Command with arguments separated by comma II (typically an easy way to write matrices)

Question

Since I am using 2 x 2 matrices very frequently, I would like to define a command which would work like this: \matr{a, b, c, d} would produce $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$.

Of course, I know how to get this result using something like \matr{a}{b}{c}{d}, but the point is to have a "comma-separated list" of arguments. A solution using \matr{a, b}{c, d} could be interesting as well (especially its generalization to 3 x 3 matrices).

Most of the answers from here, there or there seem to rely on xparse package. But I am highly unused to the LaTeX3 syntax, so I have no clue on how to tackle with my problem.

Answer 1

The argument is first split at commas in a sequence which is mapped taking into account the positions, so we can add & or \\ as needed.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\matr}{m}
 {
  \begin{pmatrix}
  \seq_set_from_clist:Nn \l__watson_matr_seq { #1 }
  \seq_indexed_map_function:NN \l__watson_matr_seq __watson_matr_entry:nn
  \end{pmatrix}
 }
\seq_new:N \l__watson_matr_seq
\cs_new:Nn __watson_matr_entry:nn
 {
  #2 % the entry
  \int_case:nn { #1 } { {1}{&} {2}{\} {3}{&} }
 }
\ExplSyntaxOff
\begin{document}
[
\matr{a,b,c,d}
]
\end{document}

Can we generalize it? Yes.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\matr}{O{2}m}
 {
  \int_set:Nn \l__watson_matr_size_int { #1 }
  \begin{pmatrix}
  \watson_matr:nn { #1 } { #2 }
  \end{pmatrix}
 }
\seq_new:N \l__watson_matr_seq
\int_new:N \l__watson_matr_size_int
\cs_new_protected:Nn \watson_matr:nn
 {
  \seq_set_from_clist:Nn \l__watson_matr_seq { #2 }
  \seq_indexed_map_function:NN \l__watson_matr_seq __watson_matr_entry:nn
 }
\cs_new_protected:Nn __watson_matr_entry:nn
 {
  #2 % the entry
  \int_compare:nTF { \int_mod:nn { #1 } { \l__watson_matr_size_int } = 0 }
   { \ }
   { & }
 }
\ExplSyntaxOff
\begin{document}
[
\matr{a,b,c,d}\ne\matr[3]{1,2,3,4,5,6,7,8,9}
]
\end{document}

If you're willing to accept a slightly different syntax, with semicolons for ending rows, you can easily produce matrices with different shapes and delimiters.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\matr}{O{p}m}
 {
  \seq_set_split:Nnn \l__watson_matr_full_seq { ; } { #2 }
  \begin{#1matrix}
  \seq_map_function:NN \l__watson_matr_full_seq __watson_matr_makerow:n
  \end{#1matrix}
 }
\seq_new:N \l__watson_matr_full_seq
\seq_new:N \l__watson_matr_row_seq
\cs_new_protected:Nn __watson_matr_makerow:n
 {
  \seq_set_split:Nnn \l__watson_matr_row_seq { , } { #1 }
  \seq_use:Nn \l__watson_matr_row_seq { & }
  \
 }
\ExplSyntaxOff
\begin{document}
[
\matr{a,b;c,d}\ne\matr[b]{1,2,3;4,5,6;7,8,9;10,11,12}
]
\end{document}

Answer 2

I am highly unused to the LaTeX3 syntax too, so I give you non-exp3 solution based only on TeX primitives. You need not any LaTeX package (and you basically don't even need LaTeX):

\documentclass[12pt]{article}
\def\addto#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}
\def\matr#1{\def\matrL{}\matrA#1\end}
\def\matrA#1{\ifx\end#1\pmatrix{\matrL}\else 
   \ifx,#1\addto\matrL{&}\else
   \ifx;#1\addto\matrL{\cr}\else
   \addto\matrL{#1}\fi\fi
   \expandafter\matrA\fi
}
\begin{document}
$$
  \matr{a,b;c,d}\ne\matr{1,2,3;4,5,6;7,8,9;10,11,12}
$$
\end{document}

Answer 3

Here I use tokcycle to replace the commas with & separators. WHile I show 2x2 and 3x3, any number of columns are acceptible, as long as the matrices contain 2 or (optionally) 3 rows.

