Singular Manual: ArnoldAction

| #### D.6.18.1 ArnoldAction Procedure from library `qhmoduli.lib` (see qhmoduli_lib). Usage: ArnoldAction(f, [Gf, B]); poly f; list Gf, B; 'Gf' is a list of two rings (coming from 'StabEqn') Purpose: compute the induced action of the stabilizer G of f on T_, where T_ is given by the upper monomials B of the Milnor algebra of f. Assume: f is quasihomogeneous Return: polynomial ring over the same ground field, containing the ideals 'actionid' and 'stabid'. - 'actionid' is the ideal defining the induced action of Gf on T_ - 'stabid' is the ideal of the stabilizer Gf in the new ring Example:
    LIB "qhmoduli.lib";
    ring B   = 0,(x,y,z), ls;
    poly f = -z5+y5+x2z+x2y;
    def R = ArnoldAction(f);
    ==> // ** redefining zz (int zz = 1;) qhmoduli.lib::StabEqnId:630
    setring R;
    actionid;
    ==> actionid[1]=-s(2)*t(1)+s(3)*t(1)
    ==> actionid[2]=-s(2)^2*t(2)+2*s(2)^2*t(3)^2+s(3)^2*t(2)
    ==> actionid[3]=s(2)*t(3)+s(3)*t(3)
    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(1)^2+s(2)^4-s(3)^4
    ==> stabid[5]=s(1)^4+s(2)^3-s(3)^3
    ==> stabid[6]=-s(1)^2*s(3)+s(3)^5

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