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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:630
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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