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diff --git a/macros/latex/contrib/rangen/README b/macros/latex/contrib/rangen/README
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+The rangen Package
+
+The rangen package is a package that generates random integers,
+rational numbers, and decimal number. Actually, the package uses the
+lcg package (by Erich Janka) to generate random integers, while
+rangen builds rational numbers and decimal numbers from the
+generated integers. My purpose in writing this package was to be
+able to create random questions for the quizzes of exerquiz (part of
+AeB). Indeed, that is what you can do with this package: Write a
+quiz question based on a template (for example, differentiate
+$\a x^{\n}$ , where \a and \n are RVs (random variables) generated with
+rangen); determine if the user input is correct; and display the
+correct answer to the question.
+
+Beta Testers wanted: The package is still in development. I would
+invite anyone interested to test the package, looking for bugs.
+Also, suggested features would be appreciated.
+
+The rangen package requires the insdljs package from AeB. The
+package can be used without exerquiz, perhaps there are some
+applications to the generation of random numbers. As pointed out in
+the documentation, the fp package can be used to manipulate the
+numbers created by rangen.
+
+The home page for rangen is
+
+    http://www.math.uakron.edu/~dpstory/rangen.html
+
+The home page for AeB is
+
+    http://www.math.uakron.edu/~dpstory/webeq.html
+
+Comments and suggestions are always gratefully accepted and seriously
+considered.
+
+D. P. Story
+09/30/09
diff --git a/macros/latex/contrib/rangen/doc/rangen_man.pdf b/macros/latex/contrib/rangen/doc/rangen_man.pdf
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+<</Size 568/Root 367 0 R/Info 567 0 R/ID[<EEE28D43EF289D22A5E5929EFF578194><1DDBB348F97C6945A42883A56B114D19>]>>

+startxref

+215462

+%%EOF

diff --git a/macros/latex/contrib/rangen/doc/rangen_man.tex b/macros/latex/contrib/rangen/doc/rangen_man.tex
new file mode 100644
index 0000000000..cfecd31ecd
--- /dev/null
+++ b/macros/latex/contrib/rangen/doc/rangen_man.tex
@@ -0,0 +1,1563 @@
+% makeindex < aebpro_man.idx > aebpro_man.ind
+\documentclass[12pt]{article}
+\usepackage[fleqn]{amsmath}
+\usepackage[
+    web={centertitlepage,designv,tight*,forcolorpaper,
+%         usesf,
+         latextoc,pro},
+         aebxmp,exerquiz,
+        dljslib={equations,ImplMulti,indefIntegral,limitArith,nodec}
+]{aeb_pro}
+\usepackage{multicol}
+\usepackage{array}
+%\usepackage{myriadpro} %[usecmtt]
+\usepackage[altbullet]{lucidbry}
+\usepackage[quiet,testmode]{rangen} % testmode
+%\usepackage[quiet,seed=98]{rangen} % 128
+%\usepackage[quiet,seed=135]{rangen} %
+
+\DeclareInitView
+{%
+    layoutmag={mag=100},
+%    windowoptions={fit}
+}
+
+
+%\usepackage{makeidx}\makeindex
+
+\usepackage{acroman}
+
+\usepackage[active]{srcltx}
+
+\def\expath{../examples}
+
+\urlstyle{tt}
+
+%\def\tutpath{doc/tutorial}
+%\def\tutpathi{tutorial}
+
+\DeclareDocInfo
+{
+    university={\AcroTeX.Net},
+    title={The \texorpdfstring{\pkg{rangen} Package\\[1em]}{: }
+        Random Generation of Integer, Rational, and Real Numbers with
+    Applications to the \texttt{exercise}, \texttt{quiz}, and \texttt{shortquiz} Environments of \textsf{Exerquiz}},
+    author={D. P. Story},
+    email={dpstory@acrotex.net},
+    subject={Documentation for annot\textunderscore pro from AcroTeX},
+    talksite={\url{www.acrotex.net}},
+    version={1.4},
+    copyrightStatus=True,
+    copyrightNotice={Copyright (C) \the\year, D. P. Story},
+    copyrightInfoURL={http://www.acrotex.net}
+}
+
+\def\anglemeta#1{\ensuremath{\langle\textit{\texttt{#1}}\rangle}}
+\def\meta#1{\textit{\texttt{#1}}}
+\let\meta\anglemeta
+\def\darg#1{\texttt{\{#1\}}}
+\def\takeMeasure{\bgroup\obeyspaces\takeMeasurei}
+\def\takeMeasurei#1{\global\setbox\webtempboxi\hbox{\ttfamily#1}\egroup}
+\def\bxSize{\wd\webtempboxi+2\fboxsep+2\fboxrule}
+\let\pkg\textsf
+\let\env\texttt
+\let\opt\texttt
+\let\app\textsf
+
+\let\amtIndent\leftmargini
+\def\SUB#1{${}_{\text{#1}}$}
+
+\newdimen\aebdimen \aebdimen 0pt %\advance\aebdimen\partopsep
+\newcommand\bVerb[1][]{\begingroup#1\vskip\aebdimen\parindent0pt}%
+\def\eVerb{\vskip\aebdimen\endgroup\noindent}
+
+\makeatletter
+\renewcommand{\paragraph}
+    {\@startsection{paragraph}{4}{0pt}{6pt}{-3pt}{\bfseries}}
+\renewcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.5em}}
+\renewcommand*\descriptionlabel[1]{\hspace\labelsep
+    \normalfont #1}
+\newcommand{\aebDescriptionlabel}[1]{%
+    \setlength\dimen@{\amtIndent+\labelsep}%
+    {\hspace*{\dimen@}#1}}
+\makeatother
+\newenvironment{aebDescript}
+    {\begin{list}{}{\setlength{\labelwidth}{0pt}%
+        \setlength{\leftmargin}{\leftmargin}%
+        \setlength{\leftmargin}{\leftmargin+\amtIndent}%
+        \setlength\itemindent{-\leftmargin}%
+        \let\makelabel\aebDescriptionlabel
+    }}{\end{list}}
+
+
+\def\dps{$\hbox{$\mathfrak D$\kern-.3em\hbox{$\mathfrak P$}%
+   \kern-.6em \hbox{$\mathcal S$}}$}
+
+\universityLayout{fontsize=Large}
+\titleLayout{fontsize=LARGE}
+\authorLayout{fontsize=Large}
+\tocLayout{fontsize=Large,color=aeb}
+\sectionLayout{indent=-62.5pt,fontsize=large,color=aeb}
+\subsectionLayout{indent=-31.25pt,color=aeb}
+\subsubsectionLayout{indent=0pt,color=aeb}
+\subsubDefaultDing{\texorpdfstring{$\bullet$}{\textrm\textbullet}}
+
+\newenvironment{eqComments}[1][\strut]{\smallskip\leftskip-\labelwidth
+\item[]\textbf{\textcolor{blue}{#1}}}{\par\smallskip}
+
+\renewcommand\nodecAlertMsg{%
+    "A decimal answer is not acceptable here.
+     Please express your answer using a fraction."}
+
+%\previewtrue
+
+%\pagestyle{empty}
+%\parindent0pt\parskip\medskipamount
+
+\definePath\bgPath{"C:/Users/Public/Documents/%
+    ManualBGs/Manual_BG_Print_AeB.pdf"}
+\begin{docassembly}
+\addWatermarkFromFile({%
+    bOnTop: false,
+    cDIPath: \bgPath
+})
+\executeSave()
+\end{docassembly}
+
+\begin{document}
+
+\maketitle
+
+\selectColors{linkColor=black}
+\tableofcontents
+\selectColors{linkColor=webgreen}
+
+\section{Introduction}\label{s:intro}
+
+This is a package that I began back in the year 2000 AD; at that
+time, I managed to obtain a working version up and running with many
+bugs, then forgot about it. Now, in my retirement, I stumbled across
+the work and decided to give it another go.
+
+The \pkg{rangen} package, as the title implies, can (pseudo-)randomly generate
+integers, rationals, and real numbers. Generate said numbers using the
+\cs{RandomZ}, \cs{RandomQ}, and \cs{RandomR} commands, respectively; in addition
+to these, there is \cs{RandomL} for creating a list of numbers, from which one number
+is selected at random, and \cs{RandomI} for generating a random index value that can
+be used in conjunction with \cs{RandomL}.
+
+The \AcroTeX{} eDucation Bundle (AeB) contains a package called \textsf{exerquiz}
+that is used to create exercises and quizzes.  My goal in writing the
+\pkg{rangen} package was to integrate it with the quiz system of \textsf{exerquiz}
+so that quiz questions could be composed using the ``natural'' syntax of \pkg{rangen},
+each time the source file is {\LaTeX}ed, new random numbers populate the question. To get your
+interest, here is an example,
+
+
+
+\begingroup\parskip0pt  %\previewtrue
+
+\def\aftershortquizskip{}
+\setlength{\multicolsep}{0pt}
+
+\begin{shortquiz}*[answer] \textbf{\textcolor{blue}{Arithmetic.}}
+A simple arithmetic problem, I've created one problem, then copied it to make
+two problems.
+
+\vskip6pt
+
+\begin{multicols}{2}
+\begin{questions}
+
+% subtraction
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+
+\item  $\displaystyle \ds\a - \ds\b =
+       \RespBoxMath[\rectW{.5in}]{ (\nOf\a * \dOf\b - \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b - \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+% subtraction
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+
+\item  $\displaystyle \ds\a - \ds\b =
+       \RespBoxMath[\rectW{.5in}]{ (\nOf\a * \dOf\b - \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b - \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+\pushquestions
+\end{multicols}
+\popquestions
+
+\vskip-6pt
+
+\begin{eqComments}[Indefinite Integration.]
+There are two integration problems, again, the second question is a copy and paste of the first.
+The parameters of the problem were, of course, populated by different random numbers.
+\end{eqComments}
+
+\RandomQ{\a}{1/6}{3/2}
+\RandomQ{\b}{1/6}{3/2}
+\RandomZ{\c}{1}{3}
+
+\item   $\displaystyle\int \cds\a x^2 + \cds\b x + \ds\c\,dx =
+        \RespBoxMath{(\a/3)x^3+(\b/2) x^2 + \c x}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{(rFrac(rEval(\nOf\a)/rEval(3*\dOf\a))) x^3
+            + (rFrac(rEval(\nOf\b)/rEval(2*\dOf\b))) x^2
+            + \c x + C}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\RandomQ{\a}{1/6}{3/2}
+\RandomQ{\b}{1/6}{3/2}
+\RandomZ{\c}{1}{3}
+
+\item   $\displaystyle\int \cds\a x^2 + \cds\b x + \ds\c\,dx =
+        \RespBoxMath{(\a/3)x^3+(\b/2) x^2 + \c x}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{(rFrac(rEval(\nOf\a)/rEval(3*\dOf\a))) x^3
+            + (rFrac(rEval(\nOf\b)/rEval(2*\dOf\b))) x^2
+            + \c x + C}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+%\vskip-6pt
+\vskip-6pt
+
+\begin{eqComments}
+Definite integration can also be posed, but is not illustrated here.
+\end{eqComments}
+
+\vskip-6pt
+
+\begin{eqComments}[Analytic Geometry.]
+Find the equation of the line that passes through $P$ and $Q$.
+\end{eqComments}
+
+\RandomZ{\a}{-10}{9}
+\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}
+\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m}{\d - \b}{\c - \a}{rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+
+\item   $P(\,\a, \b\,)$, $Q(\,\c, \d\,)$:
+        \RespBoxMath{y = \m*x + (\b - \a*\m) }(xy){3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}\hfill
+        \CorrAnsButton{y = \js\m\space x + rFrac((rEval( \b * \dOf\m - \a*\nOf\m ))/(rEval(\dOf\m)))}*{rngCorrAnsButton}%
+        \kern1bp\sqTallyBox
+
+\RandomZ{\a}{-10}{9}
+\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}
+\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m} {\d - \b} {\c - \a} {rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+
+\item   $P(\,\a, \b\,)$, $Q(\,\c, \d\,)$:
+        \RespBoxMath{y = \m*x + (\b - \a*\m) }(xy){3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}\hfill
+        \CorrAnsButton{y = \js\m\space x + rFrac((rEval( \b * \dOf\m - \a*\nOf\m ))/(rEval(\dOf\m)))}*{rngCorrAnsButton}%
+        \kern1bp\sqTallyBox\par\kern2pt
+\end{questions}
+\end{shortquiz}\hfill\sqClearButton\kern1bp\sqTallyTotal
+\par\endgroup
+\newtopic\noindent
+Each time the manual is compiled, a new set of problems of the same type is generated.
+This package is pretty impressive, I'm sure you'll agree. \dps
+
+These examples were taken from the demo file \texttt{rangen\_tst.tex}.
+
+\section{Requirements}
+
+The requirements for your {\LaTeX} system, and well as any other
+software, is highlighted in this section.
+
+\subsection{{\LaTeX} Package Requirements}
+
+The following packages, in addition to the standard {\LaTeX}
+distribution, are required:
+\begin{enumerate}
+  \item The \textsf{lcg} package (2008/09/10 v1.2) by Erich Janka.
+  \item The \textsf{hyperref} package, a recent version.
+  \item If you want to use \pkg{rangen} to create quizzes, then
+  \textsf{exerquiz} of \textcolor{blue}{AeB} is required.\footnote{AeB: \url{http://www.math.uakron.edu/~dpstory/webeq.html}}
+\end{enumerate}
+
+\subsection{PDF Creator Requirements}
+
+The package works for all PDF creators: Acrobat Distiller, pdftex, and dvipdfm.
+
+\section{Installation}
+
+Unzip \texttt{rangen.zip} into your {\LaTeX} tree, the folder \texttt{rangen} is constructed
+with to contain the installation.
+
+\section{Package Options}
+
+Currently, there is only one option, \opt{testmode}. Then this option is used,
+each time the file is run, the random number generator of \pkg{lcd} is re-seeded
+Normally, the seed is based on the time, the date and other factors; the clock
+of the {\TeX} compiler gives the time to the nearest minute, so one must wait at least
+a minute before getting a new seed, this is not acceptable when testing a package.
+When \opt{testmode} is used, the initial seed is \texttt{seed=1}, and increments
+by one thereafter; after the increment, this value is saved to the file
+\cs{jobname.seed} and input back in on the next compile.
+
+Any other options that are passed to \pkg{rangen}, are passed on to the \textsf{lcg} package.
+Useful options for \pkg{lcg} are \texttt{quiet} and \texttt{seed=\meta{number}}.
+
+
+\section{Basic Commands}
+
+This package defines the commands \cs{RandomZ},
+\cs{RandomQ}, and \cs{RandomR}, \cs{RandomL}, and \cs{RandomI}. We describe
+these commands in this section.
+
+For convenience of terminology, a number created by one of the above commands
+will be referred to as a RV (random variable).
+
+\cs{RandomZ} and \cs{RandomQ} use the count registers, so there is a restriction
+on the size of any RV generated by these two commands, we must have
+\begin{equation*}
+    -2^{31}+1 \leq \text{RV} \leq  2^{31}-1\implies
+    -2147483647 \leq \text{RV} \leq 2147483647
+\end{equation*}
+For simple applications envisioned for \pkg{rangen}, this range should be plenty
+enough.
+
+The \cs{RandomR} command uses the dimension registers, so a RV generated by
+\cs{RandomR} is restricted to
+\begin{equation*}
+    -2^{14} < \text{RV} <  2^{14}\implies
+    -16384 < \text{RV} < 16384
+\end{equation*}
+Again, this is not a package for making floating point calculations, it is a package
+for generating integers, rationals, and decimal numbers with an eye towards application
+to academic problem generation. Floating point arithmetic can be accomplished using
+the \textsf{fp} package; \pkg{rangen} and \textsf{fp} seem to be compatible.
+
+\subsection{\texorpdfstring{\protect\cs{RandomZ}}{\CMD{RandomZ}}}
+
+The command \Com{RandomZ} defines a random integer, the syntax is
+
+\takeMeasure{\string\RandomZ[\meta{key-values}]\darg{\cs{\meta{name}}}\darg{\meta{zLEP}}\darg{\meta{zUEP}}}
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomZ[!meta(key-values)]{!cs(!meta(name))}{!meta(zLEP)}{!meta(zUEP)}
+\end{dCmd*}
+\PD
+\begin{description}
+\item [\texttt{\meta{key-values}}] The key-value pairs that modify the choice of
+the variable. The key-value pairs recognize are
+\begin{description}
+  \item [\texttt{ne=\meta{value}}] Restrict the choice of the random integer by requiring
+  it \emph{not be equal} to another number, for example, \texttt{ne=0} or \texttt{ne=\cs{b}}.
+  In the latter case, \cs{b} is a number defined already by either an earlier
+  \cs{RandomZ} call, or by \Com{defineZ}, discussed later. Multiple restrictions can
+  be placed as well, for example, if \verb!ne={0,-1}!, \pkg{rangen} selects an integer
+  different from 0 or -1.
+%  \item \texttt{formatOne}: A Boolean formatting key for formatting the number 1;
+%  for example, instead of typesetting \texttt{1x} the correct syntax is to typeset \texttt{x}.
+%  To obtain this special formatting, you must use
+%  \cs{fmt} or \cs{ds}, for example \verb!\fmt\a!. Details are described below.
+%  \item \texttt{formatPMOne}: A Boolean formatting key for formatting the numbers 1 and -1;
+%  in addition to formatting of the number 1, if the random integer is -1 we want to
+%  typeset \texttt{-x} not \texttt{-1x}. To obtain this special formatting, you must use
+%  \cs{fmt} or \cs{ds}, for example \verb!\fmt\a!. Details are described below.
+\end{description}
+\item[\cs{\meta{name}}] The name of the random integer. For example,
+    \cs{a}, \cs{b}, etc.
+\item [\meta{zLEP}] An integer that is the lower endpoint of the interval
+    from which the number is randomly selected. The lower endpoint may be
+    an integer previously calculated by an earlier \cs{RandomZ} call, for
+    example, \verb!\RandomZ{\b}{\a}{5}!, this will generate an integer
+    \cs{b} such that $\cs{a}\le\cs{b}\le5$. To get strict inequality,
+    append an asterisk (\texttt{*}), for example, if the syntax
+    \verb!\RandomZ{\b}{\a*}{5}! is used, then \pkg{rangen} attempts to
+    satisfy $\cs{a}<\cs{b}\le5$. The range of \cs{a} should be such that
+    the upper limit for \cs{a} is less than the upper limit of \cs{b}. When
+    the endpoint is a number, the \texttt{*} is ignored.\smallskip
+
+    When the lower endpoint is a command created by the commands
+    \cs{Random\meta{\upshape{Z|Q|R|L}}} or by
+    \cs{define\meta{\upshape{Z|Q|R}}}, the endpoint is converted to a real
+    number.
+
+\item [\meta{zUEP}] An integer that is the upper endpoint of the interval
+    from which the number is randomly selected. The upper endpoint may be
+    an integer previously calculated by an earlier \cs{RandomZ} call, for
+    example, \verb!\RandomZ{\b}{-5}{\a}!, this will generate an integer
+    \cs{b} such that $-5\le\cs{b}\le\cs{a}$. To get strict inequality, use
+    the syntax $-5\le\cs{b}\le\cs{a}*$, then \pkg{rangen} attempts to
+    satisfy $-5\le\cs{b}<\cs{a}$. The range of \cs{a} should be such that
+    the lower limit for \cs{a} is greater than the lower limit of \cs{b}.
+    When the endpoint is a number, the \texttt{*} is ignored.\smallskip
+
+    When the upper endpoint is a command created by the commands
+    \cs{Random\meta{\upshape{Z|Q|R|L}}} or by
+    \cs{define\meta{\upshape{Z|Q|R}}}, the endpoint is converted to a real
+    number.
+
+\end{description}
+
+\noindent
+\textbf{Examples:}
+\begin{enumerate}
+    \item \verb!\RandomZ{\a}{-5}{5}!: \RandomZ{\a}{-5}{5}\cs{a}=\a. To get another
+    random integer, we repeatedly execute \verb!\RandomZ{\a}{-5}{5}! followed by
+    \cs{a}, for example, we copy and paste \verb!\RandomZ{\a}{-5}{5}\a! three times to get
+    \RandomZ{\a}{-5}{5}\a, \RandomZ{\a}{-5}{5}\a, \RandomZ{\a}{-5}{5}\a.
+
+    \item Illustrate \texttt{ne}: Consider
+        \verb!\RandomZ[ne={0,-1}]{\a}{-5}{5}\a!, copy and paste
+        repeatedly: \RandomZ[ne={0,-1}]{\a}{-5}{5}\a,
+        \RandomZ[ne={0,-1}]{\a}{-5}{5}\a, \RandomZ[ne={0,-1}]{\a}{-5}{5}\a,
+        \RandomZ[ne={0,-1}]{\a}{-5}{5}\a, and
+        \RandomZ[ne={0,-1}]{\a}{-5}{5}\a. If \pkg{rangen} worked as it
+        should, the list of five number should not contain a 0 or a -1,
+        does it?
+    \item Illustrate $\cs{a}\le\cs{b}$: We use the code
+\begin{Verbatim}
+\RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$
+\end{Verbatim}
+    We now copy and paste this code: \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$,
+    \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$. To get strict inequality we execute
+\begin{Verbatim}
+\RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$
+\end{Verbatim}
+    We now copy and paste this code: \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$,
+    \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$
+%\item\texttt{formatOne}: We execute the code
+%\begin{Verbatim}
+%\RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$
+%\end{Verbatim}
+%    to get \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$,
+%    \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$.
+%    Notice the use of the command \cs{fmt}. When \cs{fmt} is present, the special formatting
+%    is used; there are times when you want the formatting, and other times when you don't it. For example,
+%    suppose we want \cs{a} to be a constant term, we want $ 1 + x $ not $\phantom{1}+x$, to get this
+%    we use create \cs{a} as before \verb!\RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$!, but do not use
+%    the \cs{fmt} on the first term. This gets us \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$,
+%    \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$.
+%
+%\item\texttt{formatPMOne}: We execute the code
+%\begin{Verbatim}
+%\RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$
+%\end{Verbatim}
+%to obtain \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$, \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$,
+%\RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$, \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$. Let us hope
+%we get a -1 in one of those generations.
+\end{enumerate}
+
+\paragraph*{Data Type Properties.}\label{dtProperties}When a random number is created, there are several auxiliary commands that are defined.
+
+\takeMeasure{\string\nOf\darg{\cs{\meta{name}}}\quad\string\dOf\darg{\cs{\meta{name}}}}
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\nOf{!cs(!meta(name))}!quad\dOf{!cs(!meta(name))}
+\fmt{!cs(!meta(name))}!quad\ds{!cs(!meta(name))}
+\end{dCmd*}
+\CmdDescription
+\begin{description}\def\1{\hspace{-\labelsep}}
+  \item\1 \cs{nOf\darg{\cs{\meta{name}}}} is the numerator for the number
+      \cs{\meta{name}}. For an integer this is just \cs{\meta{name}}. This
+      function becomes important for rational numbers. If \cs{a} is the
+      rational number 2/3, then \verb!\nOf{\a}=2!.
+
+  \item\1 \cs{dOf\darg{\cs{\meta{name}}}} is the denominator for the number
+      \cs{\meta{name}}. For an integer this is just \texttt{1}. This
+      function becomes important for rational numbers. If \cs{a} is the
+      rational number 2/3, then \verb!\dOf{\a}=3!.
+
+  \item\1 \cs{fmt\darg{\cs{\meta{name}}}} allows for special formatting for
+      in-line numbers. Without one of the special formatting options,
+      \cs{fmt}\cs{a} is the same as \cs{a}.
+
+  \item\1 \cs{ds\darg{\cs{\meta{name}}}} allows for special formatting for
+      display style number. \cs{ds} is relevant for rational numbers. If
+      \cs{a} represents the rational 1/2, the \cs{a} expanded is 1/2, while
+      \cs{ds}\cs{a} expanded is $\frac{1}{2}$. The \cs{ds} command also
+      obeys the formatting options.
