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D.6.14.2 ModEqn
Procedure from library qhmoduli.lib (see qhmoduli_lib).
- Usage:
- ModEqn(f [, opt]); poly f; int opt;
- Purpose:
- compute equations of the moduli space of semiquasihomogenos hypersurface singularity with principal part f w.r.t. right equivalence
- Assume:
- f quasihomogeneous polynomial with an isolated singularity at 0
- Return:
- polynomial ring, possibly a simple extension of the ground field of
the basering, containing the ideal 'modid'
- 'modid' is the ideal of the moduli space if opt is even (> 0).
otherwise it contains generators of the coordinate ring R of the
moduli space (note : Spec(R) is the moduli space)
- Options:
- 1 compute equations of the mod. space,
2 use a primary decomposition,
4 compute E_f0, i.e., the image of G_f0,
to combine options, add their value, default: opt =7
Example:
| | LIB "qhmoduli.lib";
ring B = 0,(x,y), ls;
poly f = -x4 + xy5;
def R = ModEqn(f);
setring R;
modid;
==> modid[1]=Y(5)^2-Y(4)*Y(6)
==> modid[2]=Y(4)*Y(5)-Y(3)*Y(6)
==> modid[3]=Y(3)*Y(5)-Y(2)*Y(6)
==> modid[4]=Y(2)*Y(5)-Y(1)*Y(6)
==> modid[5]=Y(4)^2-Y(3)*Y(5)
==> modid[6]=Y(3)*Y(4)-Y(2)*Y(5)
==> modid[7]=Y(2)*Y(4)-Y(1)*Y(5)
==> modid[8]=Y(3)^2-Y(2)*Y(4)
==> modid[9]=Y(2)*Y(3)-Y(1)*Y(4)
==> modid[10]=Y(2)^2-Y(1)*Y(3)
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