%%%%%%%%%%%
Gchar.txt
%%%%%%%%%%%

 Help:=proc():print(`Circ(x,k),Prod(pi,sig)`):
 print(`Gdet(x,k)`):
 end:

with(linalg):
with(combinat):
Circ:=proc(x,k)
local M,i,j:

M:=matrix(k,k,[
seq(seq(x[(i+j) mod k],i=0..k-1),j=0..k-1)]):
factor(det(M)):

end:



#prod(pi,sig): the product of the perms
#pi and sig (of the same length)
Prod:=proc(pi,sig) local i,k:
k:=nops(pi):

[seq(pi[sig[i]],i=1..k)]:
end:


#Gdet(x,k), inputs a pos. integer k and outputs
#the matrix representing the multiplication
#table (for S_k)
#in symboilc form using x[i] to denote
#the i-th member of S_k . It outputs the group-det
Gdet:=proc(x,k) local S,M,i,j:
S:=permute(k):

M:=matrix(k!,k!):

for i from 1 to nops(S) do
 for j from 1 to nops(S) do
   M[i,j]:=Prod(S[i],S[j]):
 od:
od:

factor(det(subs({seq(S[i]=x[i],i=1..nops(S))}, op(M)))):

end: