texmacs/showcase2.tm

   1 <TeXmacs|1.0.6>
   2
   3 <style|generic>
   4
   5 <\body>
   6   <with|prog-language|cadabra|prog-session|default|<\session>
   7     <\output>
   8       <with|font-family|rm|<with|font-size|1.41|Cadabra 0.8> (built on Thu
   9       Jul 20 11:17:01 CEST 2006)<next-line>Copyright (c) 2001-2006 Kasper
  10       Peeters \<less\>kasper.peeters@aei.mpg.de\<gtr\><next-line>Available
  11       under the terms of the GNU General Public License.<next-line>>Default
  12       startup file ~/.cadabra not present.
  13
  14       \;
  15     </output>
  16
  17     <\input|<with|mode|math|color|red|\<gtr\>>>
  18       {m,n,p,q,r}::Integer(0..3).
  19
  20       \\bar{#}::DiracBar.\
  21
  22       \\Gamma{#}::GammaMatrix.
  23
  24       \\psi_{m}::Spinor(dimension=4).\
  25
  26       \\psi_{m}::GammaTraceless.\
  27
  28       \\delta_{m n}::KroneckerDelta.\
  29
  30       { \\delta_{m n}, A_{m}, \\psi_{m}, \\Gamma_{#} }::SortOrder.
  31     </input>
  32
  33     <\output>
  34       Assigning property Integer to m, n, p, q, r.
  35
  36       Assigning property DiracBar to \\bar.
  37
  38       Assigning property GammaMatrix to \\Gamma.
  39
  40       Assigning property Spinor to \\psi.
  41
  42       Assigning property GammaTraceless to \\psi.
  43
  44       Assigning property KroneckerDelta to \\delta.
  45
  46       Assigning property SortOrder to \\delta, A, \\psi, \\Gamma.
  47
  48       \
  49     </output>
  50
  51     <\input|<with|mode|math|color|red|\<gtr\>>>
  52       ::PostDefaultRules{ @@prodsort!(%), @@eliminate_kr!(%) }.
  53     </input>
  54
  55     <\output>
  56       Assigning property PostDefaultRules to .
  57
  58       \
  59     </output>
  60
  61     <\input|<with|mode|math|color|red|\<gtr\>>>
  62       \\bar{\\psi_{m}} (\\Gamma_{m n} + A_{m} \\Gamma_{n}) \\Gamma_{p q r}
  63       \\psi_{r};
  64     </input>
  65
  66     <\output>
  67       1:= <with|mode|math|<wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>(\<Gamma\><rsub|m*n>+A<rsub|m><space|0.25spc>\<Gamma\><rsub|n>)<space|0.25spc>\<Gamma\><rsub|p*q*r><space|0.25spc>\<psi\><rsub|r>;>
  68
  69       \
  70     </output>
  71
  72     <\input|<with|mode|math|color|red|\<gtr\>>>
  73       @distribute!(%);
  74     </input>
  75
  76     <\output>
  77       1:= <with|mode|math|<wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|m*n><space|0.25spc>\<Gamma\><rsub|p*q*r><space|0.25spc>\<psi\><rsub|r>+A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n><space|0.25spc>\<Gamma\><rsub|p*q*r><space|0.25spc>\<psi\><rsub|r>;>
  78
  79       \
  80     </output>
  81
  82     <\input|<with|mode|math|color|red|\<gtr\>>>
  83       @join!(%);
  84     </input>
  85
  86     <\output>
  87       1:= <with|mode|math|<wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>(6<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>\<Gamma\><rsub|m*q*r>+6<space|0.25spc>\<delta\><rsub|m*q><space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>\<Gamma\><rsub|r>)<space|0.25spc>\<psi\><rsub|r>+A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>(\<Gamma\><rsub|n*p*q*r>+3<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>\<Gamma\><rsub|q*r>)<space|0.25spc>\<psi\><rsub|r>;>
  88
  89       \
  90     </output>
  91
  92     <\input|<with|mode|math|color|red|\<gtr\>>>
  93       @distribute!(%);
  94     </input>
  95
  96     <\output>
  97       1:= <with|mode|math|6<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|m*q*r><space|0.25spc>\<psi\><rsub|r>+6<space|0.25spc>\<delta\><rsub|m*q><space|0.25spc>\<delta\><rsub|n*p><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|r><space|0.25spc>\<psi\><rsub|r>+A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n*p*q*r><space|0.25spc>\<psi\><rsub|r>+3<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|q*r><space|0.25spc>\<psi\><rsub|r>;>
  98
  99       \
 100     </output>
 101
 102     <\input|<with|mode|math|color|red|\<gtr\>>>
 103       @remove_gamma_trace!(%);
 104     </input>
 105
 106     <\output>
 107       1:= <with|mode|math|-6<space|0.25spc>\<delta\><rsub|m*q><space|0.25spc>\<delta\><rsub|n*p><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|r><space|0.25spc>\<psi\><rsub|r>+6<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|q><space|0.25spc>\<psi\><rsub|m>-A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n*p><space|0.25spc>\<psi\><rsub|q>+A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n*q><space|0.25spc>\<psi\><rsub|p>-A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|p*q><space|0.25spc>\<psi\><rsub|n>-3<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<psi\><rsub|q>;>
 108
 109       \
 110     </output>
 111
 112     <\input|<with|mode|math|color|red|\<gtr\>>>
 113       @remove_gamma_trace!(%);
 114     </input>
 115
 116     <\output>
 117       1:= <with|mode|math|6<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|q><space|0.25spc>\<psi\><rsub|m>-A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n*p><space|0.25spc>\<psi\><rsub|q>+A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|n*q><space|0.25spc>\<psi\><rsub|p>-A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<Gamma\><rsub|p*q><space|0.25spc>\<psi\><rsub|n>-3<space|0.25spc>\<delta\><rsub|n*p><space|0.25spc>A<rsub|m><space|0.25spc><wide|\<psi\><rsub|m>|\<bar\>><space|0.25spc>\<psi\><rsub|q>;>
 118
 119       \
 120     </output>
 121
 122     <\input|<with|mode|math|color|red|\<gtr\>>>
 123       \;
 124     </input>
 125   </session>>
 126 </body>
 127
 128 <\initial>
 129   <\collection>
 130     <associate|font-base-size|8>
 131   </collection>
 132 </initial>