Variable argument macro to define splitting polynomial

Question

I need a macro that behaves the following:

\mpoly{x}{1}{2} outputs (x+1)(x+2)

\mpoly{x}{1}{2}{3} outputs (x+1)(x+2)(x+3)

\mpoly{x}{1}{2}{3}{5} outputs (x+1)(x+2)(x+3)(x+5)

and so on. I am not at all confident with the variable length argument processing by tex. Could anyone help me with this?

Answer 1

I streamline the syntax by putting all the term data in a comma separated list in the 2nd argument. I use listofitems to parse the list (the default list separtor is a comma, but that could be changed). The package's \foreachitem macro allows easy regurgitation.

\documentclass{report}
\usepackage{listofitems}
\newcommand\mpoly[2]{%
  \readlist\myterms{#2}%
  \foreachitem\x\in\myterms{(#1+\x)}%
}
\begin{document}
$y_1 =\mpoly{x}{1,2}$

$y_2 =\mpoly{x}{1,2,3}$

$y_3 = \mpoly{x}{1,2,3,5}$
\end{document}

This can be generalized to a more inclusive format, with the use of nested parsing, to allow multiple variables as well as setting the +/- operation:

\documentclass{report}
\usepackage{listofitems}
\newcommand\mpoly[1]{%
  \setsepchar{*/+||-/,}
  \readlist\myterms{#1}%
  \foreachitem\x\in\myterms[]{
    \foreachitem\y\in\myterms[\xcnt,2]{(\myterms[\xcnt,1]\mytermssep[\xcnt,1]\y)}%
  }%
}
\begin{document}
$y_1 =\mpoly{x+1,2 * y-3,4}$

$y_2 =\mpoly{x+2,3 * x-4,5,6,7}$

$y_3 = \mpoly{x-1,2 * y+3,5 * z-6}$
\end{document}

Answer 2

Different syntax could be more flexible:

\usepackage{pgffor}
\newcommand*\mpoly[2]{\foreach\x in{#2}{(#1\x)}}

That would let you do \mpoly{x-}{1,2,3} or \mpoly{x+}{2,...,5}.

Another option could be

\newcommand*\mpolyn[3]{\foreach\x in{#3}{(#1#2\x)}}

That would let you do \mpolyn x-{1,2,3} or \mpolyn x+{2,...,5}. Or may be cleaner definition for this last synax

\newcommand\mpolyn{}
\protected\def\mpolyn#1#{\mpolynaux{#1}}
\protected\def\mpolynaux#1#2{\foreach\x in{#2}{(#1\x)}}

And that way you can \mpolyn xyz - {1,2,3} or \mpolyn \ln(x) + {2,...,5} for instance.