mjo-common.tex

   1 %
   2 % Only the most commonly-used macros. Needed by everything else.
   3 %
   4 \ifx\havemjocommon\undefined
   5 \def\havemjocommon{1}
   6
   7
   8 \ifx\mathbb\undefined
   9   \usepackage{amsfonts}
  10 \fi
  11
  12 \ifx\bigtimes\undefined
  13   \usepackage{mathtools}
  14 \fi
  15
  16 % Place the argument in matching left/right parentheses.
  17 \newcommand*{\of}[1]{ \left({#1}\right) }
  18
  19 % Group terms using parentheses.
  20 \newcommand*{\qty}[1]{ \left({#1}\right) }
  21
  22 % Group terms using square brackets.
  23 \newcommand*{\sqty}[1]{ \left[{#1}\right] }
  24
  25 % Create a set from the given elements
  26 \newcommand*{\set}[1]{\left\lbrace{#1}\right\rbrace}
  27
  28 % A set comprehension, where the ``such that...'' bar is added
  29 % automatically. The bar was chosen over a colon to avoid ambiguity
  30 % with the L : V -> V notation. We can't leverage \set here because \middle
  31 % needs \left and \right present.
  32 \newcommand*{\setc}[2]{\left\lbrace{#1}\ \middle|\ {#2} \right\rbrace}
  33
  34 % A pair of things.
  35 \newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
  36
  37 % A triple of things.
  38 \newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
  39
  40 % The Cartesian product of two things.
  41 \newcommand*{\cartprod}[2]{ {#1}\times{#2} }
  42
  43 % The Cartesian product of three things.
  44 \newcommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
  45
  46 % The direct sum of two things.
  47 \newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
  48
  49 % The direct sum of three things.
  50 \newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
  51
  52 % The factorial operator.
  53 \newcommand*{\factorial}[1]{ {#1}! }
  54
  55 %
  56 % Product spaces
  57 %
  58 % All of the product spaces (for example, R^n) that follow default to
  59 % an exponent of ``n'', but that exponent can be changed by providing
  60 % it as an optional argument. If the exponent given is ``1'', then it
  61 % will be omitted entirely.
  62 %
  63
  64 % The natural n-space, N x N x N x ... x N.
  65 \newcommand*{\Nn}[1][n]{
  66   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  67 }
  68
  69 % The integral n-space, Z x Z x Z x ... x Z.
  70 \newcommand*{\Zn}[1][n]{
  71   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  72 }
  73
  74 % The rational n-space, Q x Q x Q x ... x Q.
  75 \newcommand*{\Qn}[1][n]{
  76   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  77 }
  78
  79 % The real n-space, R x R x R x ... x R.
  80 \newcommand*{\Rn}[1][n]{
  81   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  82 }
  83
  84 % The complex n-space, C x C x C x ... x C.
  85 \newcommand*{\Cn}[1][n]{
  86   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  87 }
  88
  89 % The space of real symmetric n-by-n matrices.
  90 \newcommand*{\Sn}[1][n]{
  91   \mathcal{S}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  92 }
  93
  94 % The space of complex Hermitian n-by-n matrices.
  95 \newcommand*{\Hn}[1][n]{
  96   \mathcal{H}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  97 }
  98
  99 %
 100 % Basic set operations
 101 %
 102
 103 % The union of its two arguments.
 104 \newcommand*{\union}[2]{ {#1}\cup{#2} }
 105
 106 % A three-argument union.
 107 \newcommand*{\unionthree}[3]{ \union{\union{#1}{#2}}{#3} }
 108
 109 % The intersection of its two arguments.
 110 \newcommand*{\intersect}[2]{ {#1}\cap{#2} }
 111
 112 % A three-argument intersection.
 113 \newcommand*{\intersectthree}[3]{ \intersect{\intersect{#1}{#2}}{#3} }
 114
 115 % An indexed arbitrary binary operation such as the union or
 116 % intersection of an infinite number of sets. The first argument is
 117 % the operator symbol to use, such as \cup for a union. The second
 118 % argument is the lower index, for example k=1. The third argument is
 119 % the upper index, such as \infty. Finally the fourth argument should
 120 % contain the things (e.g. indexed sets) to be operated on.
 121 \newcommand*{\binopmany}[4]{
 122   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 123              { {#1}_{#2}^{#3}{#4} }
 124              { {#1}_{#2}^{#3}{#4} }
 125              { {#1}_{#2}^{#3}{#4} }
 126 }
 127
 128 \newcommand*{\intersectmany}[3]{ \binopmany{\bigcap}{#1}{#2}{#3} }
 129 \newcommand*{\cartprodmany}[3]{ \binopmany{\bigtimes}{#1}{#2}{#3} }
 130 \newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
 131 \newcommand*{\unionmany}[3]{ \binopmany{\bigcup}{#1}{#2}{#3} }
 132
 133
 134 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 135 % the real line.
 136 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 137 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 138 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 139 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 140
 141
 142 \fi