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D.7.1.24 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 programme 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
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