texmacs/showcase1.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       ::KeepHistory(false).
  19
  20       {m,n,p,q,r,s,t,u,v,w,a,b,c,d,e,f}::Indices(vector).
  21
  22       W_{m n p q}::WeylTensor.
  23     </input>
  24
  25     <\output>
  26       Assigning property KeepHistory to .
  27
  28       Assigning property Indices to m, n, p, q, r, s, t, u, v, w, a, b, c, d,
  29       e, f.
  30
  31       Assigning property WeylTensor to W.
  32
  33       \
  34     </output>
  35
  36     <\input|<with|mode|math|color|red|\<gtr\>>>
  37       R41:= W_{m n a b} W_{n p b c} W_{p s c d} W_{s m d a};
  38
  39       R42:= W_{m n a b} W_{n p b c} W_{m s c d} W_{s p d a};
  40
  41       R43:= W_{m n a b} W_{p s b a} W_{m n c d} W_{p s d c};
  42
  43       R44:= W_{m n a b} W_{m n b a} W_{p s c d} W_{p s d c};
  44
  45       R45:= W_{m n a b} W_{n p b a} W_{p s c d} W_{s m d c};
  46
  47       R46:= W_{m n a b} W_{p s b a} W_{m p c d} W_{n s d c};
  48
  49       R47:= W_{m n}^{m n} W_{p q}^{p q} W_{r s}^{r s} W_{t u}^{t u};\
  50     </input>
  51
  52     <\output>
  53       R41:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*c><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*m*d*a>;>
  54
  55       R42:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*c><space|0.25spc>W<space|0.25spc><rsub|m*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*p*d*a>;>
  56
  57       R43:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|p*s*b*a><space|0.25spc>W<space|0.25spc><rsub|m*n*c*d><space|0.25spc>W<space|0.25spc><rsub|p*s*d*c>;>
  58
  59       R44:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|m*n*b*a><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|p*s*d*c>;>
  60
  61       R45:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*a><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*m*d*c>;>
  62
  63       R46:= <with|mode|math|W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|p*s*b*a><space|0.25spc>W<space|0.25spc><rsub|m*p*c*d><space|0.25spc>W<space|0.25spc><rsub|n*s*d*c>;>
  64
  65       R47:= <with|mode|math|W<space|0.25spc><rsub|m*n><space|0.25spc><rsup|m*n><space|0.25spc>W<space|0.25spc><rsub|p*q><space|0.25spc><rsup|p*q><space|0.25spc>W<space|0.25spc><rsub|r*s><space|0.25spc><rsup|r*s><space|0.25spc>W<space|0.25spc><rsub|t*u><space|0.25spc><rsup|t*u>;>
  66
  67       \
  68     </output>
  69
  70     <\input|<with|mode|math|color|red|\<gtr\>>>
  71       @asym!(%){^{m},^{n},^{p},^{q},^{r},^{s},^{t},^{u}}:
  72
  73       @substitute!(%)( W_{a b}^{c d} -\<gtr\> W_{a b c d} ):
  74
  75       @indexsort!(%):
  76
  77       @collect_terms!(%):
  78
  79       @canonicalise!(%):
  80
  81       @collect_terms!(%);
  82     </input>
  83
  84     <\output>
  85       R47:= <with|mode|math|<frac|1|840><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>-<frac|2|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*p*r><space|0.25spc>W<space|0.25spc><rsub|q*s*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>+<frac|1|420><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*r*s><space|0.25spc>W<space|0.25spc><rsub|p*q*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>-<frac|4|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*r*s><space|0.25spc>W<space|0.25spc><rsub|p*t*r*u><space|0.25spc>W<space|0.25spc><rsub|q*u*s*t>+<frac|2|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*r*p*s><space|0.25spc>W<space|0.25spc><rsub|n*t*q*u><space|0.25spc>W<space|0.25spc><rsub|r*t*s*u>-<frac|4|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*r*p*s><space|0.25spc>W<space|0.25spc><rsub|n*t*r*u><space|0.25spc>W<space|0.25spc><rsub|q*t*s*u>;>