+\end{description}
+
+
+\subsection{\texorpdfstring{\protect\cs{RandomQ}}{\CMD{RandomQ}}}
+
+The command \Com{RandomQ} defines a random rational, the syntax is
+
+\takeMeasure{\small\string\RandomQ[\meta{key-values}]\darg{\cs{\meta{name}}}%
+[\meta{max\_denom}]\darg{\meta{qLEP}}\darg{\meta{qUEP}}}
+\begin{dCmd*}[commandchars=!(),fontsize=\small]{\bxSize}
+\RandomQ[!meta(key-values)]{!cs(!meta(name))}[!meta(max_denom)]{!meta(qLEP)}{!meta(qUEP)}
+\end{dCmd*}
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+\item [\meta{key-values}] The key-value pairs that modify the choice of
+the variable. The key-value pairs recognize are
+\begin{description}
+  \item [\texttt{ne=\meta{value}}] Restrict the choice of the random rational by requiring
+  it \emph{not be equal} to another number, for example, \texttt{ne=0} or \texttt{ne=\cs{b}}.
+  In the latter case, \cs{b} is a number defined already by either an earlier
+  \cs{RandomQ} call, or by \Com{defineQ}, discussed later. Multiple restrictions can
+  be placed as well, for example, if \verb!ne={0,-1}!, \pkg{rangen} selects an integer
+  different from 0 or -1.
+%  \item \texttt{formatOne}: A Boolean formatting key for formatting the number 1;
+%  for example, instead of typesetting \texttt{1x} the correct syntax is to typeset \texttt{x}.
+%  To obtain this special formatting, you must use
+%  \cs{fmt} or \cs{ds}, for example \verb!\fmt\a!. Details are described below.
+%  \item \texttt{formatPMOne}: A Boolean formatting key for formatting the numbers 1 and -1;
+%  in addition to formatting of the number 1, if the random integer is -1 we want to
+%  typeset \texttt{-x} not \texttt{-1x}. To obtain this special formatting, you must use
+%  \cs{fmt} or \cs{ds}, for example \verb!\fmt\a!. Details are described below.
+\end{description}
+\item\1\cs{\meta{name}} is the name of the random rational. For example,
+\cs{a}, \cs{b}, etc.
+
+\item\1\meta{max\_denom} is the largest denominator you want your random
+    rational to have. For example, \verb!\RandomQ{\a}[9]{1/2}{7/2}!: The
+    value of \cs{a} is a rational number between 1/2 and 7/2 having a
+    maximum denominator of 9. If this parameter is not specified, the least
+    common denominator is used; for the example, that would be 2. To
+    contrast the two, consider the following examples:
+\begin{enumerate}
+  \item \verb!\RandomQ{\a}[9]{1/2}{7/2}\a!: \RandomQ{\a}[9]{1/2}{7/2}\a, \RandomQ{\a}[9]{1/2}{7/2}\a,
+  \RandomQ{\a}[9]{1/2}{7/2}\a, and \RandomQ{\a}[9]{1/2}{7/2}\a.
+  \item \verb!\RandomQ{\a}{1/2}{7/2}\a!: \RandomQ{\a}{1/2}{7/2}\a, \RandomQ{\a}{1/2}{7/2}\a,
+  \RandomQ{\a}{1/2}{7/2}\a, \RandomQ{\a}{1/2}{7/2}\a.
+\end{enumerate}
+The fractions are reduced to lowest terms, and represented as an integer if needed.
+
+Here is more detail on the algorithm used to generate a rational: We illustrate
+using the example, \verb!\RandomQ{\a}[9]{1/2}{7/2}!, the details are simplified slightly.
+\begin{enumerate}
+    \item Convert the range so that the endpoints have a denominator of~9.
+\begin{alignat*}{2}
+    &\texttt{LEP}: \frac{1}{2}= \frac{9/2}{9}=\frac{4.5}{9}< \frac{5}{9}&&\quad\text{round up} \\[1em]
+    &\texttt{UEP}: \frac{7}{2}= \frac{63/2}{9}=\frac{31.5}{9}>\frac{31}{9}&&\quad\text{round down}
+\end{alignat*}
+\item We randomly choose an integer between 5 and 31, call it \cs{z}; our random
+rational is then \texttt{\cs{z}/9}, unless there is an \texttt{*} affixed to one of
+both endpoints.
+\item If one or both endpoints is itself a random rational (or integer) and the \texttt{*}
+character is used, then the lower end of the range is incremented (from 5 to 6) and/or
+the upper end is decremented (from 31 to 30).
+\item Reduce the fraction obtained in the previous step.
+\end{enumerate}
+
+You can see from this example, there are a lot of choices for the random
+integer, there are 27 possibilities between 5 and 32.
+
+\item\1 \meta{qLEP} is a rational (of the form a/b) that is the lower
+    endpoint of the interval from which the number is randomly selected.
+    The lower endpoint may be a rational (or integer) previously calculated
+    by an earlier \cs{RandomQ} call, for example,
+    \verb!\RandomQ{\b}{\a}{4/3}!, this will generate an integer \cs{b} such
+    that $\cs{a}\le\cs{b}\le4/3$. To get strict inequality, use the syntax
+    \verb!\RandomZ{\b}{\a*}{4/3}!, then \pkg{rangen} attempts to satisfy
+    $\cs{a}<\cs{b}\le4/3$. The range of \cs{a} should be such that the
+    upper limit for \cs{a} is less than the upper limit of \cs{b}. When the
+    endpoint is a number, the \texttt{*} is ignored.\smallskip
+
+    When the lower endpoint is a command created by any of the commands
+    \cs{Random\meta{\upshape{Z|Q|R|L}}} or \cs{define\meta{\upshape{Z|Q|R}}},
+    the endpoint is converted to a real number.
+
+\item\1\meta{qUEP} is a rational that is the upper endpoint of the interval
+    from which the number is randomly selected. The upper endpoint may be a
+    rational  (or integer) previously calculated by an earlier \cs{RandomQ}
+    call, for example, \verb!\RandomQ{\b}{-4/3}{\a}!, this will generate an
+    integer \cs{b} such that $-4/3\le\cs{b}\le\cs{a}$. To get strict
+    inequality, use the syntax $-4/3\le\cs{b}\le\cs{a}*$, then \pkg{rangen}
+    attempts to satisfy $-4/3\le\cs{b}<\cs{a}$. The range of \cs{a} should
+    be such that the lower limit for \cs{a} is greater than the lower limit
+    of \cs{b}. When the endpoint is a number, the \texttt{*} is
+    ignored.\smallskip
+
+    When the upper endpoint is a command created by any of the commands
+    \cs{Random\meta{\upshape{Z|Q|R|L}}} or \cs{define\meta{\upshape{Z|Q|R}}},
+    the endpoint is converted to a real number.
+\end{description}
+
+\paragraph*{Examples}
+\begin{enumerate}
+    \item \verb!\RandomZ{\a}{-5}{5}!: \RandomZ{\a}{-5}{5}\cs{a}=\a. To get
+        another random integer, we repeatedly execute
+        \verb!\RandomZ{\a}{-5}{5}! followed by \cs{a}, for example, we copy
+        and paste \verb!\RandomZ{\a}{-5}{5}\a! three times to get
+        \RandomZ{\a}{-5}{5}\a, \RandomZ{\a}{-5}{5}\a,
+        \RandomZ{\a}{-5}{5}\a.
+
+    \item Illustrate \texttt{ne}: Copy and paste
+\begin{Verbatim}
+\RandomZ[ne={0,-1}]{\a}{-5}{5}\a
+\end{Verbatim}
+        repeatedly to obtain:
+        \RandomZ[ne={0,-1}]{\a}{-5}{5}\a, \RandomZ[ne={0,-1}]{\a}{-5}{5}\a,
+        \RandomZ[ne={0,-1}]{\a}{-5}{5}\a, \RandomZ[ne={0,-1}]{\a}{-5}{5}\a,
+        and \RandomZ[ne={0,-1}]{\a}{-5}{5}\a. If \pkg{rangen} worked as it
+        should, the list of five number should not contain a 0 or a -1,
+        does it?
+    \item Illustrate $\cs{a}\le\cs{b}$: We use the code
+\begin{Verbatim}
+\RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$
+\end{Verbatim}
+    We now copy and paste this code: \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$,
+    \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a}{10}$\a \le \b$. To get strict inequality we execute
+\begin{Verbatim}
+\RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$
+\end{Verbatim}
+    We now copy and paste this code:
+    \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$,
+    \RandomZ{\a}{-5}{5}\RandomZ{\b}{\a*}{10}$\a < \b$
+%\item\texttt{formatOne}: We execute the code
+%\begin{Verbatim}
+%\RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$
+%\end{Verbatim}
+%    to get \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$,
+%    \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\fmt\a x$.
+%    Notice the use of the command \cs{fmt}. When \cs{fmt} is present, the special formatting
+%    is used; there are times when you want the formatting, and other times when you don't it. For example,
+%    suppose we want \cs{a} to be a constant term, we want $ 1 + x $ not $\phantom{1}+x$, to get this
+%    we use create \cs{a} as before \verb!\RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$!, but do not use
+%    the \cs{fmt} on the first term. This gets us \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$,
+%    \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$, \RandomZ[formatOne]{\a}{1}{3}$\a+\fmt\a x$.
+%
+%\item\texttt{formatPMOne}: We execute the code
+%\begin{Verbatim}
+%\RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$
+%\end{Verbatim}
+%to obtain \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$, \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$,
+%\RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$, \RandomZ[ne=0,formatPMOne]{\a}{-2}{2}$\fmt\a x$. Let us hope
+%we get a -1 in one of those generations.
+
+    \item \verb!\RandomQ{\a}{-5/2}{5/2}!: \RandomQ{\a}{-5/2}{5/2}\cs{a}=\a.
+        We repeatedly copy and paste \verb!\RandomQ{\a}{-5/2}{5/2}\a! three
+        times to get \RandomQ{\a}{-5/2}{5/2}\a, \RandomQ{\a}{-5/2}{5/2}\a,
+        \RandomQ{\a}{-5/2}{5/2}\a.
+
+    \item Illustrate \texttt{ne}:
+        \verb!\RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a!, copy and paste this
+        code repeatedly: \RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a,
+        \RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a,
+        \RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a,
+        \RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a, and
+        \RandomQ[ne={0,-1}]{\a}{-5/2}{5/2}\a. If \pkg{rangen} worked as it
+        should, the list of five number should not contain a 0 or a -1,
+        does it?
+
+    \item Illustrate $\cs{a}\le\cs{b}$: We use the code
+\begin{Verbatim}[fontsize=\small]
+\RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a}{10}$\a \le \b$
+\end{Verbatim}
+    and copy and paste: \RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a}{10}$\a \le \b$,
+    \RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a}{10}$\a \le \b$. To get strict inequality we execute
+\begin{Verbatim}[fontsize=\small]
+\RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a*}{10}$\a < \b$
+\end{Verbatim}
+    to get \RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a*}{10}$\a < \b$,
+    \RandomQ{\a}{-5/2}{5/2}\RandomQ{\b}[4]{\a*}{10}$\a < \b$
+%\item\texttt{formatOne}: We execute the code
+%\begin{Verbatim}
+%\RandomQ[formatOne]{\a}{2/3}{4/3}$\ds\a x$
+%\end{Verbatim}
+%    to get \RandomQ[formatOne]{\a}{2/3}{4/3}$\ds\a x$, \RandomQ[formatOne]{\a}{2/3}{4/3}$\ds\a x$,
+%    \RandomQ[formatOne]{\a}{2/3}{4/3}$\ds\a x$, \RandomQ[formatOne]{\a}{2/3}{4/3}$\ds\a x$.
+%    Notice the use of the command \cs{ds}. When \cs{ds} is present, the special formatting
+%    is used; there are times when you want the formatting, and other times when you don't it. For example,
+%    suppose we want \cs{a} to be a constant term, we want $ 1 + x $ not $\phantom{1}+x$, to get this
+%    we use create \cs{a} as before\\[3pt]
+%        \verb!\RandomQ[formatOne]{\a}{2/3}{4/3}$\a+\ds\a x$!,\\[3pt]
+%    but do not use
+%    the \cs{ds} on the first term. This gets us \RandomQ[formatOne]{\a}{2/3}{4/3}$\a+\ds\a x$,
+%    \RandomQ[formatOne]{\a}{2/3}{4/3}$\a+\ds\a x$, \RandomQ[formatOne]{\a}{2/3}{4/3}$\a+\ds\a x$.
+%
+%\item\texttt{formatPMOne}: We execute the code
+%\begin{Verbatim}
+%\RandomQ[formatPMOne]{\a}{-6/5}{-4/5}$\ds\a x$
+%\end{Verbatim}
+%to obtain \RandomQ[formatPMOne]{\a}{-6/5}{-4/5}$\ds\a x$, \RandomQ[formatPMOne]{\a}{-6/5}{-4/5}$\ds\a x$,
+%\RandomQ[formatPMOne]{\a}{-6/5}{-4/5}$\ds\a x$, \RandomQ[formatPMOne]{\a}{-6/5}{-4/5}$\ds\a x$. Let us hope
+%we get a -1 in one of those generations.
+\end{enumerate}
+For a rational number, the commands \cs{nOf}, \cs{dOf}, \cs{fmt}, and \cs{ds} are
+also defined, see \Nameref{dtProperties}.
+
+\subsection{\texorpdfstring{\protect\cs{RandomR}}{\CMD{RandomR}}}
+
+The command \Com{RandomR} defines a random real number, the syntax is
+
+\takeMeasure{\string\RandomR[\meta{key-values}]\darg{\cs{\meta{name}}}%
+\darg{\meta{rLEP}}\darg{\meta{rUEP}}}
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomR[!meta(key-values)]{!cs(!meta(name))}{!meta(rLEP)}{!meta(rUEP)}
+\end{dCmd*}
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+\item [\meta{key-values}] The key-value pairs that modify the choice of
+the variable. The key-value pairs recognize are
+\begin{description}
+  \item [\texttt{round=\meta{value}}] Round the generated real number so
+      that number of decimal places equals the \meta{value}, the value of
+      the \texttt{round} key; for example, \texttt{round=2} rounds the
+      result to 2 decimal places.
+
+  \item [\texttt{showzeros=\meta{\upshape{true|false}}}] Show trailing
+      zeros, only valid when the \texttt{round} key is used. For example,
+      \texttt{round=4,showzeros} might yield a result of 3.2300, whereas
+      without the \texttt{showzeros} key (or with
+      \texttt{showzeros=false}), the same result would be 3.23.
+
+  \item [\texttt{ne=\meta{value}}] Restrict the choice of the random real
+      by requiring it \emph{not be equal} to another number real, for
+      example, \texttt{ne=-1} or \texttt{ne=\cs{b}}. In the latter case,
+      \cs{b} is a number defined already by either an earlier
+      \cs{RandomR} call, or by \Com{defineR}, discussed later. Multiple
+      restrictions can be placed as well, for example, if
+      \verb!ne={0,-1}!, \pkg{rangen} selects an integer different from 0
+      or -1.\smallskip
+
+  Note, comparisons are made \emph{after} rounding.
+
+\end{description}
+
+\item\1\cs{\meta{name}} is the name of the random rational. For example,
+\cs{a}, \cs{b}, etc.
+
+\item\1 \meta{rLEP} is a real number (or integer) that is the lower
+    endpoint of the interval from which the number is randomly selected.
+    The lower endpoint may be a number previously calculated by an earlier
+    \cs{RandomR} call, for example, \verb!\RandomR{\b}{\a}{1.3}!, this will
+    generate an integer \cs{b} such that $\cs{a}\le\cs{b}\le1.3$. To get
+    strict inequality, use the syntax \verb!\RandomZ{\b}{\a*}{1.3}!, then
+    \pkg{rangen} attempts to satisfy $\cs{a}<\cs{b}\le4/3$. The range of
+    \cs{a} should be such that the upper limit for \cs{a} is less than the
+    upper limit of \cs{b}. When the endpoint is a number, the \texttt{*} is
+    ignored.\smallskip
+
+    When the lower endpoint is a command created by ant if the command
+    \cs{Random\meta{\upshape{Z|Q|R|L}}}, or by
+    \cs{define\meta{\upshape{Z|Q|R}}}, the endpoint is converted to a real
+    number.
+
+\item\1 \meta{rUEP} is a real number that is the upper endpoint of the
+    interval from which the number is randomly selected. The upper endpoint
+    may be a number previously calculated by an earlier \cs{RandomR} call,
+    for example, \verb!\RandomR{\b}{-1.3}{\a}!, this will generate an
+    integer \cs{b} such that $-1.3\le\cs{b}\le\cs{a}$. To get strict
+    inequality, use the syntax $-1.3\le\cs{b}\le\cs{a}*$, then \pkg{rangen}
+    attempts to satisfy $-1.3\le\cs{b}<\cs{a}$. The range of \cs{a} should
+    be such that the lower limit for \cs{a} is greater than the lower limit
+    of \cs{b}. When the endpoint is a number, the \texttt{*} is
+    ignored.\smallskip
+
+    When the upper endpoint is a command created by ant if the command
+    \cs{Random\meta{\upshape{Z|Q|R|L}}}, or by
+    \cs{define\meta{\upshape{Z|Q|R}}}, the endpoint is converted to a real
+    number.
+\end{description}
+The \cs{RandomR} command divides range ($\meta{rUEP}-\meta{rLEP}$) into equal
+sub-intervals, and randomly chooses node (an endpoint of one of the
+sub-intervals). The number of subdivisions is determined by
+\cs{RNGpowerOfTen}, and can be set by \cs{nDivisionsPowerOfTen}. This latter
+command takes an integer argument, $n$, $1\le n\le 4$, the number of
+subdivisions is then $10^n$.  Strictly speaking \cs{RNGpowerOfTen} does not
+have to be a power of 10, you can make the definition
+\verb!\def\RNGpowerOfTen{16}!, and that should work as well. The default is
+\verb!\nDivisionsPowerOfTen{2}!, that is, divide the range into 100 equal
+subdivisions.
+
+\paragraph*{Examples:}
+
+\begin{enumerate}
+    \item \verb!\RandomR{\a}{-2.3}{2.3}!: \RandomR{\a}{-2.3}{2.3}\cs{a}=\a.
+        To obtain more random real numbers, repeatedly execute
+        \verb!\RandomR{\a}{-2.3}{2.3}! followed by \cs{a}; for example,
+        \verb!\RandomR{\a}{-2.3}{2.3}\a! repeated three times yields the following:
+\begin{equation*}
+    \RandomR{\a}{-2.3}{2.3}\a,\ \RandomR{\a}{-2.3}{2.3}\a,\ \RandomR{\a}{-2.3}{2.3}\a
+\end{equation*}
+
+    \item \texttt{round}: We use \verb!\RandomR[round=4]{\a}{-2}{2}\a! to get
+\begin{equation*}
+    \RandomR[round=4]{\a}{-2}{2}\a,\ \RandomR[round=4]{\a}{-2}{2}\a,\
+    \RandomR[round=4]{\a}{-2}{2}\a
+\end{equation*}
+
+    \item \texttt{showzeros}: \verb!\RandomR[round=4,showzeros]{\a}{-2}{2}\a!:
+\begin{equation*}
+    \RandomR[round=4,showzeros]{\a}{-2}{2}\a,\ \RandomR[round=4,showzeros]{\a}{-2}{2}\a,\
+    \RandomR[round=4,showzeros]{\a}{-2}{2}\a,\ \RandomR[round=4,showzeros]{\a}{-2}{2}\a,\
+    \RandomR[round=4,showzeros]{\a}{-2}{2}\a
+\end{equation*}
+
+    \item Illustrate $\cs{a}\le\cs{b}$: We use the code
+\begin{Verbatim}
+\RandomR{\a}{-5}{5}\RandomR{\b}{\a}{10}$\a \le \b$
+\end{Verbatim}
+    We now copy and paste this code twice:
+\begin{equation*}
+    \RandomR{\a}{-5}{5}\RandomR{\b}{\a}{10}\a \le \b,\
+    \RandomR{\a}{-5}{5}\RandomR{\b}{\a}{10}\a \le \b
+\end{equation*}
+To get strict inequality we execute
+\begin{Verbatim}
+\RandomR{\a}{-5}{5}\RandomR{\b}{\a*}{10}$\a < \b$
+\end{Verbatim}
+    We now copy and paste this code a couple of times:
+\begin{equation*}
+    \RandomR{\a}{-5}{5}\RandomR{\b}{\a*}{10} \a < \b,\
+    \RandomR{\a}{-5}{5}\RandomR{\b}{\a*}{10} \a < \b
+\end{equation*}
+For real numbers, there is little chance the two values are equal, but just in case, strict
+inequality may be specified in this way.
+\end{enumerate}
+
+\subsection{\texorpdfstring{\protect\cs{RandomL}}{\CMD{RandomL}}}
+
+The command \Com{RandomL} defines a list of numbers (integer, rational, decimal),
+and randomly selects a number from the list.
+
+\takeMeasure{\string\RandomR[\meta{key-values}]\darg{\cs{\meta{name}}}%
+\darg{\meta{n\SUB{1},n\SUB{2},n\SUB{3},...}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomL[!meta(key-values)]{!cs(!meta(name))}{!meta(n!SUB(1),n!SUB(2),n!SUB(3),...)}
+\end{dCmd*}
+
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+\item [\texttt{\meta{key-values}}] The only key-value pairs recognized is
+    \texttt{index=\meta{posZ}}. The index is a base-1 index, thus \texttt{index=1}
+    references the first number in the list.
+
+    The \texttt{index} key can be used to retrieve a particular number from
+    this list; for example, declaring
+    \verb!\RandomL[index=2]{\a}{17,1/2,1.3}!, the value of \cs{a} is 1/2.
+
+    The value of \texttt{index} can be any positive integer, even one generated
+    using \cs{RandomI}.  If the value of \texttt{index} is greater than the
+    number of items in the list, modular arithmetic is performed to put the
+    index back into the proper range.
+
+    When the \texttt{index} key is not present, a number is randomly selected
+    from the list.
+
+\item\1\cs{\meta{name}} is the name of the number generated. The number
+    generated will be defined as integer, rational, or real; consequently
+    \cs{nOf}, \cs{dOf}, \cs{fmt}, and \cs{ds} are defined.
+
+\item \meta{n\SUB{1},n\SUB{2},n\SUB{3},...} A (possibly mixed) list of
+    numbers. The numbers can be literal (12, 1.2, 3/4), or control
+    sequences of numbers (commands) defined earlier by \cs{Random\meta{\upshape{Z|Q|R|L}}}
+    or by \cs{define\meta{\upshape{Z|Q|R}}}.
+\end{description}
+
+\paragraph*{Examples}
+
+\begin{enumerate}
+    \item After declaring \verb!\RandomL{\a}{17,3.14,88,3/4,1/2}!, the value
+        of \cs{a} is \RandomL{\a}{17,3.14,88,3/4,1/2}\texttt{\cs{a} = \a},
+        Select a number from this list at random
+        \RandomL{\a}{17,3.14,88,3/4,1/2}\texttt{\string\a=\a}, again
+        \RandomL{\a}{17,3.14,88,3/4,1/2}\texttt{\string\a=\a}, and again
+        \RandomL{\a}{17,3.14,88,3/4,1/2}\texttt{\string\a=\a}.
+    \item \verb!\RandomL[index=3]{\a}{17,3.14,88,3/4,1/2}\a!,
+    \RandomL[index=3]{\a}{17,3.14,88,3/4,1/2}\texttt{\string\a=\a}.
+\end{enumerate}
+
+\subsection{\texorpdfstring{\protect\cs{RandomI}}{\CMD{RandomI}}}
+
+The command \Com{RandomI} defines a list of integers, \verb!{1,2,3...n}!
+and randomly selects an integer, thought of as an index value, from the list.
+
+\takeMeasure{\string\RandomI\darg{\cs{\meta{name}}}\darg{\meta{n}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomI{!cs(!meta(name))}{!meta(n)}
+\end{dCmd*}
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+
+\item\1\cs{\meta{name}} is the name of the number generated, the number
+will be defined as an integer number.
+
+\item\1 \meta{n} is a positive number greater than 1. The list
+    \verb!{1,2,3...n}! is implicitly created.
+\end{description}
+
+\paragraph*{Example:} \verb!\RandomI{\indx}{20}\indx! yields \RandomI{\indx}{20}\indx,
+\RandomI{\indx}{20}\indx, \RandomI{\indx}{20}\indx, \RandomI{\indx}{20}\indx, when copied
+and pasted four times.
