D.5.7.5 StabEqnId

Procedure from library qhmoduli.lib (see qhmoduli_lib).

Usage:

StabEqn(I, w); I ideal, w intvec

Purpose:

compute the equations of the isometry group of the ideal I each generator of I is fixed by the stabilizer.

Assume:

I semiquasihomogeneous ideal wrt ’w’ 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. t(i) -> t(i)t(j) ...

Example:

LIB "qhmoduli.lib";
ring B   = 0,(x,y,z), ls;
ideal I = x2,y3,z6;
intvec w = 3,2,1;
list stab = StabEqnId(I, w);
→ // ** redefining d **
→ // ** redefining newcoMx **
→ // ** redefining coMx **
→ // ** redefining d **
→ // ** redefining newcoMx **
→ // ** redefining coMx **
def S1 = stab[1]; setring S1;  stabid;
→ stabid[1]=s(1)^2-1
→ stabid[2]=s(2)^3-1
→ stabid[3]=s(3)^6-1
def S2 = stab[2]; setring S2;  actionid;
→ actionid[1]=s(1)*x
→ actionid[2]=s(2)*y
→ actionid[3]=s(3)*z