Mapping a macro onto multiple lists simultaneously

Question

I have a macro (say \myMacro) that takes three arguments (say a, b, c) and I want to write another macro (say \otherMacro) that given three lists of parameters (comma delimited lists and all of the same length and the length of the lists is two or more) maps \myMacro onto these arguments in turn. That is

\otherMacro {a1, a2, a3}{b1, b2, b3}{c1, c2, c3}

gives the representation

\myMacro{a1}{b1}{c1} \mapsto
  (\myMacro{a2}{b2}{c2} , \myMacro{a3}{b3}{c3})

and

\otherMacro {a1, a2, a3, a4}{b1, b2, b3, b4}{c1, c2, c3, c4}

gives the representation

\myMacro{a1}{b1}{c1} \mapsto
  (\myMacro{a2}{b2}{c2} , \myMacro{a3}{b3}{c3}, \myMacro{a4}{b4}{c4})

I am a LaTeX novice and I am very sorry if similar questions have already been asked. I searched the site and found problems that were somewhat similar but I couldn't make sense of the solutions.

Answer 1

A rather crude version:

\documentclass{article}

\makeatletter
\newcount\my@index
\newcommand\otherMacro[3]
{%
  \my@index\z@
  \@othermacro#1,\@nil#2,\@nil#3,\@nil
}
\def\@othermacro#1,#2\@nil#3,#4\@nil#5,#6\@nil
{%
  \ifnum\my@index=\@ne\mapsto (\fi
  \ifnum\my@index>\@ne,\fi
  \myMacro{#1}{#3}{#5}%
  \ifx\empty#2\empty
    )%
   \else
    \advance\my@index\@ne
    \@othermacro#2\@nil#4\@nil#6\@nil
  \fi
}
\newcommand\myMacro[3]{\max(#1,#2,#3)}
\makeatother

\begin{document}

$\otherMacro {a1,a2,a3,a4}{b1,b2,b3,b4}{c1,c2,c3,c4}$


\end{document}

Answer 2

This works for arbitrarily long lists (at least two elements, of course):

\documentclass{article}
\usepackage{xparse}

\newcommand{\myMacro}[3]{[#1,#2,#3]} % define suitably

\ExplSyntaxOn
\NewDocumentCommand{\otherMacro}{mmm}{ \maps_splitargs:nnn {#1}{#2}{#3} }

\seq_new:N \l_maps_first_seq
\seq_new:N \l_maps_second_seq
\seq_new:N \l_maps_third_seq

\cs_new:Npn \maps_splitargs:nnn #1 #2 #3
 {
  \seq_set_split:Nnn \l_maps_first_seq  {,} { #1 }
  \seq_set_split:Nnn \l_maps_second_seq {,} { #2 }
  \seq_set_split:Nnn \l_maps_third_seq  {,} { #3 }
  \prg_stepwise_inline:nnnn { 0 } { 1 } { \seq_length:N \l_maps_first_seq - 1 }
   {
    \tl_set:Nx \l_tmpa_tl
     {
      { \seq_item:Nn \l_maps_first_seq { ##1 } }
      { \seq_item:Nn \l_maps_second_seq { ##1 } }
      { \seq_item:Nn \l_maps_third_seq { ##1 } }
     }
    \exp_after:wN \myMacro \l_tmpa_tl
    \int_compare:nTF { ##1 = 0 }
     { \mapsto ( }
     { \int_compare:nTF { ##1 = \seq_length:N \l_maps_first_seq - 1 } { ) } { , } }
   }
 }
\ExplSyntaxOff


\begin{document}

$\otherMacro {a1,a2}{b1,b2}{c1,c2}$

$\otherMacro {a1,a2,a3}{b1,b2,b3}{c1,c2,c3}$

$\otherMacro {a1,a2,a3,a4}{b1,b2,b3,b4}{c1,c2,c3,c4}$

$\otherMacro {a1,a2,a3,a4,a5}{b1,b2,b3,b4,b5}{c1,c2,c3,c4,c5}$

\end{document}

---

Important change

Due to the changes made to expl3 in Summer 2012, the code above should be replaced by the following:

\documentclass{article}
\usepackage{xparse}

\newcommand{\myMacro}[3]{[#1,#2,#3]} % define suitably

\ExplSyntaxOn
\NewDocumentCommand{\otherMacro}{mmm}{ \maps_splitargs:nnn {#1}{#2}{#3} }

\seq_new:N \l_maps_first_seq
\seq_new:N \l_maps_second_seq
\seq_new:N \l_maps_third_seq

\cs_new:Npn \maps_splitargs:nnn #1 #2 #3
 {
  \seq_set_split:Nnn \l_maps_first_seq  {,} { #1 }
  \seq_set_split:Nnn \l_maps_second_seq {,} { #2 }
  \seq_set_split:Nnn \l_maps_third_seq  {,} { #3 }
  \int_step_inline:nnnn { 1 } { 1 } { \seq_count:N \l_maps_first_seq }
   {
    \tl_set:Nx \l_tmpa_tl
     {
      { \seq_item:Nn \l_maps_first_seq { ##1 } }
      { \seq_item:Nn \l_maps_second_seq { ##1 } }
      { \seq_item:Nn \l_maps_third_seq { ##1 } }
     }
    \exp_after:wN \myMacro \l_tmpa_tl
    \int_compare:nTF { ##1 = 1 }
     { \mapsto ( }
     { \int_compare:nTF { ##1 = \seq_count:N \l_maps_first_seq } { ) } { , } }
   }
 }
\ExplSyntaxOff


\begin{document}

$\otherMacro {a1,a2}{b1,b2}{c1,c2}$

$\otherMacro {a1,a2,a3}{b1,b2,b3}{c1,c2,c3}$

$\otherMacro {a1,a2,a3,a4}{b1,b2,b3,b4}{c1,c2,c3,c4}$

$\otherMacro {a1,a2,a3,a4,a5}{b1,b2,b3,b4,b5}{c1,c2,c3,c4,c5}$

\end{document}