D.6.3.13 ReynoldsOperator

Procedure from library rinvar.lib (see rinvar_lib).

Usage:

ReynoldsOperator(G, action [, opt); ideal G, action; int opt

Purpose:

compute the Reynolds operator of the group G which act via ’action’

Return:

polynomial ring R over a simple extension of the ground field of the basering (the extension might be trivial), containing a list ’ROelements’, the ideals ’id’, ’actionid’ and the polynomial ’newA’. R = K(a)[s(1..r),t(1..n)].
- ’ROelements’ is a list of ideal, each ideal represents a substitution map F : R -> R according to the zero-set of G - ’id’ is the ideal of G in the new ring
- ’newA’ is the new representation of a’ in terms of a. If the basering does not contain a parameter then ’newA’ = ’a’.

Assume:

basering = K[s(1..r),t(1..n)], K = Q or K = Q(a’) and minpoly != 0, G is the ideal of a finite group in K[s(1..r)], ’action’ is a linear group action of G