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+% \iffalse
+% +AMDG  This document was begun on 7 October 11EX, the
+% feast of the Blessed Virgin Mary for the Rosary, and it is
+% humbly dedicated to her, for her prayers, and to the
+% Sacred Heart of Jesus for His mercy.
+%
+% This document is copyright 2014 by Donald P. Goodman, and is
+% released publicly under the LaTeX Project Public License.  The
+% distribution and modification of this work is constrained by the
+% conditions of that license.  See
+% 	http://www.latex-project.org/lppl.txt
+% for the text of the license.  This document is released
+% under version 1.3 of that license, and this work may be distributed
+% or modified under the terms of that license or, at your option, any
+% later version.
+% 
+% This work has the LPPL maintenance status 'maintained'.
+% 
+% The Current Maintainer of this work is Donald P. Goodman
+% (dgoodmaniii@gmail.com).
+% 
+% This work consists of basicarith.dtx, basicarith.ins, and
+% derived files basicarith.sty and basicarith.pdf.
+% \fi
+
+% \iffalse
+%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+%<package>\ProvidesPackage{basicarith}[2015/01/01 v1.1 support for typesetting basic arithmetic in the American fashion]
+%<*driver>
+\documentclass{ltxdoc}
+
+\usepackage{doc}
+\usepackage{array}
+\usepackage{lettrine}
+	\setcounter{DefaultLines}{3}
+	\setlength{\DefaultFindent}{2pt}
+	\renewcommand{\LettrineFontHook}{\color{red}}
+\usepackage{url}
+\usepackage{spverbatim}
+\usepackage[nocounters]{dozenal}
+\usepackage[noshowdivwork]{basicarith}
+\usepackage[colorlinks]{hyperref}
+\usepackage{makeidx}
+\EnableCrossrefs
+\PageIndex
+\CodelineNumbered
+\RecordChanges
+\makeindex
+\DoNotIndex{\?,\{,\},\|,\DeclareFontFamily,\DeclareFontShape,
+	\DeclareMathAccent,\DeclareMathAlphabet,\DeclareMathDelimiter,
+	\DeclareMathSymbol,\DeclareMathVersion,\DeclareSymbolFont,\def,
+	\drmsym,\encodingdefault,\familydefault,\fontencoding,\fontfamily,
+	\fontseries,\fontshape,\hfil,\hbox,\mathalpha,\mathclose,
+	\mathopen,\mathord,\mathversion,\mp,\nabla,\nbshortroman,
+	\RedefineMRmdclxvij,\relax,\renewcomand,\RequirePackage,
+	\selectfont,\SetMathAlphabet,\SetSymbolFont,\drmsymbolredef,
+	\nodefaultfalse,\nodefaultmathfalse,\nodefaultmathtrue,\nodefaulttrue,
+	\nodefaulttextfalse,\nodefaulttexttrue,\noindent,\numexpr,
+	\acute,\addtolength,\advance,\backslash,\baselineskip,
+	\char,\counterA,\counterB,\DeclareOption,\ProcessOptions,
+	\drmmathlets,\if,\else,\fi,\ifnum,\fi,\ifdim,\fi,
+	\symbolsonlyfalse,\fontsize,\newif,\newcount,
+	\loop,\iter,\let,\renewcommand,\setbox,\setlength,\the,\vss,
+	\vskip,\vbox,\newlength,\@tempboxa,\b@loopi,\b@parenfontsize,
+	\counterA,\counterB,\newcount,\r@@t,\z@,\DeclareMathRadical,
+	\DeclareRobustCommand,\bBigg@,\@ifnextchar,\@sqrt,\@makefnmark,
+	\@thefnmark,\catcode,\active,\b@spaceout,\b@xloop,\bf,
+	\b@totalprobwid,\checknil,\assignthencheck,\afterassignment,
+	\auxcountchar,\b@charcount,\gobblechar,\getdroparrowwidth,
+	\checknil,\countchar,\countunlessnil,\csname,\endcsname,
+	\divide,\multiply,\advance,\edef,\expandafter,\f@size,\ifx,\fi,
+	\ifshowdivisionwork,\fi,\linewidth,\newdimen,\next,\nil,
+	\wd,\xx,\hbox,\vbox,\vtop,\hrule,\vrule,\hskip,\hss,\footnotesize,
+	\downarrow,\leavevmode,\settowidth}
+
+\tracingmacros=3
+\begin{document}
+\DocInput{basicarith.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The |basicarith| Package, v1.1}
+% \author{Donald P.\ Goodman III}
+% \date{\today}
+%
+% \maketitle
+%
+% \begin{abstract}
+% The |basicarith| package provides means for typesetting
+% arithmetic problems, of whatever operations, in a clean
+% and open fashion, suitable for educational texts rather
+% than scholarly works.  Digits are spaced out, work (such
+% as carrying, borrowing, and dropping) can be shown
+% visibly, and individual digits can be styled independently.
