\usepackage{mathtools}
% Place the argument in matching left/right parentheses.
-\providecommand*{\of}[1]{ \left({#1}\right) }
+\newcommand*{\of}[1]{ \left({#1}\right) }
% Group terms using parentheses.
-\providecommand*{\qty}[1]{ \left({#1}\right) }
+\newcommand*{\qty}[1]{ \left({#1}\right) }
% Group terms using square brackets.
-\providecommand*{\sqty}[1]{ \left[{#1}\right] }
+\newcommand*{\sqty}[1]{ \left[{#1}\right] }
% Create a set from the given elements
-\providecommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
+\newcommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
% A set comprehension, where the ``such that...'' bar is added
% automatically. The bar was chosen over a colon to avoid ambiguity
% with the L : V -> V notation. We can't leverage \set here because \middle
% needs \left and \right present.
-\providecommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
+\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
% A pair of things.
-\providecommand*{\pair}[2]{ \left({#1},{#2}\right) }
+\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
% A triple of things.
-\providecommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
+\newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
% The Cartesian product of two things.
-\providecommand*{\cartprod}[2]{ {#1}\times{#2} }
+\newcommand*{\cartprod}[2]{ {#1}\times{#2} }
% The Cartesian product of three things.
-\providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+\newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
% The direct sum of two things.
-\providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
+\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
% The direct sum of three things.
-\providecommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
% The factorial operator.
-\providecommand*{\factorial}[1]{ {#1}! }
+\newcommand*{\factorial}[1]{ {#1}! }
%
% Product spaces
%
% The natural n-space, N x N x N x ... x N.
-\providecommand*{\Nn}[1][n]{
+\newcommand*{\Nn}[1][n]{
\mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The integral n-space, Z x Z x Z x ... x Z.
-\providecommand*{\Zn}[1][n]{
+\newcommand*{\Zn}[1][n]{
\mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The rational n-space, Q x Q x Q x ... x Q.
-\providecommand*{\Qn}[1][n]{
+\newcommand*{\Qn}[1][n]{
\mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The real n-space, R x R x R x ... x R.
-\providecommand*{\Rn}[1][n]{
+\newcommand*{\Rn}[1][n]{
\mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The complex n-space, C x C x C x ... x C.
-\providecommand*{\Cn}[1][n]{
+\newcommand*{\Cn}[1][n]{
\mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The space of real symmetric n-by-n matrices.
-\providecommand*{\Sn}[1][n]{
+\newcommand*{\Sn}[1][n]{
\mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
% The space of complex Hermitian n-by-n matrices.
-\providecommand*{\Hn}[1][n]{
+\newcommand*{\Hn}[1][n]{
\mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
}
%
% The union of its two arguments.
-\providecommand*{\union}[2]{ {#1}\cup{#2} }
+\newcommand*{\union}[2]{ {#1}\cup{#2} }
% A three-argument union.
-\providecommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
+\newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
% The intersection of its two arguments.
-\providecommand*{\intersect}[2]{ {#1}\cap{#2} }
+\newcommand*{\intersect}[2]{ {#1}\cap{#2} }
% A three-argument intersection.
-\providecommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
+\newcommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
% An indexed arbitrary binary operation such as the union or
% intersection of an infinite number of sets. The first argument is
% argument is the lower index, for example k=1. The third argument is
% the upper index, such as \infty. Finally the fourth argument should
% contain the things (e.g. indexed sets) to be operated on.
-\providecommand*{\binopmany}[4]{
+\newcommand*{\binopmany}[4]{
\mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
{ {#1}_{#2}^{#3}{#4} }
{ {#1}_{#2}^{#3}{#4} }
{ {#1}_{#2}^{#3}{#4} }
}
-\providecommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
-\providecommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
-\providecommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
-\providecommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
+\newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
+\newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
+\newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
+\newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
% The four standard (UNLESS YOU'RE FRENCH) types of intervals along
% the real line.
-\providecommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
-\providecommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
-\providecommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
-\providecommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
+\newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
+\newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
+\newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
+\newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
\fi