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 direct sum of two things.
  39 \newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
  40
  41 % The direct sum of three things.
  42 \newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
  43
  44 % The factorial operator.
  45 \newcommand*{\factorial}[1]{ {#1}! }
  46
  47 %
  48 % Product spaces
  49 %
  50 % All of the product spaces (for example, R^n) that follow default to
  51 % an exponent of ``n'', but that exponent can be changed by providing
  52 % it as an optional argument. If the exponent given is ``1'', then it
  53 % will be omitted entirely.
  54 %
  55
  56 % The natural n-space, N x N x N x ... x N.
  57 \newcommand*{\Nn}[1][n]{
  58   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  59 }
  60
  61 \ifdefined\newglossaryentry
  62   \newglossaryentry{N}{
  63     name={\ensuremath{\Nn[1]}},
  64     description={the set of natural numbers},
  65     sort=N
  66   }
  67 \fi
  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 \ifdefined\newglossaryentry
  75   \newglossaryentry{Z}{
  76     name={\ensuremath{\Zn[1]}},
  77     description={the ring of integers},
  78     sort=Z
  79   }
  80 \fi
  81
  82 % The rational n-space, Q x Q x Q x ... x Q.
  83 \newcommand*{\Qn}[1][n]{
  84   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  85 }
  86
  87 \ifdefined\newglossaryentry
  88   \newglossaryentry{Q}{
  89     name={\ensuremath{\Qn[1]}},
  90     description={the field of rational numbers},
  91     sort=Q
  92   }
  93 \fi
  94
  95 % The real n-space, R x R x R x ... x R.
  96 \newcommand*{\Rn}[1][n]{
  97   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  98 }
  99
 100 \ifdefined\newglossaryentry
 101   \newglossaryentry{R}{
 102     name={\ensuremath{\Rn[1]}},
 103     description={the field of real numbers},
 104     sort=R
 105   }
 106 \fi
 107
 108
 109 % The complex n-space, C x C x C x ... x C.
 110 \newcommand*{\Cn}[1][n]{
 111   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 112 }
 113
 114 \ifdefined\newglossaryentry
 115   \newglossaryentry{C}{
 116     name={\ensuremath{\Cn[1]}},
 117     description={the field of complex numbers},
 118     sort=C
 119   }
 120 \fi
 121
 122
 123 % An indexed arbitrary binary operation such as the union or
 124 % intersection of an infinite number of sets. The first argument is
 125 % the operator symbol to use, such as \cup for a union. The second
 126 % argument is the lower index, for example k=1. The third argument is
 127 % the upper index, such as \infty. Finally the fourth argument should
 128 % contain the things (e.g. indexed sets) to be operated on.
 129 \newcommand*{\binopmany}[4]{
 130   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 131              { {#1}_{#2}^{#3}{#4} }
 132              { {#1}_{#2}^{#3}{#4} }
 133              { {#1}_{#2}^{#3}{#4} }
 134 }
 135
 136
 137 \newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
 138
 139
 140 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 141 % the real line.
 142 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 143 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 144 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 145 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 146
 147
 148 \fi