How to Enhance an Existing Math Environment

Question

I'm taking the next step in my learning of LaTeX and starting to explore the possibility of creating custom environments; however, the resources I've consulted don't mention how to create an environment like the bmatrix environment that does not have a pre-defined number of arguments.

In particular, I'd like to define a variant of bmatrix (and similar) that allows me to colour the rows / columns.

Ideally, I'd like to figure out a way to define the environment so that I can:

• specify the colour of each row / column at the opening of the environment (or at the first element of the row / column). E.g. if \ca, \cb and \cc are macros for different colours, then something like \begin{cbmatrix}{\ca \ca \cb} would start a bmatrix environment where the entries in the first row will each be wrapped in \ca, similarly for the second row, and the entries of the third row would be wrapped in cb,

i.e. the desired output would be equivalent to:

\begin{bmatrix}
\ca{e1} & \ca{e2} & \ca{e3} & \ca{e4} \\
\ca{e5} & \ca{e6} & \ca{e7} & \ca{e8} \\
\cb{e9}& \cb{e10} & \cb{e11} & \cb{e12} \\
e13 & e14 & e15 & e16
\end{bmatrix}

• easily switch between applying the colour command to rows or columns (perhaps with a starred version of the environment)?

I realize this is a very specific end-result, but I'm generally curious to know where to begin to be able to define this type of environment, where the number of inputs / arguments isn't predefined?

Answer 1

Very fragile mixture of array, collcell, and some internal macros.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{collcell}
\usepackage{xcolor}

\newcommand\ca{\textcolor{red}}
\newcommand\cb{\textcolor{green}}
\newcommand\cc{\textcolor{blue}}

\newcounter{row}
\newcounter{col}
\makeatletter
\newenvironment{triplecolorbmatrix}[1]
  {\setcounter{row}{1}%
   \@for\name:=#1\do{%
       \expandafter\def\csname rowcolor\number\value{row}\expandafter\endcsname\expandafter{\name}%
       \stepcounter{row}%
   }%
   \setcounter{row}{0}%
   \setcounter{col}{0}%
   \newcommand\colorrow{\csname rowcolor\number\value{row}\endcsname}%
   \let\@arraycrnormal\@arraycr
   \def\@arraycr{\setcounter{col}{0}\@arraycrnormal}%
   \left[\hspace{-\tabcolsep}\array{*{10}{>{\ifnum\value{col}=0\stepcounter{row}\fi\stepcounter{col}\collectcell\colorrow}c<{\endcollectcell}}}}
  {\endmatrix\right]}
\makeatother

\begin{document}
\begin{equation*}
  \begin{triplecolorbmatrix}{\ca,\cb,\cc}
    e1  & e2  & e3  & e4  \\
    e5  & e6  & e7  & e8  \\
    e9  & e10 & e11 & e12 \\
    e13 & e14 & e15 & e16 \\
  \end{triplecolorbmatrix}
\end{equation*}
\end{document}