Unbounded number of arguments - Good practice

Question

Here is how I do to work with unbounded number of arguments of a macro. Is there a better way to do that ?

\documentclass[12pt,a4paper]{article}

\usepackage{ifmtarg}
\usepackage{nicematrix}

\makeatletter
    \def\backify#1|#2\@nil{%
        \@ifmtarg{#2}{%
            #1%
        }{%
            #1 \\ \backify#2\@nil%
        }%
    }

    \newcommand\vcoord[1]{%
        \begin{pmatrix}
            \backify#1|\@nil %
        \end{pmatrix}%
    }
\makeatother

\begin{document}

$\vcoord{3 | -4 | 0}$

\end{document}

Answer 1

Using expl3 (which is loaded by xparse) you can use the built-in sequence type. The following defines your \vcoord using only built-in functions. The result is not expandable. It also adds two macros, \readsequence that sets up a sequence variable (unexpandable), and \usesequence which expands to the sequence with each sequence element separated by its argument (expandable). You can look at interface3 for the documentation of the available functions in expl3.

\documentclass[]{article}

\usepackage{amsmath}
\usepackage{xparse}
\ExplSyntaxOn
\seq_new:N \l__projetmbc_seq
\NewDocumentCommand \readsequence { +m +m }
  {
    \seq_set_split:Nnn \l__projetmbc_seq { #1 } { #2 }
  }
\NewExpandableDocumentCommand \usesequence { +m }
  {
    \seq_use:Nnnn \l__projetmbc_seq { #1 } { #1 } { #1 }
  }
\NewDocumentCommand \vcoord { m }
  {
    \group_begin:
    \seq_set_split:Nnn \l__projetmbc_seq { | } { #1 }
    \begin { pmatrix }
      \seq_use:Nnnn \l__projetmbc_seq { \\ } { \\ } { \\ }
    \end { pmatrix }
    \group_end:
  }
\ExplSyntaxOff

\begin{document}
\readsequence{|}{a|b|c|d|e}
\[
  \begin{pmatrix}
    \usesequence{\\}
  \end{pmatrix}
\]

\[
  \vcoord{3|-4|0}
\]
\end{document}

Answer 2

Not sure about best practice, but you can simplify the definition somewhat:

\documentclass[12pt,a4paper]{article}

\usepackage{amsmath}


\long\def\backify#1|{#1\backify\\}
\def\endbackify#1#2{}

    \newcommand\vcoord[1]{%
        \begin{pmatrix}
            \backify#1|\endbackify|%
        \end{pmatrix}%
    }


\begin{document}

$\vcoord{3 | -4 | 0}$

\end{document}

Answer 3

I propose a different way to cope with what you seem to be doing.

\documentclass[12pt,a4paper]{article}

\usepackage{xparse}
\usepackage{amsmath}

\ExplSyntaxOn

% a general purpose macro for defining other macros
\NewDocumentCommand{\makemultiargument}{mmmmm}
 {
  \projetmbc_multiarg:nnnnn { #1 } { #2 } { #3 } { #4 } { #5 }
 }

% allocate a private variable
\seq_new:N \l__projetmbc_generic_seq

% the internal version of the general purpose macro
\cs_new_protected:Nn \projetmbc_multiarg:nnnnn
 {% #1 = separator
  % #2 = multiargument
  % #3 = code before
  % #4 = code between
  % #5 = code after

  % a group allows nesting
  \group_begin:
  % split the multiargument into parts
  \seq_set_split:Nnn \l__projetmbc_generic_seq { #1 } { #2 }
  % execute the <code before>
  #3
  % deliver the items, with the chosen material between them
  \seq_use:Nn \l__projetmbc_generic_seq { #4 }
  % execute the <code after>
  #5
  % end the group started at the beginning
  \group_end:
 }

\ExplSyntaxOff

% separator: |; before: \begin{pmatrix}; between: \\, after: \end{pmatrix}
\newcommand{\vcoord}[1]{%
  \makemultiargument{|}{#1}{\begin{pmatrix}}{\\}{\end{pmatrix}}%
 }

\begin{document}

$\vcoord{3 | \vcoord{-4 | -3 } | 0}$ 

\end{document}

It is possible to add formatting to each entry, with a trailing optional argument (without it the macro is the same as in the previous version).

\documentclass[12pt,a4paper]{article}

\usepackage{xparse}
\usepackage{amsmath}

\ExplSyntaxOn

\NewDocumentCommand{\makemultiargument}{mmmmmo}
 {
  \projetmbc_multiarg:nnnnnn { #1 } { #2 } { #3 } { #4 } { #5 } { #6 }
 }

\seq_new:N \l__projetmbc_generic_seq

\cs_new_protected:Nn \projetmbc_multiarg:nnnnnn
 {% #1 = separator
  % #2 = multiargument
  % #3 = code before
  % #4 = code between
  % #5 = code after
  % #6 = ornament to items

  % allow nesting
  \group_begin:
  % split the multiargument
  \seq_set_split:Nnn \l__projetmbc_generic_seq { #1 } { #2 }
  \tl_if_novalue:nF { #6 }
   {
    \seq_set_eq:NN \l__projetmbc_temp_seq \l__projetmbc_generic_seq
    \seq_set_map:NNn \l__projetmbc_generic_seq \l__projetmbc_generic_seq { #6 }
   }
  #3
  \seq_use:Nn \l__projetmbc_generic_seq { #4 }
  #5
  \group_end:
 }

\ExplSyntaxOff

\NewDocumentCommand{\vcoord}{m}
 {
  \makemultiargument{|}{#1}{\begin{pmatrix}}{\\}{\end{pmatrix}}
 }

\NewDocumentCommand{\pboxed}{m}{\boxed{#1}}

\begin{document}

$\vcoord{3 | \vcoord{-4 | -3 } | 0}$

$\makemultiargument{|}{-4 | -3  | 0}{\begin{pmatrix}}{\\}{\end{pmatrix}}[\pboxed{#1}]$

\end{document}

Beware that macros in the trailing argument have to be either fully expandable or protected (which is why I defined \pboxed; the standard \boxed would not fail, but just by chance).