D.5.7.4 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 ring ’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);
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