+% \end{abstract}
+%
+% \tableofcontents
+%
+% \section{Introduction}
+%
+% \TeX\ and \LaTeX\ are, of course, justly celebrated for
+% their ability to beautifully typeset mathematics.
+% However, there are few utilities available for typesetting
+% the sort of mathematics that we find in primary school
+% textbooks.  We can easily typeset incredibly complex
+% equations, and \TeX\ will put them together perfectly; but
+% to typeset an example addition problem, showing our work,
+% is quite difficult.  |basicarith| attempts to fill this
+% need by providing macros for typesetting and organizing
+% such problems.
+%
+% It is notable that basic arithmetic is done in several
+% different styles in various places, though of course the
+% algorithms are typically the same.  The author being an
+% American, |basicarith| typesets the problems according to
+% the American custom.  Most of these are shared with other
+% English-speaking countries; however, some, particularly
+% long division, will look quite odd to those from other
+% countries.  No option for using these other styles is
+% currently available.
+%
+% \section{Basic Macros}
+%
+% |basicarith| offers a few basic macros for formulating
+% problems.  These must be divided into two main groups:
+% long division, and other operations.  Since the latter are
+% simpler, we'll start with those.
+%
+% \subsection{Non-Division Operations}
+%
+% The fundamental macros for this are
+% \DescribeMacro{\opline}|\opline|,
+% \DescribeMacro{\probline}|\probline|, 
+% \DescribeMacro{\nextpline}|\nextpline|, and
+% \DescribeMacro{\soluline}|\soluline|.  The syntax for each
+% is simple; we'll take them in their order of use.
+%
+% \begin{center}
+% \cmd{\probline} \marg{width} \marg{number}
+% \end{center}
+% 
+% Both these arguments are mandatory.  Simply put,
+% |probline| takes first the total width of the problem you
+% are typesetting; this is equivalent to the longest line of
+% the problem.  So if your longest line is, say, eight
+% digits long, you put ``8'' here.  The second is the number
+% of the first line of the equation.
+%
+% \begin{center}
+% \cmd{\nextpline} \marg{number}
+% \end{center}
+%
+% |\nextpline| just takes the next number of the equation.
+% 
+% \begin{center}
+% \cmd{\opline} \marg{operator} \marg{number}
+% \end{center}
+%
+% |\opline| takes two mandatory arguments; first, the
+% operator to be typeset, and second, the number of the
+% final line.  It also prints a ``solution line'' underneath
+% itself; this makes it the last line in the problem before
+% we start figuring the answer.  Note that, if you want a
+% mathematical symbol for the operator (say, ``$\times$''),
+% you have to include the dollar signs yourself.  This means
+% that \emph{any} character can be your operator, not only
+% math characters.
+%
+% \begin{center}
+% \cmd{\soluline} \marg{number}
+% \end{center}
+%
+% |\soluline| is designed for the solution of the problem.
+% Functionally this is equivalent to |\nextpline|, but
+% semantically it is clearer.  Furthermore, it resets the
+% line counter, so that line styles will be correctly
+% applied in future equations.
+%
+% There remains only one more basic macro:  |\noopline|.
+%
+% \begin{center}
+% \cmd{\noopline} \marg{number}
+% \end{center}
+%
+% \DescribeMacro{\noopline}|\noopline|
+% is identical to |\opline| except that it does not print
+% the operator.  This is useful for typesetting operations
+% that require one or more intermediate solutions; for
+% example, multiplication by more than one digit.
+% Typically, in the American style the operator is printed
+% only on the final line of the first solution; subsequent
+% intermediate solutions require a rule above them but no
+% operator on that rule.  |\noopline| is what produces this.
+%
+% These are then combined in the way one might expect.  For
+% example:
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+%		\begin{spverbatim}
+%		\probline{9}{58193}
+%		\nextpline{54}
+%		\nextpline{4397}
+%		\opline{$+$}{38291374}
+%		\nextpline{38354018}
+%		\noopline{54}
+%		\soluline{38354072}
+%		\end{spverbatim}}
+%	}\hfil%
+%	\problembox{%
+%		\probline{9}{58193}
+%		\nextpline{54}
+%		\nextpline{4397}
+%		\opline{$+$}{38291374}
+%		\nextpline{38354018}
+%		\noopline{54}
+%		\soluline{38354072}
+%	}%
+%	\hfil%
+% }%
+% \bigskip
+%
+% And that's the essentials of using |basicarith| for
+% non-long division.
+%
+% \subsection{Long Division}
+%
+% Long division is typically more difficult to typeset than
+% other functions; so |basicarith| offers different macros
+% for handling it.  The examples below are meaningless
+% (unlike those above, which are actually correct); they are
+% merely meant to show the macros which are available.
