%
% Only the most commonly-used macros. Needed by everything else.
%
+\ifx\havemjocommon\undefined
+\def\havemjocommon{1}
-% Place the argument in matching left/right parntheses.
-\providecommand*{\of}[1]{ \left( {#1} \right) }
+
+\ifx\mathbb\undefined
+ \usepackage{amsfonts}
+\fi
+
+\ifx\bigtimes\undefined
+ \usepackage{mathtools}
+\fi
+
+% Place the argument in matching left/right parentheses.
+\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.
+\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.
+\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The direct sum of three things.
+\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+
+% The factorial operator.
+\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
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{N}{
+ name={\ensuremath{\Nn[1]}},
+ description={the set of natural numbers},
+ sort=N
+ }
+\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
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Z}{
+ name={\ensuremath{\Zn[1]}},
+ description={the ring of integers},
+ sort=Z
+ }
+\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
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{Q}{
+ name={\ensuremath{\Qn[1]}},
+ description={the field of rational numbers},
+ sort=Q
+ }
+\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
}
+\ifdefined\newglossaryentry
+ \newglossaryentry{R}{
+ name={\ensuremath{\Rn[1]}},
+ description={the field of real numbers},
+ sort=R
+ }
+\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
}
+
+\ifdefined\newglossaryentry
+ \newglossaryentry{C}{
+ name={\ensuremath{\Cn[1]}},
+ description={the field of complex numbers},
+ sort=C
+ }
+\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
+% 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.
+\newcommand*{\binopmany}[4]{
+ \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
+ { {#1}_{#2}^{#3}{#4} }
+ { {#1}_{#2}^{#3}{#4} }
+ { {#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.
+\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
projects / mjotex.git / blobdiff