+
+\newtopic\noindent
+My thought in creating \cs{RandomI} is to use it in conjunction with
+\cs{RandomL} (using the \texttt{index} key). For example,
+\begin{Verbatim}
+    \RandomI{\indx}{4}
+    \RandomL[index=\indx]{\a}{1/2,1/3,1/4,1/5}
+    \RandomL[index=\indx]{\b}{5/3,6/5,7/2,5/6}
+\begin{equation*}
+    (\a)+(\b) =
+\end{equation*}
+\end{Verbatim}
+
+    \RandomI{\indx}{4}
+    \RandomL[index=\indx]{\a}{1/2,1/3,1/4,1/5}
+    \RandomL[index=\indx]{\b}{5/3,6/5,7/2,5/6}
+
+\noindent
+This code results in the following arithmetic problem:
+\begin{equation*}
+    (\a)+(\b) =
+\end{equation*}
+This is probably not a good example of the usage of \cs{RandomI}. See the next section
+on \cs{RandomP}.
+
+\subsection{\texorpdfstring{\protect\cs{RandomP}}{\CMD{RandomP}}}
+
+The command \Com{RandomP} defines a list of strings (literal expressions),
+and randomly selects one from the list. (The ``P'' in \cs{RandomP} stands
+for ``Problem.'')
+
+\takeMeasure{\string\RandomP[\meta{key-values}]\darg{\cs{\meta{name}}}\darg{\meta{list of literals}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomP[!meta(key-values)]{!cs(!meta(name))}{!meta(list of literals)}
+\end{dCmd*}
+
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+
+\item [\texttt{\meta{key-values}}] The only key-value pairs recognized is
+    \texttt{index=\meta{posZ}}. The index is a base-1 index, thus index=1
+    references the first number in the list.
+
+    The \texttt{index} key can be used to retrieve a particular literal from
+    this list; for example, by executing \verb!\RandomP[index=2]{\a}{d,p,s}!,
+    the value of \cs{a} is \texttt{p}.
+
+    The value of \texttt{index} can be any positive integer, even one generated
+    using \cs{RandomI}, or by another list.  If the value of \texttt{index} is
+    greater than the number of items in the list, modular arithmetic is
+    performed to put the index back into the proper range.
+
+    When the \texttt{index} key is not present, a number is randomly selected
+    from the list.
+
+\item\1\cs{\meta{name}} is the name of the literal generated.
+
+\item\1\meta{list of literals} is a comma-delimited list of literal
+    strings, selected literal is not interpreted as a number, but is passed
+    into the definition of \cs{\meta{name}}.
+\end{description}
+
+\paragraph*{Examples}
+
+\begin{enumerate}
+    \item Executing \verb!\RandomP{\a}{1+16,\cos(\pi),%!\\
+    \verb!  \frac{d}{dx}\frac{1}{2}x^2,{\int \cos(x)\,dx}}!\\
+    \verb!$\texttt{\string\a} = \a$!, we get
+    \RandomP[index=5]{\a}{1+16,\cos(\pi),\frac{d}{dx}\frac{1}{2}x^2}%
+    $\texttt{\string\a} = \a $, and then again,
+    \RandomP{\a}{1+16,\cos(\pi),\frac{d}{dx}\frac{1}{2}x^2}%
+    $ \texttt{\string\a} = \a $.
+    \item Use \cs{RandomI} with \cs{RandomP}. You can create a series
+    of questions and answers using these two:
+\begin{Verbatim}[fontsize=\small]
+\RandomI{\indx}{5}
+\RandomP[index=\indx]{\q}{1+16,\cos(\pi),\pi\sin(\pi),%
+    \frac{d}{dx}\frac{1}{2}x^2,{\int \cos(x)\,dx}}
+\RandomP[index=\indx]{\a}{17,-1,0,x,\sin(x)+C}
+\begin{equation*}
+  \q = \a
+\end{equation*}
+\end{Verbatim}
+
+\RandomI{\indx}{5}
+%\typeout{index=\iOf{\indx}}%
+\RandomP[index=\indx]{\q}{1+16,\cos(\pi),\pi\sin(\pi),\frac{d}{dx}\frac{1}{2}x^2,{\int \cos(x)\,dx}}
+\RandomP[index=\indx]{\a}{17,-1,0,x,\sin(x)+C}
+
+The execution of these lines becomes
+\begin{equation*}
+  \q = \a
+\end{equation*}
+You can create a switch to include the answer or not.
+
+\item There is an alternate approach to this previous example.
+Random lists (\cs{RandomL} and \cs{RandomP}) define a macro \cs{iOf},
+the value of which is the index of the item selected (at random).
+We can use \cs{iOf} in the above problem as follows:
+\begin{Verbatim}[fontsize=\small]
+\RandomP{\q}{1+16,\cos(\pi),\pi\sin(\pi),%
+    \displaystyle\frac{d}{dx}\frac{1}{2}x^2,%
+    {\int \cos(x)\,dx}}
+\RandomP[index=\iOf{\q}]{\a}{17,-1,0,x,\sin(x)+C}
+\begin{equation*}
+  \q = \a
+\end{equation*}
+\end{Verbatim}
+The execution of these lines gives the output\dots
+\RandomP{\q}{1+16,\cos(\pi),\pi\sin(\pi),%
+    \displaystyle\frac{d}{dx}\frac{1}{2}x^2,{\int \cos(x)\,dx}}
+\RandomP[index=\iOf{\q}]{\a}{17,-1,0,x,\sin(x)+C}
+\begin{equation*}
+  \q = \a
+\end{equation*}
+Here, we select the answer to the randomly chosen question.
+\end{enumerate}
+
+\subsection{\texorpdfstring{\protect\cs{RandomS}}{\CMD{RandomS}}}
+
+The command \cs{RandomS} generates a random sign, either \texttt{+}
+or \texttt{-}. This may be useful for creating addition/subtraction
+problems.
+
+\takeMeasure{\string\RandomS[\meta{dec}]\darg{\cs{\meta{name}}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\RandomS[!meta(dec)]{!cs(!meta(name))}
+\end{dCmd*}
+
+\PD
+\begin{description}\def\1{\hspace{-\labelsep}}
+
+\item\1\meta{dec} is a number between 0 and 1. This command generates a
+    \texttt{+} sign with probability \meta{dec}. The default value is
+    0.5.
+
+\item\1\cs{\meta{name}} is the name that references the generated random sign.
+
+\end{description}
+
+\paragraph*{Examples}
+
+\begin{enumerate}
+  \item Random addition problem:
+\begin{Verbatim}
+\RandomZ{\a}{1}{20}\RandomZ{\b}{1}{20}\RandomS{\s}
+\begin{equation*}
+    \a \s \b
+\end{equation*}
+\end{Verbatim}
+
+\RandomZ{\a}{1}{20}\RandomZ{\b}{1}{20}\RandomS{\s}
+
+This code expands to
+\begin{equation*}
+    \a \s \b
+\end{equation*}
+Whether we add or subtract the summands is determined by the command \cs{s}.
+
+\item Random Differentiation problem:
+\begin{Verbatim}
+\RandomQ{\a}[8]{1}{2}\RandomQ{\b}[8]{2}{3}
+\RandomZ{\n}{1}{6}\RandomS{\si}\RandomS{\sii}
+
+Differentiate
+\begin{equation*}
+    \frac{d}{dx}(\bigl (\a) \si (\b) x^{\sii\n}\bigr)
+\end{equation*}
+\end{Verbatim}
+
+\RandomQ{\a}[8]{1}{2}\RandomQ{\b}[8]{2}{3}
+\RandomZ{\n}{1}{6}\RandomS{\si}\RandomS{\sii}
+
+Differentiate
+\begin{equation*}
+    \frac{d}{dx}\bigl( (\a) \si (\b) x^{\sii\n}\bigr)
+\end{equation*}
+\end{enumerate}
+
+\subsection{Commands that Operate on Numbers}
+
+Associated with each data type (integer, rational, and real) are several
+useful commands \cs{nOf}, \cs{dOf}, \cs{iOf}, \cs{fmt}, and \cs{ds}.
+
+\subsubsection{\texorpdfstring{\protect\cs{nOf} and \protect\cs{dOf}}{\CMD{nOf} and \CMD{dOf}}}
+
+For integer, rational, and real numbers \cs{nOf} and \cs{dOf} are
+the numerator and denominator, respectively.
+\begin{itemize}
+  \item Integer: \cs{nOf} is the integer, and \cs{dOf} is 1; for example,
+  define an integer by \verb!\RandomZ{\a}{-5}{5}!,\RandomZ{\a}{-5}{5} \cs{a}=\a,
+  \verb!\nOf{\a}!=\nOf{\a}, \verb!\dOf{\a}!=\dOf{\a}, as advertised.
+
+  \item Rational: \cs{nOf} is the numerator (an integer), and \cs{dOf} is the
+  denominator (an integer) of the reduced fraction. For example, define \cs{a} by
+  \verb!\RandomQ[ne=0]{\a}[9]{-3/2}{3/2}!,\RandomQ[ne=0]{\a}[9]{-3/2}{3/2} then
+  \begin{equation*}
+  \cs{a}=\a,\ \verb!\nOf{\a}!=\nOf{\a},\ \text{and}\ \verb!\dOf{\a}!=\dOf{\a}.
+  \end{equation*}
+  \item Real: \cs{nOf} is the numerator (an integer), and \cs{dOf} is the
+  denominator (an integer) of the reduced fraction, after the real is converted
+  into a rational number. For example, \verb!\RandomR{\a}{.25}{.75}!,\RandomR{\a}{.25}{.75}
+  then
+  \begin{equation*}
+  \cs{a}=\a,\ \verb!\nOf{\a}!=\nOf{\a},\ \text{and}\ \verb!\dOf{\a}!=\dOf{\a}
+  \end{equation*}
+  If we round using with \verb!\RandomR[round=2]{\a}{.25}{.75}!, we get
+  \begin{equation*}
+  \RandomR[round=2]{\a}{.25}{.75}\cs{a}=\a,\ \verb!\nOf{\a}!=\nOf{\a},\ \text{and}\ \verb!\dOf{\a}!=\dOf{\a}
+  \end{equation*}
+%  \cs{a}=\a, \verb!\nOf{\a}!=\nOf{\a}, and \verb!\dOf{\a}!=\dOf{\a}
+\end{itemize}
+
+
+\subsubsection{Special Formatting Commands: The \texorpdfstring{\protect\cs{ds}}{\CMD{ds}}
+and \texorpdfstring{\protect\cs{fmt}}{\CMD{fmt}} families}
+
+When a RV, such as \cs{a}, is a rational number type, say \cs{a}=1/3, the command \cs{a} expands
+to 1/3. To get a display style formatting of the rational use the \Com{ds} command.
+The expansion of \texttt{\$\cs{ds}\cs{a}\$} is $\frac13$.
+
+We have seen in several examples in which the formatting was not always what we'd like.
+Expressions like $x^{1}$ should be $x$, $1x$ should be $x$, $-1x$ should be $-x$.
+The formatting commands \cs{cfmt} and \cs{efmt} (and their display style counterparts
+\cs{cds} and \cs{eds}) attempt to format the special cases of 1 and -1, as they appear
+in an exponent (the `e' variations) and as they appear as a coefficient (the `c' variations).
+
+All the formatting commands \cs{cfmt}, \cs{efmt}, \cs{ds}, \cs{cds}, and
+\cs{eds} take a RV as its argument.
+\cs{\meta{\upshape{c|e}}fmt}|\cs{\meta{\upshape{c|e}}ds}\cs{a} expands to
+\cs{a} when \cs{a} is not 1 or -1. These cases are covered below.
+
+\begin{itemize}
+    \item For \cs{a}=1,
+        \cs{cfmt}\cs{a}=\cs{efmt}\cs{a}=\cs{cds}\cs{a}=\cs{eds}\cs{a}=\darg{},
+        the empty string. Thus, \defineZ{\a}{1}if \cs{a}=\a, and we typeset
+        \verb!$\a x^{\a}$!, we get $\a x^{\a}$, which is not the standard
+        way of writing this expression, but if we typeset \verb!$\cfmt\a x^{\efmt\a}$! we get $\cfmt\a x^{\efmt\a}$, which is correct.
+        Notice that we used \cs{cfmt} on the baseline, and \cs{efmt} in the
+        exponent. It does not make any difference here, but it does if
+        \cs{a}=-1, see the next bullet point.
+
+    \item \cs{a}=-1, then
+    \begin{align*}
+        &\cs{cfmt}\cs{a}=\cs{cds}\cs{a}=\texttt{-}\quad\text{(minus sign)}\\
+        &\cs{efmt}\cs{a}=\cs{eds}\cs{a}=\texttt{-1}\quad\text{(minus one)}
+    \end{align*}
+    Returning to the same expression in the previous bullet, if
+    \defineZ{\a}{-1}\cs{a}=\a, and we typeset
+    \verb!$\a x^{\a}$!, we get $\a x^{\a}$, which is not the standard way
+    of writing this expression, but, on the other hand, if we typeset
+    \verb!$\cfmt\ax^{\efmt\a}$! we get $\cfmt\a x^{\efmt\a}$, which is correct. Notice
+    the difference cases if I had typeset \verb!$\cfmt\a x^{\cfmt\a}$!, I
+    would have gotten $\cfmt\a x^{\cfmt\a}$, not good.
+
+    The `c'-variation is used for unitary signs, not binary signs. For example,
+    \defineZ{\a}{-1}, if \cs{a}=\a, and we typeset \verb!$2 + \cfmt\a x$!, we get
+    $2 + \cfmt\a x$, which may be fine is some situations, but most of the time
+    it is not. As a work around, make coefficients positive, and generate a random sign
+    using \cs{RandomS}; for example, after declaring
+\begin{Verbatim}
+\RandomS{\s}\RandomZ{\a}{1}{3}
+\end{Verbatim}
+    and typeseting \verb!$2 \s \cfmt\a x$!, we get an addition half the
+    time and subtraction the other half: \RandomS{\s}\RandomZ{\a}{1}{3}$2
+    \s \cfmt\a x$, \RandomS{\s}\RandomZ{\a}{1}{3}$2 \s \cfmt\a x$,
+    \RandomS{\s}\RandomZ{\a}{1}{3}$2 \s \cfmt\a x$,
+    \RandomS{\s}\RandomZ{\a}{1}{3}$2 \s \cfmt\a x$,
+    \RandomS{\s}\RandomZ{\a}{1}{3}$2 \s \cfmt\a x$,
+    \RandomS{\s}\RandomZ{\a}{1}{3}$2 \s \cfmt\a x$.
+
+    Similarly, the `e'-variation is for unitary sign in the exponent, and
+    should be used when there is a need for these special format rules.
+
+  \item Random Sign: The formatting commands are defined for a random sign
+      created by \cs{RandomS} and following the same definitions outline
+      above. These are of marginal value in this context.
+%  \item[] \verb!\RandomL{\a}{-1,1}\RandomS{\s}$\a \s x^{\efmt\s x}$! yields the
+%  expression \RandomL{\a}{-1,1}\RandomS{\s}$\a \s e^{\efmt\a x}$
+\end{itemize}
+
+\subsubsection{Getting the Data type with \texorpdfstring{\protect\cs{typeOf}}{\CMD{typeOf}}}
+
+There may be occasions where you want to know the data type of a RV. The \pkg{rangen}
+does change the data type in special cases. For example, if \cs{a} is created by
+\verb~\cs{RandomQ}{\a}[2]{1}{3}~, and its value happens to be an integer, \pkg{rangen}
+changes its type of integer. You can determine the type of a RV with the \cs{typeOf}
+command, which takes a RV as its argument,  the value of \cs{typeOf} is a nonnegative integer. The following table gives
+the values of \cs{typeOf}, and associated data types.
+\begin{flushleft}
+\hspace{\amtIndent}\begin{tabular}{lc}
+Data type & \cs{typeOf}\\\hline
+Integer & 0 \\
+Rational & 1 \\
+Real & 2 \\
+Literal & 3
+\end{tabular}
+\end{flushleft}
+
+\paragraph*{A suggested application to \cs{typeOf}.} Suppose, \cs{a} is a rational RV
+(for example, \verb!\RandomQ{\a}[2]{1}{3}!), and we want to typeset the
+expression \verb!$\cfmt\a x$!. One instance might be
+\defineQ{\a}{3}{2}$\cfmt\a x$, this is not good syntax; so we typeset
+\verb!$(\cfmt\a) x$! to get $(\cfmt\a) x$, that's good. But if \cs{a} is an
+integer, such as 1, 2, or 3, we get \defineQ{\a}{2}{1}$(\cfmt\a) x$, which
+contains redundant parentheses. Now we come to the use of \cs{typeof}. We now
+typeset the expression
+\begin{Verbatim}
+$ \ifnum\typeOf\a=0\relax\cfmt\a\else(\cfmt\a)\fi x $
+\end{Verbatim}
+If \cs{a} is \emph{not an integer} we get, \defineQ{\a}{3}{2}for \cs{a}=\a, we obtain
+$\ifnum\typeOf\a=0\relax\cfmt\a\else(\cfmt\a)\fi x$, but for
+\defineQ{\a}{2}{1}for \cs{a}=\a, we get
+$\ifnum\typeOf\a=0\relax\cfmt\a\else(\cfmt\a)\fi x$.
+
+\subsection{\texorpdfstring{\protect\cs{defineZ}}{\CMD{defineZ}},
+\texorpdfstring{\protect\cs{defineQ}}{\CMD{defineQ}}, and
+\texorpdfstring{\protect\cs{defineR}}{\CMD{defineR}}}
+
+The \pkg{rangen} package internally uses \cs{defineZ}, \cs{defineQ},
+and \cs{defineR} to define an integer, a rational number, and a real (decimal) number.
+These command may be used by the document author as well to create non-random variables.
+
+\takeMeasure{\string\defineQ\darg{\cs{\meta{name}}}\darg{\meta{zNumer}}\darg{\meta{zDenom}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\defineZ{!cs(!meta(name))}{!meta(zValue)}
+\defineQ{!cs(!meta(name))}{!meta(zNumer)}{!meta(zDenom)}
+\defineR{!cs(!meta(name))}{!meta(rValue)}
+\end{dCmd*}
+Thus, \verb!\defineZ{\a}{17}!\defineZ{\a}{17} defines \cs{a}=\a, \verb!\defineQ{\a}{-3}{2}!
+\defineQ{\a}{-3}{2} defines \cs{a}=\a, and \verb!\defineR{\a}{17.88}!\defineR{\a}{17.88} defines
+\cs{a}=\a.
+
+The various properties data types are created by \cs{defineZ}, \cs{defineQ},
+and \cs{defineR}; these are \cs{nOf}, \cs{dOf}, \cs{typeOf}, \cs{ds}, \cs{eds},
+\cs{cds}, \cs{efmt}, and \cs{cfmt}.
+
+\newtopic\noindent
+The following are other important points to remember.
+\begin{itemize}
+\item \textbf{Positive Denominators.} Notice that if \verb!\defineQ{\a}{3}{-2}!,\defineQ{\a}{3}{-2} then \cs{a}=\a, and
+\cs{nOf}\cs{a}=\nOf\a, and \cs{dOf}\cs{a}=\dOf\a. Thus, \pkg{rangen} does not allow a
+negative denominator.
+
+\item \textbf{Automatic Reduction.} If we declare
+    \verb!\defineQ{\a}{6}{4}!,\defineQ{\a}{6}{4} then \cs{a}=\a, a rational
+    number is automatically reduced to lowest terms.
+
+\item \textbf{Re-classification.} If we make the definition \verb!\defineQ{\a}{6}{2}!,\defineQ{\a}{6}{2} then \cs{a}={\a} is reduced
+to lowest terms and re-classified as an integer \cs{typeOf}\cs{a}=\typeOf\a~(an integer).
+\end{itemize}
+
+\section{\textsf{rangen} and \textsf{fp}}
+
+After a little bit of testing, it appears that \textsf{fp} can work with the \texttt{rangen} package.
+The \texttt{rangen} package does not provide any command for combining RVs using such operations
+as addition, subtraction, multiplication, division, etc.
+
+The \texttt{rangen} package package does provide several useful commands that \textsf{fp} does not,
+these are \cs{reduceFrac}, \cs{gcd}, and \cs{lcm}.
+
+\Com{reduceFrac} takes two arguments (numerator and denominator), both integers, and attempts to reduce the implied fraction
+to lowest terms, and returns the result in two macros \cs{rfNumer} and \cs{rfDenom}. For example,
+to reduce the fraction $4/12$, we execute \verb!\reduceFrac{4}{12}!, which returns\reduceFrac{4}{12} \cs{rfNumer}=\rfNumer, and
+\cs{rfDenom}=\rfDenom, forming the reduced fraction $\rfNumer/\rfDenom$; thus,
+$4/12 = \rfNumer/\rfDenom$.
+
+The \emph{greatest common divisor} command \cs{gcd} takes two integers as its arguments
+and returns its result in the macro \cs{thegcd}. For example, the \verb!\gcd{4,8}! is
+\gcd{4}{8}\thegcd, while the \verb!\gcd{4}{6}! is \gcd{4}{6}\thegcd.
+
+The \emph{least common multiple} command \cs{lcd} takes two integers as its arguments,
+and returns its result in the macro \cs{thelcd}. For example, \verb!\lcm{4}{5}! is
+\lcm{4}{5}\cs{thelcm}=\thelcm, while, \verb!\lcm{4}{6}! is  \lcm{4}{6}\cs{thelcm}=\thelcm.
+
+The following example illustrates the use of the \texttt{rangen} and \texttt{fp} packages to pose a random
+arithmetic problem, and present a detailed solution.
+\begin{Verbatim}[fontsize=\footnotesize]
+\RandomQ{\a}[6]{2}{4}\RandomQ{\b}[6]{2}{4}
+\gcd{\dOf\a}{\dOf\b}
+\FPeval\lcd{clip((\dOf\a)*(\dOf\b)/\thegcd)}
+\FPeval\si{clip(\lcd/(\dOf\a))}
+\FPeval\sii{clip(\lcd/(\dOf\b))}
+\FPeval\finalnum{clip((\si)*(\nOf\a)+(\sii)*(\nOf\b))}
+\defineQ{\ans}{\finalnum}{\lcd}
+$$
+    \ds\a \thisop \ds\b = \frac{(\si)(\nOf\a)+(\sii)(\nOf\b)}{\lcd}
+        = \frac{\finalnum}{\lcd}\ifnum\lcd=\dOf\ans\else =\ds\ans\fi
+$$
+\end{Verbatim}
+An instance of this code might look like this:
+$$
+    \frac{8}{3}+\frac{17}{6}=\frac{(2)(8)+(1)(17)}{6}=\frac{33}{6}=\frac{11}{2}
+$$
+If there is any reduction of the fraction (brought on by the \cs{defineQ} command),
+this additional expression is included.
+
+\paragraph*{Demo file.}
+See the demo file \texttt{rangen\_fp.tex} for a complete example.
+
+\section{\textsf{rangen} and \textsf{exerquiz}}
+
+Developing a package for randomly generating numbers that could be
+used as a basis for creating random quizzes (see the example back in
+\hyperref[s:intro]{Section~\ref*{s:intro}}, page~\pageref*{s:intro})
+was my original motivation for writing the original package back in
+the year 2000 AD. In this section, we introduce the techniques that
+I've developed for creating random quizzes, and, more importantly,
+how to grade them and to exhibit to the user the correct answer.
+This system is not a computer algebra system, so, it is difficult,
+but not impossible to also supply a solution (a opposed to just the
+answer) to the problem as well.
+
+\paragraph*{Demo file.}  Now, let's see how its done! Examples of this section were taken from the
+demo file \texttt{rangen\_tst.tex}.
+
+\subsection{Creating Quizzes using \textsf{rangen}}
+
+
+The \pkg{rangen} package provides three JavaScript functions that are used with \textsf{exerquiz}
+quizzes, these are
+\begin{itemize}
+    \item \texttt{rEval(str)}: The function \texttt{rEval} evaluates its
+        argument. The \texttt{rEval} function searches its argument for
+        \texttt{rEval} and \texttt{rFrac}, and executes any inner nested
+        functions first.
