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7.7.9.0. 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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