+%
+% \begin{center}
+% \cmd{\longdiv} \marg{length} \marg{dividend} \marg{divisor}
+% \end{center}
+%
+% The \DescribeMacro{\longdiv}|\longdiv| macro is,
+% obviously, the most important; it typesets the
+% all-important first line of a long division problem.
+% |\longdiv| takes three arguments, all mandatory; the first
+% is the length of the dividend in number of digits (it uses
+% this to calculate the appropriate length of the line over
+% of the dividend); the second is the dividend itself; and
+% the third is the divisor.  It uses a simple
+% close-parenthesis between the dividend and divisor, scaled
+% to 1.2 times the current font size.  
+%
+% \begin{center}
+% \cmd{\ldsoluline} \marg{solution} \marg{remainder}
+% \end{center}
+%
+% \DescribeMacro{\ldsoluline}|\ldsoluline| typesets
+% the answer.  This is a bit tricky, because as mentioned
+% before, in American-style long division, the answer is
+% typeset \emph{above} the question, not below it; but we
+% don't know how much space we will need for that answer
+% until we've typeset the first line, containing the
+% dividend, divisor, and close-parenthesis.  So
+% |\ldsoluline| should be input \emph{after} the |\longdiv|
+% command but \emph{before} any |\nextldline|s; otherwise,
+% |basicarith| won't be able to place it correctly.
+%
+% The second argument to |\ldsoluline| is the remainder; if
+% you don't want to typeset a remainder, you still must
+% include this argument, but it can be left blank.
+%
+% \begin{center}
+% \cmd{\nextldline} \marg{cutoff} \marg{number}
+% \end{center}
+%
+% In the American style of long division, intermediate
+% values are placed \emph{underneath} the dividend, while
+% the solution itself is placed \emph{above} it.
+% \DescribeMacro{\nextldline}|\nextldline| typesets these
+% intermediate values.  It takes two arguments, both
+% mandatory.  The first is the number of digits of the
+% dividend that are encompassed by this intermediate result
+% (that is, in purely visual terms, the number of digits in
+% the dividend which will not have a number underneath
+% them); the second is the number itself.
+%
+% Notice that |basicarith| does not keep track of how much
+% it must indent subsequent lines when you're showing your
+% work.  This has the benefit that you can skip steps as you
+% see fit; it has the drawback that you have to tell
+% |basicarith| how much each |\nextldline| must skip ahead
+% in order to get the number properly placed.
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+% 	\begin{spverbatim}
+% 		\longdiv{6}{430;932}{983}
+% 		\ldsoluline{837;61}{4}
+% 		\nextldline{3}{43}
+% 		\nextldline{2}{4389}
+% 	\end{spverbatim}}
+% 	}\hfil%
+% 		\problembox{%
+% 		\longdiv{6}{430;932}{983}
+% 		\ldsoluline{837;61}{4}
+% 		\nextldline{3}{43}
+% 		\nextldline{2}{4389}
+% 		}%
+%	\hfil%
+% }
+%
+%
+% And this suffices for basic usage of |basicarith|.
+% However, there are many other settings available with the
+% package, which we will address in the next section.
+%
+% \section{Advanced Usage}
+%
+% |basicarith| allows each line of a mathematical problem to
+% be specially styled.  For example, say you are trying to
+% draw particular attention to the subtrahend of a given
+% problem:
+%
+% \hbox to\linewidth{\LARGE\hfil%
+% \linestyle{2}{\color{red}}
+% \problembox{%
+%	\probline{4}{548}
+%	\opline{$-$}{27}
+%	\soluline{521}
+% }%
+% \hfil}%
+%
+% Or for some reason you want to highlight each line of a
+% subtraction problem differently, perhaps to visually
+% demonstrate which part is which:
+%
+% \hbox to\linewidth{\LARGE\hfil%
+% \linestyle{1}{\color{blue}}%
+% \linestyle{2}{\color{red}}%
+% \linestyle{3}{\color{green}}%
+% \problembox{%
+%	\probline{4}{548}%
+%	\opline{$-$}{27}%
+%	\soluline{521}%
+% }%
+% \hfil}%
+%
+% This is accomplished using the
+% \DescribeMacro{\linestyle}|\linestyle| command, which
+% takes two arguments:  the number of the line of the
+% problem to be styled (starting with 1 at the top), and the
+% style to be applied to that line.
+%
+% \begin{center}
+% \cmd{\linestyle} \marg{line number} \marg{style}
+% \end{center}
+%
+% The style commands can be anything at all; colors,
+% weights, shapes, or any combination of the above.  These
+% commands will typically be confined to the innermost box
+% (particularly, they will not span |\problembox|es), but if
+% you do need to manually clear all these values back to
+% default (which is no styling at all), issue the command
+% \DescribeMacro{\clearlinestyles}|\clearlinestyles|.
