One of the more frustrating features of TeX's macro-expansion based language is that the control code and the code it controls can interact unexpectedly. This means that if you want a conditional block \ifwhatever...\fi to control some macro \macro that affects stuff after the block, you need to leapfrog \macro to finish the conditional first:
\ifwhatever
\expandafter\macro
\fi
<stuff taken as an argument by \macro>
You see, the \expandafter eats the \fi before \macro can. Using this trick, you can write some code that conditionally executes some following code. Say you have a conditional \ifwhatever, and you want to execute <code> if it is true, but not if it is false. Then you can write (here I am assuming \makeatletter is active):
\ifwhatever
\expandafter\@firstofone
\else
\expandafter\@gobble
\fi
{<code>}
This can be generalized if you want to select among two different pieces of code, which by the way is how the LaTeX-style conditionals \ifwhatever{<true code>}{<false code>} work:
\ifwhatever
\expandafter\@firstoftwo
\else
\expandafter\@secondoftwo
\fi
{<code 1>}
{<code 2>}
I wouldn't advise doing this with more than one conditional, though: if you want to execute <code> when \ifwhatever or \ifnot is true, you have to write:
\ifwhatever
\expandafter\@gobble
\else
\ifnot
\expandafter\expandafter\expandafter\@firstoftwo
\else
\expandafter\expandafter\expandafter\@gobble
\fi
\fi
{<code>}
This profusion of \expandafters is to skip \@firstoftwo or \@gobble and expand first one token, then another after it, before going back to expand the macro you actually want once there is nothing in its way.
Of course, the technique of using multiple \expandafters to skip ahead is itself an idiom. For example, you can expand the first token in a group once:
\expandafter{\macro}
or twice:
\expandafter\expandafter
\expandafter{\macro}
or three times:
\expandafter\expandafter\expandafter\expandafter
\expandafter\expandafter
\expandafter{\macro}
and you see the pattern. I may as well explain why this works. When the first \expandafter goes off, it expands in turn the third, then the first in the next row, then the first in the following row, and finally, \macro. The intervening tokens are not expanded in this "run", but just stuck back in order. The effect is that every other column of \expandafters vanishes, \macro is expanded once, and then TeX starts expanding again with what is now the first \expandater, which was the second. The configuration has become the one for expanding \macro twice, and so we end up expanding it three times.
My idea is very similar to egreg's, but I'd like to add an optional argument, so the math command could process arguments itself. The code:
\documentclass{article}
\usepackage{xparse}
\DeclareDocumentCommand{\mathdef}{mO{0}m}{%
\expandafter\let\csname old\string#1\endcsname=#1
\expandafter\newcommand\csname new\string#1\endcsname[#2]{#3}
\DeclareRobustCommand#1{%
\ifmmode
\expandafter\let\expandafter\next\csname new\string#1\endcsname
\else
\expandafter\let\expandafter\next\csname old\string#1\endcsname
\fi
\next
}%
}
\mathdef{\v}[1]{\tilde{#1}}
\mathdef{\d}{\mathrm{d}}
\begin{document}
Ha\v{c}ek and tilde $\v{a}+\v{b}=1$.
\d x is an x with a dot below and $\int f(x) \d x$ is an integral over $x$.
\end{document}
The result:
Best Answer
This directly prints the symbols but you could of course make the macros increment some counter instead and defer all printing until after the whole collection is known.