D.6.1.28 secondary_not_cohen_macaulay

Procedure from library finvar.lib (see finvar_lib).

Usage:

secondary_not_cohen_macaulay(P,G1,G2,...[,v]);
P: a 1xn <matrix> with primary invariants, G1,G2,...: nxn <matrices> generating a finite matrix group, v: an optional <int>

Assume:

n is the number of variables of the basering

Return:

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

Display:

information if v does not equal 0

Theory:

Secondary invariants are generated following "Generating Invariant Rings of Finite Groups over Arbitrary Fields" by Kemper (1996).

Example:

LIB "finvar.lib";
ring R=2,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
list L=primary_invariants(A);
matrix S=secondary_not_cohen_macaulay(L[1],A);
print(S);
→ 1