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D.7.1.12 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
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