D.6.1.13 primary_char0

Procedure from library finvar.lib (see finvar_lib).

Usage:

primary_char0(REY,M[,v]);
REY: a <matrix> representing the Reynolds operator, M: a 1x2 <matrix> representing the Molien series, v: an optional <int>

Assume:

REY is the first return value of group_reynolds or reynolds_molien and M the one of molien or the second one of reynolds_molien

Display:

information about the various stages of the program if v does not equal 0

Return:

primary invariants (type <matrix>) of the invariant ring

Theory:

Bases of homogeneous invariants are generated successively and those are chosen as primary invariants that lower the dimension of the ideal generated by the previously found invariants (see paper "Generating a Noetherian Normalization of the Invariant Ring of a Finite Group" by Decker, Heydtmann, Schreyer (1998)).

Example:

LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
matrix REY,M=reynolds_molien(A);
matrix P=primary_char0(REY,M);
print(P);
→ z2,x2+y2,x2y2