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 % The Cartesian product of three things.
  30 \providecommand*{\cartprodthree}[3]{ \cartprod{{#1}}{\cartprod{{#2}}{{#3}}} }
  31
  32 %
  33 % Product spaces
  34 %
  35 % All of the product spaces (for example, R^n) that follow default to
  36 % an exponent of ``n'', but that exponent can be changed by providing
  37 % it as an optional argument. If the exponent given is ``1'', then it
  38 % will be omitted entirely.
  39 %
  40
  41 % The natural n-space, N x N x N x ... x N.
  42 \providecommand*{\Nn}[1][n]{
  43   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  44 }
  45
  46 % The integral n-space, Z x Z x Z x ... x Z.
  47 \providecommand*{\Zn}[1][n]{
  48   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  49 }
  50
  51 % The rational n-space, Q x Q x Q x ... x Q.
  52 \providecommand*{\Qn}[1][n]{
  53   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  54 }
  55
  56 % The real n-space, R x R x R x ... x R.
  57 \providecommand*{\Rn}[1][n]{
  58   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  59 }
  60
  61 % The complex n-space, C x C x C x ... x C.
  62 \providecommand*{\Cn}[1][n]{
  63   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  64 }