Help:=proc(): print(`Cramer(a,b,n),DenC(a,b,n)`):
print(`DenCC(a,n)`):
end:

#Cramer(a,b,n): inputs symbols a and b
#and pos. integer n, outputs the
#symbolic solution of a[1,1]x[1]+...+a[1,n]x[n]=b[1]
#... a[n,1]x[1]+ ... + a[n,n]x[n]=b[n]
Cramer:=proc(a,b,n) local x,i,j,eq,var:

var:=[seq(x[i],i=1..n)]:

eq:={seq(add(a[i,j]*x[j],j=1..n) - b[i], 
i=1..n)}:

subs(solve(eq,{op(var)}),var ):

end:


DenC:=proc(a,n) local b: 
denom(Cramer(a,b,n)[1]):end:

Sign1:= proc(pi) local n,i,j:n:=nops(pi):

sign(mul(mul(pi[j]-pi[i],j=i+1..n),i=1..n)):

end:


Weight:=proc(a,pi) local i:
 Sign1(pi)*mul(a[i,pi[i]],i=1..nops(pi)):
end:

DenCC:=proc(a,n) local S,i:

with(combinat):
S:=permute(n):

add(Weight(a,S[i]),i=1..nops(S)):
end: