alignment mark inside box can't be seen from outside this box

Question

I didn't really know how to write the title, hope it's clear enough (I'm willing to change it if anyone suggests anything better).

My problem is the following: I want to align different items with respect to each other, but with the anchor inside an already aligned environment (this of course fails as it isn't seen outside this environment). Typically I'm giving several definitions of functions, and I'd like to have a pleasing horizontal and vertical alignment between them: horizontal with respect to the column and vertical with respect to the base of first line. Here's a MWE:

\documentclass{minimal}

\usepackage{amsmath}
\usepackage{amsfonts}

\newcommand*\Rset{\mathbb{R}}

\newcommand*\mapping[5]{%
   \begingroup
      \setlength\arraycolsep{0.2em}%
      \begin{array}{ccccc}%
         {#1}&\colon&{#2}&\longrightarrow&{#3}\\
         &&{#4}&\longmapsto&{#5}%
      \end{array}%
   \endgroup
}%

\begin{document}
\begin{align*}
&\mapping f\Rset\Rset x{x^2,}&
&\mapping M\Rset\Rset x{x^{42},}\\*[2ex]
&\mapping{\mathrm{Function}}XYx{\dfrac1{1+\dfrac1{1+x^2}},}&
&\mapping U\Rset\Rset x{x.}
\end{align*}
\end{document}

So far my only option is to put the & for the align* environment in front of the \mapping command, so the horizontal alignment is from the beginning of the name of the function. How can I somehow put the & inside the array environment so that it is not seen by the array environment but by the outer align* environment?

Not mentioning the awful vertical alignment!

Maybe you'll have an altogether different (and better) method to achieve this, but anyways, I'd like to know if it is at all possible (in an easy way) or not.

Answer 1

One way to stick with the way you are doing is to add an optional first parameter to the \mapping macro which specifies the widest element that is to go before the colon and use \makebox to ensure that that element takes up the appropriate amount of space:

Notes:

• As per egreg's comment, specifying [t] as the optional first parameter to array provides the desired vertically alignment.
• The first parameter to \mapping is optional and defaults to the first mandatory parameter if not specified. \IfStrEq from the xstring package was used to test that the first parameter is empty. If you do not wish to use an additional package, this comparison can be done without it.
• The \widthof macro is from the calc package.
• The macros \makebox and \widthof expect text parmaters hence the nede to go into math mode within the parameters to those macros.

Code:

\documentclass{article}

\usepackage{xstring}
\usepackage{calc}
\usepackage{amsmath}
\usepackage{amsfonts}

\newcommand*\Rset{\mathbb{R}}

\newcommand*{\WidestElement}{}%
\newcommand*\mapping[6][]{%
   \begingroup
      \setlength\arraycolsep{0.2em}%
      \IfStrEq{#1}{}{%
            \def\WidestElement{#2}% default \WidestElement to same as #2
        }{%
            \def\WidestElement{#1}% \WidestElement was specified
        }%
      \begin{array}[t]{ccccc}%
         \makebox[\widthof{$\WidestElement$}][r]{$#2$}&\colon&{#3}&\longrightarrow&{#4}\\
         &&{#5}&\longmapsto&{#6}%
      \end{array}%
   \endgroup
}%

\begin{document}
\begin{align*}
&\mapping[\mathrm{Function}]{f}{\Rset}{\Rset}{x}{x^2,}&
&\mapping{M}{\Rset}{\Rset}{x}{x^{42},}\\*[2ex]
&\mapping{\mathrm{Function}}{X}{Y}{x}{\dfrac1{1+\dfrac1{1+x^2}},}&
&\mapping{U}{\Rset}{\Rset}{x}{x.}
\end{align*}
\end{document}

Answer 2

If I understand correctly you just want to move the & into your definition, after the first argument:

\documentclass{minimal}

\usepackage{amsmath}
\usepackage{amsfonts}

\newcommand*\Rset{\mathbb{R}}

\newcommand*\mapping[5]{%
#1&%
   \begingroup
      \setlength\arraycolsep{0.2em}%
      \begin{array}[t]{cccc}%
         \colon&#2&\longrightarrow&#3\\
         &#4&\longmapsto&#5%
      \end{array}%
   \endgroup
}

\begin{document}
\begin{align*}
\mapping f\Rset\Rset x{x^2,}&
\mapping M\Rset\Rset x{x^{42},}\\*[2ex]
\mapping{\mathrm{Function}}XYx{\dfrac1{1+\dfrac1{1+x^2}},}&
\mapping U\Rset\Rset x{x.}
\end{align*}
\end{document}