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 \ifx\restriction\undefined
  12   \usepackage{amssymb}
  13 \fi
  14
  15 % Place the argument in matching left/right parentheses.
  16 \newcommand*{\of}[1]{ \left({#1}\right) }
  17
  18 % Group terms using parentheses.
  19 \newcommand*{\qty}[1]{ \left({#1}\right) }
  20
  21 % Group terms using square brackets.
  22 \newcommand*{\sqty}[1]{ \left[{#1}\right] }
  23
  24 % A pair of things.
  25 \newcommand*{\pair}[2]{ \left({#1},{#2}\right) }
  26
  27 % A triple of things.
  28 \newcommand*{\triple}[3]{ \left({#1},{#2},{#3}\right) }
  29
  30 % A four-tuple of things.
  31 \newcommand*{\quadruple}[4]{ \left({#1},{#2},{#3},{#4}\right) }
  32
  33 % A five-tuple of things.
  34 \newcommand*{\quintuple}[5]{ \left({#1},{#2},{#3},{#4},{#5}\right) }
  35
  36 % A six-tuple of things.
  37 \newcommand*{\sextuple}[6]{ \left({#1},{#2},{#3},{#4},{#5},{#6}\right) }
  38
  39 % A seven-tuple of things.
  40 \newcommand*{\septuple}[7]{ \left({#1},{#2},{#3},{#4},{#5},{#6},{#7}\right) }
  41
  42 % The factorial operator.
  43 \newcommand*{\factorial}[1]{ {#1}! }
  44
  45 % Restrict the first argument (a function) to the second argument (a
  46 % subset of that functions domain). Abused for polynomials to specify
  47 % an associated function with a particular domain (also its codomain,
  48 % in the case of univariate polynomials).
  49 \newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
  50 \ifdefined\newglossaryentry
  51   \newglossaryentry{restriction}{
  52     name={\ensuremath{\restrict{f}{X}}},
  53     description={the restriction of $f$ to $X$},
  54     sort=r
  55   }
  56 \fi
  57
  58 %
  59 % Product spaces
  60 %
  61 % All of the product spaces (for example, R^n) that follow default to
  62 % an exponent of ``n'', but that exponent can be changed by providing
  63 % it as an optional argument. If the exponent given is ``1'', then it
  64 % will be omitted entirely.
  65 %
  66
  67 % The natural n-space, N x N x N x ... x N.
  68 \newcommand*{\Nn}[1][n]{
  69   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  70 }
  71
  72 \ifdefined\newglossaryentry
  73   \newglossaryentry{N}{
  74     name={\ensuremath{\Nn[1]}},
  75     description={the set of natural numbers},
  76     sort=N
  77   }
  78 \fi
  79
  80 % The integral n-space, Z x Z x Z x ... x Z.
  81 \newcommand*{\Zn}[1][n]{
  82   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  83 }
  84
  85 \ifdefined\newglossaryentry
  86   \newglossaryentry{Z}{
  87     name={\ensuremath{\Zn[1]}},
  88     description={the ring of integers},
  89     sort=Z
  90   }
  91 \fi
  92
  93 % The rational n-space, Q x Q x Q x ... x Q.
  94 \newcommand*{\Qn}[1][n]{
  95   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  96 }
  97
  98 \ifdefined\newglossaryentry
  99   \newglossaryentry{Q}{
 100     name={\ensuremath{\Qn[1]}},
 101     description={the field of rational numbers},
 102     sort=Q
 103   }
 104 \fi
 105
 106 % The real n-space, R x R x R x ... x R.
 107 \newcommand*{\Rn}[1][n]{
 108   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 109 }
 110
 111 \ifdefined\newglossaryentry
 112   \newglossaryentry{R}{
 113     name={\ensuremath{\Rn[1]}},
 114     description={the field of real numbers},
 115     sort=R
 116   }
 117 \fi
 118
 119
 120 % The complex n-space, C x C x C x ... x C.
 121 \newcommand*{\Cn}[1][n]{
 122   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 123 }
 124
 125 \ifdefined\newglossaryentry
 126   \newglossaryentry{C}{
 127     name={\ensuremath{\Cn[1]}},
 128     description={the field of complex numbers},
 129     sort=C
 130   }
 131 \fi
 132
 133
 134 % An indexed arbitrary binary operation such as the union or
 135 % intersection of an infinite number of sets. The first argument is
 136 % the operator symbol to use, such as \cup for a union. The second
 137 % argument is the lower index, for example k=1. The third argument is
 138 % the upper index, such as \infty. Finally the fourth argument should
 139 % contain the things (e.g. indexed sets) to be operated on.
 140 \newcommand*{\binopmany}[4]{
 141   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 142              { {#1}_{#2}^{#3}{#4} }
 143              { {#1}_{#2}^{#3}{#4} }
 144              { {#1}_{#2}^{#3}{#4} }
 145 }
 146
 147
 148 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 149 % the real line.
 150 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 151 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 152 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 153 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 154
 155
 156 \fi