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+% 	\begin{spverbatim}
+%  \linestyle{1}{\color{blue}}%
+%  \linestyle{2}{\color{red}}%
+%  \linestyle{3}{\color{green}}%
+%  \probline{4}{548}%
+%  \opline{$-$}{27}%
+%  \soluline{521}%
+% 	\end{spverbatim}}
+% 	}\hfil%
+%  \vbox{\linestyle{1}{\color{blue}}%
+%  \linestyle{2}{\color{red}}%
+%  \linestyle{3}{\color{green}}%
+%	\vskip-1em%
+%	\LARGE
+%	\problembox{
+%  \probline{4}{548}%
+%  \opline{$-$}{27}%
+%  \soluline{521}%
+%	}}%
+%	\hfil%
+% }
+%
+% Digits can also be individually styled by means of the
+% \DescribeMacro{\digstyle}|\digstyle| command.
+%
+% \begin{center}
+% \cmd{\digstyle} \marg{column number} \marg{style}
+% \end{center}
+%
+% Note that these are really styling \emph{columns}, not
+% merely digits; the style will be applied to every number
+% in that column until either another |\digstyle| for that
+% column number is issued or a
+% \DescribeMacro{\cleardigitstyles}|\cleardigitstyles|
+% command is encountered.  (This latter is like
+% |\clearlinestyles|, and is pretty self-explanatory.)
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+% 	\begin{spverbatim}
+%  \linestyle{1}{\color{blue}}%
+%  \linestyle{2}{\color{red}}%
+%  \linestyle{3}{\color{green}}%
+%  \digstyle{3}{\color{black}\itshape}%
+%  \probline{4}{548}%
+%  \opline{$-$}{27}%
+%  \soluline{521}%
+% 	\end{spverbatim}}
+% 	}\hfil%
+%  \vbox{%
+%	\linestyle{1}{\color{blue}}%
+%  \linestyle{2}{\color{red}}%
+%  \linestyle{3}{\color{green}}%
+%  \digstyle{3}{\color{black}\itshape}%
+%  \vskip-1em%
+%	\LARGE
+%	\problembox{
+%  \probline{6}{21;\x48}%
+%  \opline{$-$}{27}%
+%  \soluline{5;21}%
+%	}}%
+%	\hfil%
+% }
+% 
+% Notice also that |\digstyle| commands always take precedence over
+% |\linestyle| commands, no matter what order they are
+% issued in.
+%
+% Oftentimes we want to show our work explicitly, including
+% our carrying (in the case of addition or multiplication)
+% and our borrowing (in the case of subtraction).  We can
+% show this work by using the
+% \DescribeMacro{\carryline}|\carryline|
+% macro.  |\carryline| takes two arguments, the number of
+% digits you'll be putting carries over, and the line
+% with the carries or borrows that you wish to display.
+%
+% \begin{center}
+% \cmd{\carryline} \marg{number of digits} \marg{carries}
+% \end{center}
+%
+% |\carryline| will respect all |\linestyle| and |\digstyle|
+% commands, and it \emph{does} count as a line for
+% |\linestyle| purposes.
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+% 	\begin{spverbatim}
+%  \carryline{4}{{3}{\strike{18}17}}
+%  \probline{4}{548}%
+%  \opline{$-$}{29}%
+%  \soluline{519}%
+% 	\end{spverbatim}}
+% 	}\hfil%
+%  \vbox{
+%  \vskip-1em%
+%	\LARGE
+%	\problembox{
+%	\carryline{4}{{3}{\strike{18}17}}
+%  \probline{4}{548}%
+%  \opline{$-$}{29}%
+%  \soluline{519}%
+%	}}%
+%	\hfil%
+% }
+% \bigskip
+%
+% The first argument must be the same as that in the
+% |\probline| that the carries will be a part of.  This is a
+% clunkiness in the interface that I haven't been able to
+% resolve.
+%
+% Multiple digits can be put in a single carry place by enclosing
+% them in brackets.  Further, styling can be applied in a
+% limited way within those brackets; most basic styling,
+% such as italics and boldface, will work, but more complex
+% styling will not.  Experimentally, at the very least
+% |soul| and |ulem| styling will not work here.  For this
+% reason, |basicarith| provides the
+% \DescribeMacro{\strike}|\strike| command, which will
+% strike out a borrow when another borrow is required.  It
+% is used as shown in the example above (quite erroneously
+% applied there for the sake of example).  |\strike| takes a
+% single argument, the number to be struck out.  It is
+% implemented quite na\"\i{}vly, and will consequently only
+% strike out one or two digit numbers.