+    \item \texttt{rFrac(str)}: Evaluates a rational number by evaluating
+        the value of the numerator and denominator separately. The function
+        \texttt{rFrac} searches its argument for \texttt{rEval} and
+        \texttt{rFrac}, and executes any inner nested functions first.
+    \item \texttt{rngCorrAnsButton}: A function that is used to represent
+        the correct answer to the user.
+\end{itemize}
+The best way of illustrating these function is by discussing an example or two.
+
+\renewcommand\titleQuizfmt{\bfseries\color{red}}
+\titleQuiz*{Example~1. }
+\begin{shortquiz}*[sq1] We create two RVs, \cs{a} and \cs{b} that are rational numbers. We want to
+add them, and present the answer as a rational number.
+\begin{Verbatim}[fontsize=\small]
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+\end{Verbatim}
+\begin{questions}
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+
+\item  $\displaystyle\ds\a - \ds\b =
+       \RespBoxMath[\rectW{.5in}]{ (\nOf\a * \dOf\b - \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b - \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqClearButton
+\end{questions}
+\end{shortquiz}
+\vskip-.5\baselineskip
+The question is posed using \cs{RespBoxMath}.
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+$\displaystyle\ds\a - \ds\b =
+\RespBoxMath[\rectW{.5in}]{
+    (\nOf\a*\dOf\b-\nOf\b*\dOf\a)/(\dOf\a*\dOf\b)}
+    {2}{.0001}{[0,2]}
+    [{priorParse: \Array(nodec,NoAddOrSub)}]$
+\end{Verbatim}
+\textsf{Exerquiz} determines whether the user's answer is correct, it by evaluating
+the author's answer at randomly selected points. Exerquiz uses the floating point arithmetic
+of JavaScript to evaluate the user's answer. The author's correct answer is given
+in line (1), and it is just the formula for combining two fractions \cs{a} and \cs{b};
+note the use of \cs{nOf} and \cs{dOf}. Line~(2) is standard parameters for \cs{RespBoxMath},
+the number of random points to use, the precision, and the interval from which to select the
+points. Line~(3) specifies a couple of routines from the \textsf{dljslib} package, these
+prevent the user from using decimals and rational arithmetic to answer the question. (The latter
+function would, for example, prevent the user from copying the question and pasting it into the
+answer.)
+
+Now comes the most interesting part, at least to me: The presentation of the correct
+answer to the user. These is where the JavaScript functions \texttt{rEval} and \texttt{rFrac} are used.
+The code for the answer button is shown below.
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+\CorrAnsButton{rFrac(
+   rEval(\nOf\a*\dOf\b-\nOf\b*\dOf\a)/rEval(\dOf\a*\dOf\b)
+)}*{rngCorrAnsButton}
+\end{Verbatim}
+Here, this code is broken across several lines to fit on the page. We direct the \cs{CorrAnsButton}
+to use the function \texttt{rngCorrAnsButton}, as seen in line~(3). This is a special function
+define by \pkg{rangen} to help in the presentation of the answer to the user.
+
+Keep in mind, the inner-most \texttt{rEval} and \texttt{rFrac}
+functions are evaluated first; consequently, the two \texttt{rEval}
+functions in line~(2) are evaluated first. These two evaluations
+calculate the numerator and denominator separately, this results in
+a numerical numerator and denominator. The function \texttt{rFrac}
+is then executed on the resulting rational number, this function
+reduces the fraction to lowers terms. This final calculation is what
+the user sees when the correct answer button is pressed.
+
+The next example will illustrate a decimal presentation of the answer, and introduces
+a new command, \Com{RNGprintf}.
+
+\titleQuiz*{Example~2. }
+\begin{shortquiz}*[sq2] We create four RVs, \cs{a}, \cs{b}, \cs{c}, and \cs{n}, three rational and one integer.
+The exponent of the power is rational, hence, we represent a decimal answer to the user.
+\begin{Verbatim}[fontsize=\small]
+\RandomQ{\a}[8]{1/4}{7/6}\RandomZ{\b}{1}{3}
+\RandomQ{\n}[8]{1/2}{3/2}\RandomZ[ne=\zZero]{\c}{-3}{3}
+\end{Verbatim}
+\begin{questions}\setcounter{eqquestionnoi}{1}
+\RandomQ{\a}[8]{1/4}{7/6}
+\RandomZ{\b}{1}{3}
+\RandomQ{\n}[8]{1/2}{3/2}
+\RandomZ[ne=\zZero]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1))}*{rngCorrAnsButton\RNGprintf{\%.4f}}\kern1bp\sqClearButton
+\end{questions}
+\end{shortquiz}
+\vskip-.5\baselineskip
+The question is posed using \cs{RespBoxMath}.
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+$\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+    \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}
+        {3}{.0001}{[0,2]}$
+\end{Verbatim}
+The correct answer is given on line~(2), and is based on the known form of the integrand; here,
+we use standard integration formulas.
+
+The code for the correct answer button has a new element in it
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+\CorrAnsButton{rEval(
+    \c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)
+)}*{rngCorrAnsButton\RNGprintf{\%.4f}}}\kern1bp\sqTallyBox
+\end{Verbatim}
+The \texttt{rEval} function evaluates the expression on line~(2), the result
+is a decimal number. As before, we use the \texttt{rngCorrAnsButton}, but we've
+added the \Com{RNGprintf} command to the end of the function name. This is a kludge
+that I've developed to be able to format a numerical answer. The \cs{RNGprintf} command
+uses the Acrobat JavaScript function \texttt{util.printf}. The argument of \cs{RNGprintf}
+is passed to \texttt{util.printf} as its formatting string. Here, we use
+\verb!\%.4f!, so the number is presented as a floating point number with four decimal places.
+See the documentation of \texttt{util.printf} in the \textsl{JavaScript for Acrobat API Reference.}\footnote
+{\url{{http://livedocs.adobe.com/acrobat_sdk/9/Acrobat9_HTMLHelp}}}
+
+
+The final example it the one seen in \Nameref{s:intro}, it uses another new command,
+\Com{defineDepQJS}. This command is used to define a new RV as a rational function of other RVs,
+and to define special JavaScript formatting, \cs{js}. The results of this command are used
+exclusively for JavaScript, and are not meant to be typeset.
+
+\takeMeasure{\string\defineDepQJS\darg{\cs{\meta{name}}}%
+\darg{\meta{numer}}\darg{\meta{denom}}\darg{\meta{script}}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\defineDepQJS{!cs(!meta(name))}{!meta(numer)}{!meta(denom)}{!meta(script)}
+\end{dCmd*}
+\noindent This function defines \cs{\meta{name}} to be
+\texttt{(\meta{numer})/(\meta{denom})}.  The expression \meta{numer} and
+\meta{denom} can be functions of RV defined earlier. The $4^{\text{th}}$
+argument is JavaScript for evaluating \cs{\meta{name}}; \meta{script} is
+accessed by \cs{js\cs{\meta{name}}} and is used from within a
+\cs{CorrAnsButton}. The $4^{\text{th}}$ argument can include such
+commands as \cs{\meta{name}}, \cs{nOf}\cs{\meta{name}}, and
+\cs{dOf}\cs{\meta{name}}. An example will perhaps illustrate.
+
+\titleQuiz*{Example~3. }
+\begin{shortquiz}*[sq3] Find the equation of the line that passes through $P$ and $Q$.
+
+We begin by defining our variables:
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+\RandomZ{\a}{-10}{9}\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m}{\d - \b}{\c - \a}
+    {rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+\defineDepQJS{\yIntercept}{\b - \a*\m}{1}
+    {rFrac((rEval(\b*\dOf\m-\a*\nOf\m))/(rEval(\dOf\m)))}
+\end{Verbatim}
+Our big problem is to compute the slope of the line, \cs{m}. I define \cs{m}
+as using \cs{defineDepQJS}. The numerator and denominator are those in the
+slope calculation, given two points. The expansion of \cs{m} is
+\verb!(\d-\b)/(\c-\a)!, and the JavaScript will perform the arithmetic
+operations. The expression that is accessed with the \cs{js} is the fourth
+argument, line~(4); here, we calculate slope as a rational number. We make a
+similar definition for the \cs{yIntercept} of the line.
+
+Below are the two points \verb!$P(\a, \b)$! and \verb!$Q(\c, \d)$!.
+\begin{questions}\setcounter{eqquestionnoi}{2}
+\RandomZ{\a}{-10}{9}\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m}{\d - \b}{\c - \a}{rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+\defineDepQJS{\yIntercept}{\b - \a*\m}{1}{rFrac((rEval( \b * \dOf\m - \a*\nOf\m ))/(rEval(\dOf\m)))}
+
+\item   $P(\,\a, \b\,)$, $Q(\,\c, \d\,)$:
+        \RespBoxMath{y = \m*x + \yIntercept}(xy){3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}\hfill
+        \CorrAnsButton{y = \js\m\space x + \js\yIntercept}*{rngCorrAnsButton}%
+        \kern1bp\sqClearButton
+\end{questions}
+\end{shortquiz}
+\vskip-.5\baselineskip
+The question is posed using \cs{RespBoxMath}.
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+$P(\,\a, \b\,)$, $Q(\,\c, \d\,)$:
+    \RespBoxMath{y=\m*x + \yIntercept}(xy)
+    {3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}
+\end{Verbatim}
+The answer is given in line~(2), and will be evaluated numerically, and compared numerically
+with the user's response.
+
+The code for the correct answer button has a new element in it
+\begin{Verbatim}[xleftmargin=20pt,numbers=left,fontsize=\small]
+\CorrAnsButton{y = \js\m\space x + \js\yIntercept}
+    *{rngCorrAnsButton}
+\end{Verbatim}
+The display of the answer is done using \cs{js}\cs{m} and
+\cs{js}\cs{yIntercept} to represent the slope and intercept as a rational
+number.
+
+Think of \cs{defineDepQJS} a convenient way of defining (JavaScript) expressions
+that will appear in \cs{RespBoxMath} and for \cs{CorrAnsButton}.
+
+\subsection{Creating Solutions to Random Quizzes}
+
+Writing a solution to a question that is based on a formula or template can be difficult.
+{\LaTeX} is not a computer algebra system, so the possibilities are limited. Still,
+\pkg{rangen} supplies the \texttt{writeRVsTo} environment to support a solution.
+
+\titleQuiz*{Example~4. }
+\begin{shortquiz}*[sq1] We create two RVs, \cs{a} and \cs{b} that are rational numbers. We want to
+add them, and present the answer as a rational number.
+\begin{Verbatim}[fontsize=\small]
+\begin{writeRVsTo}{quizzes}
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+\end{writeRVsTo}
+\end{Verbatim}
+We make that same definitions as in \textbf{\textcolor{red}{Example~1}}, but we enclose
+these definitions within the \texttt{writeRVsTo}. This environment writes its contents
+to the quiz solutions file, and also executes its contents. This way, the definitions are
+make both here, and just before the solution to this problem in the solutions file.
+\begin{questions}\setcounter{eqquestionnoi}{3}
+\begin{writeRVsTo}{quizzes}
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+\end{writeRVsTo}
+
+\item  $\displaystyle\ds\a + \ds\b =
+       \RespBoxMath[\rectW{.5in}]{ (\nOf\a * \dOf\b + \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }*{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b + \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqClearButton
+\begin{solution}\relax\RNGadd\a\b\defineQ{\ans}{\rfNumer}{\rfDenom}%
+The solution to this problem is
+\begin{equation*}
+        \boxed{\ds\a +  \ds\b = \ds\ans}
+\end{equation*}
+Did I forget to tell you that a simple command \cs{RNGadd} for adding two rational numbers
+is defined by \pkg{rangen}. Sorry about that! \dps
+\end{solution}
+\end{questions}
+\end{shortquiz}
+\vskip-.5\baselineskip
+The verbatim listing of this quiz is
+\begin{Verbatim}[fontsize=\footnotesize]
+\item  $\displaystyle\ds\a + \ds\b =
+\RespBoxMath[\rectW{.5in}]{
+    (\nOf\a*\dOf\b+\nOf\b*\dOf\a)/(\dOf\a*\dOf\b)}*{2}
+    {.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+\CorrAnsButton{rFrac(rEval(
+    \nOf\a * \dOf\b + \nOf\b * \dOf\a)/rEval(\dOf\a * \dOf\b))
+}*{rngCorrAnsButton}\kern1bp\sqClearButton
+\begin{solution}\relax\RNGadd\a\b\defineQ{\ans}{\rfNumer}{\rfDenom}%
+The solution to this problem is
+\begin{equation*}
+    \boxed{\ds\a - \ds\b = \ds\ans}
+\end{equation*}
+Did I forget to tell you that a simple command \cs{RNGadd}
+for adding two rational numbers is defined by
+\pkg{rangen}. Sorry about that! \dps
+\end{solution}
+\end{Verbatim}
+
+\newtopic\noindent
+The \texttt{writeRVsTo} has the following syntax
+
+\takeMeasure{\string\begin\darg{writeRVsTo}\darg{quizzes|exercises}}%
+\begin{dCmd*}[commandchars=!()]{\bxSize}
+\begin{writeRVsTo}{quizzes|exercises}
+    !meta(rangen commands creating RVs)
+\end{writeRVsTo}
+\end{dCmd*}
+The argument can be either the string \texttt{quizzes} or \texttt{exercises}. In the first case,
+the content of the environment is written to the solutions file for quizzes, and in the latter case,
+to the solutions file for the exercises.
+
+\bigskip
+
+That's all for now, I simply must get back to my retirement. \dps
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/randomLIP.tex b/macros/latex/contrib/rangen/examples/randomLIP.tex
new file mode 100644
index 0000000000..9917038150
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/randomLIP.tex
@@ -0,0 +1,53 @@
+\documentclass{article}
+\usepackage[tight,designv]{web}
+\usepackage{insdljs}
+\usepackage[testmode,quiet]{rangen}
+%\usepackage[seed=30,quiet]{rangen}
+
+\parindent0pt\parskip6pt
+
+\begin{document}
+
+\RandomL{\a}{1,-1}$\texttt{\string\a}=\a, \cfmt\a x$
+
+\RandomP[index=5]{\a}{1,x,x^2,x^3}$\a$
+
+\RandomI{\indx}{5}
+\RandomP[index=\indx]{\q}{1+16,\cos(\pi),\pi\sin(\pi),\frac{d}{dx}\frac{1}{2}x^2,{\int \cos(x)\,dx}}
+
+$\displaystyle\q$
+
+\RandomI{\i}{2}\i
+\RandomP[index=\i]{\q}{1+16, \frac{d}{dx}\frac{1}{2}x^2}
+\RandomP[index=\i]{\a}{17,x}
+
+$ \q = \a $
+
+\RandomP{\q}{1+16,\frac{d}{dx}\frac{1}{2}x^2}
+\RandomP[index=\iOf\q]{\a}{17,x}
+
+$\displaystyle\q = \a $
+
+\RandomI{\i}{6}RandomI=\i
+
+\RandomL[index=1]{\a}{17,\rPI,3/4,\rE,88,1/2}\a\quad index=\iOf{\a}
+
+\RandomL[index=\i]{\a}{17,\rPI,3/4,\rE,88,1/2}\a\quad index=\iOf{\a}
+
+\RandomL{\a}{17,\rPI,3/4,\rE,88,1/2}\a\quad index=\iOf{\a}
+
+In practice, \verb!\RandomI! can be used to select one of n problems. Here, we have
+selected the
+\RandomI{\i}{6}
+\ifcase\i\relax\or
+first\or
+second\or
+third\or
+fourth\or
+fifth\or
+sixth\fi\space problem.
+
+
+
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/randomQ.tex b/macros/latex/contrib/rangen/examples/randomQ.tex
new file mode 100644
index 0000000000..ec2a9081a6
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/randomQ.tex
@@ -0,0 +1,27 @@
+\documentclass{article}
+\usepackage[dvipsone]{insdljs}
+\usepackage[testmode,quiet]{rangen}
+
+
+\parindent0pt\parskip6pt
+
+\begin{document}
+
+\RandomQ{\a}[16]{1/8}{3/7}$ 1/8 \le \a \le 3/7 $
+
+\RandomQ{\b}[7]{\a}{15/16}$\a \le \b$
+
+\RandomQ[ne={0,-1}]{\n}{-3}{2/3}$x^{\efmt\n}$
+
+
+\defineQ{\a}{5}{3}\RandomQ{\b}[8]{\a*}{10}$ \a < \b $
+
+\RandomQ{\a}[8]{1}{5}\RandomQ{\b}[8]{\a}{10}$ \a \le \b $
+
+\RandomQ{\a}[8]{1}{5}\RandomQ{\b}[8]{1}{\a*}$ \a > \b $
+
+\RandomQ{\a}[2]{1}{5}\RandomQ{\b}[8]{1}{\a}$ \a \ge \b $
+
+\RandomQ{\a}[2]{1}{5}$\ifnum\typeOf\a=0\relax\cfmt\a\else(\cfmt\a)\fi x$
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/randomR.tex b/macros/latex/contrib/rangen/examples/randomR.tex
new file mode 100644
index 0000000000..69f2f2ba1a
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/randomR.tex
@@ -0,0 +1,44 @@
+\documentclass{article}
+\usepackage[tight,designv]{web}
+\usepackage{insdljs}
+\usepackage[testmode,quiet]{rangen}
+
+\parindent0pt\parskip6pt
+
+\begin{document}
+
+\RandomR{\a}{-2.3}{2.3}\a
+
+\RandomL{\a}{17,\rPI,3/4,\rE,88,1/2}
+
+Choose at random a number from the list \verb!{17,\rPI,3/4,\rE,88,1/2}!:
+The choice is $\texttt{\a}$
+
+\rule{\linewidth}{.4pt}
+
+
+\defineR{\a}{-4.5}\defineR{\b}{5.343}
+
+\RandomR[round=2,showzeros]{\c}{\a}{\b}
+
+Random Real from the interval \texttt{[\a, \b ]} is \texttt{\c}
+
+\RandomR[round=2]{\a}{0}{10}\RandomR[round=2]{\b}{0}{12}
+
+\RandomR[round=2]{\c}{\a}{\b}
+
+A random Real taken from a random interval \texttt{[\a, \b ]} is \texttt{\c}
+
+
+\rule{\linewidth}{.4pt}
+
+
+\RandomR[round=2,showzeros]{\b}{0}{9.5}
+\RandomR[round=2]{\a}{-3}{\b}
+
+We require \verb!\b! to be greater than \texttt{\string\a}:
+$ \texttt{\string\b=\b} > \texttt{\a=\string\a} $
+
+$\texttt{\string\a}=\a\approx\nOf{\a}/\dOf{\a}$
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/randomZ.tex b/macros/latex/contrib/rangen/examples/randomZ.tex
new file mode 100644
index 0000000000..233b8efd16
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/randomZ.tex
@@ -0,0 +1,38 @@
+\documentclass{article}
+\usepackage[dvipsone]{insdljs}
+\usepackage[testmode,quiet]{rangen}
+
+
+
+\parindent0pt\parskip6pt
+
+\begin{document}
+
+\RandomZ[ne={0,-1}]{\n}{-2}{2}$x^{\efmt\n}$
+
+\RandomZ[ne=\zZero]{\b}{-1}{1}
+The value of \texttt{\string\b=\b} and should be
+different from zero. Is it?
+
+\RandomZ{\a}{1}{5}\RandomZ{\b}{\a*}{10}$ \a < \b $
+
+\RandomZ{\a}{1}{5}\RandomZ{\b}{\a*}{10}$ \a \le \b $
+
+\RandomZ{\a}{1}{5}\RandomZ{\b}{1}{\a*}$ \a > \b $
+
+\RandomZ{\a}{1}{5}\RandomZ{\b}{1}{\a}$ \a \ge \b $
+
+\RandomZ[ne=0]{\b}{-1}{1}Is \texttt{\string\b}=\b\space zero?
+
+\RandomL{\a}{-2,4,6,-12,9,5,17}Select a number from a list \texttt{\string\a=\a}
+
+\RandomS{\si}\RandomS{\sii}
+\RandomZ[ne=0]{\a}{-5}{5}
+\RandomZ[ne=0]{\b}{1}{5}
+\RandomZ[ne=0]{\c}{1}{5}
+\RandomZ[ne=0]{\n}{1}{5}
+
+$ \cfmt\a x^{\efmt\n} \si \cfmt\b x \sii \c $
+
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/rangen_fp.tex b/macros/latex/contrib/rangen/examples/rangen_fp.tex
new file mode 100644
index 0000000000..e7e4fcffda
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/rangen_fp.tex
@@ -0,0 +1,24 @@
+\documentclass{article}
+\usepackage[tight,dvipsone,designv,nodirectory]{web}
+\usepackage{insdljs}
+\usepackage[testmode,quiet]{rangen}
+\usepackage{fp}
+
+\parindent0pt\parskip6pt
+
+\begin{document}
+
+\RandomQ{\a}[6]{2}{4}\RandomQ{\b}[6]{2}{4}\RandomS{\thisop}
+\gcd{\dOf\a}{\dOf\b}
+\FPeval\lcd{clip((\dOf\a)*(\dOf\b)/\thegcd)}
+\FPeval\si{clip(\lcd/(\dOf\a))}
+\FPeval\sii{clip(\lcd/(\dOf\b))}\def\thisop{+}
+\if\thisop+\FPeval\finalnum{clip((\si)*(\nOf\a)+(\sii)*(\nOf\b))}
+\else\FPeval\finalnum{clip((\si)*(\nOf\a)-(\sii)*(\nOf\b))}\fi
+\defineQ{\ans}{\finalnum}{\lcd}
+$$
+\ds\a \thisop \ds\b = \frac{(\si)(\nOf\a)+(\sii)(\nOf\b)}{\lcd}
+    = \frac{\finalnum}{\lcd}\ifnum\lcd=\dOf\ans\else =\ds\ans\fi
+$$
+
+\end{document}
diff --git a/macros/latex/contrib/rangen/examples/rangen_tst.tex b/macros/latex/contrib/rangen/examples/rangen_tst.tex
new file mode 100644
index 0000000000..c89a5964ce
--- /dev/null
+++ b/macros/latex/contrib/rangen/examples/rangen_tst.tex
@@ -0,0 +1,280 @@
+\documentclass{article}
+\usepackage[fleqn]{amsmath}
+\usepackage[tight,designiii,usesf]{web}
+\usepackage{exerquiz}
+\usepackage[equations,ImplMulti,indefIntegral,limitArith,nodec]{dljslib}
+\usepackage[quiet,testmode]{rangen}
+
+\title{Experiments in Creating Random Problems}
+\author{D. P. Story}
+\subject{Test file for the rangen Package}
+\keywords{LaTeX, rangen, quizzes, random}
+
+\university{NORTHWEST FLORIDA STATE COLLEGE\\
+   Department of Mathematics}
+\email{dpstory@acrotex.net}
+\version{1.0}
+
+%\nocopyright
+\norevisionLabel
+\makeatletter
+\def\eq@textFont{/TiRo}
+\makeatother
+
+\everyTextField{\BG{1 1 1}}
+\everyCheckBox{\BG{1 1 1}}
+\everyRespBoxMath{\rectW{1.9in}\textSize{0}}
+\everyRespBoxTxt{\rectW{1.9in}\textSize{0}}
+
+\newcommand{\cs}[1]{\texttt{\char`\\#1}}
+
+\renewcommand\nodecAlertMsg{%
+    "A decimal answer is not acceptable here.
+     Please express your answer using a fraction."}
+\newenvironment{eqComments}[1][\strut]{\smallskip\leftskip-\labelwidth
+\item[]\textbf{\textcolor{blue}{#1}}}{\par\smallskip}
+
+\begin{document}
+
+\maketitle
+
+\begin{shortquiz}*[sq] Answer each of the following. Passing is 100\%.
