D.6.1.22 primary_charp_without_random

Procedure from library finvar.lib (see finvar_lib).

Usage:

primary_charp_without_random(G1,G2,...,r[,v]);
G1,G2,...: <matrices> generating a finite matrix group, r: an <int> where -|r| to |r| is the range of coefficients of the random combinations of bases elements, 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 random linear combinations are chosen as primary invariants that lower the dimension of the ideal generated by the previously found invariants (see "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_random(A,1);
print(P);
→ x+y,z,xy