Polynomial Long Division Using Polynom

Question

I have been toiling around polynom package to typeset polynomial long division. The polynom package produces wonderful long division with step by step process. But I just have two problems. Let me tell you what I need exactly

Here is the output that I produced with polynom for \polylongdiv{X^3+X^2-1}{X-1}

But instead of spaces for the missing x, I want to have 0x. Is it possible to do that? I checked the documentation and I couldn't find a way to do this.

You can read the documentation here: http://www.cs.brown.edu/system/software/latex/doc/polynom.pdf

I also realized that the polynomials aren't formatted inside the math environment. So is there anyway to format these equations inside math environment also? I tried putting $ signs around \polylongdiv{X^3+X^2-1}{X-1}, but that didn't change anything. Equations inside math environment produces something like this

I am very new to latex. So please help me.

Update: @polgab helped me solve the second question of producing math environment like output. I just need the solution for question 1 now which is I want to have 0x in the place of missing x instead of a space which is being produced by polynom.

Answer 1

Changing the internal macros that are responsible for omitting zero terms you get what you want (but you have to specify the zero term in the input):

\documentclass{article}
\usepackage{polynom}
\makeatletter
\def\pld@CF@loop#1+{%
    \ifx\relax#1\else
        \begingroup
          \pld@AccuSetX11%
          \def\pld@frac{{}{}}\let\pld@symbols\@empty\let\pld@vars\@empty
          \pld@false
          #1%
          \let\pld@temp\@empty
          \pld@AccuIfOne{}{\pld@AccuGet\pld@temp
                            \edef\pld@temp{\noexpand\pld@R\pld@temp}}%
           \pld@if \pld@Extend\pld@temp{\expandafter\pld@F\pld@frac}\fi
           \expandafter\pld@CF@loop@\pld@symbols\relax\@empty
           \expandafter\pld@CF@loop@\pld@vars\relax\@empty
           \ifx\@empty\pld@temp
               \def\pld@temp{\pld@R11}%
           \fi
          \global\let\@gtempa\pld@temp
        \endgroup
        \ifx\@empty\@gtempa\else
            \pld@ExtendPoly\pld@tempoly\@gtempa
        \fi
        \expandafter\pld@CF@loop
    \fi}
\def\pld@CMAddToTempoly{%
    \pld@AccuGet\pld@temp\edef\pld@temp{\noexpand\pld@R\pld@temp}%
    \pld@CondenseMonomials\pld@false\pld@symbols
    \ifx\pld@symbols\@empty \else
        \pld@ExtendPoly\pld@temp\pld@symbols
    \fi
    \ifx\pld@temp\@empty \else
        \pld@if
            \expandafter\pld@IfSum\expandafter{\pld@temp}%
                {\expandafter\def\expandafter\pld@temp\expandafter
                    {\expandafter\pld@F\expandafter{\pld@temp}{}}}%
                {}%
        \fi
        \pld@ExtendPoly\pld@tempoly\pld@temp
        \pld@Extend\pld@tempoly{\pld@monom}%
    \fi}
\makeatother
\begin{document}
\polylongdiv{X^3+X^2+0X-1}{X-1}
\end{document}