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7.10.2.2 serreRelations
Procedure from library fpalgebras.lib (see fpalgebras_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 "fpalgebras.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 = freeAlgebra(r, uptodeg);
setring R;
ideal I = serreRelations(A,1); I = simplify(I,1+2+8);
I;
==> I[1]=f2*f2*f1-2*f2*f1*f2+f1*f2*f2
==> I[2]=f3*f1-f1*f3
==> I[3]=f2*f1*f1-2*f1*f2*f1+f1*f1*f2
==> I[4]=f3*f3*f3*f3*f2-4*f3*f3*f3*f2*f3+6*f3*f3*f2*f3*f3-4*f3*f2*f3*f3*f3+f2\
*f3*f3*f3*f3
==> I[5]=f3*f2*f2-2*f2*f3*f2+f2*f2*f3
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