  86
  87       \
  88     </output>
  89
  90     <\input|<with|mode|math|color|red|\<gtr\>>>
  91       basisR4:= { @(R41), @(R42), @(R43), @(R44), @(R45), @(R46), @(R47) };
  92     </input>
  93
  94     <\output>
  95       basisR4:= <with|mode|math|{W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*c><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*m*d*a>,W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*c><space|0.25spc>W<space|0.25spc><rsub|m*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*p*d*a>,W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|p*s*b*a><space|0.25spc>W<space|0.25spc><rsub|m*n*c*d><space|0.25spc>W<space|0.25spc><rsub|p*s*d*c>,W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|m*n*b*a><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|p*s*d*c>,W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|n*p*b*a><space|0.25spc>W<space|0.25spc><rsub|p*s*c*d><space|0.25spc>W<space|0.25spc><rsub|s*m*d*c>,W<space|0.25spc><rsub|m*n*a*b><space|0.25spc>W<space|0.25spc><rsub|p*s*b*a><space|0.25spc>W<space|0.25spc><rsub|m*p*c*d><space|0.25spc>W<space|0.25spc><rsub|n*s*d*c>,<frac|1|840><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>-<frac|2|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*p*r><space|0.25spc>W<space|0.25spc><rsub|q*s*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>+<frac|1|420><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*r*s><space|0.25spc>W<space|0.25spc><rsub|p*q*t*u><space|0.25spc>W<space|0.25spc><rsub|r*s*t*u>-<frac|4|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*n*r*s><space|0.25spc>W<space|0.25spc><rsub|p*t*r*u><space|0.25spc>W<space|0.25spc><rsub|q*u*s*t>+<frac|2|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*r*p*s><space|0.25spc>W<space|0.25spc><rsub|n*t*q*u><space|0.25spc>W<space|0.25spc><rsub|r*t*s*u>-<frac|4|105><space|0.25spc>W<space|0.25spc><rsub|m*n*p*q><space|0.25spc>W<space|0.25spc><rsub|m*r*p*s><space|0.25spc>W<space|0.25spc><rsub|n*t*r*u><space|0.25spc>W<space|0.25spc><rsub|q*t*s*u>};>
  96
  97       \
  98     </output>
  99
 100     <\input|<with|mode|math|color|red|\<gtr\>>>
 101       W_{p q r s} W_{p t r u} W_{t v q w} W_{u v s w} - W_{p q r s} W_{p q t
 102       u} W_{r v t w} W_{s v u w};
 103     </input>
 104
 105     <\output>
 106       10:= <with|mode|math|W<space|0.25spc><rsub|p*q*r*s><space|0.25spc>W<space|0.25spc><rsub|p*t*r*u><space|0.25spc>W<space|0.25spc><rsub|t*v*q*w><space|0.25spc>W<space|0.25spc><rsub|u*v*s*w>-W<space|0.25spc><rsub|p*q*r*s><space|0.25spc>W<space|0.25spc><rsub|p*q*t*u><space|0.25spc>W<space|0.25spc><rsub|r*v*t*w><space|0.25spc>W<space|0.25spc><rsub|s*v*u*w>;>
 107
 108       \
 109     </output>
 110
 111     <\input|<with|mode|math|color|red|\<gtr\>>>
 112       @decompose!(%){ @(basisR4) }:
 113
 114       @list_sum(%):
 115
 116       @collect_terms!(%);
 117     </input>
 118
 119     <\output>
 120       10:= <with|mode|math|{0,1,0,0,0,(<frac|-1|4>),0};>
 121
 122       \
 123     </output>
 124
 125     <\input|<with|mode|math|color|red|\<gtr\>>>
 126       \;
 127     </input>
 128   </session>>
 129 </body>
 130
 131 <\initial>
 132   <\collection>
 133     <associate|font-base-size|8>
 134   </collection>
 135 </initial>