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 "least common multiple of" function. Takes a nonempty set of
  43 % things that can be multiplied and ordered as its argument. Name
  44 % chosen for synergy with \gcd, which *does* exist already.
  45 \newcommand*{\lcm}[1]{ \operatorname{lcm}\of{{#1}} }
  46 \ifdefined\newglossaryentry
  47   \newglossaryentry{lcm}{
  48     name={\ensuremath{\lcm{X}}},
  49     description={the least common multiple of the elements of $X$},
  50     sort=l
  51   }
  52 \fi
  53
  54 % The factorial operator.
  55 \newcommand*{\factorial}[1]{ {#1}! }
  56
  57 % Restrict the first argument (a function) to the second argument (a
  58 % subset of that functions domain). Abused for polynomials to specify
  59 % an associated function with a particular domain (also its codomain,
  60 % in the case of univariate polynomials).
  61 \newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
  62 \ifdefined\newglossaryentry
  63   \newglossaryentry{restriction}{
  64     name={\ensuremath{\restrict{f}{X}}},
  65     description={the restriction of $f$ to $X$},
  66     sort=r
  67   }
  68 \fi
  69
  70 %
  71 % Product spaces
  72 %
  73 % All of the product spaces (for example, R^n) that follow default to
  74 % an exponent of ``n'', but that exponent can be changed by providing
  75 % it as an optional argument. If the exponent given is ``1'', then it
  76 % will be omitted entirely.
  77 %
  78
  79 % The natural n-space, N x N x N x ... x N.
  80 \newcommand*{\Nn}[1][n]{
  81   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  82 }
  83
  84 \ifdefined\newglossaryentry
  85   \newglossaryentry{N}{
  86     name={\ensuremath{\Nn[1]}},
  87     description={the set of natural numbers},
  88     sort=N
  89   }
  90 \fi
  91
  92 % The integral n-space, Z x Z x Z x ... x Z.
  93 \newcommand*{\Zn}[1][n]{
  94   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  95 }
  96
  97 \ifdefined\newglossaryentry
  98   \newglossaryentry{Z}{
  99     name={\ensuremath{\Zn[1]}},
 100     description={the ring of integers},
 101     sort=Z
 102   }
 103 \fi
 104
 105 % The rational n-space, Q x Q x Q x ... x Q.
 106 \newcommand*{\Qn}[1][n]{
 107   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 108 }
 109
 110 \ifdefined\newglossaryentry
 111   \newglossaryentry{Q}{
 112     name={\ensuremath{\Qn[1]}},
 113     description={the field of rational numbers},
 114     sort=Q
 115   }
 116 \fi
 117
 118 % The real n-space, R x R x R x ... x R.
 119 \newcommand*{\Rn}[1][n]{
 120   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 121 }
 122
 123 \ifdefined\newglossaryentry
 124   \newglossaryentry{R}{
 125     name={\ensuremath{\Rn[1]}},
 126     description={the field of real numbers},
 127     sort=R
 128   }
 129 \fi
 130
 131
 132 % The complex n-space, C x C x C x ... x C.
 133 \newcommand*{\Cn}[1][n]{
 134   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 135 }
 136
 137 \ifdefined\newglossaryentry
 138   \newglossaryentry{C}{
 139     name={\ensuremath{\Cn[1]}},
 140     description={the field of complex numbers},
 141     sort=C
 142   }
 143 \fi
 144
 145 % The n-dimensional product space of a generic field F.
 146 \newcommand*{\Fn}[1][n]{
 147   \mathbb{F}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 148 }
 149
 150 \ifdefined\newglossaryentry
 151   \newglossaryentry{F}{
 152     name={\ensuremath{\Fn[1]}},
 153     description={a generic field},
 154     sort=F
 155   }
 156 \fi
 157
 158
 159 % An indexed arbitrary binary operation such as the union or
 160 % intersection of an infinite number of sets. The first argument is
 161 % the operator symbol to use, such as \cup for a union. The second
 162 % argument is the lower index, for example k=1. The third argument is
 163 % the upper index, such as \infty. Finally the fourth argument should
 164 % contain the things (e.g. indexed sets) to be operated on.
 165 \newcommand*{\binopmany}[4]{
 166   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 167              { {#1}_{#2}^{#3}{#4} }
 168              { {#1}_{#2}^{#3}{#4} }
 169              { {#1}_{#2}^{#3}{#4} }
 170 }
 171
 172
 173 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 174 % the real line.
 175 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 176 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 177 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 178 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 179
 180
 181 \fi