf{makecmds}, both of which are included in \TeX\ distributions
% and at \href{http://www.ctan.org}{The Comprehensive TeX Archive Network}.
%
%\subsection{Counter Prefixes}
%
% Counter prefixes are stored in an internal macro whose default value is an
% empty string.
%\DescribeMacro{\setcounterprefix}
% The command \cs{setcounterprefix}\marg{prefix} is used to change this value.
% For example, to change the prefix to \textit{PurpleMonkey}, use
%
%\begin{verbatim}
%\setcounterprefix{PurpleMonkey}
%\end{verbatim}
%
% \noindent
% and to change it from \textit{PurpleMonkey} to \textit{Dishwasher}, use
%
%\begin{verbatim}
%\setcounterprefix{Dishwasher}
%\end{verbatim}
%
% \noindent
%\DescribeMacro{\clearcounterprefix}
% The command \cs{clearcounterprefix} returns the prefix to its empty default.
%
%\subsection{Manipulating Counters}
%
%\DescribeMacro{\xnewcounter}
% The command \cs{xnewcounter}\marg{countername} creates a counter with a
% prefixed name.
%\DescribeMacro{\xsetcounter}
% The command \cs{xsetcounter}\marg{countername}\marg{integer} assigns the
% specified value to the counter with the prefixed name. For example, suppose
% that the file \textsf{BoringFile1.tex} contains the following:
%
%\begin{verbatim}
%\xnewcounter{bestcounterever}
%\xsetcounter{bestcounterever}{100}
%\end{verbatim}
%
% \noindent
% and suppose that the file \textsf{BoringFile2.tex} contains the following:
%
%\begin{verbatim}
%\xnewcounter{bestcounterever}
%\xsetcounter{bestcounterever}{-29}
%\end{verbatim}
%
% \noindent
% and, finally, suppose that the file Main.tex contains (in part) the following:
%
%\begin{verbatim}
%\setcounterprefix{PurpleMonkey}
%\input{BoringFile1}
%\setcounterprefix{Dishwasher}
%\input{BoringFile2}
%\end{verbatim}
%
% \noindent
% Then typesetting \textsf{Main.tex} will create a counter
% \textit{PurpleMonkeybestcounterever} with the value 100 and a counter
% \textit{Dishwasherbestcounterever} with the value $-29$. By using commands
% \cs{xnewcounter} and \cs{xsetcounter} instead of \cs{newcounter} and
% \cs{setcounter}, \textsf{BoringFile1.tex} and \textsf{BoringFile2.tex}
% may be written independently without considering any counter name conflicts.
% The distinction between the counters is determined by the prefixes defined
% in the file \textsf{Main.tex}. By changing prefixes, \textsf{Main.tex} can
% even input the same file multiple times without conflict.
%
%\DescribeMacro{\xprovidecounter}
% The commands \cs{xprovidecounter}, \cs{xaddtocounter}, and \cs{xvalue} are
% likewise prefix versions of commands \cs{providecounter}, \cs{addtocounter},
%\DescribeMacro{\xaddtocounter}
% and \cs{value}, respectively. When the prefix is empty, the commands expand
%\DescribeMacro{\xvalue}
% like their standard counterparts. (Note: \cs{providecounter} defines a counter
% if it has not already been defined. See the documentation for the package
% \textsf{makecmds} for details.)
%
%\subsection{Conditional Statements}
%
%\DescribeMacro{\ifctrequal}
% The command \cs{ifctrequal}\marg{counter1}\marg{counter2}\marg{foo}\marg{bar}
% uses the command \cs{xvalue} to compare the values of the (prefixed) counters
% and then executes \meta{foo} if the values are equal and otherwise executes
% \meta{bar}. The commands
%\DescribeMacro{\ifctrless}
% \cs{ifctrless} and \cs{ifctrmore} work analogously, based on whether the value
% of prefixed \meta{counter1} is less than that of of prefixed \meta{counter2}
%\DescribeMacro{\ifctrmore}
% or more than that of prefixed \meta{counter2}, respectively. Consider the
% example code
%
%\begin{verbatim}
%\setcounterprefix{TigerTiger}
%\xnewcounter{Small}
%\xsetcounter{Small}{7}
%\xnewcounter{Large}
%\xsetcounter{Large}{11}
%\ifctrequal{Small}{Large}{January}{February}
%\ifctrless{Small}{Large}{March}{April}
%\ifctrmore{Small}{Large}{May}{June}
%\end{verbatim}
%
% \noindent
% which produces the output
%
% \bigskip
%\setcounterprefix{TigerTiger}
%\xnewcounter{Small}
%\xsetcounter{Small}{7}
%\xnewcounter{Large}
%\xsetcounter{Large}{11}
%\ifctrequal{Small}{Large}{January}{February}
%\ifctrless{Small}{Large}{March}{April}
%\ifctrmore{Small}{Large}{May}{June}
%
% \bigskip
% \noindent
% because the value of the counter \textit{TigerTigerSmall} is 7 which is less
% than 11, the value of the counter \textit{TigerTigerLarge}.
%
%\DescribeMacro{\ifctrzero}
% The command \cs{ifctrzero}\marg{counter}\marg{foo}\marg{bar} executes
% \meta{foo} if the value of the (prefixed) counter is zero and otherwise
% executes \meta{bar}. The commands 
%\DescribeMacro{\ifctrneg}
% \cs{ifctrneg} and \cs{ifctrpos} work analogously based on whether the value
%\DescribeMacro{\ifctrpos}
% is negative or positive, respectively. The example code
%
%\begin{verbatim}
%\setcounterprefix{TigerTiger}
%\xprovidecounter{Small}
%\xsetcounter{Small}{7}
%\ifctrzero{Small}{January}{February}
%\ifctrneg{Small}{March}{April}
%\ifctrpos{Small}{May}{June}
%\end{verbatim}
%
% \noindent
% produces the output
%
% \bigskip
%\setcounterprefix{TigerTiger}
%\xprovidecounter{Small}
%\xsetcounter{Small}{7}
%\ifctrzero{Small}{January}{February}
%\ifctrneg{Small}{March}{April}
%\ifctrpos{Small}{May}{June}
%
% \bigskip
% \noindent
% because the value of the counter \textit{TigerTigerSmall} is 7 which is
% positive (and thus nonzero, as well).
