mjo-common.tex

   1 %
   2 % Only the most commonly-used macros. Needed by everything else.
   3 %
   4
   5 % Place the argument in matching left/right parntheses.
   6 \providecommand*{\of}[1]{ \left( {#1} \right) }
   7
   8 % Group terms using parentheses.
   9 \providecommand*{\qty}[1]{ \left( {#1} \right) }
  10
  11 % Group terms using square brackets.
  12 \providecommand*{\sqty}[1]{ \left[ {#1} \right] }
  13
  14 % Create a set from the given elements
  15 \providecommand*{\set}[1]{ \left\lbrace {#1} \right\rbrace }
  16
  17 % A set comprehension, where the ``such that...'' bar is added
  18 % automatically. The bar was chosen over a colon to avoid ambiguity
  19 % with the L : V -> V notation. We can't leverage \set here because \middle
  20 % needs \left and \right present.
  21 \providecommand*{\setc}[2]{ \left\lbrace {#1}\ \middle|\ {#2} \right\rbrace }
  22
  23 % A pair of things.
  24 \providecommand*{\pair}[2]{ \left( {#1}, {#2} \right) }
  25
  26 % The Cartesian product of two things.
  27 \providecommand*{\cartprod}[2]{ {#1} \times {#2} }
  28
  29 %
  30 % Product spaces
  31 %
  32 % All of the product spaces (for example, R^n) that follow default to
  33 % an exponent of ``n'', but that exponent can be changed by providing
  34 % it as an optional argument. If the exponent given is ``1'', then it
  35 % will be omitted entirely.
  36 %
  37
  38 % The natural n-space, N x N x N x ... x N.
  39 \providecommand*{\Nn}[1][n]{
  40   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  41 }
  42
  43 % The integral n-space, Z x Z x Z x ... x Z.
  44 \providecommand*{\Zn}[1][n]{
  45   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  46 }
  47
  48 % The rational n-space, Q x Q x Q x ... x Q.
  49 \providecommand*{\Qn}[1][n]{
  50   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  51 }
  52
  53 % The real n-space, R x R x R x ... x R.
  54 \providecommand*{\Rn}[1][n]{
  55   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  56 }
  57
  58 % The complex n-space, C x C x C x ... x C.
  59 \providecommand*{\Cn}[1][n]{
  60   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  61 }