+
+\begin{questions}
+
+\begin{eqComments}[Arithmetic]\end{eqComments}
+
+%% addition
+\RandomQ{\a}[9]{1/8}{6/7}\RandomQ{\b}[8]{1/16}{15/16}
+
+\item  $\displaystyle \ds\a +  \ds\b =
+       \RespBoxMath{ (\nOf\a * \dOf\b + \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b + \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+% subtraction
+\RandomQ{\a}[16]{1/16}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+
+\item  $\displaystyle  \ds\a - \ds\b =
+       \RespBoxMath{ (\nOf\a * \dOf\b - \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b - \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+% subtraction
+\RandomQ{\a}[16]{1/8}{15/16}\RandomQ[ne=\a]{\b}[16]{1/8}{15/16}
+
+\item  $\displaystyle \ds\a - \ds\b =
+       \RespBoxMath{ (\nOf\a * \dOf\b - \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b - \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\begin{eqComments}
+This next problem illustrates the use of \cs{RandomL} and \cs{RansomAS}. The summands are
+determined from a list of rational numbers. Addition or subtraction of the summands is determined
+by \cs{RandomAS}.
+\end{eqComments}
+
+%% Random add/subtr using RandomL and RandomAS
+\RandomL{\a}{1/2,2/3,5/3,2/5,6/5}\RandomL{\b}{4/3,3/4,8/7,3/2}\RandomS{\as}
+
+\item $\displaystyle \ds\a \as  \ds\b =
+       \RespBoxMath{ (\nOf\a * \dOf\b \as \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b \as \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+
+\begin{eqComments}
+This next example illustrates how you can create a solution to a problem. This is a simple
+addition problem using the built-in command \cs{qAdd}. Solutions to more advanced problems
+might be obtained using the \textsf{fp} package.
+\end{eqComments}
+
+\begin{writeRVsTo}{quizzes}
+\RandomQ{\a}[9]{1/8}{6/7}\RandomQ{\b}[7]{1/16}{15/16}
+\end{writeRVsTo}
+
+%% addition
+\item $\displaystyle \ds\a +  \ds\b =
+       \RespBoxMath{ (\nOf\a * \dOf\b + \nOf\b * \dOf\a )/( \dOf\a * \dOf\b ) }*{2}{.0001}{[0,2]}[{priorParse: \Array(nodec,NoAddOrSub)}]$\hfill
+       \CorrAnsButton{rFrac( rEval( \nOf\a * \dOf\b + \nOf\b * \dOf\a )/rEval( \dOf\a * \dOf\b ) )}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\begin{solution}\relax\RNGadd\a\b\defineQ{\ans}{\rfNumer}{\rfDenom}%
+The solution to this problem is
+\begin{equation*}
+        \boxed{\ds\a +  \ds\b = \ds\ans}
+\end{equation*}
+\end{solution}
+
+
+\newpage
+\begin{eqComments}[Definite Integrals]\end{eqComments}
+
+\RandomQ{\a}[8]{1/4}{7/6}
+\RandomZ{\b}{1}{3}
+\RandomQ{\n}[8]{1/2}{3/2}
+\RandomZ[ne=0]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+
+\RandomQ{\a}{1/6}{2/9}
+\RandomZ{\b}{1}{10}
+\RandomQ[ne={0,-1}]{\n}[5]{-1}{1}
+\RandomZ[ne=0]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\RandomZ{\a}{1}{6}
+\RandomZ{\b}{\a*}{8}
+\RandomZ{\n}{1}{5}
+\RandomZ[ne=0]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rFrac(rEval(\c ( (\b)^(\n+1)-(\a)^(\n+1)))/rEval(\n+1))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\RandomZ{\a}{1}{5}
+\RandomZ{\b}{\a*}{10}
+\RandomQ[ne={0,-1}]{\n}{-3}{2/3}
+\RandomZ[ne=0]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\RandomQ{\a}{1/4}{2/3}
+\RandomQ{\b}{\a*}{7/6}
+\RandomQ[ne={0,-1}]{\n}{-3}{2/3}
+\RandomZ[ne=0]{\c}{-3}{3}
+
+\item   $\displaystyle\int_{\a}^{\b} \cfmt\c x^{\efmt\n}\,dx =
+        \RespBoxMath{\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1)}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\c((\b)^(\n+1)-(\a)^(\n+1))/(\n+1))}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\begin{eqComments}
+This next problem was created from random lists of values using \cs{RandomL}.
+\end{eqComments}
+
+\RandomL{\c}{1/6,1/4,1/6,1/2}
+\RandomL{\a}{1,2,3,4,5,6}
+\ifnum\a=1
+    \def\strAns{sin(PI/\dOf\c)}
+\else
+    \def\strAns{(1/\a)(sin(\a*PI/\dOf\c))}
+\fi
+
+\item $\displaystyle\int_0^{\pi/\dOf\c} \cos(\cfmt\a x) \,dx =
+        \RespBoxMath{(1/\a)(sin(\a*PI/\dOf\c))}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{rEval(\strAns)}*{rngCorrAnsButton\RNGprintf{\%.4f}}\kern1bp\sqTallyBox
+
+
+\newpage
+\begin{eqComments}[Indefinite Integration]\end{eqComments}
+
+\RandomQ{\a}{1/6}{3/2}
+\RandomQ{\b}{1/6}{3/2}
+\RandomZ{\c}{1}{3}
+
+\item   $\displaystyle\int \cds\a x^2 + \ds\b x + \c\,dx =
+        \RespBoxMath{(\a/3)x^3+(\b/2) x^2 + \c x}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{(rFrac(rEval(\nOf\a)/rEval(3*\dOf\a))) x^3
+            + (rFrac(rEval(\nOf\b)/rEval(2*\dOf\b))) x^2
+            + \c x + C}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\RandomQ{\a}{1/3}{3}
+\RandomQ{\b}{1/6}{3/2}
+\RandomZ{\c}{1}{3}
+
+\item   $\displaystyle\int \cds\a x^2 + \ds\b x + \c\,dx =
+        \RespBoxMath{(\a/3)x^3+(\b/2) x^2 + \c x}{3}{.0001}{[0,2]}$\hfill
+        \CorrAnsButton{(rFrac(rEval(\nOf\a)/rEval(3*\dOf\a))) x^3
+            + (rFrac(rEval(\nOf\b)/rEval(2*\dOf\b))) x^2
+            + \c x + C}*{rngCorrAnsButton}\kern1bp\sqTallyBox
+
+\newpage
+\begin{eqComments}[Differentiation]\end{eqComments}
+
+\RandomQ[ne=0]{\c}[4]{-2}{2}
+\RandomQ[ne=0]{\n}[1]{-3}{2}
+
+\item   $\displaystyle \frac{d}{dx} \cds\c x^{\efmt\n} =
+        \ifnum\nOf\n=\dOf\n
+            \RespBoxMath{\c}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{rFrac(\nOf\c/\dOf\c)}*{rngCorrAnsButton}%
+        \else
+            \RespBoxMath{\c*\n*x^(\n-1)}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{rFrac(rEval(\nOf\c*\nOf\n)/rEval(\dOf\c*\dOf\n))
+                x^(rFrac(rEval(\nOf\n-\dOf\n)/\dOf\n))}*{rngCorrAnsButton}%
+        \fi
+        \kern1bp\sqTallyBox
+
+\begin{eqComments}
+This next problem uses a random sign, defined by \cs{RandomS}.
+\end{eqComments}
+
+\RandomQ{\c}[4]{2}{3}\RandomS{\s}
+\RandomQ[ne=0]{\n}[2]{-3}{2}
+
+\item   $\displaystyle \frac{d}{dx} \cfmt\s\ds\c x^{\efmt\n} =
+        \ifnum\nOf\n=\dOf\n
+            \RespBoxMath{\s\c}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{\s\nOf\c/\dOf\c}*{rngCorrAnsButton}%
+        \else
+            \RespBoxMath{\s\c*\n*x^(\n-1)}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{rFrac(rEval(\s\nOf\c*\nOf\n)/rEval(\dOf\c*\dOf\n))
+                x^(rFrac(rEval(\nOf\n-\dOf\n)/\dOf\n))}*{rngCorrAnsButton}%
+        \fi
+        \kern1bp\sqTallyBox
+
+
+\RandomQ[ne=0]{\c}[4]{-2}{5}
+\RandomQ{\n}[4]{2}{5}
+
+\item   $\displaystyle \frac{d}{dx} \ds\c x^{\efmt\n} =
+        \ifnum\nOf\n=\dOf\n
+            \RespBoxMath{\c}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{\nOf\c/\dOf\c}*{rngCorrAnsButton}%
+        \else
+            \RespBoxMath{\c*\n*x^(\n-1)}{3}{.0001}{[0,2]}$\hfill
+            \CorrAnsButton{rFrac(rEval(\nOf\c*\nOf\n)/rEval(\dOf\c*\dOf\n))
+                x^(rFrac(rEval(\nOf\n-\dOf\n)/\dOf\n))}*{rngCorrAnsButton}%
+        \fi
+        \kern1bp\sqTallyBox
+
+\newpage
+
+\begin{eqComments}[Analytic Geometry]\end{eqComments}
+
+\RandomZ{\a}{-10}{9}
+\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}
+\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m}{\d - \b}{\c - \a}{rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+\defineDepQJS{\yIntercept}{\b - \a*\m}{1}{rFrac((rEval( \b * \dOf\m - \a*\nOf\m ))/(rEval(\dOf\m)))}
+
+
+\item   Let $P(\,\a, \b\,)$ be a point and $Q(\,\c, \d\,)$ be a point. Find the equation of the line that
+        passes through $P$ and $Q$.\par\kern3pt
+        \RespBoxMath{y = \m*x + \yIntercept }(xy){3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}\hfill
+        \CorrAnsButton{y = \js\m\space x + \js\yIntercept}*{rngCorrAnsButton}%
+        \kern1bp\sqTallyBox
+
+\RandomZ{\a}{-10}{9}
+\RandomZ{\b}{-10}{9}
+\RandomZ{\c}{\a*}{10}
+\RandomZ{\d}{\b*}{10}
+\defineDepQJS{\m}{\d - \b}{\c - \a}{rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+\defineDepQJS{\yIntercept}{\b - \a*\m}{1}{rFrac((rEval( \b * \dOf\m - \a*\nOf\m ))/(rEval(\dOf\m)))}
+
+\item  Let $P(\,\a, \b\,)$ be a point and $Q(\,\c, \d\,)$ be a point. Find the equation of the line that
+        passes through $P$ and $Q$.\par\kern3pt
+        \RespBoxMath{y = \m*x + (\b - \a*\m) }(xy){3}{.0001}{[0,2]x[0,2]}*{ProcRespEq}\hfill
+        \CorrAnsButton{y = \js\m\space x + \js\yIntercept}*{rngCorrAnsButton}%
+        \kern1bp\sqTallyBox
+
+\end{questions}
+\end{shortquiz}
+\begin{flushright}
+\sqClearButton\kern1bp\sqTallyTotal
+\end{flushright}
+\end{document}
diff --git a/macros/latex/contrib/rangen/rangen.dtx b/macros/latex/contrib/rangen/rangen.dtx
new file mode 100644
index 0000000000..637775f9c3
--- /dev/null
+++ b/macros/latex/contrib/rangen/rangen.dtx
@@ -0,0 +1,1988 @@
+%\iffalse
+%<*copyright>
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Rangen.sty package,                       2016-02-19 %%
+%% Copyright (C) 1999-2016  D. P. Story                 %%
+%%   dpstory@uakron.edu                                 %%
+%%                                                      %%
+%% This program can 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 (at your option) any later version.      %%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%</copyright>
+%<package>\NeedsTeXFormat{LaTeX2e}[1997/12/01]
+%<package>\ProvidesPackage{rangen}
+%<package> [2014/10/17 v1.4 Rangen: Generate Random Questions (dps)]
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage[colorlinks,hyperindex]{hyperref}
+%\pdfstringdefDisableCommands{\let\\\textbackslash}
+%\EnableCrossrefs \CodelineIndex
+\begin{document}
+  \GetFileInfo{rangen.sty}
+%  \settowidth{\oddsidemargin}{0pt}%
+%   \setlength{\evensidemargin}{0pt}
+%   \setlength{\marginparsep}{0pt}
+%    \setlength{\marginparwidth}{0pt}
+%  \setlength\textwidth{6in}
+%  \hoffset=.5in
+%  \hsize = 6in
+  \title{\textsf{Rangen}\texorpdfstring{\\}{:} Random Generation of Integer, Rational, and Real Numbers with
+    Applications to the \texttt{exercise}, \texttt{quiz}, and \texttt{shortquiz} environments of \textsf{Exerquiz}}
+  \author{D. P. Story\\
+    Email: \texttt{dpstory@uakron.edu}}
+  \date{processed \today}
+  \maketitle
+  \tableofcontents
+  \let\Email\texttt
+  \DocInput{rangen.dtx}
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+% \MakeShortVerb{|}
+% \StopEventually{}
+%
+% \DoNotIndex{\def,\edef,\gdef,\xdef,\global,\long,\let}
+% \DoNotIndex{\expandafter,\string,\the,\ifx,\else,\fi}
+% \DoNotIndex{\csname,\endcsname,\relax,\begingroup,\endgroup}
+% \DoNotIndex{\DeclareTextCommand,\DeclareTextCompositeCommand}
+% \DoNotIndex{\space,\@empty,\special}
+%
+%    \begin{macrocode}
+%<*package>
+%    \end{macrocode}
+% \section{Introduction}
+%
+% This package provides some  commands for creating randomly generated integers, rational,
+% and real numbers.  There are options for specifying constraints on the generation of the numbers.
+% Companion JavaScript functions are developed to use these random numbers as part of a
+% question in a \texttt{shortquiz} or \texttt{quiz}. The syntax of this package can be used
+% to pose number-related questions, the JavaScript can be used to create the answer to the
+% question based on a formula. You'll have to see it to believe it.
+%
+% \section{The Main Code}
+%
+% \subsection{Declare Options}
+%
+% This package has one option, other options are passed to the really nice \textsf{lcg} Package,
+% by Erich Janka (\texttt{janka@utanet.at}).
+%    \begin{macrocode}
+\newcount\seedCnt
+\DeclareOption{testmode}{%
+    \InputIfFileExists{\jobname.seed}{}{\def\thisseed{1}}%
+    \PassOptionsToPackage{seed=\thisseed}{lcg}%
+    \AtEndOfPackage{\reseedEachRun}%
+}
+\def\reseedEachRun{%
+    \seedCnt=\thisseed
+    \advance\seedCnt1\relax
+    \newwrite \rngWrite
+    \immediate\openout\rngWrite \jobname.seed
+    \immediate\write\rngWrite{\string\def\string\thisseed{\the\seedCnt}}
+    \immediate\closeout\rngWrite
+}
+\def\RNG@Dec{.}
+\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{lcg}}
+\ProcessOptions
+\RequirePackage{lcg}[2008/09/10]
+%    \end{macrocode}
+% Save the seed value so we can reproduce the same pseudo-random number sequence.
+%    \begin{macrocode}
+\edef\rng@saveSeed{\the\cr@nd}
+%    \end{macrocode}
+% There are three data types: Integer, Rational, and Real. The following macros
+% gives each of these types a numerical value, 0, 1 and 2, respectively.
+%    \begin{macrocode}
+\newcount\loopCnt
+\def\maxLoopLimit{10}
+\def\typeCodeForz{0}
+\def\typeCodeForq{1}
+\def\typeCodeForr{2}
+%    \end{macrocode}
+% Some scratch count registers
+%    \begin{macrocode}
+\newcount\rng@cnta
+\newcount\rng@cntb
+%    \end{macrocode}
+% A random variable is specified using a control sequence, e.g. \cs{a}. The following macro
+% extracts the underlying name of the command, e.g. \verb+\@gtVarName{\a}+ expands to \texttt{a},
+% and returns the name as the expansion of the macro \cs{@varName}.
+%    \begin{macrocode}
+\def\@getVarName#1{%
+    \edef\@varName{\expandafter\@gobble\string#1}%
+}
+%    \end{macrocode}
+% The command \cs{@getVarType} takes one argument, a random variable, e.g., \cs{a}. This
+% command defines a macro \cs{varType} which expands to the data type the random variable is.
+%    \begin{macrocode}
+\def\@getVarType#1{%
+    \@getVarName{#1}\edef\varType{\csname typeof@\@varName\endcsname}}
+%    \end{macrocode}
+% \subsection{GCD and Rational Reduction Commands}
+%    \begin{macro}{\gcd}
+% Here we use Euclid's Algorithm to find the greatest common divisor of two integers.
+%    \begin{macrocode}
+\def\gcd#1#2{{% #1 = a, #2 = b
+    \ifnum#2=0 \edef\next{#1}\else
+        \@tempcnta=#1 \@tempcntb=#2 \divide\@tempcnta by\@tempcntb
+        \multiply\@tempcnta by\@tempcntb  % q*b
+        \@tempcntb=#1
+        \advance\@tempcntb by-\@tempcnta % remainder in \@tempcntb
+        \ifnum\@tempcntb=0
+            \@tempcnta=#2
+            \ifnum\@tempcnta < 0 \@tempcnta=-\@tempcnta\fi
+            \xdef\gcd@next{\noexpand%
+                \def\noexpand\thegcd{\the\@tempcnta}}%
+        \else
+            \xdef\gcd@next{\noexpand\gcd{#2}{\the\@tempcntb}}%
+        \fi
+    \fi}\gcd@next
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\lcm}
+% Now compute the least common multiple
+%    \begin{macrocode}
+\def\lcm#1#2{% #1 = a, #2 = b
+    \gcd{#1}{#2}%
+    {\@tempcnta=#1
+    \multiply\@tempcnta by#2
+    \divide\@tempcnta by\thegcd
+    \xdef\thelcm{\the\@tempcnta}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\amodb}
+% Modular arithmetic \texttt{a mod b}, returns its results
+% as a macro \cs{retnmod}.
+%    \begin{macrocode}
+\def\amodb#1#2{% #1 = a, #2 = b
+    {\@tempcnta=#1
+    \divide\@tempcnta by#2
+    \multiply\@tempcnta by#2
+    \@tempcntb=#1
+    \advance\@tempcntb by-\@tempcnta
+    \xdef\retnmod{\the\@tempcntb}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\reduceFrac}
+% Reduce a fraction to lowest terms. The first argument is the numerator and the second
+% argument is the denominator. This command computes the \texttt{gcd} of the two integers,
+% divides each by the \texttt{gcd}, and returns the results in the two scratch count
+% registers \cs{@tempcnta} and \cs{@tempcntb}.
+%    \begin{macrocode}
+\newcommand\reduceFrac[2]
+{%
+    \gcd{#1}{#2}{\@tempcnta=#1 \divide\@tempcnta by\thegcd
+    \@tempcntb=#2 \divide\@tempcntb by\thegcd
+    \ifnum\@tempcntb<0\relax
+%    \end{macrocode}
+% Always have the denominator as positive.
+%    \begin{macrocode}
+        \@tempcntb=-\@tempcntb
+        \@tempcnta=-\@tempcnta
+    \fi
+    \xdef\rfNumer{\the\@tempcnta}\xdef\rfDenom{\the\@tempcntb}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\convertRatTo}
+% Converts a fraction \texttt{a/b} (\texttt{\#1/\#2}) to a denominator of \texttt{\#3}. Will return
+% new numerator in \cs{rnd@Cnta} register.  This will be exact if
+% \texttt{\#2} divides \texttt{\#3}.
+%    \begin{macrocode}
+\def\convertRatTo#1#2#3{{%
+    \@tempcnta=#3
+    \multiply\@tempcnta by#1
+    \divide\@tempcnta by#2
+    \xdef\rng@retn@num{\the\@tempcnta}%
+}}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\RNGadd}
+% This is the support for rational arithmetic (addition and subtraction).
+% Adds two rational numbers, \texttt{\#1} and \texttt{\#2} together. These two rational numbers must have been defined
+% already, possibly by \cs{defineQ}. Usage: \verb+\RNGadd\a\b+. This macro returns a rational number:
+% the numerator in the \cs{rfNumer} command, and the denominator in the \cs{rfDenom} command.
+% For example,
+%\begin{verbatim}
+%\defineQ\a{1}{3}\defineQ\b{3}{5}\RNGadd\a\b
+%\makeatletter
+%The sum of $\frac{\nOf\a}{\dOf\a} + \frac{\nOf\b}{\dOf\b}
+%        = \frac{\rfNumer}{\rfDenom}$
+%\makeatother
+%\end{verbatim}
+%This code typesets as $\frac{1}{3}+\frac{3}{5}=\frac{14}{15}$.
+%    \begin{macrocode}
+\newcommand\RNGadd[2]{%
+    \rng@cnta=\nOf#1 \multiply\rng@cnta by\dOf#2
+    \rng@cntb=\nOf#2 \multiply\rng@cntb by\dOf#1
+    \advance\rng@cnta by\the\rng@cntb
+    \rng@cntb=\dOf#1 \multiply\rng@cntb by\dOf#2
+    \reduceFrac{\the\rng@cnta}{\the\rng@cntb}
+}
+%    \end{macrocode}
+%    \end{macro}
+% This is a simple macro for detecting if the argument \texttt{\#1}
+% is a macro or not. Used when interval definitions of the
+% \cs{RandomZ/Q/R} macros.
+%    \begin{macrocode}
+\def\rng@isControl#1{\@ifundefined{\expandafter\@gobble\string#1}%
+    {\let\rng@isC@ntrol=0}{\let\rng@isC@ntrol=1}}
+%    \end{macrocode}
+% This command determines if its argument has an \texttt{*}
+% prefixed or post-fixed to its argument.
+% If \cs{rng@isStariii} equals \texttt{*}, then an \texttt{*} exists.
+% \begin{itemize}
+%   \item If there is no \texttt{*}, then the argument is \texttt{\#1}
+%   \item \cs{rng@isStariii} equals \texttt{*}, there is \texttt{*},
+%   If the argument has the form \cs{*a}, then \cs{rng@isStari} is \cs{@empty}
+%   and the argument, stripped of the \texttt{*}, is given as \cs{rng@isStarii}
+%   \item \cs{rng@isStariii} equals \texttt{*}, there is \texttt{*},
+%   If the argument has the form \cs{a*}, then \cs{rng@isStarii} is \cs{@empty}
+%   and the argument, stripped of the \texttt{*}, is given as \cs{rng@isStari}
+%\end{itemize}
+%    \begin{macrocode}
+\def\rng@existStar#1{\rng@existSt@r#1**\@nil}
+\def\rng@existSt@r#1*#2*#3\@nil{\def\rng@isStari{#1}%
+    \def\rng@isStarii{#2}\def\rng@isStariii{#3}%
+}
+\def\rng@NameEndpoint#1{%
+    \ifx\rng@isStari\@empty
+        \edef#1{\expandafter\noexpand\rng@isStarii}%
+    \else\ifx\rng@isStarii\@empty
+        \edef#1{\expandafter\noexpand\rng@isStari}%
+    \fi\fi
+}
+%    \end{macrocode}
+% \subsection{Define an Integer and a Rational}
+%    \begin{macro}{\defineZ}
+% Define a integer for use in other macros.
+%    \begin{macrocode}
+\newcommand\defineZ[2]
+{%
+    \@getVarName#1\relax
+    \expandafter\def\csname typeof@\@varName\endcsname{0}%
+    \expandafter\edef\csname n@\@varName\endcsname{#2}%
+    \expandafter\edef\csname d@\@varName\endcsname{1}%
+    \edef\display@TeXfmt{#2}\edef\inline@TeXfmt{#2}%
+    \ifnum#2=1\relax\rng@makeOneFmtDefns
+    \else\ifnum#2=-1\relax\rng@makeMinusOneFmtDefns
+    \else\rng@makeOtherFmtDefns\fi\fi
+    \expandafter\let\csname\@varName*\endcsname\display@TeXfmt
+    \expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
+    \expandafter\edef\csname\@varName\endcsname{#2}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\defineQ}
+% The following macro defines a rational number. Usage
+% \verb+\defineQ\a{1}{2}+. This defines the rational number 1/2 and
+% gives it a name, \cs{a}.