%
%\subsection{Displaying Counters}
%
%\DescribeMacro{\xarabic}
% The command \cs{xarabic}\marg{counter} is simply a prefix version of the
% standard display command \cs{arabic}.
%\DescribeMacro{\xroman}
% The commands \cs{xroman}, \cs{xRoman}, \cs{xalph}, \cs{xAlph}, and
%\DescribeMacro{\xRoman}
% \cs{xfnsymbol} are likewise prefix versions of the standard display commands
%\DescribeMacro{\xalph}
% \cs{roman}, \cs{Roman}, \cs{alph}, \cs{Alph}, and \cs{fnsymbol}, inheriting
% the restrictions of their
%\DescribeMacro{\xAlph}
% parent commands.
%
%\DescribeMacro{\xfnsymbol}
% Note that the code
%
%\begin{verbatim}
%\setcounterprefix{Sneaky}
%\xprovidecounter{Pete}
%\xsetcounter{Pete}{42}
%\arabic{Pete}
%\end{verbatim}
%
% \noindent
% produces an error because the counter \textit{Pete} is not defined, but the
% code
%
%\begin{verbatim}
%\setcounterprefix{Sneaky}
%\xprovidecounter{Pete}
%\xsetcounter{Pete}{42}
%\xarabic{Pete}
%\end{verbatim}
%
% \noindent
% produces the output
%
% \bigskip
%\setcounterprefix{Sneaky}
%\xprovidecounter{Pete}
%\xsetcounter{Pete}{42}
%\xarabic{Pete}
%
% \bigskip
% \noindent
% which is the value of the counter \textit{SneakyPete}. The code
%
%\begin{verbatim}
%\setcounterprefix{Sneaky}
%\xprovidecounter{Pete}
%\xsetcounter{Pete}{42}
%\clearcounterprefix
%\xarabic{Pete}
%\end{verbatim}
%
% \noindent
% also generates error because the final line is trying to use the
% undefined counter \textit{Pete} after the prefix was returned to its
% default value.
%
% In addition to prefix versions of the standard display commands, the package
% \textsf{counterz} defines some variants of \cs{xarabic} that are useful in
% the display of mathematical expressions. For example, consider the following
% code:
%
%\begin{verbatim}
%\xprovidecounter{a}
%\xsetcounter{a}{5}
%\xprovidecounter{b}
%\xsetcounter{b}{0}
%\xprovidecounter{c}
%\xsetcounter{c}{-7}
%$\xarabic{a}+\xarabic{b}+\xarabic{c}$
%\end{verbatim}
%
% \noindent
% which produces
%
% \bigskip
%\xprovidecounter{a}
%\xsetcounter{a}{5}
%\xprovidecounter{b}
%\xsetcounter{b}{0}
%\xprovidecounter{c}
%\xsetcounter{c}{-7}
%$\xarabic{a}+\xarabic{b}+\xarabic{c}$
%
% \bigskip
% \noindent
% Using \cs{arabicx} causes the expression to contain the consecutive pair $+-$.
% The command \cs{xsigned}\marg{counter} is like \cs{xarabic} except that
%\DescribeMacro{\xsigned}
% nonnegative values are preceded by a plus sign ``+''. The code
%
%\begin{verbatim}
%$\xarabic{a}\xsigned{b}\xsigned{c}$
%\end{verbatim}
%
% \noindent
% produces
%
% \bigskip
%$\xarabic{a}\xsigned{b}\xsigned{c}$
%
% \bigskip
% \noindent
% If we wish to suppress the $0$, we can instead use the command
%\DescribeMacro{\xsignednz}
% \cs{xsignednz}\marg{counter} which is a nonzero version of \cs{xsigned} and,
% if desired or necessary, the command \cs{xarabicnz}\marg{counter} which is a
%\DescribeMacro{\xarabicnz}
% nonzero version of \cs{xarabic}. The code
%
%\begin{verbatim}
%$\xarabicnz{a}\xsignednz{b}\xsignednz{c}$
%\end{verbatim}
%
% \noindent
% produces
%
% \bigskip
%$\xarabicnz{a}\xsignednz{b}\xsignednz{c}$
%
% \bigskip
% \noindent
%\DescribeMacro{\xnegof}
% The command \cs{xnegof}\marg{counter} displays the negative of \meta{counter}.
% The command \cs{xnegofnz} does the same except that it suppresses the number
%\DescribeMacro{\xnegofnz}
% zero. The command \cs{xnegsigned} includes the appropriate signs of plus ``+''
%\DescribeMacro{\xnegsigned}
% and minus ``-'' (assigning a minus to zero in this case).
%\DescribeMacro{\xnegsignednz}
% Finally, the command \cs{xnegsignednz} does the same except that it suppresses
% the number zero., as demonstrated by the following code:
%
%\begin{verbatim}
%\xprovidecounter{d}
%\xsetcounter{d}{-2}
%
%$\xarabic{a}\xsigned{b}\xsigned{c}=\xarabic{d}$
%
%$\xnegof{d}=\xnegof{a}\xnegsigned{b}\xnegsigned{c}$
%
%$\xnegofnz{d}=\xnegofnz{a}\xnegsignednz{b}\xnegsignednz{c}$
%\end{verbatim}
%
% \noindent
% which produces
%
% \bigskip
%\xprovidecounter{d}
%\xsetcounter{d}{-2}
%
%$\xarabic{a}\xsigned{b}\xsigned{c}=\xarabic{d}$
%
%$\xnegof{d}=\xnegof{a}\xnegsigned{b}\xnegsigned{c}$
%
%$\xnegofnz{d}=\xnegofnz{a}\xnegsignednz{b}\xnegsignednz{c}$
%
% \bigskip
% The preceding commands for displaying values related to counters were created
% by using some other commands that we make available in case they prove useful.
%\DescribeMacro{\xabsof}
% The command \cs{xabsof}\marg{counter} prints the absolute value of
% \meta{counter}. The command \cs{xsignof}\marg{counter} prints a minus sign
%\DescribeMacro{\xsignof}
% ``-'' if \meta{counter} is negative and otherwise prints a plus sign ``+''.
