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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
should 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
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