On Auto-Updating References in LaTeX Documents

I am using LaTeX for almost all of my documents since my third semester, but I just recently (1-2 months ago) stumbled upon two packages I definitely would not like to miss anymore (besides the usual ones for writing math texts, of course): cleveref and xparse.

Auto-updating your references

When writing up mathematical statements I am sometimes unsure if it should be a theorem, proposition, lemma or claim. A proposition would certainly be renamed to a claim if I do not plan to prove it; or a lemma if it turns out later that I do need it part way to prove a theorem. It is a painful and laborious task to go through the document and change all uses of proposition, Proposition \ref or Prop.~\ref to the respective claim or Claim \ref. Package cleveref solves this problem elegantly:

Thm.~\ref{s:A} is based on Lem.~\ref{s:B} and Prop.~\ref{s:C},
and specializes Eqn.~(\ref{eqn:D}).

becomes

% Part of the preamble
\usepackage[capitalise]{cleveref}
\crefname{theorem}{Thm.}{Thm.}
\crefname{lemma}{Lem.}{Lem.}
\crefname{proposition}{Prop.}{Prop.}
\crefname{equation}{Eqn.}{Eqn.}
\creflabelformat{equation}{#2(#1)#3}

% New code
\Cref{s:A} is based on \cref{s:B,s:C}, and specializes \cref{eqn:D}.

which produces

Thm. 1.4 is based on Lem. 1.1 and Prop. 1.2, and specializes Eqn. (1).

Customizing newcommand

Writing up the math you have discovered is certainly important—but I think, just like in programming, you want to spend your time thinking and solving problems, and on explaining them well to your readers, but certainly not typing. Take sets for example: Instead of

\big\{ x \in \mathbb{R} \middle| \int^x_{-1} f(x) dx < 1 \big\}

we could introduce a new command for sets thus saving us a few keystrokes and giving us a highly customizable command through

% Shortcut for proper scalings of braces
\newcommand{\sd}[2] {
    \ifthenelse{\equal{#1}{0}}{}{
        \ifthenelse{\equal{#1}{1}}{\big}{
            \ifthenelse{\equal{#1}{2}}{\Big}{
                \ifthenelse{\equal{#1}{3}}{\bigg}{
                    \ifthenelse{\equal{#1}{4}}{\Bigg}{#2}}}}}
}

% Shorthand for sets
\newcommand{\st}[3][auto]{
    \sd{#1}{\left}\{ #2 \middle| #3 \sd{#1}{\right}\}
}

% Usage
\st[1]{x \in \IR}{\int^x_{-1} f(x) dx < 1}

Using xparse we can even add (optional) parameters at almost any position. This is very handy for things when you have many annotations to add to a mathematical expression, but want to have the freedom to change your notation later on without having to go through all of your document and alter each call one by one:

\usepackage{xparse}
% Closed balls with optional annotation
\NewDocumentCommand{\clb}{D(){auto} D[]{\empty} m m}{%
    \overline{\mathrm{ball}}_{#2} \sd{#1}{\left}( #3, #4 \sd{#1}{\right})
}

% Usage
... and $x \in \clb[\infty]{0}{2^{-n}}$.

producing the output \overline{\mathrm{ball}}_\infty\big( 0, 2^{-n} \big)—which is the same as if we had wrote

... and $x \in \clb(1)[\infty]{0}{2^{-n}}$.