% (Note that the latter case includes the value zero.) The command
%\DescribeMacro{\xnegsignof}
% \cs{xnegsignof}\marg{counter} prints a plus sign ``+'' if \meta{counter} is
% negative and otherwise prints a minus sign ``-''. (Note that the latter case
% includes the value zero.)
%
% Additional variants of these commands suppress certain output, as is
% conventional when using integers as coefficients in algebraic expressions.
% The command \cs{xabsofcoef}\marg{counter} prints the absolute value of
%\DescribeMacro{\xabsofcoef}
% \meta{counter} except that it suppresses the values of 1 and 0. The command
%\DescribeMacro{\xsignofcoef}
% \cs{xsignofcoef}\marg{counter} prints the sign of \meta{counter} if the value
% of \meta{counter} is nonzero. The command \cs{xnegsignofcoef}\marg{counter}
%\DescribeMacro{\xnegsignofcoef}
% prints the opposite sign of \meta{counter} if the value of \meta{counter} is
% nonzero. These commands are used to build versions of \cs{xarabic} and
% \cs{xsigned} specific to typesetting coefficients, as we now illustrate.
%
% Consider the following code
%
%\begin{verbatim}
%\xprovidecounter{a0}
%\xsetcounter{a0}{-10}
%\xprovidecounter{a1}
%\xsetcounter{a1}{1}
%\xprovidecounter{a2}
%\xsetcounter{a2}{-5}
%\xprovidecounter{a3}
%\xsetcounter{a3}{-1}
%\xprovidecounter{a4}
%\xsetcounter{a4}{0}
%\xprovidecounter{a5}
%\xsetcounter{a5}{11}
%$\xarabic{a5}x^5 + \xarabic{a4}x^4 + \xarabic{a3}x^3 + \xarabic{a2}x^2
%                 + \xarabic{a1}x   + \xarabic{a0}    = 42$
%\end{verbatim}
%
% \noindent
% and its output
%
% \bigskip
%\xprovidecounter{a0}
%\xsetcounter{a0}{-10}
%\xprovidecounter{a1}
%\xsetcounter{a1}{1}
%\xprovidecounter{a2}
%\xsetcounter{a2}{-5}
%\xprovidecounter{a3}
%\xsetcounter{a3}{-1}
%\xprovidecounter{a4}
%\xsetcounter{a4}{0}
%\xprovidecounter{a5}
%\xsetcounter{a5}{11}
%$\xarabic{a5}x^5 + \xarabic{a4}x^4 + \xarabic{a3}x^3 + \xarabic{a2}x^2
%                 + \xarabic{a1}x   + \xarabic{a0}    = 42$
%
% \bigskip
% \noindent
% We seek a better way to handle the coefficients, especially $1$ and $-1$. The
% command \cs{xcoef}\marg{counter} prints the value of \meta{counter} except
%\DescribeMacro{\xcoef}
% that it suppresses the values of 1, 0, and -1, printing a minus sign ``-'' in
% the latter case. The command \cs{xsignedcoef}\marg{counter} is like \cs{xcoef}
%\DescribeMacro{\xsignedcoef}
% except that positive values are preceded by a plus sign ``+''. We use these to
% write the code
%
%\begin{verbatim}
%$\xarabic{a5}x^5 + \xarabic{a4}x^4 + \xarabic{a3}x^3 + \xarabic{a2}x^2
%                 + \xarabic{a1}x   + \xarabic{a0}    = 42$
%
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignedcoef{a1}\ifctrzero{a1}{}{x}
%   \xsignednz{a0}
%   = 42$
%\end{verbatim}
%
% \noindent
% whose output is
%
% \bigskip
%$\xarabic{a5}x^5 + \xarabic{a4}x^4 + \xarabic{a3}x^3 + \xarabic{a2}x^2
%                 + \xarabic{a1}x   + \xarabic{a0}    = 42$
%
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignedcoef{a1}\ifctrzero{a1}{}{x}
%   \xsignednz{a0}
%   = 42$
%
% \bigskip
%\DescribeMacro{\xnegcoef}
% The command \cs{xnegcoef}\marg{counter} prints the negative of the value of
% \meta{counter} except that it suppresses the values of 1, 0, and -1, printing
% a ``-'' in the latter case. The command \cs{xnegsignedcoef}\marg{counter} is
%\DescribeMacro{\xnegsignedcoef}
% like \cs{xnegcoef} except that positive values are preceded by a plus sign
% ``+''. We use these to write the code
%
%\begin{verbatim}
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignedcoef{a1}\ifctrzero{a1}{}{x}
%   \xsignednz{a0}
%   = 42$
%
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignednz{a0}
%   = \xnegcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xnegsignedcoef{a1}\ifctrzero{a1}{}{x}
%   +42$
%\end{verbatim}
%
% \noindent
% whose output is
%
% \bigskip
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignedcoef{a1}\ifctrzero{a1}{}{x}
%   \xsignednz{a0}
%   = 42$
%
%$\xcoef{a5}\ifctrzero{a5}{}{x^5}
%   \xsignedcoef{a4}\ifctrzero{a4}{}{x^4}
%   \xsignedcoef{a2}\ifctrzero{a2}{}{x^2}
%   \xsignednz{a0}
%   = \xnegcoef{a3}\ifctrzero{a3}{}{x^3}
%   \xnegsignedcoef{a1}\ifctrzero{a1}{}{x}
%   +42$
%
% \bigskip
% As the reader has probably already observed in the code above, these display
% commands appear to be less efficient than a manual adjustment of signs and
% numbers. For fixed, known values of counters, this assessment is correct. The
% real utility of these commands is not apparent until they are combined with
% randomly generated counter values.
%
%\subsection{Random Counters}
%
% We first define random versions of \cs{setcounter} and \cs{addtocounter}.
% The command \cs{randsetcounter}\marg{counter}\marg{min}\marg{max} assigns
%\DescribeMacro{\randsetcounter}
% to \meta{counter} a random integer value between \meta{min} and \meta{max}.
%\DescribeMacro{\xrandsetcounter}
% The command \cs{xrandsetcounter} is a prefix version of \cs{randsetcounter}.
