D.5.7.3 QuotientEquations

Procedure from library qhmoduli.lib (see qhmoduli_lib).

Usage:

QuotientEquations(G,action,emb [, opt]); ideal G,action,emb;int opt

Purpose:

compute the quotient of the variety given by the parameterization ’emb’ by the linear action ’action’ of the algebraic group G.

Assume:

’action’ is linear, G must be finite if the Reynolds operator is needed (i.e., NullCone(G,action) returns some non-invariant polys)

Return:

polynomial ring over a simple extension of the ground field of the basering, containing the ideals ’id’ and ’embedid’.
- ’id’ contains the equations of the quotient, if opt = 1; if opt = 0, 2, ’id’ contains generators of the coordinate ring R of the quotient (Spec(R) is the quotient)
- ’embedid’ = 0, if opt = 1;
if opt = 0, 2, it is the ideal defining the equivariant embedding

Options:

1 compute equations of the quotient,
2 use a primary decomposition when computing the Reynolds operator
To combine options, add their value, default: opt =3.