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