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 \ifx\mathbb\undefined
   8   \usepackage{amsfonts}
   9 \fi
  10
  11 % Place the argument in matching left/right parentheses.
  12 \newcommand*{\of}[1]{ \left({#1}\right) }
  13
  14 % Group terms using parentheses.
  15 \newcommand*{\qty}[1]{ \left({#1}\right) }
  16
  17 % Group terms using square brackets.
  18 \newcommand*{\sqty}[1]{ \left[{#1}\right] }
  19
  20 % A pair of things.
  21 \newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
  22
  23 % A triple of things.
  24 \newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
  25
  26 % A four-tuple of things.
  27 \newcommand*{\quadruple}[4]{ \left({#1},{#2},{#3},{#4}\right) }
  28
  29 % A five-tuple of things.
  30 \newcommand*{\quintuple}[5]{ \left({#1},{#2},{#3},{#4},{#5}\right) }
  31
  32 % A six-tuple of things.
  33 \newcommand*{\sextuple}[6]{ \left({#1},{#2},{#3},{#4},{#5},{#6}\right) }
  34
  35 % A seven-tuple of things.
  36 \newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
  37
  38 % The factorial operator.
  39 \newcommand*{\factorial}[1]{ {#1}! }
  40
  41 %
  42 % Product spaces
  43 %
  44 % All of the product spaces (for example, R^n) that follow default to
  45 % an exponent of ``n'', but that exponent can be changed by providing
  46 % it as an optional argument. If the exponent given is ``1'', then it
  47 % will be omitted entirely.
  48 %
  49
  50 % The natural n-space, N x N x N x ... x N.
  51 \newcommand*{\Nn}[1][n]{
  52   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  53 }
  54
  55 \ifdefined\newglossaryentry
  56   \newglossaryentry{N}{
  57     name={\ensuremath{\Nn[1]}},
  58     description={the set of natural numbers},
  59     sort=N
  60   }
  61 \fi
  62
  63 % The integral n-space, Z x Z x Z x ... x Z.
  64 \newcommand*{\Zn}[1][n]{
  65   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  66 }
  67
  68 \ifdefined\newglossaryentry
  69   \newglossaryentry{Z}{
  70     name={\ensuremath{\Zn[1]}},
  71     description={the ring of integers},
  72     sort=Z
  73   }
  74 \fi
  75
  76 % The rational n-space, Q x Q x Q x ... x Q.
  77 \newcommand*{\Qn}[1][n]{
  78   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  79 }
  80
  81 \ifdefined\newglossaryentry
  82   \newglossaryentry{Q}{
  83     name={\ensuremath{\Qn[1]}},
  84     description={the field of rational numbers},
  85     sort=Q
  86   }
  87 \fi
  88
  89 % The real n-space, R x R x R x ... x R.
  90 \newcommand*{\Rn}[1][n]{
  91   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  92 }
  93
  94 \ifdefined\newglossaryentry
  95   \newglossaryentry{R}{
  96     name={\ensuremath{\Rn[1]}},
  97     description={the field of real numbers},
  98     sort=R
  99   }
 100 \fi
 101
 102
 103 % The complex n-space, C x C x C x ... x C.
 104 \newcommand*{\Cn}[1][n]{
 105   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 106 }
 107
 108 \ifdefined\newglossaryentry
 109   \newglossaryentry{C}{
 110     name={\ensuremath{\Cn[1]}},
 111     description={the field of complex numbers},
 112     sort=C
 113   }
 114 \fi
 115
 116
 117 % An indexed arbitrary binary operation such as the union or
 118 % intersection of an infinite number of sets. The first argument is
 119 % the operator symbol to use, such as \cup for a union. The second
 120 % argument is the lower index, for example k=1. The third argument is
 121 % the upper index, such as \infty. Finally the fourth argument should
 122 % contain the things (e.g. indexed sets) to be operated on.
 123 \newcommand*{\binopmany}[4]{
 124   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 125              { {#1}_{#2}^{#3}{#4} }
 126              { {#1}_{#2}^{#3}{#4} }
 127              { {#1}_{#2}^{#3}{#4} }
 128 }
 129
 130
 131 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 132 % the real line.
 133 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 134 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 135 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 136 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 137
 138
 139 \fi