Singular Manual: StabEqn

| #### D.6.18.4 StabEqn Procedure from library `qhmoduli.lib` (see qhmoduli_lib). Usage: StabEqn(f); f polynomial Purpose: compute the equations of the isometry group of f. Assume: f semiquasihomogeneous polynomial with an isolated singularity at 0 Return: list of two rings 'S1', 'S2' - 'S1' contains the equations of the stabilizer (ideal 'stabid') - 'S2' contains the action of the stabilizer (ideal 'actionid') Global: varSubsList, contains the index j s.t. x(i) -> x(i)t(j) ... Example:
    LIB "qhmoduli.lib";
    ring B = 0,(x,y,z), ls;
    poly f = -z5+y5+x2z+x2y;
    list stab = StabEqn(f);
    ==> // ** redefining zz (int zz = 1;) qhmoduli.lib::StabEqnId:629
    def S1 = stab[1]; setring S1;  stabid;
    ==> stabid[1]=s(2)*s(3)
    ==> stabid[2]=s(1)^2*s(2)+s(1)^2*s(3)-1
    ==> stabid[3]=s(1)^2*s(3)^2-s(3)
    ==> stabid[4]=s(2)^4-s(3)^4+s(1)^2
    ==> stabid[5]=s(1)^4+s(2)^3-s(3)^3
    ==> stabid[6]=s(3)^5-s(1)^2*s(3)
    def S2 = stab[2]; setring S2;  actionid;
    ==> actionid[1]=s(1)*x
    ==> actionid[2]=s(3)*y+s(2)*z
    ==> actionid[3]=s(2)*y+s(3)*z

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