+%
+% Oftentimes we want to arrange our equations in the page,
+% and |basicarith|'s setup, with each line being a separate
+% |\hbox|, can sometimes make this difficult.  We therefore
+% have \DescribeMacro{\problembox}|\problembox|, which can
+% enclose any number of |basicarith| statements and make it
+% easier to position it on the page.  For example, a
+% |basicarith| equation in a |center| environment will not
+% be centered, due to some deep \TeX\ magic that we don't
+% need to go into here.  Wrap the equation up in
+% |\problembox|, however, with the |basicarith| equation as
+% the only element, and it will work just fine:
+%
+% \begin{center}
+% \problembox{%
+%	\carryline{4}{{3}{\strike{18}17}}
+%  \probline{4}{548}%
+%  \opline{$-$}{29}%
+%  \soluline{519}%
+% }%
+% \end{center}
+% 
+% \section{Configuration Commands}
+%
+% There are a variety of other bits and pieces of
+% |basicarith| that can be customized.  The width of
+% solution line is held in the macro
+% \DescribeMacro{\b@solverulewidth}|\b@solverulewidth|.  As
+% implied by the \@ in its name, this is considered an
+% ``internal'' command, but with |\makeatletter| and
+% |\makeatother| it can still be reset by a user, to values
+% reasonable or ridiculous.  For example,
+% |\b@solverulewidth=2pt| (or
+% |\setlength{\b@solverulewidth}{2pt}|) gives:
+%
+% \bigskip
+% \makeatletter\b@solverulewidth=2pt\makeatother
+% \hbox to\linewidth{\hfil%
+% \problembox{
+% \probline{3}{44}
+% \opline{$+$}{44}
+% }\hfil}
+% \makeatletter\b@solverulewidth=0.4pt\makeatother
+% \bigskip
+%
+% The longdivision equivalent is
+% \DescribeMacro{\b@longdivlinewidth}|\b@longdivlinewidth|;
+% setting it equal to 2pt gives:
+%
+% \bigskip
+% \makeatletter\b@longdivlinewidth=2pt\makeatother
+% \hbox to\linewidth{\hfil%
+% \problembox{\longdiv{4}{3298}{24}}
+% \hfil}%
+% \makeatletter\b@longdivlinewidth=0.4pt\makeatother
+% \bigskip
+%
+% Both of these values are the \TeX-default 0.4pt unless
+% changed by the user.
+%
+% For adminstrative reasons, the sizes of problems are
+% limited both in number of \emph{rows} and in number of
+% \emph{columns}.  The parameters controlling these things
+% are, unsurprisingly,
+% \DescribeMacro{\b@maxcols}|\b@maxcols| and
+% \DescribeMacro{\b@maxrows}|\b@maxrows|.  Both of these are
+% set at twenty to begin with, which ought to be more than
+% enough; but they can be changed if needed.
+%
+% By default, when a remainder is displayed in a long
+% division problem, it is prefixed by ``R,'' in the American
+% custom.  If you'd like something different, you can
+% redefine
+% \DescribeMacro{\b@remaindertext}|\b@remaindertext|; its
+% contents will be printed instead.
+%
+% When doing long division, sometimes work is shown in a
+% more explicit way.  In addition to writing intermediate
+% solutions beneath the appropriate digits of the dividend,
+% we often show visibly how digits are ``dropped'' from the
+% dividend into those intermediate problems, by drawing an
+% arrow down from those digits to the appropriate place.
+% With |basicarith|, we do this by issuing the
+% \DescribeMacro{\showdivwork}|\showdivwork|, and turn it
+% off with \DescribeMacro{\noshowdivwork}|\noshowdivwork|.
+% Showing work is turned \emph{on} by default.
+%
+% \def\fractionsymbol{.}
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\hbox to0.5\linewidth{\vbox{%
+% 	\begin{spverbatim}
+% 		\showdivwork
+% 		\longdiv{6}{430.932}{983}
+% 		\ldsoluline{837.61}{4}
+% 		\nextldline{3}{43}
+% 		\nextldline{2}{4389}
+% 	\end{spverbatim}}
+% 	}\hfil%
+% 		\problembox{%
+%		\showdivwork
+% 		\longdiv{6}{430.932}{983}
+% 		\ldsoluline{837.61}{4}
+% 		\nextldline{1}{40}
+% 		\nextldline{2}{69}
+% 		\nextldline{3}{73}
+% 		\nextldline{4}{22}
+% 		}%
+%	\hfil%
+% }
+% \bigskip
+%
+% These settings can also be set globally for the package at
+% loading time, with the package options
+% \DescribeMacro{noshowdivwork}|noshowdivwork| and
+% \DescribeMacro{showdivwork}|showdivwork|.  The latter is,
+% of course, the default.
