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The Maxima on-line user's manual

Algebra Calculator

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Todd_coxeter Calculator

Todd_coxeter

Function: todd_coxeter (<relations>, <subgroup>)

Function: todd_coxeter (<relations>) Find the order of G/H where G is the Free Group modulo <relations>, and H is the subgroup of G generated by <subgroup>. <subgroup> is an optional argument, defaulting to []. In doing this it produces a multiplication table for the right action of G on G/H, where the cosets are enumerated [H,Hg2,Hg3,...]. This can be seen internally in the variable todd_coxeter_state.

Example:

          (%i1) symet(n):=create_list(
                  if (j - i) = 1 then (p(i,j))^^3 else
                      if (not i = j) then (p(i,j))^^2 else
                          p(i,i) , j, 1, n-1, i, 1, j);
                                                                 <3>
          (%o1) symet(n) := create_list(if j - i = 1 then p(i, j)

<2> else (if not i = j then p(i, j) else p(i, i)), j, 1, n - 1,

          i, 1, j)
          (%i2) p(i,j) := concat(x,i).concat(x,j);
          (%o2)        p(i, j) := concat(x, i) . concat(x, j)
          (%i3) symet(5);
                   <2>           <3>    <2>           <2>           <3>
          (%o3) [x1   , (x1 . x2)   , x2   , (x1 . x3)   , (x2 . x3)   ,

<2> <2> <2> <3> <2> x3 , (x1 . x4) , (x2 . x4) , (x3 . x4) , x4 ]

          (%i4) todd_coxeter(%o3);

          Rows tried 426
          (%o4)                          120
          (%i5) todd_coxeter(%o3,[x1]);

          Rows tried 213
          (%o5)                          60
          (%i6) todd_coxeter(%o3,[x1,x2]);

          Rows tried 71
          (%o6)                          20

(%o1)                                true
(%i2) 

Todd_coxeter Example

Related Examples

todd_coxeter

? todd_coxeter;

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todd_coxeter

? todd_coxeter;

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