| #### 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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