D.6.1.10 evaluate_reynolds

Procedure from library finvar.lib (see finvar_lib).

Usage:

evaluate_reynolds(REY,I);
REY: a <matrix> representing the Reynolds operator, I: an arbitrary <ideal>

Assume:

REY is the first return value of group_reynolds() or reynolds_molien()

Returns:

image of the polynomials defining I under the Reynolds operator (type <ideal>)

Note:

the characteristic of the coefficient field of the polynomial ring should not divide the order of the finite matrix group

Theory:

REY has been constructed in such a way that each row serves as a ring mapping of which the Reynolds operator is made up.

Example:

LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
list L=group_reynolds(A);
ideal I=x2,y2,z2;
print(evaluate_reynolds(L[1],I));
→ 1/2x2+1/2y2,
→ 1/2x2+1/2y2,
→ z2