D.6.1.17 primary_charp_without

Procedure from library finvar.lib (see finvar_lib).

Usage:

primary_charp_without(G1,G2,...[,v]);
G1,G2,...: <matrices> generating a finite matrix group, v: an optional <int>

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)). No Reynolds
operator or Molien series is used.

Example:

LIB "finvar.lib";
ring R=2,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
matrix P=primary_charp_without(A);
print(P);
→ x+y,z,xy