Singular Manual: serreRelations

| #### 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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