\documentclass{article}
\usepackage{amsmath,tokcycle}
\newcommand\matr[1][2]{\tctestifnum{3=#1}{\matrTHREE}{\matrTWO}}
\newcommand\matrTWO[2]{%
  \tokcyclexpress{#1\\#2}%
  \begin{pmatrix}\the\cytoks\end{pmatrix}}
\newcommand\matrTHREE[3]{%
  \tokcyclexpress{#1\\#2\\#3}%
  \begin{pmatrix}\the\cytoks\end{pmatrix}}
\Characterdirective{\tctestifx{,#1}{\addcytoks{&}}{\addcytoks{#1}}}
\begin{document}
\[
\matr{a, b}{c, d}
\]
\[
\matr[3]{a, b,c}{d, e, f}{g, h, i}
\]
\end{document}

OPTIONAL SINGLE ARGUMENT APPROACH

This allows any combination of rows and columns within a single argument with the syntax \matr{ a, b / c, d} Here, commas are taken a column separators and / tokens are taken as row separators:

\documentclass{article}
\usepackage{amsmath,tokcycle}
\newcommand\matr[1]{\tokcyclexpress{#1}%
  \begin{pmatrix}\the\cytoks\end{pmatrix}}
\Characterdirective{\tctestifx{,#1}{\addcytoks{&}}{%
  \tctestifx{/#1}{\addcytoks{\\}}{\addcytoks{#1}}}}
\begin{document}
\[
\matr{a, b / c, d}
\]
\[
\matr{a, b,c / d, e, f/ g, h, i}
\]
\end{document}

Answer 4

A solution without any packages that is based on two fast loops to replace , with & and ; with \\ (so the syntax is the same as in @wipet's answer, but the execution is marginally faster, and it has no problems with braced groups, e.g., \matr{\mathbf{stuff},b;c,d} works as intended). To change to other parsing tokens than , and ; just swap out these two in every definition...

Also, I separated the parsing macro from the pmatrix, so that you could also use other matrix/tabular like enviroments (e.g., \begin{tabular}{cc}\matrinp{a,b;c,d}\end{tabular} would work as well).

\documentclass[]{article}
\usepackage[]{amsmath}
\makeatletter
\newcommand\matr[1]
  {%
    \begin{pmatrix}
      \matrinp{#1}%
    \end{pmatrix}
  }
\newcommand\matrinp[1]
  {%
    \expandafter@firstofone\expandafter
      {%
        \romannumeral
        \matr@commas
          \matr@nil#1\matr@mark
          \matr@stop\matr@commas
          ,\matr@stop\matr@commas@done
      }%
  }
\long\def\matr@commas#1,#2\matr@stop#3{#3#1&#2\matr@stop#3}
\long\def\matr@commas@done#1\matr@stop#2\matr@commas@done
  {\matr@semicolon#1\matr@stop\matr@semicolon;\matr@stop\matr@done}
\long\def\matr@semicolon#1;#2\matr@stop#3{#3#1\#2\matr@stop#3}
\long\def\matr@done#1\matr@mark#2\matr@done{\expandafter\z@@gobble#1}
\makeatother
\begin{document}
[
  \matr{a,b;c,d}\ne\matr{1,2,3;4,5,6;7,8,9;10,11,12}
]
\end{document}

Answer 5

A little bit late to the party, but for the sake of variety, here's a LuaLaTeX-based solution. Regarding input syntax, I make the assumption that , is used as the separator between cells in a given row, while ; is used as the separator between rows.

\documentclass{article}
\usepackage{amsmath} % for 'pmatrix' environment
\usepackage{luacode} % for '\luaexec' macro
\luaexec{
    function matr ( s ) 
       s = s:gsub ( ";" , "\\" )
       s = s:gsub ( "," , "&" )
       tex.sprint ( "\begin{pmatrix}" .. s .. "\end{pmatrix}" )
    end
}
\newcommand\matr[1]{\directlua{ matr ( "#1" ) }}
\begin{document}
$\matr{ a, b ; c, d  }$
\end{document}

Answer 6

If you are a Emacs user, such a command already exists. You just type (for example)

\[ [[a b][c d]]\]

and when the point is on this formula, call the Calc-embedded command (C-x * e) . Emacs immediately returns:

\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix}\]

As a bonus, Calc allows you to perform many matrix operations.

You have to call again Calc-embedded to return to normal latex-mode.