% Analogously, we define the command 
%\DescribeMacro{\randaddtocounter}
% \cs{randaddtocounter}\marg{counter}\marg{min}\marg{max} which adds to
% \meta{counter} a random integer value between \meta{min} and \meta{max}.
%\DescribeMacro{\xrandaddtocounter}
% \cs{xrandaddtocounter} is a prefix version of \cs{randaddtocounter}.
% The following code may be used to produce an expression in the form
% $ax+b$, where $a$ and $b$ are random integers between $-10$ and $10$:
%
%\begin{verbatim}
%\xprovidecounter{a}
%\xprovidecounter{b}
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$
%\end{verbatim}
%
% \noindent
% Organized in the following table are sixty instances of output that are
% randomly generated by the typesetting of this document:
%
% \bigskip
%\noindent
%\xprovidecounter{a}
%\xprovidecounter{b}
%\begin{tabular}{rrrrrr}
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ &
%\xrandsetcounter{a}{-10}{10}
%\xrandsetcounter{b}{-10}{10}
%$\xcoef{a}\ifctrzero{a}{\xarabic{b}}{x \xsignednz{b}}$ \\
%\end{tabular}
%
% \bigskip
% In order to effectively manage the options of randomizing counter values or
%\DescribeMacro{\randomizectr}
% reusing counter values, the commands \cs{randomizectr} and \cs{norandomizectr}
% are used to toggle an internal boolean variable. The internal boolean
%\DescribeMacro{\norandomizectr}
% is initialized as TRUE when the \textsf{counterz} package is loaded. A
% conditional command \cs{ifrandomizectr}\marg{foo}\marg{bar} executes
%\DescribeMacro{\ifrandomizectr}
% \meta{foo} when the boolean is true and otherwise executes \meta{bar}.
%
% If our document contains randomly generated counters, but we wish to typeset
% the document again without changing those values, then we need a way to save
%\DescribeMacro{\opencountersfile}
% them. The command \cs{opencountersfile} creates and opens the write stream to
% the file \textsf{\meta{jobname}.counters.tex} to store the necessary
% information. For example, if the document is
% named \textsf{Yellowdog.tex}, then the previously generated counters and their
% assigned values will be stored the file \textsf{Yellowdog.counters.tex}. 
% The author only has to include this command once, prior to any commands used
% to save the counter values. Additional instances of \cs{opencountersfile} will
% report an error, as will trying to use the command when the document is set to
% not randomize (e.g. \cs{norandomizectr}). These error reports are designed to
% prevent the accidental overwriting of \textsf{\meta{jobname}.counters.tex}.
%
% After opening the write stream to \textsf{\meta{jobname}.counters.tex}, the
% command \cs{savecounter}\marg{counter} may be used to ``save'' the value of
%\DescribeMacro{\savecounter}
% \textit{counter} by writing to the file the relevant \cs{providecounter} and
% \cs{setcounter} commands. The command \cs{xsavecounter} is a prefix version of
%\DescribeMacro{\xsavecounter}
% \cs{savecounter}. When using \cs{xsavecounter}, the commands that are written
% to the file include the necessary counter prefixes. Consequently, an author
% can, if necessary or desired, manually search the file for the value assigned
% to any randomly generated counter.
%
% Once we have generated a file for storing counters, we need a way to recover
% those values during a subsequent typesetting. The command
%\DescribeMacro{\inputcountersfile}
% \cs{inputcountersfile} will input the necessary file, if it exists, and report
% an error if it does not. Keep in mind that inputting the file will override
% any previous assignments of those counters, so it is probably best to invoke
% this command near the beginning of a document. For example, after including an
% instance of either \cs{randomizectr} or \cs{norandomizectr}, a document named
% \textsf{Yellowdog.tex} might include the code
%
%\begin{verbatim}
%\ifrandomizectr{\opencountersfile}{\inputcountersfile}
%\end{verbatim}
%
% \noindent
% to determine whether to preload previously stored counter values or open the
% write stream in anticipation of randomly generating new counter values.
%
%\DescribeMacro{\promptrandomizectr}
% The command \cs{promptrandomizectr}\oarg{macro}\marg{message}\marg{string}
% offers an alternative to manually switching between the commands
% \cs{randomizectr} and \cs{norandomizectr} for different typesettings. The
% contents of \meta{message} are displayed in the terminal, awaiting a response
% from the user at the prompt \meta{macro}. If the optional argument is not used
% then the default prompt is \cs{@typein}. If the optional argument is given, it
% must be a macro name that includes the backslash. The user's response is
% stored as a string in \meta{macro} and compared to \meta{string}. If they are
% equal, then the command \cs{randomizectr} is executed. If they are not equal
% then \cs{norandomizectr} is executed. 
%
% Consider the following example code:
%
%\begin{verbatim}
%\promptrandomizectr[\EnterResponse]{%
%   ^^J Enter 1 to randomize.
%   ^^J Enter 2 to not randomize.
%}{%
%   1%
%}%
%\ifrandomizectr{%
%   \opencountersfile
%}{%
%   \inputcountersfile
%}%
%\end{verbatim}
%
% \noindent
% which displays the following in the terminal:
%
%\begin{verbatim}
% Enter 1 to randomize.
% Enter 2 to not randomize.
%
%\EnterResponse=
%\end{verbatim}
%
% \noindent
% Notice that the first (optional) argument \cs{EnterResponse} begins with a
% backslash and is displayed with an equals sign ``='' at the prompt. Also note
% that the second argument contains two instances of the text \texttt{\^{}\^{}J}
% which is used to produce a line break in the terminal output. Next, note that
% the third argument \texttt{1} is immediately followed by a percent symbol
% \texttt{\%} to prevent extra space being included in the string. (If the
% \texttt{1} was immediately followed by a closing brace instead of a line break
% in the code, the percent symbol would not be used.) Finally, note that if the
% user types a \texttt{1} in the terminal and presses Enter, then the commands
% \cs{randomizectr} and \cs{opencountersfile} will be executed. If the user
% enters \textit{any other text} or simply presses Enter with no text, then the
% commands \cs{norandomizectr} and \cs{inputcountersfile} will be executed,
% despite the instructions to enter a \texttt{2} to achieve this outcome.