+%    \begin{macrocode}
+\newcommand\defineQ[3]
+{%
+    \@getVarName#1\relax
+    \expandafter\def\csname typeof@\@varName\endcsname{1}%
+    \expandafter\edef\csname n@\@varName\endcsname{#2}%
+    \expandafter\edef\csname d@\@varName\endcsname{#3}%
+    \edef\display@TeXfmt{\frac{#2}{#3}}\edef\inline@TeXfmt{#2/#3}%
+    \ifnum#2=#3\relax\rng@makeOneFmtDefns
+    \else\ifnum#2=-#3\relax\rng@makeMinusOneFmtDefns
+    \else\rng@makeOtherFmtDefns\fi\fi
+    \expandafter\let\csname\@varName*\endcsname\display@TeXfmt
+    \expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
+    \expandafter\edef\csname\@varName\endcsname{#2/#3}%
+    \simplifyCurrentQ
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\defineR}
+% This macro computes: (1) \cs{rng@intpart}; (2) \cs{rng@fracpart};
+% (3) \cs{rndnDec} (the number of decimals of the fractional part);
+% (4) \cs{rndPower} (the power of ten determined by \cs{rndnDec}).
+%    \begin{macrocode}
+\newcommand{\defineR}[2]{%
+    \@getVarName{#1}\RNGparseDec{#2}%
+    \expandafter\def\csname typeof@\@varName\endcsname{2}%
+    \reduceFrac{\rng@intpart\rng@fracpart}{\rndPower}%
+    \expandafter\edef\csname n@\@varName\endcsname{\rfNumer}%
+    \expandafter\edef\csname d@\@varName\endcsname{\rfDenom}%
+    \edef\display@TeXfmt{#2}\edef\inline@TeXfmt{#2}%
+    \ifnum\rfNumer=1\relax\rng@makeOneFmtDefns
+    \else\ifnum\rfNumer=-1\relax\rng@makeMinusOneFmtDefns
+    \else\rng@makeOtherFmtDefns\fi\fi
+    \expandafter\let\csname\@varName*\endcsname\display@TeXfmt
+    \expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
+    \expandafter\edef\csname\@varName\endcsname{#2}%
+    \simplifyCurrentR
+}
+\newcommand{\simplifyCurrentR}{%
+    \ifnum\csname d@\@varName\endcsname=1
+    \expandafter\defineZ
+    \csname\@varName\endcsname{\csname n@\@varName\endcsname}\fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macrocode}
+\def\rng@makeOneFmtDefns{%
+% inline
+    \expandafter\def\csname\@varName!e\endcsname{}%
+    \expandafter\def\csname\@varName!c\endcsname{}%
+% display
+    \expandafter\def\csname\@varName*e\endcsname{}%
+    \expandafter\def\csname\@varName*c\endcsname{}%
+}
+\def\rng@makeMinusOneFmtDefns{%
+% inline
+    \expandafter\def\csname\@varName!e\endcsname{-1}%
+    \expandafter\def\csname\@varName!c\endcsname{-}%
+% display
+    \expandafter\def\csname\@varName*e\endcsname{-1}%
+    \expandafter\def\csname\@varName*c\endcsname{-}%
+}
+\def\rng@makeOtherFmtDefns{%
+% inline
+    \expandafter\let\csname\@varName!e\endcsname\inline@TeXfmt
+    \expandafter\let\csname\@varName!c\endcsname\inline@TeXfmt
+% display
+    \expandafter\let\csname\@varName*e\endcsname\display@TeXfmt
+    \expandafter\let\csname\@varName*c\endcsname\display@TeXfmt
+}
+%    \end{macrocode}
+%
+% \subsection{Parse a Number}
+%
+% \subsubsection{Parsing a Rational}
+%
+%    \begin{macro}{\RNGparseRat}
+%    \begin{macrocode}
+\def\RNGparseRat#1{\expandafter\@chkslash#1//\@nil}
+\def\@chkslash#1/#2/#3\@nil{%
+    \def\rng@num{#1}\def\rng@denom{#2}%
+    \def\rng@parseQ@iii{#3}%
+    \ifx\rng@denom\@empty\def\rng@denom{1}\fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \subsubsection{Parsing a Real}
+%
+%    \begin{macro}{\RNGparseDec}
+% The argument \texttt{\#1} is a decimal number (or integer)
+% This macro computes: (1) \cs{rng@intpart}; (2) \cs{rng@fracpart};
+% (3) \cs{rndnDec} (the number of decimals of the fractional part);
+% (4) \cs{rndPower} (the power of ten determined by \cs{rndnDec}).
+% These variables will be overwritten the next time this command
+% is executed.
+%    \begin{macrocode}
+\newcommand{\RNGparseDec}[1]{\edef\parse@argi{#1}%
+    \expandafter\@chkdec\parse@argi..\@nil}
+\def\@chkdec#1.#2.#3\@nil{%
+    \def\rng@intpart{#1}\def\rng@fracpart{#2}%
+    \def\rng@parseR@iii{#3}\rng@getnDec}
+\def\rng@getnDec{%
+    \begingroup
+        \ifx\rng@fracpart\@empty\gdef\rndnDec{0}\gdef\rndPower{1}\else
+        \count0=0\relax\count2=1\relax
+        \expandafter\cntNumDec\rng@fracpart\end\fi
+    \endgroup}
+\def\cntNumDec#1#2\end{%
+    \advance\count0by1
+    \def\rng@arg{#2}%
+    \ifx\rng@arg\@empty
+        \xdef\rndnDec{\the\count0}%
+        \xdef\rndPower{1\@nameuse{rng@tz\the\count0}}%
+        \let\rng@next\relax
+    \else
+        \def\rng@next{\cntNumDec#2\end}%
+    \fi\rng@next
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\nDivisionsPowerOfTen}
+% This is a control of how many nodes to create in an interval
+% of real numbers, as defined by \cs{RandomR}. The argument is
+% an integer between 1 and 4 inclusive.
+%    \begin{macrocode}
+\newcommand{\nDivisionsPowerOfTen}[1]{%
+    \begingroup
+    \count0=#1\relax
+    \ifnum\count0>4\relax
+        \PackageError{rangen}{Number of subdivisions too large}%
+        {Reduce the argument of \string\nDivisionsPowerOfTen.}%
+    \else
+        \ifnum\count0<1\relax
+        \PackageError{rangen}{Number of subdivisions too large}%
+        {Increase the argument of \string\nDivisionsPowerOfTen.}%
+    \fi\fi
+    \xdef\RNGpowerOfTen{1\@nameuse{rng@tz#1}}%
+    \endgroup
+}
+\nDivisionsPowerOfTen{2}
+%    \end{macrocode}
+%    \end{macro}
+%\subsection{Creating Random Things}
+%\subsubsection{Random Integer}
+%    \begin{macro}{\RandomZ}
+% Randomly generates an integer in the specified range of values.
+%\begin{verbatim}
+%[#1] Optional parameter to modify the variable.
+% #2  The random variable being defined, e.g., \a
+% #3  lower limit of random integer
+% #4  upper limit of random integer
+%\end{verbatim}
+%    \begin{macrocode}
+\newcommand\RandomZ[4][]
+{%
+    \def\rng@ne@values{}%
+    \setkeys{rangen}{ne,#1}%
+%    \end{macrocode}
+% Now see if there is an \texttt{*}, and get un-stripped
+% argument.
+%
+% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
+% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
+% Check the left endpoint:
+%    \begin{macrocode}
+    \let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
+    \let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
+%    \end{macrocode}
+% \paragraph*{Left endpoint.}
+%    \begin{macrocode}
+    \rng@existStar{#3}\rng@NameEndpoint{\rng@LEP}%
+    \if\rng@isStariii*\edef\tmp@exp{%
+        \noexpand\rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
+%    \end{macrocode}
+% The LEP is a control sequence with a star, we need to increment the value
+% of \cs{rng@LEP} to the next largest integer.
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
+            \ifcase\varType % integer
+                \rng@cnta=\rng@LEP
+            \or % rational
+                \rng@dima=\expandafter\nOf\rng@LEP pt
+                \divide\rng@dima by\expandafter\dOf\rng@LEP
+                \defineR{\rng@LEP}{\strip@pt\rng@dima}%
+                \RNGparseDec{\rng@LEP}%
+                \rng@cnta=\rng@intpart
+            \or % real
+                \defineR{\rng@LEP}{\rng@LEP}%
+                \RNGparseDec{\rng@LEP}%
+                \rng@cnta=\rng@intpart
+            \fi
+            \advance\rng@cnta by1\relax
+            \defineZ{\rng@LEP}{\the\rng@cnta}%
+        \else
+%    \end{macrocode}
+% Not a control sequence but has a star
+%    \begin{macrocode}
+            \defineZ{\rng@LEP}{\rng@LEP}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#3}%
+        \if\rng@isC@ntrol1% control sequence
+            \let\rng@CtrlLEP=1%
+            \def\rng@LEP{#3}%
+            \@getVarType{#3}%
+            \ifcase\varType % integer
+                \defineZ{\rng@LEP}{#3}%
+            \or % rational
+                \rng@dima=\nOf{#3}pt
+                \divide\rng@dima by\dOf{#3}%
+                \defineR{\rng@LEP}{\strip@pt\rng@dima}%
+                \RNGparseDec{\rng@LEP}%
+                \defineZ{\rng@LEP}{\rng@intpart}%
+            \or % real
+                \defineR{\rng@LEP}{\rng@LEP}%
+                \RNGparseDec{\rng@LEP}%
+                \defineZ{\rng@LEP}{\rng@intpart}%
+            \fi
+        \else
+%    \end{macrocode}
+% A number, no star
+%    \begin{macrocode}
+            \defineZ{\rng@LEP}{#3}%
+        \fi
+    \fi
+%    \end{macrocode}
+% \paragraph*{Right endpoint.}
+%    \begin{macrocode}
+    \rng@existStar{#4}\rng@NameEndpoint{\rng@UEP}%
+    \if\rng@isStariii*\edef\tmp@exp{%
+        \noexpand\rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
+%    \end{macrocode}
+% The UEP is a control sequence with a star, we need to increment the value
+% of \cs{rng@UEP} to the next largest integer.
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
+            \ifcase\varType % integer
+                \rng@cnta=\rng@UEP
+            \or % rational
+                \rng@dima=\expandafter\nOf\rng@UEP pt
+                \divide\rng@dima by\expandafter\dOf\rng@UEP
+                \defineR{\rng@UEP}{\strip@pt\rng@dima}%
+                \RNGparseDec{\rng@UEP}%
+                \rng@cnta=\rng@intpart
+            \or % real
+                \defineR{\rng@UEP}{\rng@UEP}%
+                \RNGparseDec{\rng@UEP}%
+                \rng@cnta=\rng@intpart
+            \fi
+            \advance\rng@cnta by-1\relax
+            \defineZ{\rng@UEP}{\the\rng@cnta}%
+        \else
+%    \end{macrocode}
+% Not a control sequence but has a star
+%    \begin{macrocode}
+            \defineZ{\rng@UEP}{\rng@UEP}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#4}%
+        \if\rng@isC@ntrol1% control sequence
+            \let\rng@CtrlUEP=1%
+            \def\rng@UEP{#4}%
+            \@getVarType{#4}%
+            \ifcase\varType % integer
+                \defineZ{\rng@UEP}{#4}%
+            \or % rational
+                \rng@dima=\nOf{#4}pt
+                \divide\rng@dima by\dOf{#4}%
+                \defineR{\rng@UEP}{\strip@pt\rng@dima}%
+                \RNGparseDec{\rng@UEP}%
+                \defineZ{\rng@UEP}{\rng@intpart}%
+            \or % real
+                \defineR{\rng@UEP}{\rng@UEP}%
+                \RNGparseDec{\rng@UEP}%
+                \defineZ{\rng@UEP}{\rng@intpart}%
+            \fi
+        \else
+%    \end{macrocode}
+% A number, no star, assume it is an integer
+%    \begin{macrocode}
+            \defineZ{\rng@UEP}{#4}%
+        \fi
+    \fi
+%    \end{macrocode}
+% \textbf{To Do.} Check if LEP is less than UEP, if not, notify user.
+% Save the random variable, e.g., \cs{a}
+%    \begin{macrocode}
+    \def\@currentName{#2}%
+%    \end{macrocode}
+% Record the variable type
+%    \begin{macrocode}
+    \@getVarName{#2}%
+    \expandafter\def\csname typeof@\@varName\endcsname{0}%
+%    \end{macrocode}
+% Save the range of this variable
+%    \begin{macrocode}
+    \expandafter\edef\csname first@\@varName\endcsname{\rng@LEP}%
+    \expandafter\edef\csname last@\@varName\endcsname{\rng@UEP}%
+%    \end{macrocode}
+% Now get a value for the variable using \cs{rand}, defined in \texttt{lcg}
+%    \begin{macrocode}
+    \rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
+%    \end{macrocode}
+% Now define the integer.
+%    \begin{macrocode}
+    \defineZ{#2}{\arabic{rand}}%
+%    \end{macrocode}
+% \paragraph*{Constraints}
+% We have a random Z, we now try to satisfy the \texttt{ne} condition.
+%
+% The macro \cs{rangen@ne} can be of the form \verb!{1,3,4,5}!. We try to
+% satisfy all the conditions specified by \cs{rangen@ne}
+%    \begin{macrocode}
+    \ifx\rangen@ne\@empty\else\loopCnt=0\relax
+%    \end{macrocode}
+% We will try a total number of \cs{maxLoopLimit} to meet the required
+% conditions.
+%    \begin{macrocode}
+        \@whilenum\loopCnt<\maxLoopLimit\do{%
+%    \end{macrocode}
+% Set \cs{rng@cnta=1}, if \cs{rng@cnta} is still 1 at the end of this
+% loop, the condition is satisfied.
+% conditions.
+%    \begin{macrocode}
+            \rng@cnta=1\relax
+%    \end{macrocode}
+% We use a \cs{@for} loop to run through all the NE values
+%    \begin{macrocode}
+            \@for\ne@@tmp:=\rangen@ne\do{%
+%    \end{macrocode}
+% If the current RV is equal to the current NE value, we fail, so we
+% ``and'' a zero into the \cs{rng@cnta} register.
+%    \begin{macrocode}
+                \ifnum\value{rand}=\ne@@tmp\relax
+                    \multiply\rng@cnta0\relax
+                \else
+%    \end{macrocode}
+% \dots otherwise, we ``and'' a one.
+%    \begin{macrocode}
+                    \multiply\rng@cnta1\relax
+                \fi
+            }%
+%    \end{macrocode}
+% If \cs{rng@cnt} is still equal to 1, all conditions have been met,
+% in this case we set \verb!\loopCnt=\maxLoopLimit! so we can exit the outer loop.
+%    \begin{macrocode}
+            \ifnum\rng@cnta=1\relax % all conditions met
+                \loopCnt=\maxLoopLimit
+            \else % if \rng@cnta \ne 1, try again
+%    \end{macrocode}
+% Otherwise, we increment the loop, see if we have gone the limit, if
+% not, loop back with a new random choice.
+%    \begin{macrocode}
+                \advance\loopCnt1\relax
+                \ifnum\loopCnt=\maxLoopLimit
+                    \PackageWarning{rangen}{Not all conditions met
+                        after \maxLoopLimit\space tries}%
+                \else
+                    \rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
+                \fi
+            \fi
+        }%
+    \fi
+%    \end{macrocode}
+% Whether we fail or succeed, we'll go with the last RV. Hopefully, the
+% author is aware of the log file, and re-compile, possibly with a
+% wider range for the variable, or with a larger value of \cs{maxLoopLimit}.
+%
+%    \begin{macrocode}
+    \defineZ{#2}{\arabic{rand}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macrocode}
+\def\updateZ#1#2{%
+    \@getVarName#1\relax
+    \expandafter\edef\csname\@varName\endcsname{#2}%
+    \expandafter\edef\csname n@\@varName\endcsname{#2}%
+    \expandafter\edef\csname d@\@varName\endcsname{1}%
+}
+%    \end{macrocode}
+%\subsubsection{Random Rational}
+%    \begin{macro}{\RandomQ}
+% Randomly generate a rational number. The parameters for \cs{RandomQ} are
+%\begin{verbatim}
+%[#1] Optional parameter to modify the variable.
+% #2  The random variable being defined, e.g., \a
+%[#3] maximum denominator permitted (optional)
+% #4  rational number for lower endpoint of range
+% #5  rational number for upper endpoint of range
+%\end{verbatim}
+% Here, it is assume that the first rational number is less than the second.  This macro
+% will randomly generate a rational number between rat1 and rat2, with a maximum denominator
+% specified in \texttt{\#3}.
+%
+% \medskip\noindent\textbf{Note: }To allow for random endpoints, if one or both are real numbers, we convert
+% them to rational numbers in \cs{@RandomQ}.
+%
+% We begin by getting the first two parameters:
+%\begin{verbatim}
+%[#1] Optional parameter to modify the variable.
+% #2  The random variable being defined, e.g., \a
+%\end{verbatim}
+%    \begin{macrocode}
+\newcommand{\RandomQ}[2][]
+{%
+    \setkeys{rangen}{ne,#1}%
+    \def\rq@currentName{#2}%
+    \@RandomQ
+}
+%    \end{macrocode}
+% We use \cs{@RandomQ} to get the last three parameters of \cs{RandomQ}.
+% If the endpoints are not rational, they are converted to rationals.
+%\begin{verbatim}
+%[#1] maximum denominator permitted (optional)
+% #2  rational number for lower endpoint of range
+% #3  rational number for upper endpoint of range
+%\end{verbatim}
+%    \begin{macrocode}
+\newcommand{\@RandomQ}[3][]
+{%
+%    \end{macrocode}
+% Now see if there is an \texttt{*}, and get un-stripped
+% argument.
+%
+% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
+% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
+% Check the left endpoint:
+%    \begin{macrocode}
+    \let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
+    \let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
+%    \end{macrocode}
+% \paragraph*{Left endpoint}
+%    \begin{macrocode}
+    \rng@existStar{#2}\rng@NameEndpoint{\rng@LEP}%
+    \if\rng@isStariii*\edef\tmp@exp{\noexpand%
+            \rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
+%    \end{macrocode}
+% The LEP is a control sequence we get its type and convert to rational
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
+            \ifcase\varType % integer
+                \defineQ{\rng@LEP}{\rng@LEP}{1}%
+            \or % rational
+                \edef\tmp@exp{\noexpand%
+                \defineQ{\noexpand\rng@LEP}{\expandafter\nOf\rng@LEP}%
+                    {\expandafter\dOf\rng@LEP}}\tmp@exp
+            \or % real
+                \defineR{\rng@LEP}{\rng@LEP}%
+                \RNGparseDec{\rng@LEP}%
+                \defineQ{\rng@LEP}{\rng@intpart}{\rng@fracpart}%
+            \fi
+        \else
+%    \end{macrocode}
+% Not a control sequence but has a star, a number, we assume rational
+%    \begin{macrocode}
+            \RNGparseRat{\rng@LEP}%
+            \defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, is it a control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#2}%
+        \if\rng@isC@ntrol1% a control sequence
+            \@getVarType{#2}%
+            \ifcase\varType % integer
+                \defineQ{\rng@LEP}{#2}{1}%
+            \or % rational
+                \defineQ{\rng@LEP}{\nOf{#2}}{\dOf{#2}}%
+            \or % real
+                \defineR{\rng@LEP}{#2}%
+                \RNGparseDec{\rng@LEP}%
+                \defineQ{\rng@LEP}{\rng@intpart}{\rng@fracpart}%
+            \fi
+        \else % a number, required to be rational
+            \RNGparseRat{#2}%
+            \defineQ{\rng@LEP}{\rng@num}{\rng@denom}%
+        \fi
+    \fi
+%    \end{macrocode}
+% \paragraph*{Right endpoint}
+%    \begin{macrocode}
+    \rng@existStar{#3}\rng@NameEndpoint{\rng@UEP}%%
+    \if\rng@isStariii*%
+        \edef\tmp@exp{\noexpand%
+            \rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
+%    \end{macrocode}
+% The UEP is a control sequence we get its type and convert to rational
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
+            \ifcase\varType % integer
+                \defineQ{\rng@UEP}{\rng@UEP}{1}%
+            \or % rational
+                \edef\tmp@exp{\noexpand%
+                \defineQ{\noexpand\rng@UEP}{\expandafter\nOf\rng@UEP}%
+                    {\expandafter\dOf\rng@UEP}}\tmp@exp
+            \or % real
+                \defineR{\rng@UEP}{\rng@UEP}%
+                \RNGparseDec{\rng@UEP}%
+                \defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
+            \fi
+        \else
+%    \end{macrocode}
+% Not a control sequence but has a star, a number, we assume rational
+%    \begin{macrocode}
+            \RNGparseRat{\rng@UEP}%
+            \defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, is it a control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#3}%
+        \if\rng@isC@ntrol1% a control sequence
+            \@getVarType{#3}%
+            \ifcase\varType % integer
+                \defineQ{\rng@UEP}{#3}{1}%
+            \or % rational
+                \defineQ{\rng@UEP}{\nOf{#3}}{\dOf{#3}}%
+            \or % real
+                \defineR{\rng@UEP}{#3}%
+                \RNGparseDec{\rng@UEP}%
+                \defineQ{\rng@UEP}{\rng@intpart}{\rng@fracpart}%
+            \fi
+        \else % a number, required to be rational
+            \RNGparseRat{#3}%
+            \defineQ{\rng@UEP}{\rng@num}{\rng@denom}%
+        \fi
+    \fi
+    \@@RandomQ{#1}{\nOf{\rng@LEP}}{\dOf{\rng@LEP}}%
+        {\nOf{\rng@UEP}}{\dOf{\rng@UEP}}%
+}
+%    \end{macrocode}
+% Once all the parameters have been acquired, and
+% any needed conversions are made, we call \cs{@@RandomQ} which
+% actually generates the random rational.
+%\begin{verbatim}
+% #1 maximum denominator permitted
+% #2 numerator of first rational
+% #3 denominator of first rational
+% #4 numerator of second rational
+% #5 denominator of second rational
+%\end{verbatim}
+%    \begin{macrocode}
+\newcommand{\@@RandomQ}[5]
+{%
+%    \end{macrocode}
+% Now take parameters \texttt{\#2}--\texttt{\#5}, and make into two rationals
+%    \begin{macrocode}
+    \updateQ\@rqi{#2}{#3}\updateQ\@rqii{#4}{#5}%
+%    \end{macrocode}
+% Find least common multiple between \texttt{\#3}, \texttt{\#5} and \texttt{\#1}
+%    \begin{macrocode}
+    \lcm{#3}{#5}\edef\@thelcm{\thelcm}%
+    \def\@maxDenom{#1}%
+    \ifx\@maxDenom\@empty\edef\@maxDenom{\@thelcm}\else
+        \lcm{\@thelcm}{#1}\edef\@thelcm{\thelcm}\fi
+%    \end{macrocode}
+% Now convert all rationals to have a denominator of \cs{@thelcm}
+%    \begin{macrocode}
+    \convertRatTo{\nOf\@rqi}{\dOf\@rqi}{\@thelcm}%
+    \updateQ\@@rqi{\rng@retn@num}{\@thelcm}%
+    \convertRatTo{\nOf\@rqii}{\dOf\@rqii}{\@thelcm}%
+    \updateQ\@@rqii{\rng@retn@num}{\@thelcm}%
+%    \end{macrocode}
+% get divisor
+%    \begin{macrocode}
+    \rng@cnta=\@thelcm \divide\rng@cnta by\@maxDenom
+    \edef\@divisor{\the\rng@cnta}%
+%    \end{macrocode}
+% Round up lower limit
+%    \begin{macrocode}
+    \rng@cnta=\nOf\@@rqi
+    \divide\rng@cnta by\@divisor
+    \advance\rng@cnta by1
+%    \end{macrocode}
+% Round down the upper limit
+%    \begin{macrocode}
+    \rng@cntb=\nOf\@@rqii\divide\rng@cntb by\@divisor
+%    \end{macrocode}
+% If a strict inequality is requested, we creep in a little.
+%    \begin{macrocode}
+    \if\rng@makeLEPStrict1\advance\rng@cnta1\relax\fi
+    \if\rng@makeUEPStrict1\advance\rng@cntb-1\relax\fi
+%    \end{macrocode}
+% construct numerator
+%    \begin{macrocode}
+    \expandafter\@getVarName\rq@currentName
+    \let\save@varName\@varName
+    \expandafter\edef\csname first@n@\@varName\endcsname{\the\rng@cnta}%
+    \expandafter\edef\csname last@n@\@varName\endcsname{\the\rng@cntb}%
+    \expandafter\edef\csname first@d@\@varName\endcsname{\@maxDenom}%
+    \expandafter\edef\csname last@d@\@varName\endcsname{\@maxDenom}%
+    \edef\rng@LEP{\csname first@n@\@varName\endcsname}%
+    \edef\rng@UEP{\csname last@n@\@varName\endcsname}%
+%\typeout{\@varName: first=\rng@LEP,last=\rng@UEP}%
+    \rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
+%    \end{macrocode}
+% Record the random variable name, e.g., \cs{a}, ...
