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7.7.8.0. serreRelations
Procedure from library freegb.lib (see freegb_lib).

Usage:
serreRelations(A,z); A an intmat, z an int

Return:
ideal

Assume:
basering has a letterplace ring structure and
A is a generalized Cartan matrix with integer entries

Purpose:
compute the ideal of Serre's relations associated to A

Example:
 
LIB "freegb.lib";
intmat A[3][3] =
2, -1, 0,
-1, 2, -3,
0, -1, 2; // G^1_2 Cartan matrix
ring r = 0,(f1,f2,f3),dp;
int uptodeg = 5;
def R = makeLetterplaceRing(uptodeg);
setring R;
ideal I = serreRelations(A,1); I = simplify(I,1+2+8);
I;
==> I[1]=f1(1)*f2(2)*f2(3)-2*f2(1)*f1(2)*f2(3)+f2(1)*f2(2)*f1(3)
==> I[2]=f1(1)*f3(2)-f3(1)*f1(2)
==> I[3]=f1(1)*f1(2)*f2(3)-2*f1(1)*f2(2)*f1(3)+f2(1)*f1(2)*f1(3)
==> I[4]=f2(1)*f3(2)*f3(3)*f3(4)*f3(5)-4*f3(1)*f2(2)*f3(3)*f3(4)*f3(5)+6*f3(1\
   )*f3(2)*f2(3)*f3(4)*f3(5)-4*f3(1)*f3(2)*f3(3)*f2(4)*f3(5)+f3(1)*f3(2)*f3(\
   3)*f3(4)*f2(5)
==> I[5]=f2(1)*f2(2)*f3(3)-2*f2(1)*f3(2)*f2(3)+f3(1)*f2(2)*f2(3)


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