%
%\DescribeMacro{\randprovidecounter}
% The command \cs{randprovidecounter}\marg{counter}\marg{min}\marg{max}
% combines the four commands \cs{providecounter}, \cs{ifrandomizectr},
% \cs{randsetcounter}, and \cs{savecounter}. The command creates \meta{counter}
% if it has not already been defined and, if the document is
% randomized, assigns to \meta{counter} a random integer value between
% \meta{min} and \meta{max} and saves this value to the counters file. The
%\DescribeMacro{\randprovidecounternz}
% command \cs{randprovidecounternz} is like \cs{randprovidecounter} except
%\DescribeMacro{\xrandprovidecounter}
% that the generated value is nonzero. The commands \cs{xrandprovidecounter} and
%\DescribeMacro{\xrandprovidecounternz}
% \cs{xrandprovidecounternz} are prefix versions of \cs{randprovidecounter} and
% \cs{randprovidecounternz}, respectively. Suppose that \textsf{Neverending.tex}
% contains the code
%
%\begin{verbatim}
%\randomizectr
%\ifrandomizectr{\opencountersfile}{}
%\setcounterprefix{Southern}
%\xrandprovidecounternz{Oracle}{-10}{10}
%\xcoef{Oracle}x+42
%\end{verbatim}
%
% \noindent
% After typesetting once, the resulting document might display an expression
% such as $-9x+42$ and print to \textsf{Neverending.counters.tex} the line
%
%\begin{verbatim}
%\providecounter {SouthernOracle} \setcounter {SouthernOracle}{-9}
%\end{verbatim}
%
% \noindent
% After typesetting a second time, the resulting document might display $4x+42$
% and print to \textsf{Neverending.counters.tex} the line
%
%\begin{verbatim}
%\providecounter {SouthernOracle} \setcounter {SouthernOracle}{4}
%\end{verbatim}
%
% \noindent
% If, however, the command \cs{randomizectr} is replaced by \cs{norandomizectr},
% then a third typesetting will leave both the displayed text and the counters
% file unchanged.
%
%\StopEventually{^^A
%  \PrintChanges
%  \PrintIndex
%}
%
%\section{Implementation}
%
% The \textsf{counterz} package loads the two packages \textsf{etoolbox} and
% \textsf{makecmds} for the use of conditional tests (boolean and numerical)
% and the macro \cs{providecounter}.
%
%    \begin{macrocode}
%<*package>
\ProvidesPackage{counterz}[%
   2023/05/30 v1.1.0 Additional tools for counters
]%
\RequirePackage{etoolbox,makecmds}
%    \end{macrocode}
%
%\subsection{Counter Prefixes}
%
%\begin{macro}{\@counterz@counterprefix}
%\begin{macro}{\setcounterprefix}
%\begin{macro}{\clearcounterprefix}
%
% The default expansion of \cs{@counterz@counterprefix} is null, but it can be
% changed with the commands \cs{setcounterprefix} and \cs{clearcounterprefix}.
%
%    \begin{macrocode}
\newcommand{\@counterz@counterprefix}{}
\newcommand{\setcounterprefix}[1]{%
   \renewcommand{\@counterz@counterprefix}{#1}
}%
\newcommand{\clearcounterprefix}{%
   \setcounterprefix{}
}%
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%\end{macro}
%
%\subsection{Manipulating Counters}
%
%\begin{macro}{\xnewcounter}
%\begin{macro}{\xprovidecounter}
%\begin{macro}{\xsetcounter}
%\begin{macro}{\xaddtocounter}
%\begin{macro}{\xvalue}
%
% These commands are prefix versions of commands \cs{newcounter},
% \cs{providecounter}, \cs{setcounter}, \cs{addtocounter}, and \cs{value},
% respectively. The creation, modification, or use of the counters is carried
% out on a prefixed version of the specified counter name. When
% \cs{@counterz@counterprefix} is null, the commands expand like their standard
% counterparts.
%
%    \begin{macrocode}
\newcommand{\xnewcounter}[1]{%
   \newcounter{\@counterz@counterprefix #1}
}%
\newcommand{\xprovidecounter}[1]{%
   \providecounter{\@counterz@counterprefix #1}
}%
\newcommand{\xsetcounter}[2]{%
   \setcounter{\@counterz@counterprefix #1}{#2}
}%
\newcommand{\xaddtocounter}[2]{%
   \addtocounter{\@counterz@counterprefix #1}{#2}
}%
\newcommand{\xvalue}[1]{%
   \value{\@counterz@counterprefix #1}
}%
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%
%\subsection{Conditional Statements}
%
% The following commands provide if-then-else constructs analogous to those in
% the package \textsf{etoolbox}. The notable difference is that the arguments
% are counter names. The command \cs{xvalue} is used to determine the values of
% the counters, so that the stored prefix is applied to the specified counter
% names before execution.
%
%\begin{macro}{\ifctrequal}
%
% \cs{ifctrequal}\marg{counter1}\marg{counter2}\marg{foo}\marg{bar} executes
% \meta{foo} if the value of \meta{counter1} is equal to the value of
% \meta{counter2} and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrequal}[4]{%
   \ifnumequal{\xvalue{#1}}{\xvalue{#2}}{#3}{#4}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\ifctrless}
%
% \cs{ifctrless}\marg{counter1}\marg{counter2}\marg{foo}\marg{bar} executes
% \meta{foo} if the value of \meta{counter1} is less than the value of
% \meta{counter2} and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrless}[4]{%
   \ifnumless{\xvalue{#1}}{\xvalue{#2}}{#3}{#4}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\ifctrmore}
%
% \cs{ifctrmore}\marg{counter1}\marg{counter2}\marg{foo}\marg{bar} executes
% \meta{foo} if the value of \meta{counter1} is more than the value of
% \meta{counter2} and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrmore}[4]{%
   \ifnumless{\xvalue{#2}}{\xvalue{#1}}{#3}{#4}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\ifctrzero}
%
% \cs{ifctrzero}\marg{counter}\marg{foo}\marg{bar} executes \meta{foo} if
% the value of \meta{counter} is zero and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrzero}[3]{%
   \ifnumequal{\xvalue{#1}}{0}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\ifctrneg}
%
% \cs{ifctrneg}\marg{counter}\marg{foo}\marg{bar} executes \meta{foo} if the
% value of \meta{counter} is negative and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrneg}[3]{%
   \ifnumless{\xvalue{#1}}{0}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\ifctrpos}
%
% \cs{ifctrpos}\marg{counter}\marg{foo}\marg{bar} executes \meta{foo} if the
% value of \meta{counter} is positive and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifctrpos}[3]{%
   \ifnumless{\xvalue{#1}}{1}{#3}{#2}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\subsection{Displaying Counters}
%
%\begin{macro}{\xarabic}
%\begin{macro}{\xroman}
%\begin{macro}{\xRoman}
%\begin{macro}{\xalph}
%\begin{macro}{\xAlph}
%\begin{macro}{\xfnsymbol}
%
% These commands include prefix versions of the standard display commands.
