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 % A free-form tuple of things. Useful for when the exact number is not
  43 % known, such as when \ldots will be stuck in the middle of the list,
  44 % and when you don't want to think in column-vector terms, e.g. with
  45 % elements of an abstract Cartesian product space.
  46 \newcommand*{\tuple}[1]{ \left({#1}\right) }
  47
  48 % The "least common multiple of" function. Takes a nonempty set of
  49 % things that can be multiplied and ordered as its argument. Name
  50 % chosen for synergy with \gcd, which *does* exist already.
  51 \newcommand*{\lcm}[1]{ \operatorname{lcm}\of{{#1}} }
  52 \ifdefined\newglossaryentry
  53   \newglossaryentry{lcm}{
  54     name={\ensuremath{\lcm{X}}},
  55     description={the least common multiple of the elements of $X$},
  56     sort=l
  57   }
  58 \fi
  59
  60 % The factorial operator.
  61 \newcommand*{\factorial}[1]{ {#1}! }
  62
  63 % Restrict the first argument (a function) to the second argument (a
  64 % subset of that functions domain). Abused for polynomials to specify
  65 % an associated function with a particular domain (also its codomain,
  66 % in the case of univariate polynomials).
  67 \newcommand*{\restrict}[2]{{#1}{\restriction}_{#2}}
  68 \ifdefined\newglossaryentry
  69   \newglossaryentry{restriction}{
  70     name={\ensuremath{\restrict{f}{X}}},
  71     description={the restriction of $f$ to $X$},
  72     sort=r
  73   }
  74 \fi
  75
  76 %
  77 % Product spaces
  78 %
  79 % All of the product spaces (for example, R^n) that follow default to
  80 % an exponent of ``n'', but that exponent can be changed by providing
  81 % it as an optional argument. If the exponent given is ``1'', then it
  82 % will be omitted entirely.
  83 %
  84
  85 % The natural n-space, N x N x N x ... x N.
  86 \newcommand*{\Nn}[1][n]{
  87   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  88 }
  89
  90 \ifdefined\newglossaryentry
  91   \newglossaryentry{N}{
  92     name={\ensuremath{\Nn[1]}},
  93     description={the set of natural numbers},
  94     sort=N
  95   }
  96 \fi
  97
  98 % The integral n-space, Z x Z x Z x ... x Z.
  99 \newcommand*{\Zn}[1][n]{
 100   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 101 }
 102
 103 \ifdefined\newglossaryentry
 104   \newglossaryentry{Z}{
 105     name={\ensuremath{\Zn[1]}},
 106     description={the ring of integers},
 107     sort=Z
 108   }
 109 \fi
 110
 111 % The rational n-space, Q x Q x Q x ... x Q.
 112 \newcommand*{\Qn}[1][n]{
 113   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 114 }
 115
 116 \ifdefined\newglossaryentry
 117   \newglossaryentry{Q}{
 118     name={\ensuremath{\Qn[1]}},
 119     description={the field of rational numbers},
 120     sort=Q
 121   }
 122 \fi
 123
 124 % The real n-space, R x R x R x ... x R.
 125 \newcommand*{\Rn}[1][n]{
 126   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 127 }
 128
 129 \ifdefined\newglossaryentry
 130   \newglossaryentry{R}{
 131     name={\ensuremath{\Rn[1]}},
 132     description={the field of real numbers},
 133     sort=R
 134   }
 135 \fi
 136
 137
 138 % The complex n-space, C x C x C x ... x C.
 139 \newcommand*{\Cn}[1][n]{
 140   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 141 }
 142
 143 \ifdefined\newglossaryentry
 144   \newglossaryentry{C}{
 145     name={\ensuremath{\Cn[1]}},
 146     description={the field of complex numbers},
 147     sort=C
 148   }
 149 \fi
 150
 151 % The n-dimensional product space of a generic field F.
 152 \newcommand*{\Fn}[1][n]{
 153   \mathbb{F}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
 154 }
 155
 156 \ifdefined\newglossaryentry
 157   \newglossaryentry{F}{
 158     name={\ensuremath{\Fn[1]}},
 159     description={a generic field},
 160     sort=F
 161   }
 162 \fi
 163
 164
 165 % An indexed arbitrary binary operation such as the union or
 166 % intersection of an infinite number of sets. The first argument is
 167 % the operator symbol to use, such as \cup for a union. The second
 168 % argument is the lower index, for example k=1. The third argument is
 169 % the upper index, such as \infty. Finally the fourth argument should
 170 % contain the things (e.g. indexed sets) to be operated on.
 171 \newcommand*{\binopmany}[4]{
 172   \mathchoice{ \underset{#2}{\overset{#3}{#1}}{#4} }
 173              { {#1}_{#2}^{#3}{#4} }
 174              { {#1}_{#2}^{#3}{#4} }
 175              { {#1}_{#2}^{#3}{#4} }
 176 }
 177
 178
 179 % The four standard (UNLESS YOU'RE FRENCH) types of intervals along
 180 % the real line.
 181 \newcommand*{\intervaloo}[2]{ \left({#1},{#2}\right) } % open-open
 182 \newcommand*{\intervaloc}[2]{ \left({#1},{#2}\right] } % open-closed
 183 \newcommand*{\intervalco}[2]{ \left[{#1},{#2}\right) } % closed-open
 184 \newcommand*{\intervalcc}[2]{ \left[{#1},{#2}\right] } % closed-closed
 185
 186
 187 \fi