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