%
%    \begin{macrocode}
\newcommand{\xarabic}[1]{\arabic{\@counterz@counterprefix #1}}
\newcommand{\xroman}[1]{\roman{\@counterz@counterprefix #1}}
\newcommand{\xRoman}[1]{\Roman{\@counterz@counterprefix #1}}
\newcommand{\xalph}[1]{\alph{\@counterz@counterprefix #1}}
\newcommand{\xAlph}[1]{\Alph{\@counterz@counterprefix #1}}
\newcommand{\xfnsymbol}[1]{\fnsymbol{\@counterz@counterprefix #1}}
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
% The following commands likewise apply the stored prefix to the counter name.
% These commands are designed to aid in the typesetting of counter values within
% algebraic expressions while observing particular conventions about the display
% of numbers and their and their signs.
%
%\begin{macro}{\xabsof}
%
% \cs{xabsof}\marg{counter} prints the absolute value of \meta{counter}.
%
%    \begin{macrocode}
\newcommand{\xabsof}[1]{%
   \ifctrneg{#1}{%
      \the \numexpr 0 - \xvalue{#1} \relax%
   }{%
      \xarabic{#1}%
   }%
}
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xsignof}
%
% \cs{xsignof}\marg{counter} prints a minus sign ``-'' if \meta{counter} is
% negative and otherwise prints a plus sign ``+''. Note that the latter case
% includes the value zero.
%
%    \begin{macrocode}
\newcommand{\xsignof}[1]{%
   \ifctrneg{#1}{-}{+}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegsignof}
%
% \cs{xnegsignof}\marg{counter} prints a plus sign ``+'' if \meta{counter} is
% negative and otherwise prints a minus sign ``-''. Note that the latter case
% includes the value zero.
%
%    \begin{macrocode}
\newcommand{\xnegsignof}[1]{%
   \ifctrneg{#1}{+}{-}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xsigned}
%
% \cs{xsigned}\marg{counter} prints the absolute value of \meta{counter},
% preceded by a plus sign ``+'' or a minus sign ``-'' as defined by
% \cs{xsignof}.
%
%    \begin{macrocode}
\newcommand{\xsigned}[1]{%
   \xsignof{#1} \xabsof{#1}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xsignednz}
%
% \cs{xsignednz}\marg{counter} is like \cs{xsigned} but suppresses the number
% zero.
%
%    \begin{macrocode}
\newcommand{\xsignednz}[1]{%
   \ifctrzero{#1}{}{\xsigned{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xarabicnz}
%
% \cs{xarabicnz}\marg{counter} is like \cs{xarabic} but suppresses the number
% zero.
%
%    \begin{macrocode}
\newcommand{\xarabicnz}[1]{%
   \ifctrzero{#1}{}{\xarabic{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegsigned}
%
% \cs{xnegsigned}\marg{counter} prints the absolute value of \meta{counter},
% preceded by a plus sign ``+'' or a minus sign ``-'' as defined by
% \cs{xnegsignof}.
%
%    \begin{macrocode}
\newcommand{\xnegsigned}[1]{%
   \xnegsignof{#1} \xabsof{#1}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegsignednz}
%
% \cs{xnegsignednz}\marg{counter} is like \cs{xnegsigned} but suppresses the
% number zero.
%
%    \begin{macrocode}
\newcommand{\xnegsignednz}[1]{%
   \ifctrzero{#1}{}{\xnegsigned{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegof}
%
% \cs{xnegof}\marg{counter} prints the negative of the value of \meta{counter}.
%
%    \begin{macrocode}
\newcommand{\xnegof}[1]{%
   \ifctrpos{#1}{-}{}\xabsof{#1}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegofnz}
%
% \cs{xnegofnz}\marg{counter} is like \cs{xnegof} but suppresses the number
% zero.
%
%    \begin{macrocode}
\newcommand{\xnegofnz}[1]{%
   \ifctrzero{#1}{}{\xnegof{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xcoef}
%
% \cs{xcoef}\marg{counter} prints the value of \meta{counter} except that it
% suppresses the values of 1, 0, and -1, printing a ``-'' in the latter case.
%
%    \begin{macrocode}
\newcommand{\xcoef}[1]{%
   \ifboolexpr{%
      test {\ifnumless{\xvalue{#1}}{-1}}
      or test {\ifnumgreater{\xvalue{#1}}{1}}
   }{%
      \xarabic{#1}
   }{%
   }%
   \ifnumequal{\xvalue{#1}}{-1}{-}{}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegcoef}
%
% \cs{xnegcoef}\marg{counter} prints the value of \meta{counter} except that it
% suppresses the values of 1, 0, and -1, printing a ``-'' in the former case.
%
%    \begin{macrocode}
\newcommand{\xnegcoef}[1]{%
   \ifboolexpr{%
      test {\ifnumless{\xvalue{#1}}{-1}}
      or test {\ifnumgreater{\xvalue{#1}}{1}}
   }{%
      \xnegof{#1}
   }{%
   }%
   \ifnumequal{\xvalue{#1}}{1}{-}{}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xabsofcoef}
%
% \cs{xabsofcoef}\marg{counter} prints the absolute value of \meta{counter}
% except that it suppresses the values of 1 and 0.
%
%    \begin{macrocode}
\newcommand{\xabsofcoef}[1]{%
   \ifboolexpr{%
      test {\ifnumless{\xvalue{#1}}{-1}}
      or test {\ifnumgreater{\xvalue{#1}}{1}}
   }{%
      \xabsof{#1}
   }{%
   }%
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xsignofcoef}
%
% \cs{xsignofcoef}\marg{counter} prints the sign of \meta{counter} if
% \meta{counter} is nonzero.