+%
+% Incidentally, the last of these examples demonstrates
+% another configuration option:
+% \DescribeMacro{\fractionsymbol}|\fractionsymbol|.  The
+% author is a dozenalist, and dozenalists customarily use a
+% semicolon as a fractional point; but most people are
+% decimalists, and usually use either a dot or a comma.
+% With |basicarith|, you can use any symbol you want; the
+% default is ``;'', but by redefining |\fractionsymbol|, you
+% can get anything else.  The above was typeset with:
+%
+% \begin{center}
+% |\def\fractionsymbol{.}|
+% \end{center}
+%
+% \def\fractionsymbol{;}
+% The width of the box which encloses each digit is
+% controlled by a macro called
+% \DescribeMacro{\b@widthofdigit}|\b@widthofdigits|;
+% redefining this will result in different size digit boxes.
+% The following two lines show this macro set at 3ex and
+% 1ex, respectively.
+%
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\makeatletter\def\b@widthofdigit{3ex}\probline{4}{24;56}\makeatother
+%	\hfil%
+% }
+% \bigskip
+% \hbox to\linewidth{%
+%	\hfil%
+%	\makeatletter\def\b@widthofdigit{1ex}\probline{4}{24;56}\makeatother
+%	\hfil%
+% }
+% \def\b@widthofdigit{2ex}
+%
+% The default for this setting is 2ex.  Note that this is a
+% macro, not a dimen; change it using |\def| or
+% |\renewcommand|, not with |\setlength|.
+%
+% \section{Implementation}
+%
+% We begin by defining the necessary conditional for
+% determining whether long division work should be shown
+% (that is, whether to draw drop arrows), and then defining
+% and processing the package options.
+%    \begin{macrocode}
+\newif\ifshowdivisionwork		% switch for drop arrows
+\showdivisionworktrue
+\DeclareOption{noshowdivwork}{\showdivisionworkfalse}
+\DeclareOption{showdivwork}{\showdivisionworktrue}
+\ProcessOptions
+%    \end{macrocode}
+% We move on by defining the many dimensions and counters that
+% are required to typeset basic arithmetic problems.  Most
+% of these are described afterward by a comment.  First, we
+% define those which rarely change; think limitations on the
+% numbers of rows and columns; in the documentation we call
+% these ``configuration options.''
+%    \begin{macrocode}
+\newdimen\b@solverulewidth		% rule under the operator line
+\b@solverulewidth=0.4pt
+\newcount\b@maxcols				% maximum length of a problem
+\b@maxcols=20
+\newcount\b@maxrows				% maximum lines of a problem
+\b@maxrows=20
+\newdimen\b@longdivlinewidth	% width of above
+\def\fractionsymbol{;}
+%    \end{macrocode}
+% Next, we define those variables which change frequently;
+% these are the counters that keep track of which row and
+% column we're on and things of that nature.
+%    \begin{macrocode}
+\newdimen\b@topdivline			% length of the above
+\newdimen\b@totalprobwid		% width of widest line of problem
+\newdimen\b@digitwid				% width of a digit
+\def\b@widthofdigit{2ex}
+\newcount\b@colnum					% row number of problem
+\b@colnum=0%
+\def\specialdigitstyle{}		% style for a given digit
+\def\speciallinestyle{}			% style for a given digit
+\b@longdivlinewidth=0.4pt
+\newdimen\b@parenfontsize			% size of parenthesis in longdiv
+\newcount\b@linenum				% row number of problem
+\newdimen\b@divisorlen				% length of divisor
+\newdimen\b@divparenlen			% width of the paren in ld
+\newdimen\b@ldrowlen				% length to add to b@divisorlen
+\newdimen\b@fulldivlen				% length of divisor + dividend
+\b@fulldivlen=0pt
+\newcount\b@charcount				% number of chars in an argument
+\b@charcount=0
+\newcount\b@loopi					% generic loop counter
+\b@loopi=0
+\def\b@remaindertext{R}			% text for the remainder
+\newdimen\b@droparrowlen		% drop arrow length
+\b@droparrowlen=0pt
+%    \end{macrocode}
+% Now we define the macros that are used for counting the
+% number of characters in various strings; these are adapted
+% from macros by ``Florent'' at
+% \url{tex-and-stuff.blogspot.com}.
+%    \begin{macrocode}
+\def\gobblechar{\let\char= }
+\def\assignthencheck{\afterassignment\checknil\gobblechar}
+\def\countunlessnil{%
+	\ifx\char\nil \let\next=\relax%
+	\else%
+		\let\next=\auxcountchar%
+		\advance\b@charcount by1%
+	\fi%
+	\ifx\char;\advance\b@charcount by-1\fi%
+	\next%
+}%
+\def\auxcountchar{%
+	\afterassignment\countunlessnil\gobblechar%
+}%
+\def\countchar#1{\def\xx{#1}\b@charcount=0 \expandafter\auxcountchar\xx\nil}
+%    \end{macrocode}
+% Now we define some macros for splitting a string into
+% individual characters and putting them in boxes; these are
+% adapted from David Carlisle's answer on
+% \url{tex.stackexchange.com}, question 57598.