+%    \begin{macrocode}
+    \let\@currentName\rq@currentName
+    \expandafter\@getVarName\rq@currentName
+    \expandafter\defineQ\@currentName{\arabic{rand}}{\@maxDenom}%
+    \simplifyCurrentQ
+    \expandafter\defineQ\@currentName{\expandafter\nOf\@currentName}%
+        {\expandafter\dOf\@currentName}%
+%    \end{macrocode}
+%
+% \paragraph*{Constraints}
+%
+% We now attempt to satisfy the NE constraints.
+%    \begin{macrocode}
+    \ifx\rangen@ne\@empty\else\loopCnt=0\relax
+        \@whilenum\loopCnt<\maxLoopLimit\do{%
+            \rng@cnta=1\relax
+            \@for\ne@@tmp:=\rangen@ne\do{%
+%    \end{macrocode}
+% Define a rational by the name of \cs{cmp@Name}, then make  it have
+% the same denominator as \cs{@currentName}.
+%    \begin{macrocode}
+                \let\save@currentName\rq@currentName
+                \RNGparseRat{\ne@@tmp}%
+                \defineQ{\cmp@Name}{\rng@num}{\rng@denom}%
+                \let\@varName\save@varName
+                \syncronizeQs{\@varName}%
+                \ifnum\csname n@\@varName\endcsname=\n@cmp@Name
+                    \multiply\rng@cnta0\relax
+                \else
+                    \multiply\rng@cnta1\relax
+                \fi
+            }%
+            \ifnum\rng@cnta=1\relax % all conditions met
+                \loopCnt=\maxLoopLimit
+            \else % if \rng@cnta \ne 1, try again
+                \advance\loopCnt1\relax
+                \ifnum\loopCnt=\maxLoopLimit
+                    \PackageWarning{rangen}{Not all conditions met
+                        after \maxLoopLimit\space tries}%
+                \else
+                    \rng@chgrand[first=\rng@LEP,last=\rng@UEP]\rand
+                    \expandafter\@getVarName\rq@currentName
+                    \expandafter\defineQ\@currentName{\arabic{rand}}%
+                        {\@maxDenom}%
+                \fi
+            \fi
+        }%
+    \fi
+    \simplifyCurrentQ
+    \expandafter\defineQ\@currentName{\expandafter\nOf\@currentName}%
+        {\expandafter\dOf\@currentName}%
+%    \end{macrocode}
+% If the denominator is equal to 1, let's change the data type to an integer.
+%    \begin{macrocode}
+    \let\@currentName\rq@currentName
+    \expandafter\@getVarName\rq@currentName
+    \ifnum\csname d@\@varName\endcsname=1\relax\expandafter
+        \defineZ\@currentName{\expandafter\nOf\@currentName}%
+    \fi
+    \simplifyCurrentQ
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\updateQ}
+% Updates the value of a rational number, its  numerator and denominator
+% without changing any of the format macros.
+%    \begin{macrocode}
+\newcommand\updateQ[3]
+{%
+    \@getVarName#1\relax
+    \expandafter\edef\csname\@varName\endcsname{#2/#3}%
+    \expandafter\edef\csname n@\@varName\endcsname{#2}%
+    \expandafter\edef\csname d@\@varName\endcsname{#3}%
+}
+%    \end{macrocode}
+%    \end{macro}
+% A macro for performing routine adjustments on a rational number.
+%    \begin{macrocode}
+\def\simplifyCurrentQ
+{%
+%    \end{macrocode}
+% Reduce fraction: Reduce the fraction to its lowest terms.
+%    \begin{macrocode}
+    \reduceFrac{\csname n@\@varName\endcsname}%
+        {\csname d@\@varName\endcsname}%
+%    \end{macrocode}
+% \cs{reduceFrac} returns results in \cs{@tempcnta} and \cs{@tempcntb}, now
+% update the numerator and denominator
+%    \begin{macrocode}
+    \expandafter\edef\csname n@\@varName\endcsname{\rfNumer}%
+    \expandafter\edef\csname d@\@varName\endcsname{\rfDenom}%
+%    \end{macrocode}
+% If the numerator is zero, then zero out \cs{@varName} and special format
+%    \begin{macrocode}
+    \ifnum\csname n@\@varName\endcsname=0
+        \expandafter\edef\csname\@varName\endcsname{0}%
+        \edef\display@TeXfmt{0}\edef\inline@TeXfmt{0}%
+    \else
+%    \end{macrocode}
+% If numerator equals denominator, just replace by 1
+%    \begin{macrocode}
+       \ifnum\csname n@\@varName\endcsname=\csname d@\@varName\endcsname
+            \expandafter\defineZ\csname\@varName\endcsname{1}%
+       \else
+%    \end{macrocode}
+% If numerator equals -denominator, just replace by -1
+%    \begin{macrocode}
+            \ifnum\csname n@\@varName\endcsname
+                =-\csname d@\@varName\endcsname
+                \expandafter\defineZ\csname\@varName\endcsname{-1}%
+            \else
+%    \end{macrocode}
+% If denominator equals 1, modify value; otherwise, ok.
+%    \begin{macrocode}
+                \ifnum\csname d@\@varName\endcsname=1
+                    \expandafter\defineZ\csname\@varName\endcsname
+                        {\csname n@\@varName\endcsname}%
+                \else
+                    \expandafter\edef\csname \@varName\endcsname{%
+                    \csname n@\@varName\endcsname/%
+                        \csname d@\@varName\endcsname}%
+                    \edef\display@TeXfmt{%
+                        \frac{\csname n@\@varName\endcsname}
+                            {\csname d@\@varName\endcsname}}%
+                    \edef\inline@TeXfmt{%
+                        \csname n@\@varName\endcsname/%
+                            \csname d@\@varName\endcsname}%
+                    \expandafter\let
+                    \csname\@varName*\endcsname\display@TeXfmt
+                \fi
+            \fi
+        \fi
+    \fi
+}
+%    \end{macrocode}
+%    \begin{macro}{\nOf}
+%    \begin{macro}{\dOf}
+%    \begin{macro}{\iOf}
+%    \begin{macro}{\typeOf}
+% User access to numerator and denominator of random variables.
+%    \begin{macrocode}
+\newcommand\nOf[1]{\csname n@\expandafter\@gobble\string#1\endcsname}
+\newcommand\dOf[1]{\csname d@\expandafter\@gobble\string#1\endcsname}
+%    \end{macrocode}
+% For a variable created by \cs{RandomL}, the index of the number chosen (1-based)
+% can be accessed through the \cs{iOf} command.
+%    \begin{macrocode}
+\newcommand{\iOf}[1]{\csname i@\expandafter\@gobble\string#1\endcsname}
+%    \end{macrocode}
+% Get the type of a RV, \cs{ifnum}\cs{typeOf}\cs{a}=0 (integer), 1 (rational), 2 (real),
+% 3 (literal, created by \cs{RandomP}).
+%    \begin{macrocode}
+\newcommand\typeOf[1]{%
+    \csname typeof@\expandafter\@gobble\string#1\endcsname}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+%\subsubsection{Random Real}
+%
+% We attempt to generate a random real number, in a given interval of real numbers.
+%
+% The following are some data and switches used by \cs{RandomReal}.
+%    \begin{macrocode}
+\newif\iftrailingzeros\trailingzerosfalse
+\@namedef{rng@tz1}{0}
+\@namedef{rng@tz2}{00}
+\@namedef{rng@tz3}{000}
+\@namedef{rng@tz4}{0000}
+\@namedef{rng@tz5}{00000}
+\@namedef{rng@tz6}{000000}
+\@namedef{rng@tz7}{0000000}
+\@namedef{rng@tz8}{00000000}
+\def\rng@true{true}\def\rng@false{false}
+\newdimen\rng@dima
+\newdimen\rng@dimb
+\newdimen\rng@dimc
+%    \end{macrocode}
+%    \begin{macro}{\RandomR}
+% Create a real number at random within the given interval. For example,
+%\begin{verbatim}
+%   \RandomR[<key-values>]{\a}{3.45}{6.45}
+%\end{verbatim}
+%    \begin{macro}{round}
+%    \begin{macro}{showzeros}
+% The key-value pairs recognized by \cs{RandomZ|Q|R}.
+%    \begin{macrocode}
+\define@key{rangen}{ne}[]{\edef\rangen@ne{#1}}
+\define@key{rangen}{round}[]{\def\rangen@round{#1}}
+\define@key{rangen}{showzeros}[]{\def\rangen@showzeros{#1}%
+    \ifx\rangen@showzeros\@empty\global\trailingzerostrue\else
+    \ifx\rangen@showzeros\rng@true\global\trailingzerostrue\else
+    \global\trailingzerosfalse\fi\fi}
+\define@key{rangen}{index}[]{\edef\rangen@index{#1}}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%\begin{verbatim}
+%[#1] = options
+% #2  = name of real to correct
+% #3  = lower endpoint of interval
+% #4  = upper endpoint of interval
+%\end{verbatim}
+%    \begin{macrocode}
+\newcommand{\RandomR}[4][]{%
+     \setkeys{rangen}{ne,round,showzeros=false,#1}%
+%    \end{macrocode}
+% Now see if there is an \texttt{*}, and get un-stripped
+% argument.
+%
+% The \cs{rng@isControl} lets \cs{rng@isC@ntrol} to 0 if the arg is undefined,
+% and lets \cs{rng@isC@ntrol} to 1 if it is defined.
+% Check the left endpoint:
+%    \begin{macrocode}
+    \let\rng@CtrlLEP=0\let\rng@CtrlUEP=0%
+    \let\rng@makeLEPStrict=0\let\rng@makeUEPStrict=0%
+    \def\rng@lcg@first{0}\edef\rng@lcg@last{\RNGpowerOfTen}%
+%    \end{macrocode}
+% \paragraph{Left endpoint.} Check the left endpoint:
+%    \begin{macrocode}
+    \rng@existStar{#3}\rng@NameEndpoint{\rng@LEP}%
+    \if\rng@isStariii*\edef\tmp@exp{\noexpand%
+            \rng@isControl{\expandafter\noexpand\rng@LEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlLEP=1\let\rng@makeLEPStrict=1%
+            \def\rng@lcg@first{1}%
+%    \end{macrocode}
+% The LEP is a control sequence with a star. Convert LEP to a real
+% number as needed.
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@LEP}}\tmp@exp
+            \ifcase\varType % integer
+                \defineR{\rng@LEP}{\rng@LEP\RNG@Dec}%
+            \or % rational
+                \rng@dima=\expandafter\nOf\rng@LEP pt
+                \divide\rng@dima by\expandafter\dOf\rng@LEP
+                \defineR{\rng@LEP}{\strip@pt\rng@dima}%
+            \or % real
+                \defineR{\rng@LEP}{\rng@LEP}%
+            \fi
+%    \end{macrocode}
+% Not a control sequence, but has a star
+%    \begin{macrocode}
+        \else
+            \defineR{\rng@LEP}{\rng@LEP}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#3}%
+        \if\rng@isC@ntrol1% control sequence
+            \let\rng@CtrlLEP=1\def\rng@LEP{#3}%
+            \@getVarType{#3}%
+            \ifcase\varType % integer
+                \defineR{\rng@LEP}{\rng@LEP\RNG@Dec}%
+            \or % rational
+                \rng@dima=\nOf{#3}pt
+                \divide\rng@dima by\dOf{#3}%
+                \defineR{\rng@LEP}{\strip@pt\rng@dima}%
+            \or % real
+                \defineR{\rng@LEP}{\rng@LEP}%
+            \fi
+        \else
+%    \end{macrocode}
+% A number, no star, number is required to be real
+%    \begin{macrocode}
+            \defineR{\rng@LEP}{#3}%
+        \fi
+    \fi
+%    \end{macrocode}
+% \paragraph{Right endpoint.} Check the right endpoint:
+%    \begin{macrocode}
+    \rng@existStar{#4}\rng@NameEndpoint{\rng@UEP}%
+    \if\rng@isStariii*\edef\tmp@exp{\noexpand%
+            \rng@isControl{\expandafter\noexpand\rng@UEP}}\tmp@exp
+        \if\rng@isC@ntrol1% a control sequence
+            \let\rng@CtrlUEP=1\let\rng@makeUEPStrict=1%
+            \rng@cnta=\rng@lcg@last\advance\rng@cnta-1\relax
+            \edef\rng@lcg@last{\the\rng@cnta}%
+%    \end{macrocode}
+% The UEP is a control sequence with a star. Convert UEP to a real
+% number as needed.
+%    \begin{macrocode}
+            \edef\tmp@exp{\noexpand%
+                \@getVarType{\expandafter\noexpand\rng@UEP}}\tmp@exp
+            \ifcase\varType % integer
+                \defineR{\rng@UEP}{\rng@UEP\RNG@Dec}%
+            \or % rational
+                \rng@dima=\expandafter\nOf\rng@UEP pt
+                \divide\rng@dima by\expandafter\dOf\rng@UEP
+                \defineR{\rng@UEP}{\strip@pt\rng@dima}%
+            \or % real
+                \defineR{\rng@UEP}{\rng@UEP}%
+            \fi
+%    \end{macrocode}
+% Not a control sequence, but has a star
+%    \begin{macrocode}
+        \else
+            \defineR{\rng@UEP}{\rng@UEP}%
+        \fi
+    \else
+%    \end{macrocode}
+% No star, control sequence or not?
+%    \begin{macrocode}
+        \rng@isControl{#4}%
+        \if\rng@isC@ntrol1% control sequence
+            \let\rng@CtrlUEP=1\def\rng@UEP{#4}%
+            \@getVarType{#4}%
+            \ifcase\varType % integer
+                \defineR{\rng@UEP}{\rng@UEP\RNG@Dec}%
+            \or % rational
+                \rng@dima=\nOf{#4}pt
+                \divide\rng@dima by\dOf{#4}%
+                \defineR{\rng@UEP}{\strip@pt\rng@dima}%
+            \or % real
+                \defineR{\rng@UEP}{\rng@UEP}%
+            \fi
+        \else
+%    \end{macrocode}
+% A number, no star, number is required to be real
+%    \begin{macrocode}
+            \defineR{\rng@UEP}{#4}%
+        \fi
+    \fi
+%    \end{macrocode}
+% Prepare to generate the random real
+%    \begin{macrocode}
+    \def\@currentName{#2}\@getVarName{#2}%
+%    \end{macrocode}
+% Save upper and lower endpoints where they are expected to be.
+%    \begin{macrocode}
+    \expandafter\edef\csname first@\@varName\endcsname{\rng@LEP}%
+    \expandafter\edef\csname last@\@varName\endcsname{\rng@UEP}%
+%    \end{macrocode}
+% Get a random real, and declare it to be a real number using \cs{defineR}.
+%    \begin{macrocode}
+    \rng@getRandomR
+    \defineR{#2}{\strip@pt\rng@dima}%
+%    \end{macrocode}
+% Round and remove trailing zeros.
+%    \begin{macrocode}
+    \ifx\rangen@round\@empty\else
+        \RNGround{#2}{#2}{\rangen@round}%
+        \rng@dima=#2pt\relax
+        \defineR{#2}{\strip@pt\rng@dima}%
+    \fi
+%    \end{macrocode}
+% \paragraph{Constraints.} Let's try to apply constraints. We only allow one constraint.
+%    \begin{macrocode}
+    \ifx\rangen@ne\@empty\else\loopCnt=0\relax
+        \@whilenum\loopCnt<\maxLoopLimit\do{%
+            \rng@cnta=1\relax
+            \@for\ne@@tmp:=\rangen@ne\do{%
+                \rng@dima=#2pt
+                \ifdim\rng@dima=\ne@@tmp pt\relax
+                \multiply\rng@cnta0\relax\else
+                \multiply\rng@cnta1\relax\fi
+            }%
+            \ifnum\rng@cnta=1\relax % all conditions met
+                \loopCnt=\maxLoopLimit
+            \else % if \rng@cnta \ne 1, try again
+                \advance\loopCnt1\relax
+                \ifnum\loopCnt=\maxLoopLimit
+                    \PackageWarning{rangen}{Not all conditions met
+                        after \maxLoopLimit\space tries}%
+                \else
+                    \rng@getRandomR
+                    \defineR{#2}{\strip@pt\rng@dima}%
+%    \end{macrocode}
+% Round and remove trailing zeros.
+%    \begin{macrocode}
+                    \ifx\rangen@round\@empty\else
+                        \RNGround{#2}{#2}{\rangen@round}%
+                        \rng@dima=#2pt\relax
+                        \defineR{#2}{\strip@pt\rng@dima}%
+                    \fi
+                \fi
+            \fi
+        }%
+    \fi
+%    \end{macrocode}
+% \paragraph{Formatting.} Begin formatting of the real, keys recognized are
+% \texttt{round} and \texttt{showzeros}.
+%    \begin{macrocode}
+    \rnd@ProcessRealFormat{#2}%
+%    \end{macrocode}
+% We declare our number.
+%    \begin{macrocode}
+    \def\@currentName{#2}%
+    \defineR{#2}{#2}%
+}
+%    \end{macrocode}
+% Get a new random real and return it in the  \cs{rng@dima}
+%    \begin{macrocode}
+\def\rng@getRandomR{%
+%    \end{macrocode}
+% Put the endpoints in dimension registers so we can subtract them.
+%    \begin{macrocode}
+    \rng@dima=\rng@LEP pt
+    \rng@dimb=\rng@UEP pt
+%    \end{macrocode}
+% Compute the difference between upper and lower, then strip off the \texttt{pt},
+% to make it a decimal number.
+%    \begin{macrocode}
+    \advance\rng@dimb-\rng@dima
+%    \edef\r@getDiff{\strip@pt\rng@dimb}%
+%    \end{macrocode}
+% Get a random integer from the interval 0 to \cs{RNGpowerOfTen}.
+% the default value of the latter command is 100, and it can be changed
+% using \cs{nDivisionsPowerOfTen}. The idea is to divide the interval
+% from the lower bound to the upper bound into \cs{RNGpowerOfTen} nodes,
+% and we choose one of these nodes are random.
+%
+% If the endpoints where strict, then we changed \cs{rng@lcg@first}
+% from 0 to 1 (if the lower endpoint is strict); and changed
+% \cs{rng@lcg@last} from \cs{RNGpowerOfTen} to \texttt{\string\RNGpowerOfTen-1}
+% (if the upper end point is strict).
+%    \begin{macrocode}
+    \rng@chgrand[first=\rng@lcg@first,last=\rng@lcg@last]\rand
+%    \end{macrocode}
+% Divide the length of the interval by \cs{RNGpowerOfTen},
+% and store the result in \cs{rng@dimb}, then multiply
+% that by \verb!\arabic{rand}!.
+%    \begin{macrocode}
+    \divide\rng@dimb by\RNGpowerOfTen\relax
+    \rng@dimb=\arabic{rand}\rng@dimb
+%    \end{macrocode}
+% Finally, the left-end point is still in \cs{rng@dima}
+% we add the result in \cs{rng@dimb} to \cs{rng@dima}
+% to compute our random rational.
+%    \begin{macrocode}
+    \advance\rng@dima by\rng@dimb
+}
+\def\rnd@ProcessRealFormat#1{%
+    \ifx\rangen@round\@empty
+        \rng@dima=#1pt\relax
+        \defineR{#1}{\strip@pt\rng@dima}%
+    \else
+        \RNGround{#1}{#1}{\rangen@round}%
+        \rng@dima=#1pt\relax
+        \defineR{#1}{\strip@pt\rng@dima}%
+        \iftrailingzeros
+            {\RNGparseDec{#1}\count0=\decPls\relax
+             \advance\count0-\rndnDec\relax
+             \ifnum\count0>0\relax\xdef#1{%
+                \rng@intpart\RNG@Dec\rng@fracpart%
+\@nameuse{rng@tz\the\count0}}%
+             \fi}%
+             \defineR{#1}{#1}%
+        \fi
+    \fi
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \subsubsection{Random Sign}
+%    \begin{macro}{\RandomS}
+% We randomly generate a \texttt{+} or \texttt{-} sign
+% for addition and subtraction. The first optional argument
+% is a rational number between 0 and 1. The default is \texttt{1/2}.
+% This number represents the probably of a \texttt{+} sign.
+%    \begin{macrocode}
+\newcommand{\RandomS}[2][1/2]{%
+    \RNGparseRat{#1}%
+    \ifnum\rng@num<0\relax
+        \PackageError{rangen}{A positive numerator is required}%
+        {The rational number must be between 0 and 1}\fi
+    \ifnum\rng@denom<0\relax
+    \PackageError{rangen}{A positive denominator is required}%
+    {The rational number must be between 0 and 1}\fi
+    \ifnum\rng@num>\rng@denom\relax
+    \PackageError{rangen}{The rational must be between 0 and 1}%
+    {The rational number must be between 0 and 1}\fi
+    \rng@chgrand[first=1,last=\rng@denom]\rand
+    \@getVarName{#2}%
+    \ifnum\value{rand}>\rng@num\relax\def#2{-}%
+    \rng@makeMinusOneFmtDefns
+    \def\display@TeXfmt{-}\def\inline@TeXfmt{-}%
+    \else\def#2{+}\rng@makeOneFmtDefns
+    \def\display@TeXfmt{}\def\inline@TeXfmt{}\fi
+    \expandafter\let\csname\@varName*\endcsname\display@TeXfmt
+    \expandafter\let\csname\@varName!\endcsname\inline@TeXfmt
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \subsubsection{Random Number from a List}
+%
+%    \begin{macro}{\RandomL}
+% Select a number of any type from a comma-delimited list.
+%\begin{verbatim}
+% \RandomL[key-values]{\RV}{<comma-delimited list>}
+%\end{verbatim}
+% Currently, the only key recognized is the \texttt{index} key.
+% If the \texttt{index} key is specified, the number whose index is specified
+% is retrieved from the list.
+%    \begin{macrocode}
+\newcommand{\RandomL}[3][]{%
+    \let\rangen@index\@empty
+    \setkeys{rangen}{#1}%
+    \rng@cnta=0\relax\@for\@@tmp:=#3\do{%
+    \advance\rng@cnta1\relax}\edef\n@rng@listItems{\the\rng@cnta}%
+    \ifx\rangen@index\@empty
+        \rng@chgrand[first=1,last=\n@rng@listItems]\rand
+    \else
+        \rng@cnta=\rangen@index
+        \advance\rng@cnta-1\relax
+        \amodb{\rng@cnta}{\n@rng@listItems}%
+        \rng@cnta=\retnmod
+        \advance\rng@cnta1\relax
+        \value{rand}=\rng@cnta
+    \fi
+    \@getVarName{#2}%
+    \expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
+    \rng@cnta=0\relax\@for\@@tmp:=#3\do{%
+    \advance\rng@cnta1\relax\ifnum\rng@cnta=\arabic{rand}%
+    \edef\rng@choice{\@@tmp}\fi}%
+    \def\@currentName{#2}%
+%    \end{macrocode}
+% Now, determine the type of this choice, and make appropriate
+% data type definition.
+%    \begin{macrocode}
+    \RNGparseDec{\rng@choice}%
+    \if\rng@parseR@iii\RNG@Dec\defineR{#2}{\rng@choice}%
+    \else\RNGparseRat{\rng@choice}%
+    \if\rng@parseQ@iii/\defineQ{#2}{\rng@num}{\rng@denom}%
+    \else\defineZ{#2}{\rng@choice}\fi\fi
+}
+%    \end{macrocode}
+%    \end{macro}
+
+%    \subsubsection{Random Problem from a List}
+%
+%    \begin{macro}{\RandomP}
+% Select a literal from a comma-delimited list of literals.
+%\begin{verbatim}
+% \RandomP[key-values]{\RV}{<comma-delimited list>}
+%\end{verbatim}
+% Currently, the only key recognized is the \texttt{index} key.
+% If the \texttt{index} key is specified, the number whose index is specified
+% is retrieved from the list.