%
%    \begin{macrocode}
\newcommand{\xsignofcoef}[1]{%
   \ifctrzero{#1}{}{\xsignof{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegsignofcoef}
%
% \cs{xnegsignofcoef}\marg{counter} prints the opposite sign of \meta{counter}
% if \meta{counter} is nonzero.
%
%    \begin{macrocode}
\newcommand{\xnegsignofcoef}[1]{%
   \ifctrzero{#1}{}{\xnegsignof{#1}}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xsignedcoef}
%
% \cs{xsignedcoef}\marg{counter} is like \cs{xcoef} except that positive values
% are preceded by a plus sign ``+''. 
%
%    \begin{macrocode}
\newcommand{\xsignedcoef}[1]{%
   \xsignofcoef{#1} \xabsofcoef{#1}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xnegsignedcoef}
%
% \cs{xnegsignedcoef}\marg{counter} is like \cs{xsignedcoef} except using the
% opposite sign. 
%
%    \begin{macrocode}
\newcommand{\xnegsignedcoef}[1]{%
   \xnegsignofcoef{#1} \xabsofcoef{#1}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\subsection{Random Counters}
%
% The commands \cs{randsetcounter} and \cs{randaddtocounter} use the pdf\TeX\
% primitive \cs{pdfuniformdeviate} to provide random versions of
% \cs{setcounter} and \cs{addtocounter}. The commands \cs{xrandsetcounter} and
% \cs{xrandaddtocounter} are prefix versions of \cs{randsetcounter} and
% \cs{randaddtocounter}, respectively.
%
%\begin{macro}{\randsetcounter}
%\changes{v1.1.0}{2023/05/30}{new}
%\begin{macro}{\xrandsetcounter}
%\changes{v1.1.0}{2023/05/30}{now based on a new \cs{randsetcounter}}
%
% \cs{randsetcounter}\marg{counter}\marg{min}\marg{max} assigns to
% \meta{counter} a random integer value between \meta{min} and \meta{max}.
%
%    \begin{macrocode}
\newcommand{\randsetcounter}[3]{%
   \setcounter{#1}{%
      \the \numexpr #2+\pdfuniformdeviate \numexpr #3-#2+1 \relax
   }%
}%
\newcommand{\xrandsetcounter}[3]{%
   \randsetcounter{\@counterz@counterprefix#1}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%
%\begin{macro}{\randaddtocounter}
%\changes{v1.1.0}{2023/05/30}{new}
%\begin{macro}{\xrandaddtocounter}
%\changes{v1.1.0}{2023/05/30}{now based on a new \cs{randaddtocounter}}
%
% \cs{randaddtocounter}\marg{counter}\marg{min}\marg{max} adds to \meta{counter}
% a random integer value between \meta{min} and \meta{max}.
%
%    \begin{macrocode}
\newcommand{\randaddtocounter}[3]{%
   \addtocounter{#1}{%
      \the \numexpr #2+\pdfuniformdeviate \numexpr #3-#2+1 \relax
   }%
}%
\newcommand{\xrandaddtocounter}[3]{%
   \randaddtocounter{\@counterz@counterprefix#1}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
% The following commands are designed to provide a means by which authors can
% generate random values for counters but also preserve those values for future
% typesettings. This is accomplished by storing counters and their values in an
% external file and then inputting the file before a subsequent typesetting.
%
%\begin{macro}{\randomizectr}
%\begin{macro}{\norandomizectr}
%
% In order to assign a random value to a counter during one typesetting and
% avoid overwriting this value with a random assignment during another
% typesetting, the boolean \textit{@counterz@random} is used to distinguish
% between the two typesetting options. The value of \textit{@counterz@random} may
% be changed by the commands \cs{randomizectr} and \cs{norandomizectr}.
%
%    \begin{macrocode}
\newbool{@counterz@random}
\booltrue{@counterz@random}
\newcommand{\randomizectr}{\booltrue{@counterz@random}}
\newcommand{\norandomizectr}{\boolfalse{@counterz@random}}
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%
%\begin{macro}{\ifrandomizectr}
%
% \cs{ifrandomizectr}\marg{foo}\marg{bar} executes \meta{foo} if the boolean
% \textit{@counterz@random} is true and otherwise executes \meta{bar}.
%
%    \begin{macrocode}
\newcommand{\ifrandomizectr}[2]{%
   \ifbool{@counterz@random}{#1}{#2}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\promptrandomizectr}
%\changes{v1.1.0}{2023/05/30}{new}
%
% \cs{promptrandomizectr}\oarg{command}\marg{message}\marg{string} writes
% \meta{message} to the terminal and awaits a response from the user at the
% prompt. The user's response is stored in \meta{command} and compared to the
% text of \meta{string}. If they are equal, then \cs{randomizectr} is executed.
% If they are not equal, then \cs{norandomizectr} is executed.
%
%    \begin{macrocode}
\newcommand{\promptrandomizectr}[3][\@typein]{%
   \typein[#1]{#2}
   \ifdefstring{#1}{#3}{%
      \randomizectr
   }{%
      \norandomizectr
   }%
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\opencountersfile}
%\changes{v1.1.0}{2023/05/30}{new error reports}
%
% The command \cs{opencountersfile} creates and opens the write stream to the
% file \textsf{\meta{jobname}.counters.tex}, referenced by the macro
% \cs{countersfile}. If the file already exists, it is overwritten. For this
% reason, 
%
%    \begin{macrocode}
\newbool{@counterz@fileISopen}
\boolfalse{@counterz@fileISopen}
\newcommand{\opencountersfile}{%
   \ifbool{@counterz@fileISopen}{%
      \PackageError{counterz}{%
         The write stream is already open!
         \MessageBreak Process interrupted to prevent overwriting
         \MessageBreak \jobname.counters.tex
      }{%
         Be sure to include only one instance of
         \protect\opencountersfile.
