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D.7.1.13 invariant_basis

Procedure from library finvar.lib (see finvar_lib).

Usage:
invariant_basis(g,G1,G2,...);
g: an <int> indicating of which degree (>0) the homogeneous basis shoud be, G1,G2,...: <matrices> generating a finite matrix group

Returns:
the basis (type <ideal>) of the space of invariants of degree g

Theory:
A general polynomial of degree g is generated and the generators of the matrix group applied. The difference ought to be 0 and this way a system of linear equations is created. It is solved by computing syzygies.

Example:
 
LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
print(invariant_basis(2,A));
==> x2+y2,
==> z2