\ifx\havemjocommon\undefined
\def\havemjocommon{1}
-
\ifx\mathbb\undefined
\usepackage{amsfonts}
\fi
-\ifx\bigtimes\undefined
- \usepackage{mathtools}
+\ifx\restriction\undefined
+ \usepackage{amssymb}
\fi
% Place the argument in matching left/right parentheses.
% Group terms using square brackets.
\newcommand*{\sqty}[1]{ \left[{#1}\right] }
-% Create a set from the given elements
-\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.
-\newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
-
% A pair of things.
\newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
% A triple of things.
\newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
-% The Cartesian product of two things.
-\newcommand*{\cartprod}[2]{ {#1}\times{#2} }
+% A four-tuple of things.
+\newcommand*{\quadruple}[4]{ \left({#1},{#2},{#3},{#4}\right) }
-% The Cartesian product of three things.
-\newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
+% A five-tuple of things.
+\newcommand*{\quintuple}[5]{ \left({#1},{#2},{#3},{#4},{#5}\right) }
-% The direct sum of two things.
-\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
+% A six-tuple of things.
+\newcommand*{\sextuple}[6]{ \left({#1},{#2},{#3},{#4},{#5},{#6}\right) }
-% The direct sum of three things.
-\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+% A seven-tuple of things.
+\newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
% The factorial operator.
\newcommand*{\factorial}[1]{ {#1}! }
+% Restrict the first argument (a function) to the second argument (a
+% subset of that functions domain). Abused for polynomials to specify
+% an associated function with a particular domain (also its codomain,
+% in the case of univariate polynomials).
+\newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
+\ifdefined\newglossaryentry
+ \newglossaryentry{restriction}{
+ name={\ensuremath{\restrict{f}{X}}},
+ description={the restriction of $f$ to $X$},
+ sort=r
+ }
+\fi
+
%
% Product spaces
%
\fi
-% The space of real symmetric n-by-n matrices.
-\newcommand*{\Sn}[1][n]{
- \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
-\ifdefined\newglossaryentry
- \newglossaryentry{Sn}{
- name={\ensuremath{\Sn}},
- description={the set of $n$-by-$n$ real symmetric matrices},
- sort=Sn
- }
-\fi
-
-% The space of complex Hermitian n-by-n matrices.
-\newcommand*{\Hn}[1][n]{
- \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
-}
-
-\ifdefined\newglossaryentry
- \newglossaryentry{Hn}{
- name={\ensuremath{\Hn}},
- description={the set of $n$-by-$n$ complex Hermitian matrices},
- sort=Hn
- }
-\fi
-
-%
-% Basic set operations
-%
-
-% The union of its two arguments.
-\newcommand*{\union}[2]{ {#1}\cup{#2} }
-
-% A three-argument union.
-\newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
-
-% The intersection of its two arguments.
-\newcommand*{\intersect}[2]{ {#1}\cap{#2} }
-
-% A three-argument intersection.
-\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
% the operator symbol to use, such as \cup for a union. The second
{ {#1}_{#2}^{#3}{#4} }
}
-\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.