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 % The direct sum of two things.
  33 \providecommand*{\directsum}[2]{ {#1}\oplus{#2} }
  34
  35 % The factorial operator.
  36 \providecommand*{\factorial}[1]{ {#1}! }
  37
  38 %
  39 % Product spaces
  40 %
  41 % All of the product spaces (for example, R^n) that follow default to
  42 % an exponent of ``n'', but that exponent can be changed by providing
  43 % it as an optional argument. If the exponent given is ``1'', then it
  44 % will be omitted entirely.
  45 %
  46
  47 % The natural n-space, N x N x N x ... x N.
  48 \providecommand*{\Nn}[1][n]{
  49   \mathbb{N}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  50 }
  51
  52 % The integral n-space, Z x Z x Z x ... x Z.
  53 \providecommand*{\Zn}[1][n]{
  54   \mathbb{Z}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  55 }
  56
  57 % The rational n-space, Q x Q x Q x ... x Q.
  58 \providecommand*{\Qn}[1][n]{
  59   \mathbb{Q}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  60 }
  61
  62 % The real n-space, R x R x R x ... x R.
  63 \providecommand*{\Rn}[1][n]{
  64   \mathbb{R}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  65 }
  66
  67 % The complex n-space, C x C x C x ... x C.
  68 \providecommand*{\Cn}[1][n]{
  69   \mathbb{C}\if\detokenize{#1}\detokenize{1}{}\else^{#1}\fi
  70 }