+%    \begin{macrocode}
+\def\b@expandloop#1{%
+	\hbox{%
+		\b@xloop#1\relax
+	}%
+}
+\def\b@xloop#1{%
+		\if#1\fractionsymbol\else\advance\b@colnum by-1\fi%
+		\ifx\relax#1%
+		\else%
+				\if#1\fractionsymbol%
+					\rlap{\hbox to0pt{\hss#1\hss}}%
+				\else%
+					\hbox to\b@digitwid{\hfil{%
+						\csname speciallinestyle\romannumeral\b@linenum\endcsname%
+						\csname specialdigitstyle\romannumeral\b@colnum\endcsname%
+						#1%
+						}\hfil}%
+				\fi%
+			\expandafter\b@xloop%
+		\fi%
+}
+\def\b@spaceout#1{%
+	\countchar{#1}%
+	\b@colnum=\b@charcount%
+	\advance\b@colnum by1%
+	\b@expandloop{#1}%
+}%
+%    \end{macrocode}
+% Now we define our macros for non-long-division problems.
+%    \begin{macrocode}
+\def\probline#1#2{%
+	\advance\b@linenum by1%
+	\b@digitwid=\b@widthofdigit%
+	\b@totalprobwid=\b@digitwid%
+	\multiply\b@totalprobwid by#1%
+	\hbox to\b@totalprobwid{%
+		\hfil\b@spaceout{#2}%
+	}%
+}%
+\def\opline#1#2{%
+	\advance\b@linenum by1%
+	\hbox{%
+		\hbox to\b@digitwid{\hfil#1}%
+		\advance\b@totalprobwid by-\b@digitwid%
+		\hbox to\b@totalprobwid{%
+			\hfil\b@spaceout{#2}%
+		}%
+	}%
+	\vskip0.5ex%
+	\hrule width\b@totalprobwid height\b@solverulewidth%
+	\vskip0.5ex%
+}%
+\def\noopline#1{%
+	\opline{}{#1}%
+}%
+\def\nextpline#1{%
+	\advance\b@linenum by1%
+	\hbox{%
+		\hbox to\b@totalprobwid{%
+			\hfil\b@spaceout{#1}%
+		}%
+	}%
+}%
+\def\soluline#1{%
+	\advance\b@linenum by1%
+	\hbox{%
+		\hbox to\b@totalprobwid{%
+			\hfil\b@spaceout{#1}%
+		}%
+	}%
+	\b@linenum=0%
+}%
+\def\carryline#1#2{%
+	{%
+	\advance\b@linenum by1%
+	\b@digitwid=\b@widthofdigit%
+	\b@totalprobwid=\b@digitwid%
+	\multiply\b@totalprobwid by#1%
+	\footnotesize%
+	\hbox to\b@totalprobwid{%
+		\hfil\b@spaceout{#2}%
+	}%
+	\hrule width\b@totalprobwid height0pt%
+	\vskip0.4em%
+	}%
+}
+%    \end{macrocode}
+% Now we proceed to define the macros for long division.
+%    \begin{macrocode}
+\def\longdiv#1#2#3{%
+	\advance\b@linenum by1%
+	\vskip\baselineskip%
+	\b@digitwid=\b@widthofdigit%
+	\b@topdivline=\b@digitwid%
+	\settowidth{\b@divisorlen}{\b@spaceout{#3}}
+	\b@parenfontsize=\f@size pt%
+	\multiply\b@parenfontsize by12%
+	\divide\b@parenfontsize by10%
+	\settowidth{\b@divparenlen}{%
+		\fontsize{\b@parenfontsize}{\b@parenfontsize}\selectfont)}%
+	\multiply\b@topdivline by#1%
+	\advance\b@topdivline by0.5\b@digitwid%
+	\vskip0.5ex%
+	\vbox{%
+		\hbox{%
+			\hskip\b@divisorlen%
+			\vrule width\b@topdivline height\b@longdivlinewidth%
+		}%
+		\nointerlineskip%
+		\hbox{%
+			\b@spaceout{#3}%
+			\hfil{\fontsize{\b@parenfontsize}{\b@parenfontsize}\selectfont)}%
+			\b@spaceout{#2}%
+		}%
+	}%
+	\advance\b@divisorlen by\b@divparenlen%
+}%
+\def\ldsoluline#1#2{%
+	\advance\b@fulldivlen by\b@divisorlen%
+	\advance\b@fulldivlen by\b@topdivline%
+	\advance\b@fulldivlen by-\b@digitwid%
+	\advance\b@fulldivlen by\b@divparenlen%
+	\vskip-2\baselineskip%
+	\hbox to\b@fulldivlen{%
+		\hfil%
+		\b@spaceout{#1}%
+		\if#2\relax\else\rlap{\hskip1em \b@remaindertext{ }#2}\fi%
+	}%
+	\vskip\baselineskip%
+}%
+%    \end{macrocode}
+% This is an interesting little trick which gets the width
+% of a box; we use this to determine the placement of the
+% drop arrows when we're showing our long division work.