      }%
   }{%
      \ifrandomizectr{%
         \newwrite\countersfile
         \immediate\openout\countersfile=\jobname.counters.tex
         \booltrue{@counterz@fileISopen}
      }{%
         \PackageError{counterz}{%
            \protect\opencountersfile\space requires
            \protect\randomizectr
            \MessageBreak Process interrupted to prevent overwriting
            \MessageBreak \jobname.counters.tex
         }{%
            \protect\opencountersfile\space is designed to open a file
            for saving newly randomized counters. See the Random
            Counters section of the counterz package documentation for
            details.
         }%
      }%
   }%
}
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\inputcountersfile}
%\changes{v1.1.0}{2023/05/30}{new}
%
% The command \cs{inputcountersfile} inputs \textsf{\meta{jobname}.counters.tex}
% if the file exists and reports a package error if the file does not exist.
%
%    \begin{macrocode}
\newcommand{\inputcountersfile}{%
   \InputIfFileExists{\jobname.counters}{%
   }{%
      \PackageError{counterz}{%
         The file \jobname.counters.tex does not exist.
      }{%
         See the Random Counters section of the counterz package
         documentation.
      }%
   }%
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\@counterz@openbrace}
%\begin{macro}{\@counterz@closebrace}
%
% The commands \cs{@counterz@openbrace} and \cs{@counterz@closebrace}
% facilitate the writing of the brace delimiters to \cs{countersfile}.
%
%    \begin{macrocode}
\begingroup
   \catcode`<=1 \catcode`>=2
   \catcode`{=12 \catcode`}=12
   \gdef\@counterz@openbrace<{>
   \gdef\@counterz@closebrace<}>
\endgroup
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%
%\begin{macro}{\savecounter}
%\changes{v1.1.0}{2023/05/30}{new}
%\begin{macro}{\xsavecounter}
%\changes{v1.1.0}{2023/05/30}{now based on a new \cs{savecounter}}
%
% \cs{savecounter}\marg{counter} writes \cs{providecounter} and \cs{setcounter}
% commands to the file \textsf{\meta{jobname}.counters.tex} so that they may be
% inputted as part of a future typesetting. The command reports a package error
% if the write stream to \textsf{\meta{jobname}.counters.tex} is not open. The
% command \cs{xsavecounter} is a prefix version of \cs{savecounter}.
%
%
%    \begin{macrocode}
\newcommand{\savecounter}[1]{%
   \ifbool{@counterz@fileISopen}{%
      \immediate\write\countersfile{%
         \unexpanded{\providecounter}
         \@counterz@openbrace#1\@counterz@closebrace
         \unexpanded{\setcounter}
         \@counterz@openbrace#1\@counterz@closebrace
         \@counterz@openbrace\arabic{#1}\@counterz@closebrace
      }%
   }{%
      \PackageError{counterz}{%
         The write stream to the file \jobname.counters.tex must be
         opened before \protect\savecounter\space can be executed.
      }{%
         See \protect\opencountersfile\space and
         \protect\savecounter\space in the counterz package
         documentation.
      }%
   }%
}%

\newcommand{\xsavecounter}[1]{%
   \savecounter{\@counterz@counterprefix#1}%
}%
%    \end{macrocode}
%
%\end{macro}
%\end{macro}
%
%\begin{macro}{\randprovidecounter}
%\changes{v1.1.0}{2023/05/30}{new}
%
% \cs{randprovidecounter}\marg{counter}\marg{min}\marg{max} creates
% \meta{counter} if it does not already exist, and if the boolean
% \textit{@counterz@random} is true then \meta{counter} is assigned a
% random integer value between \meta{min} and \meta{max} and then saved.
%
%    \begin{macrocode}
\newcommand{\randprovidecounter}[3]{%
   \ifltxcounter{#1}{%
      \@ifnextchar]{%
         \m@k@gobbleendoptarg
      }{%
      }%
   }{%
      \newcounter{#1}
      \ifrandomizectr{%
         \randsetcounter{#1}{#2}{#3}
         \savecounter{#1}
      }{%
      }%
   }%
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\xrandprovidecounter}
%\changes{v1.1.0}{2023/05/30}{no longer randomizes if already defined;
%now based on a new \cs{randprovidecounter}}
%
% \cs{xrandprovidecounter}\marg{counter}\marg{min}\marg{max} creates
% \meta{counter} if it does not already exist, and if the boolean
% \textit{@counterz@random} is true then \meta{counter} is assigned a
% random integer value between \meta{min} and \meta{max} and then saved.
%
%    \begin{macrocode}
\newcommand{\xrandprovidecounter}[3]{%
   \randprovidecounter{\@counterz@counterprefix#1}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}
%
%\begin{macro}{\randprovidecounternz}
%\changes{v1.1.0}{2023/05/30}{new}
%
% \cs{randprovidecounternz}\marg{counter}\marg{min}\marg{max} does the same
% job as the command \cs{xrandprovidecounter} except that the value of
% \meta{counter} is randomized until it is nonzero.
%
%    \begin{macrocode}
\newcommand{\randprovidecounternz}[3]{%
   \ifltxcounter{#1}{%
      \@ifnextchar]{%
         \m@k@gobbleendoptarg
      }{%
      }%
   }{%
      \newcounter{#1}
      \ifrandomizectr{%
         \setcounter{#1}{0}
         \whileboolexpr{test {\ifnumequal{\value{#1}}{0}}}{%
            \randsetcounter{#1}{#2}{#3}
         }%
         \savecounter{#1}
      }{%
      }%
   }%
}%
%    \end{macrocode}
%
%\end{macro}%
%
%\begin{macro}{\xrandprovidecounternz}
%\changes{v1.1.0}{2023/05/30}{no longer randomizes if already defined;
%now based on a new \cs{randprovidecounternz}}
%
% \cs{xrandprovidecounternz}\marg{counter}\marg{min}\marg{max} does the same
% job as the command \cs{xrandprovidecounter} except that the value of
% \meta{counter} is randomized until it is nonzero.
%
%    \begin{macrocode}
\newcommand{\xrandprovidecounternz}[3]{%
   \randprovidecounternz{\@counterz@counterprefix#1}{#2}{#3}
}%
%    \end{macrocode}
%
%\end{macro}%
%
%    \begin{macrocode}
%</package>
%    \end{macrocode}
%\Finale