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gitweb.michael.orlitzky.com - mjotex.git/blob - mjo-common.tex
2 % Only the most commonly-used macros. Needed by everything else.
8 % Needed for \bigtimes.
11 % Place the argument in matching left/right parntheses.
12 \providecommand*
{\of}[1]{ \left(
{#1}\right)
}
14 % Group terms using parentheses.
15 \providecommand*
{\qty}[1]{ \left(
{#1}\right)
}
17 % Group terms using square brackets.
18 \providecommand*
{\sqty}[1]{ \left[{#1}\right] }
20 % Create a set from the given elements
21 \providecommand*
{\set}[1]{\left\lbrace{#1}\right\rbrace}
23 % A set comprehension, where the ``such that...'' bar is added
24 % automatically. The bar was chosen over a colon to avoid ambiguity
25 % with the L : V -> V notation. We can't leverage \set here because \middle
26 % needs \left and \right present.
27 \providecommand*
{\setc}[2]{\left\lbrace{#1}\
\middle|\
{#2} \right\rbrace}
30 \providecommand*
{\pair}[2]{ \left(
{#1},
{#2}\right)
}
33 \providecommand*
{\triple}[3]{ \left(
{#1},
{#2},
{#3}\right)
}
35 % The Cartesian product of two things.
36 \providecommand*
{\cartprod}[2]{ {#1}\times{#2} }
38 % The Cartesian product of three things.
39 \providecommand*
{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
41 % The direct sum of two things.
42 \providecommand*
{\directsum}[2]{ {#1}\oplus{#2} }
44 % The direct sum of three things.
45 \providecommand*
{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
47 % The factorial operator.
48 \providecommand*
{\factorial}[1]{ {#1}!
}
53 % All of the product spaces (for example, R^n) that follow default to
54 % an exponent of ``n'', but that exponent can be changed by providing
55 % it as an optional argument. If the exponent given is ``1'', then it
56 % will be omitted entirely.
59 % The natural n-space, N x N x N x ... x N.
60 \providecommand*
{\Nn}[1][n
]{
61 \mathbb{N
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
64 % The integral n-space, Z x Z x Z x ... x Z.
65 \providecommand*
{\Zn}[1][n
]{
66 \mathbb{Z
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
69 % The rational n-space, Q x Q x Q x ... x Q.
70 \providecommand*
{\Qn}[1][n
]{
71 \mathbb{Q
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
74 % The real n-space, R x R x R x ... x R.
75 \providecommand*
{\Rn}[1][n
]{
76 \mathbb{R
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
79 % The complex n-space, C x C x C x ... x C.
80 \providecommand*
{\Cn}[1][n
]{
81 \mathbb{C
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
84 % The space of real symmetric n-by-n matrices.
85 \providecommand*
{\Sn}[1][n
]{
86 \mathcal{S
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
89 % The space of complex Hermitian n-by-n matrices.
90 \providecommand*
{\Hn}[1][n
]{
91 \mathcal{H
}\if\detokenize{#1}\detokenize{1}{}\else^
{#1}\fi
95 % Basic set operations
98 % The union of its two arguments.
99 \providecommand*
{\union}[2]{ {#1}\cup{#2} }
101 % A three-argument union.
102 \providecommand*
{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
104 % The intersection of its two arguments.
105 \providecommand*
{\intersect}[2]{ {#1}\cap{#2} }
107 % A three-argument intersection.
108 \providecommand*
{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
110 % An indexed arbitrary binary operation such as the union or
111 % intersection of an infinite number of sets. The first argument is
112 % the operator symbol to use, such as \cup for a union. The second
113 % argument is the lower index, for example k=1. The third argument is
114 % the upper index, such as \infty. Finally the fourth argument should
115 % contain the things (e.g. indexed sets) to be operated on.
116 \providecommand*
{\binopmany}[4]{
117 \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
118 { {#1}_
{#2}^
{#3}{#4} }
119 { {#1}_
{#2}^
{#3}{#4} }
120 { {#1}_
{#2}^
{#3}{#4} }
123 \providecommand*
{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
124 \providecommand*
{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
125 \providecommand*
{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
126 \providecommand*
{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
129 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
131 \providecommand*
{\intervaloo}[2]{ \left(
{#1},
{#2}\right)
} % open-open
132 \providecommand*
{\intervaloc}[2]{ \left(
{#1},
{#2}\right] } % open-closed
133 \providecommand*
{\intervalco}[2]{ \left[{#1},
{#2}\right)
} % closed-open
134 \providecommand*
{\intervalcc}[2]{ \left[{#1},
{#2}\right] } % closed-closed