# Singular

#### D.6.12.2 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) ```