+%    \begin{macrocode}
+\newdimen\b@droparrowwidth
+\def\getdroparrowwidth{%
+	\setbox\@tempboxa\hbox{$\downarrow$}%
+	\b@droparrowwidth=\wd\@tempboxa%
+}%
+%    \end{macrocode}
+% Now we get back to long division macros (yes, these do
+% take a rather long time).  We start with the macro for
+% subsequent long division lines.
+%    \begin{macrocode}
+\def\nextldline#1#2{%
+	\advance\b@linenum by1%
+	\b@ldrowlen=\b@digitwid%
+	\multiply\b@ldrowlen by#1%
+	\hbox{%
+		\hskip\b@divisorlen%
+		\hskip\b@ldrowlen%
+		\b@spaceout{#2}%
+		\b@droparrowlen=\baselineskip%
+		\ifshowdivisionwork%
+			\ifnum\b@linenum>2%
+				\getdroparrowwidth%
+				\multiply\b@droparrowlen by\b@linenum%
+				\advance\b@droparrowlen by-2\baselineskip%
+				\hskip-0.5\b@digitwid%
+				\vtop{\vskip-\baselineskip\vskip-\b@droparrowlen%
+					\rlap{%
+						\vrule width0.4pt height\b@droparrowlen%
+						\hskip-0.5\b@droparrowwidth{$\downarrow$}%
+					}
+				}%
+			\fi%
+		\fi%
+	}%
+}%
+%    \end{macrocode}
+% Now we move on to the styling macros; this requires a lot
+% of looping and other weirdities (weirdities for \TeX\
+% programming, anyway).  First we style lines; then we style
+% columns.
+%    \begin{macrocode}
+\def\linestyle#1#2{%
+	\b@loopi=0%
+	\loop\ifnum\the\b@loopi<\the\b@maxrows%
+		\advance\b@loopi by1%
+		\ifnum#1=\the\b@loopi
+			\expandafter\def\csname speciallinestyle\romannumeral\b@loopi\endcsname{#2}%
+		\fi
+	\repeat
+}%
+\def\digstyle#1#2{%
+	\b@loopi=0%
+	\loop\ifnum\the\b@loopi<\the\b@maxcols%
+		\advance\b@loopi by1%
+		\ifnum#1=\the\b@loopi
+			\expandafter\def\csname specialdigitstyle\romannumeral\b@loopi\endcsname{#2}%
+		\fi
+	\repeat
+}%
+%    \end{macrocode}
+% Now we get our commands to clear the styling; again, first
+% lines, then columns.
+%    \begin{macrocode}
+\def\clearlinestyles{%
+	\b@loopi=0%
+	\loop\ifnum\the\b@loopi<\the\b@maxrows%
+		\advance\b@loopi by1%
+		\expandafter\def\csname speciallinestyle\romannumeral\b@loopi\endcsname{}%
+	\repeat
+}%
+\def\cleardigitstyles{%
+	\b@loopi=0%
+	\loop\ifnum\the\b@loopi<\the\b@maxcols%
+		\advance\b@loopi by1%
+		\expandafter\def\csname specialdigitstyle\romannumeral\b@loopi\endcsname{}%
+	\repeat
+}%
+%    \end{macrocode}
+% A few miscellanies; a box for binding together problems,
+% so that they can be positioned on the page more easily; a
+% macro for doing strikethroughts, quite useful in the
+% carries; and macros for showing or not showing our long
+% division work.
+%    \begin{macrocode}
+\def\problembox#1{%
+	\leavevmode\vbox{#1}%
+}%
+\def\strike#1{%
+	{\rlap{\bf---}#1}%
+}
+\def\showdivwork{%
+	\showdivisionworktrue%
+}
+\def\noshowdivwork{%
+	\showdivisionworkfalse%
+}
+%    \end{macrocode}
+% Now, finally, we clear all the digit styles (so that they
+% at least exist), and then we're done.  Thanks for reading;
+% happy \TeX{}ing!
+%    \begin{macrocode}
+\cleardigitstyles
+%    \end{macrocode}
+% \PrintIndex