+%    \begin{macrocode}
+\newcommand{\RandomP}[3][]{%
+    \let\rangen@index\@empty
+    \setkeys{rangen}{#1}%
+    \rng@cnta=0\relax\@for\@@tmp:=#3\do{%
+    \advance\rng@cnta1\relax}\edef\n@rng@listItems{\the\rng@cnta}%
+    \ifx\rangen@index\@empty
+        \rng@chgrand[first=1,last=\n@rng@listItems]\rand
+    \else
+        \rng@cnta=\rangen@index
+        \advance\rng@cnta-1\relax
+        \amodb{\rng@cnta}{\n@rng@listItems}%
+        \rng@cnta=\retnmod
+        \advance\rng@cnta1\relax
+        \value{rand}=\rng@cnta
+    \fi
+    \@getVarName{#2}%
+    \expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
+    \rng@cnta=0\relax\@for\@@tmp:=#3\do{%
+    \advance\rng@cnta1\relax\ifnum\rng@cnta=\arabic{rand}%
+    \rng@toks=\expandafter{\@@tmp}\edef#2{\the\rng@toks}%
+    \expandafter\def\csname typeof@\@varName\endcsname{3}\fi}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%    \subsubsection{Random Index}
+%
+%    \begin{macro}{\RandomI}
+% This command creates an implied list of \verb!{1, 2, 3,...,n}!,
+% and randomly selects a number from this list. The result is
+% defined as an integer, and held in the macro \texttt{\#1}.
+%\begin{verbatim}
+%   \Random{\i}{n} --> select \i from {1, 2, 3,...,n} at random
+%\end{verbatim}
+%A random index, \cs{i}, created by \cs{RandomI}, can be used
+%in the \cs{RandomL} command; for example,
+%\begin{verbatim}
+%   \RandomL[index=\i]{\a}{17,\rPI,3/4,\rE,88,1/2}
+%\end{verbatim}
+%The value of \cs{a} is determined by the index \cs{i}.
+%    \begin{macrocode}
+\newcommand{\RandomI}[2]{%
+    \rng@chgrand[first=1,last=#2]\rand
+    \defineZ{#1}{\arabic{rand}}%
+    \expandafter\edef\csname i@\@varName\endcsname{\arabic{rand}}%
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+%   \subsection{Some Constants}
+%
+%    \begin{macro}{\zZero}
+%    \begin{macro}{\zOne}
+%    \begin{macro}{\zMinusOne}
+%    \begin{macro}{\rPI}
+%    \begin{macro}{\rE}
+% Define three convenience integers corresponding to $0$, $1$, and $-1$.
+%    \begin{macrocode}
+\defineZ{\zZero}{0}
+\defineZ{\zOne}{1}
+\defineZ{\zMinusOne}{-1}
+\defineR{\rPI}{3.1415927}
+\defineR{\rE}{2.7182818}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%
+% This macro takes \cs{@varName} and \cs{cmp@Name} and converts to the same common
+% denominator. This makes it easy to make comparisons between two rational numbers.
+%    \begin{macrocode}
+\def\syncronizeQs#1{\edef\sync@arg{#1}%
+    \lcm{\csname d@\sync@arg\endcsname}{\d@cmp@Name}%
+    \edef\@thelcm{\thelcm}%
+    \convertRatTo{\n@cmp@Name}{\d@cmp@Name}{\@thelcm}%
+    \updateQ\cmp@Name{\rng@retn@num}{\@thelcm}%
+    \convertRatTo{\csname n@\sync@arg\endcsname}%
+        {\csname d@\sync@arg\endcsname}{\@thelcm}\expandafter
+    \defineQ\csname\sync@arg\endcsname{\rng@retn@num}{\@thelcm}%
+}
+%    \end{macrocode}
+% \subsection{Formatting Commands}
+%    \begin{macro}{\ds}
+%    \begin{macro}{\eds}
+%    \begin{macro}{\cds}
+% Displays an alternate representation (\textbf display\textbf style) of the random variable. Usage \cs{ds}\cs{a}.
+% This displays the contents of \cs{display@TeXfmt} for this variable. The value of \cs{display@TeXfmt}
+% is effected by the formatting commands above.
+%
+% For a rational number \cs{a}, the expression \cs{ds}\cs{a} expands either to the special format representation, or
+% to a rational of the form $\frac{p}{q}$.
+%    \begin{macrocode}
+\newcommand\ds[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1*\endcsname
+}
+\newcommand\eds[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1*e\endcsname
+}
+\newcommand\cds[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1*c\endcsname
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macro}{\fmt}
+%    \begin{macro}{\efmt}
+%    \begin{macro}{\cfmt}
+% Displays a special format for the random variable. Usage \cs{ds}\cs{a}.
+% This displays the contents of \cs{display@TeXfmt} for this variable.
+% Same as \cs{ds}, but does not display a display style if there is not
+% special formatting.
+%
+% For a rational number \cs{a}, the expression \cs{ds}\cs{a} expands either to the special format representation, or
+% to a rational of the form $p/q$.
+%    \begin{macrocode}
+\newcommand\fmt[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1!\endcsname
+}
+\newcommand\efmt[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1!e\endcsname
+}
+\newcommand\cfmt[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1!c\endcsname
+}
+%    \end{macrocode}
+%    \end{macro}
+%    \end{macro}
+%    \end{macro}
+%    \begin{macro}{\js}
+% Used within \cs{CorrAnsButton} to get a more precise expansion of a variable. Used with variables
+% that have been defined using \cs{defineDepVar}. When you say \verb+\js\m+, for example,
+% the \cs{eval@JSfmt} is expanded.
+% \par\medskip\noindent
+% \textbf{Usage:} \verb+\CorrAnsButton*{y = \js\m\space x }+
+%    \begin{macrocode}
+\newcommand\js[1]{%
+    \expandafter\csname\expandafter\@gobble\string#1!*\endcsname
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \subsection{Commands specialized to Reals}
+
+%    \begin{macro}{\RNGround}
+% Round \texttt{\#1} to \texttt{\#3} decimal places, and leave result in \texttt{\#2}.
+%    \begin{macrocode}
+\def\RNGround#1#2#3{%
+    \begingroup
+    \def\rng@ctrlName{#1}%
+    \def\rng@sourceName{#2}%
+    \def\rng@nDecPl{#3}%
+    \RNGparseDec{#2}%
+    \ifnum\rndnDec<#3\relax
+        \xdef\theseDigits{\rng@fracpart}%
+        \let\rng@next\relax
+    \else
+        \count0=0\relax
+        \gdef\theseDigits{}%
+        \def\rng@next{\expandafter\@rng@round\rng@fracpart\end}%
+    \fi
+    \rng@next
+    \xdef\decPls{\@ifundefined{save@rng@nDecPl}%
+        {\rng@nDecPl}{\save@rng@nDecPl}}%
+    \ifx\theseDigits\@empty
+    \xdef#1{\rng@intpart}\else
+    \xdef#1{\rng@intpart\RNG@Dec\theseDigits}\fi
+    \endgroup
+}
+\def\@rng@round#1{%
+    \ifx#1\end\let\rng@next\relax
+    \else
+        \ifnum\rng@nDecPl=0\relax
+            \ifnum#1>4\relax
+                \count0=\rng@intpart\relax
+                \ifnum\rng@intpart<0\relax
+                    \advance\count0by-1\relax
+                \else
+                    \advance\count0by1\relax
+                \fi
+                \xdef\rng@intpart{\the\count0}%
+            \fi
+            \gdef\theseDigits{}%
+            \let\rng@next\rng@gobbletoend
+        \else
+            \advance\count0by1\relax
+            \ifnum\count0=\rng@nDecPl\relax
+                \def\rng@next{\@@rng@round#1}%
+            \else
+                \xdef\theseDigits{\theseDigits#1}%
+                \let\rng@next\@rng@round
+            \fi
+        \fi
+    \fi
+    \rng@next
+}
+\def\rng@gobbletoend#1\end{}
+\def\@@rng@round#1#2{%
+    \ifx#2\end%
+        \xdef\theseDigits{\theseDigits#1}%
+        \let\rng@next\relax
+    \else
+        \ifnum#2>4\relax\count2=#1\relax
+            \ifnum\count2=9\relax
+                \count0=\rng@nDecPl\relax
+                \ifnum\count0=1\relax
+                    \count0=\rng@intpart\relax
+                    \ifnum\rng@intpart<0\relax
+                        \advance\count0by-1\relax
+                    \else
+                        \advance\count0by1\relax
+                    \fi
+                    \xdef\rng@intpart{\the\count0}%
+                    \let\rng@next\rng@gobbletoend
+                \else
+                    \advance\count0by-1\relax\expandafter
+                    \xdef\rng@sourceName{%
+                        \rng@intpart\RNG@Dec\theseDigits#1}%
+                    \edef\save@rng@nDecPl{\rng@nDecPl}%
+                    \edef\rng@next{\noexpand\RNGround{%
+                        \expandafter\noexpand\rng@ctrlName}%
+                        {\expandafter\noexpand\rng@sourceName}%
+                        {\the\count0}\noexpand\rng@gobbletoend}%
+                \fi
+            \else
+                \advance\count2by1\relax
+                \xdef\theseDigits{\theseDigits\the\count2}%
+                \let\rng@next\rng@gobbletoend
+            \fi
+        \else % \ifnum#2<=4
+            \xdef\theseDigits{\theseDigits#1}%
+            \let\rng@next\rng@gobbletoend
+        \fi
+    \fi
+    \rng@next
+}
+%    \end{macrocode}
+%    \end{macro}
+% Used with \cs{CorrAnsButton} and \texttt{rngCorrAnsButton}, like so,
+%\begin{verbatim}
+% \CorrAnsButton{rEval(\strAns)}*{rngCorrAnsButton\RNGprintf{\%.2f}}
+%\end{verbatim}
+%    \begin{macrocode}
+\def\RNGprintf#1{("#1",\@gobble}
+%    \end{macrocode}
+%
+% \subsection{User Defined Dependent Variables for JavaScript}
+%    \begin{macro}{\defineDepQJS}
+% Define a rational as a function of other integers. This macro defines
+% \cs{fmt} and \cs{ds} for the variable, but its primary use it
+% for \cs{js}. This command is aimed at the JavaScript side of things
+%\begin{verbatim}
+%#1 = name of rational to be defined, e.g., \a
+%#2 = numerator
+%#3 = denominator
+%#4 = \js expression for #1
+%\end{verbatim}
+% Usage:
+%\begin{verbatim}
+%   \defineDepQJS{\m}{\d-\b}{\c-\a}
+%       {rFrac(rEval(\nOf\m)/rEval(\dOf\m))}
+% ...
+% \CorrAnsButton{y = \js\m\space x}*{rngCorrAnsButton}%
+%\end{verbatim}
+% The above example would calculate equation of the line passing through
+% the two points \verb!P(\a,\b)! and \verb!Q(\c,\d)!. The code is used
+% in the \cs{CorrAnsButton} to have the answer appear.
+%    \begin{macrocode}
+\newcommand\defineDepQJS[4]{%
+    \@getVarName#1
+    \expandafter\edef\csname\@varName\endcsname{(#2)/(#3)}%
+    \expandafter\edef\csname n@\@varName\endcsname{(#2)}%
+    \expandafter\edef\csname d@\@varName\endcsname{(#3)}%
+    \edef\display@TeXfmt{\csname\@varName\endcsname}%
+    \edef\inline@TeXfmt{\csname\@varName\endcsname}%
+    \def\dv@argiv{#4}\ifx\dv@argiv\@empty
+    \edef\eval@JSfmt{\csname\@varName\endcsname}\else
+    \edef\eval@JSfmt{#4}\fi
+    \expandafter\let\csname\@varName!*\endcsname\eval@JSfmt
+}
+%    \end{macrocode}
+%    \end{macro}
+%
+% \subsection{Writing RVs to Solution Files}
+%    \begin{macrocode}
+\def\rng@writeCurrentSeed#1{\immediate\write#1{\string\makeatletter
+    \string\global\string\cr@nd=\the\cr@nd\string\relax
+    \string\makeatother}}
+%    \end{macrocode}
+% Token register to hold the verbatim contents of the \texttt{writeRVsTo} environment.
+%    \begin{macrocode}
+\newtoks\rng@toks
+\def\wrv@ex@solns{exercises}%
+\def\wrv@ex@quiz{quizzes}%
+%    \end{macrocode}
+%    \begin{environment}{writeRVsTo}
+% This environment takes its environment contents and writes it to
+% two files, one file is \cs{jobname\_rvs.cut} which is input back
+% into the source file immediately. The second parameter
+% accepts the string \texttt{exercises} or \texttt{quizzes}, or a write
+% handle to write to an auxiliary file. The environment was designed for
+% use with the \texttt{exercise}, \texttt{quiz}, and \texttt{shortquiz} environments
+% of \textsf{exerquiz}.
+%    \begin{macrocode}
+\newenvironment{writeRVsTo}[2][]
+{%
+    \def\wrv@argii{#2}%
+    \ifx\wrv@argii\wrv@ex@quiz\let\wrv@out\quiz@solns
+    \else\ifx\wrv@argii\wrv@ex@solns\let\wrv@out\ex@solns\else
+    \let\wrv@out#2\fi\fi
+    \rng@writeCurrentSeed\wrv@out
+    \rng@toks={}%
+    \def\verbatim@processline{%
+        \xdef\rng@temp{\the\rng@toks\the\verbatim@line}%
+        \global\rng@toks=\expandafter{\rng@temp}}%
+    \let\do\@makeother\dospecials\catcode`\^^M\active
+    #1%
+    \verbatim@start
+}{  \immediate\write\wrv@out{\the\rng@toks}%
+    \newwrite\rng@writeRVs
+    \immediate\openout\rng@writeRVs\jobname_rvs.cut
+    \immediate\write\rng@writeRVs{\the\rng@toks}%
+    \immediate\closeout\rng@writeRVs
+    \aftergroup\rng@Input@RVs
+}
+%    \end{macrocode}
+%    \end{environment}
+% After the \texttt{writeRVsTo} environment writes the RVs to
+% \cs{jobname\_rvs.cut}. The environment executes
+% \cs{rng@Input@RVs} to input the file back into the source file.
+%    \begin{macrocode}
+\def\rng@Input@RVs{\InputIfFileExists{\jobname_rvs.cut}{}{}}
+%    \end{macrocode}
+% \subsection{Redefine lcg Package Macro}
+%    \begin{macrocode}
+\def\rng@p@stkeysr@nd{%
+   \@rderr@nd%                  last < first  -> swap
+   \cutr@nger@nd%               range too big -> cut
+} % end of \def\p@stkeysr@nd
+\def\rng@chgrand{\@ifnextchar[\rng@chgr@nd{\rng@chgr@nd[]}}
+\def\rng@chgr@nd[#1]{%
+    \@tempcnta=\z@
+    \@tempcntb=\z@
+    \setkeys{Init}{#1}%
+    \rng@p@stkeysr@nd%
+    \@utputr@nd%
+}  % end of \def\rng@chgrand
+%    \end{macrocode}
+% \subsection{DLJS Support}
+%    \begin{macrocode}
+\begin{insDLJS}[partialExpand]{partial}{Rangen}
+var partre = /rEval|rFrac/;
+%    \end{macrocode}
+% The arguments for this function take two forms
+% (1) \texttt{fieldname}, \texttt{theanswer} (the default); (2)
+% \texttt{theformat}, \texttt{fieldname}, \texttt{theanswer}. The later case
+% is created by using the \cs{RNGprintf} command that inserts allows the
+% document author to insert a \texttt{printf} formatting template. For example,
+%\begin{verbatim}
+%   \CorrAnsButton{rEval(\strAns)}*{rngCorrAnsButton\RNGprintf{\%.4f}}
+%\end{verbatim}
+%    \begin{macrocode}
+function rngCorrAnsButton()
+{
+    var theprecision,fieldname,theanswer;
+    if (arguments.length==4) {
+        var theformat=arguments[0];
+        var fieldname=arguments[1];
+        var theanswer=arguments[2];
+        var thequiz=arguments[3];
+    } else {
+        var fieldname=arguments[0];
+        var theanswer=arguments[1];
+        var thequiz=arguments[2];
+    }
+    theanswer = partialExpand(0,theanswer);
+    if (arguments.length==4)
+        theanswer=util.printf(theformat,eval(theanswer));
+    DisplayAnswer(fieldname,theanswer,thequiz);
+}
+%    \end{macrocode}
+% The JavaScript function \texttt{partialExpand} searches through \texttt{Ans} in search of
+% \texttt{rEval} and \texttt{rFrac}. It calls itself recursively to search for the inner most
+% appearances of these two functions. It evaluates these two functions starting with the inner
+% most and working its way outward.
+%    \begin{macrocode}
+function partialExpand(level,Ans)
+{
+    Ans = correctPlusMinus(Ans)
+    level += 1;
+\db console.println("Enter level = " + level +": Ans: " + Ans);\db%
+    var n=0, m, bP, eP, subExp;
+    while ( true ) {
+\db     console.println("Searching a level " + level);\db%
+        try { m = Ans.match(partre); }
+        catch (e) { break; }
+        if ( m != null ) {
+            bP = m.index + m[0].length;
+            eP = FindBalP(Ans, bP, true);
+\db         console.println("bP = " + bP + " : eP = " + eP);\db%
+            var subExp = Ans.substring(bP+1, eP);
+\db         console.println("Found \'" + subExp%
+                + "\' at level = " + level);\db%
+%            subExp = partialExpand(level, subExp);
+            // n = beginning of "rEval",
+            // eP = beginning of balanced parens,
+            // bP = end of balanced parens
+            Ans = Ans.substring(0, m.index)
+                + eval(m[0]+"(level,subExp)") + Ans.substring(eP+1);
+\db         console.println("level = " + level%
+                             +": New Ans: " + Ans);\db %
+        } else {
+            if ( level == 1 ) {
+\db             console.println("Level 1 break");\db %
+                break;
+            }
+        }
+    }
+\db console.println("Return Ans: " + Ans);\db%
+    Ans = correctPlusMinus(Ans);
+    return Ans;
+}
+%    \end{macrocode}
+% Evaluates the value of \texttt{Ans}.
+%    \begin{macrocode}
+function rEval(level, Ans)
+{
+    level += 1;
+\db console.println("Enter rEval: level = "%
+        + level +": Ans: " + Ans);\db%
+    var n=0, m, bP, eP, subExp;
+    while ( true )
+    {
+\db     console.println("Searching a level " + level);\db%
+        try { m = Ans.match(partre); }
+        catch (e) { break; }
+        if ( m != null ) {
+            bP = m.index + m[0].length;
+            eP = FindBalP(Ans, bP, true);
+\db         console.println("bP = " + bP + " : eP = " + eP);\db%
+            var subExp = Ans.substring(bP+1, eP);
+\db         console.println("Found \'" + subExp%
+                + "\' at level = " + level);\db%
+            // n = beginning of "rEval",
+            // eP = beginning of balanced parens,
+            // bP = end of balanced parens
+            Ans = Ans.substring(0, m.index)
+                +eval(m[0]+"(level,subExp)")+Ans.substring(eP+1);
+\db         console.println("level = "%
+                + level +": New Ans: " + Ans);\db %
+        } else {
+            Ans = ParseInput(Ans);
+\db         console.println("Ready to eval at level = "%
+                + level + ": Ans = " + Ans);\db%
+            with(Math) { Ans = eval( Ans ) };
+\db         console.println("After eval at level = "%
+                + level + ": Ans = " + Ans);\db%
+            break;
+        }
+    }
+\db console.println("Return Ans: " + Ans);\db%
+    return Ans;
+}
+%    \end{macrocode}
+% Evaluates an rational number by evaluating the value of the numerator and denominator separately.
+%    \begin{macrocode}
+function rFrac(level, Ans)
+{
+    level += 1;
+\db console.println("Enter rFrac level = "%
+        + level +": Ans: " + Ans);\db%
+    var n=0, m, bP, eP, subExp;
+    while ( true ) {
+\db     console.println("Searching a level " + level);\db%
+        try { m = Ans.match(partre); }
+        catch (e) { break; }
+        if ( m != null ) {
+            bP = m.index + m[0].length;
+            eP = FindBalP(Ans, bP, true);
+\db         console.println("bP = "%
+                + bP + " : eP = " + eP);\db%
+            var subExp = Ans.substring(bP+1, eP);
+\db         console.println("Found \'" + subExp%
+                + "\' at level = " + level);\db%
+            // n = beginning of "rEval",
+            // eP = beginning of balanced parens,
+            // bP = end of balanced parens
+            Ans = Ans.substring(0, m.index)
+                + eval(m[0]+"(level,subExp)") + Ans.substring(eP+1);
+\db         console.println("level = " + level%
+                +": New Ans: " + Ans);\db %
+        } else {
+            var numDenom = Ans.split("/");
+            numDenom[0] = eval(numDenom[0]);
+            numDenom[1] = eval(numDenom[1]);
+            var g = gcd(numDenom[0], numDenom[1]);
+            numDenom[0] /= g;
+            numDenom[1] /= g;
+            if ( numDenom[1] == 1)
+                Ans = numDenom[0];
+            else
+                Ans = numDenom.join("/");
+\db         console.println("Reduce: " + numDenom.join("/"));\db%
+            break;
+        }
+    }
+\db console.println("Return Ans: " + Ans);\db%
+    return Ans;
+}
+function correctPlusMinus(Ans)
+{
+    Ans = "" + Ans;
+    Ans  = Ans.replace(/\s*([\+-])\s*\1\s*/g, " + ");
+    Ans  = Ans.replace(/\s*\+\s*-\s*/g, " - ");
+%    Ans  = Ans.replace(/\s*\+\s*\+\s*/g, " + ");
+%    Ans  = Ans.replace(/\s*-\s*-\s*/g, " + ");
+    Ans  = Ans.replace(/\s*-\s*\+\s*/g, " - ");
+    return Ans;
+}
+function gcd(a,b)
+{
+    var x = a, y = b, r;
+    while (true)
+    {
+        r = x \% y;
+        if ( r == 0 ) break;
+        x = y;
+        y = r;
+    }
+    return Math.abs(y);
+}
+function lcm (a,b) { return (a*b)/gcd(a,b); }
+\end{insDLJS}
+%</package>
+%    \end{macrocode}
+\endinput
diff --git a/macros/latex/contrib/rangen/rangen.ins b/macros/latex/contrib/rangen/rangen.ins
new file mode 100644
index 0000000000..c9335e7f87
--- /dev/null
+++ b/macros/latex/contrib/rangen/rangen.ins
@@ -0,0 +1,64 @@
+%%
+%% This file will generate fast loadable files and documentation
+%% driver files from the doc files in this package when run through
+%% LaTeX or TeX.
+%%
+%% Copyright 1999-2002 D. P. Story
+%%
+%% This file is part of the `Web and Exerquiz Distribution'.
+%% -------------------------------------------
+%%
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.2 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 1.2 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%%
+%% --------------- start of docstrip commands ------------------
+%%
+\def\filedate{2001/05/26}
+\def\batchfile{rangen.ins}
+%
+% If you can assume that the target audience for the document all have
+% Acrobat Reader 5.0 or later, then chance the following switch to true,
+% else, leave it as false.
+
+\input docstrip
+\ifx\generate\undefined
+  \Msg{**********************************************}
+  \Msg{*}
+  \Msg{* This installation requires docstrip}
+  \Msg{* version 2.4 or later.}
+  \Msg{*}
+  \Msg{* An older version of docstrip has been input}
+  \Msg{*}
+  \Msg{**********************************************}
+  \errhelp{Move or rename old docstrip.tex and get a newer one.}
+  \errmessage{Old docstrip in input path}
+  \batchmode
+  \csname @@end\endcsname\end
+\fi
+
+\keepsilent
+\askforoverwritefalse
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\preamble
+\endpreamble
+
+\generate
+{%
+    \file{rangen.sty}{\from{rangen.dtx}{copyright,package}}
+}
+
+\Msg{***************************************************************}
+\Msg{*}
+\Msg{* \space To finish the installation you have to copy the files }
+\Msg{*}
+\Msg{* \space *.sty, *.cfg and *.def into a directory searched by TeX}
+\Msg{*}
+\Msg{***************************************************************}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\endinput