[OS X TeX] Long Division redux

[Alain Schremmer]

I once appealed to this list for help setting up long divisions. I 
remember not using Arseneau's longdiv, for whatever reason, but someone 
gave me some code which I have been using ever since.

Now I want to set up long divisions for polynomials. I was able to fudge 
what I had but I have the strong feeling that I am defeating the code 
that was given to me and I don't understand it enough to adapt it.

I wonder if, as mostly a matter of esthetics, someone might be williing 
to do so.

Below is the template that I am using, in the form of a document, should 
anyone be interested by the exercise.

Regards for the New Year
--schremmer

\documentclass[11pt]{book}
\begin{document}

\begin{center}
\newdimen\digitwidth \settowidth\digitwidth{0}
\def~{\hspace{\digitwidth}}
\def\divrule#1#2{%
\noalign{\moveright#1\digitwidth%
\vbox{\hrule width#2\digitwidth}}}
%This is the divisor
            $0$
            $+0h$
            $+0h^{2}$
            $+0h^{3}$
                \hspace{0mm}
        \begin{tabular}[b]{@{}l@{}}
%This is the quotient (Its length controls the line.)
                \hspace{5mm}
            $0$
                \hspace{5mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
            \\
            \hline
        \big)
        \begin{tabular}[t]{@{}l@{}l@{}}
%This is the dividend
                \hspace{2mm}
            $0$
                \hspace{5mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
        \\
%This is the first multiplication
                \hspace{2mm}
            $0$
                \hspace{5mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
           \divrule{0}{30}
%This is the first subtraction
                \hspace{2mm}
            $0$
                \hspace{5mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
%This is the second multiplication
                \hspace{2mm}
            $ð$
                \hspace{7mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
           \divrule{7}{23}
%This is the second subtraction
                \hspace{2mm}
            $ð$
                \hspace{7mm}
            $+0h$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
%This is the third multiplication
                \hspace{6mm}
            $ð$
                \hspace{10mm}
            $ð$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
           \divrule{13}{17}
%This is the third subtraction
                \hspace{8mm}
            $ð$
                \hspace{8mm}
            $ð$
                \hspace{5mm}
            $+0h^{2}$
                \hspace{5mm}
            $+0h^{3}$
           \\
%This is the fourth multiplication
                \hspace{10mm}
            $ð$
                \hspace{10mm}
            $ð$
                \hspace{10mm}
            $ð$
                \hspace{5mm}
            $+0h^{3}$
           \\
           \divrule{20}{10}
%This is the fourth subtraction
                \hspace{10mm}
            $ð$
                \hspace{10mm}
            $ð$
                \hspace{10mm}
            $ð$
                \hspace{5mm}
            $+0h^{3}$
           \\
           \end{tabular}
           \end{tabular}
\end{center}       

\end{document}

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