inline bracket, similar to a permutation and binomial, but aligned

Question

I'm often experiencing instances, when I need to define a function on two sets in a domain. I'd like to create a command \newcommand{\func}[4]{...}, which makes an inline bracket, that shows how the function maps both sets of points.

So far, I've managed to do this

via the command $\binom{\tiny(x,s,t)\mapsto(x,s(1-t))}{\tiny(y,t)\mapsto y~~~~~~~~~}. As you can see, I'm having problems with the alignment of both \mapstos and also with the size of the both outer brackets.

Could anyone please help me write such a command? I tried it with an inline table, but it is way too large. It would be desirable (but not necessary) that both outer brackets would respond to \left and \right or \big.

COMMENT: this is how my current solution (via \binom with no alignment) looks like:

Any solution that produces larger brackets is not acceptable. The only thing that is missing is alignment.

Answer 1

Ideally, one would have a version of aligned with smaller spacing. I'm not aware of any implementation of that though.

Here is a non-automatic solution with \mathllap and psmallmatrix* from mathtools:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
abc 
$\begin{psmallmatrix*}[l]
    (x,s,t)                           \mapsto (x,s(1-t)) \\ 
    \phantom{(x,s,t)}\mathllap{(y,t)} \mapsto y
\end{psmallmatrix*}$
abc
\end{document}

Answer 2

Here's an option, building on Tobi's answer. Now the command offers three different sizes depending on the first (optional argument): with no optional argument, it can be used in in-line expressions; using Big or bigg as the optional argument, you can increase the size and use the command in displayed expressions.

\documentclass[12pt,a4paper]{scrartcl}
\usepackage{ifthen}
\usepackage{amsmath,mathtools}

% default values
\newcommand\OpenS{\bigl(}
\newcommand\CloseS{\bigr)}
\newcommand\Vspace{-0.85em}
\newcommand\Msize{\scriptstyle}

\newcommand{\func}[5][]{%
  \ensuremath{% 
    \ifthenelse{\equal{#1}{Big}}
      {\renewcommand\OpenS{\Bigl(}%
        \renewcommand\CloseS{\Bigr)}%
        \renewcommand\Vspace{-0.55em}%
        \renewcommand\Msize{\textstyle}}%
      {\ifthenelse{\equal{#1}{bigg}}%
        {\renewcommand\OpenS{\biggl(}%
          \renewcommand\CloseS{\biggr)}%
          \renewcommand\Vspace{-0.2em}%
          \renewcommand\Msize{\displaystyle}}%
          {}}
          \OpenS%
            \begin{aligned}\Msize
            {\Msize#2} &\mapsto {\Msize#3}\\[\Vspace]
            {\Msize#4} &\mapsto {\Msize#5}
            \end{aligned}
        \CloseS%
    }%
}

\begin{document}
text text  text text t text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text text text $k(g)=\func{(x,s,t)}{(x,s(t-1))}{(y,t)}{y}$ text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  
\[
k(g)=\func[Big]{(x,s,t)}{(x,s(t-1))}{(y,t)}{y}
\]
text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text 
\[
k(g)=\func[bigg]{(x,s,t)}{\big(x,s(t-1)\big)}{(y,t)}{y}
\]
text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text text  text text 

\end{document}

The result:

Answer 3

Try this (note that you’ll need the amsmath-package):

\documentclass[11pt,a4paper]{scrartcl}
\usepackage{amsmath}
\newcommand{\func}[4]{%
    \ensuremath{%
        \left(%
            \begin{aligned}
            #1 &\rightarrow #2\\
            #3 &\rightarrow  #4
            \end{aligned}
        \right)%
    }%
}

\begin{document}
\[k(g)=\func{abcd}{ef}{gh}{ijklm}\]
\end{document}

output:

You just have to replace the arrows …

Answer 4

This is a streamlined version of Gonzalo's answer

\makeatletter
\newcommand{\ho@func}[8]{
  %#1 = opening delimiter
  %#2 = closing delimiter
  %#3 = vertical space 
  %#4 = size of symbols
  %#5 = top left
  %#6 = top right
  %#7 = bottom left
  %#8 = bottom right
  #1\vcenter{\halign{\hfil$##\mapsto{}$&$##$\hfil\cr
    #4#5&#4#6\cr\noalign{\vskip#3}#4#7&#4#8\cr}}#2}
\@namedef{ho@}{\ho@func{\bigl(}{\bigr)}{-1ex}{\scriptstyle}}
\@namedef{ho@Big}{\ho@func{\Bigl(}{\Bigr)}{-.2ex}{\textstyle}}
\@namedef{ho@bigg}{\ho@func{\biggl(}{\biggr)}{0ex}{\textstyle}}
\newcommand{\func}[1][]{\@nameuse{ho@#1}}
\makeatother

The optional argument to \func decides which one of the \ho@... commands to use; the command \ho@... expands to \ho@func followed by four of the eight arguments it requires, the following four are in the input stream,where they appear to the user as arguments to \func.

I too, as Phil, would never define such a thing using \ensuremath: putting math formulas where they belong helps to confine syntax errors.

Note: edited to use directly \halign. The example text can be the same as in Gonzalo's answer, no extra package is needed.

Answer 5

Here's a version using Xy-pic:

\documentclass[12pt]{article}
\usepackage[all,cmtip]{xy}

\newcommand{\func}[4]{
  \begingroup
  \let\objectstyle=\scriptstyle
  \ensuremath{
    \left(
      \vcenter{
        \xymatrix@R=0ex@C=1em{
          {#1} \ar@{|->}[r]& {#2}\\
          {#3} \ar@{|->}[r]& {#4}
        }
      }
    \right)
  }
  \endgroup
}

\begin{document}

Here we are in math mode: $\func{(x,y)}{x+y}{(s,t)}{s^{2}-t}$

Here we are not in math mode: \func{(x,s,t)}{(x,s(1-t))}{(y,t)}{y}

\end{document}

(I would never have thought of using \ensuremath, but I saw it in @Tobi's answer.)