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D.7.1.23 primary_charp_no_molien_random
Procedure from library finvar.lib (see finvar_lib).
- Usage:
- primary_charp_no_molien_random(REY,r[,v]);
REY: a <matrix> representing the Reynolds operator, r: an <int> where
-|r| to |r| is the range of coefficients of the random combinations of
bases elements, v: an optional <int>
- Assume:
- REY is the first return value of group_reynolds or reynolds_molien
- Display:
- information about the various stages of the programme if v does not
equal 0
- Return:
- primary invariants (type <matrix>) of the invariant ring and an
<intvec> listing some of the degrees where no non-trivial homogeneous
invariants are to be found
- 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)).
Example:
| | LIB "finvar.lib";
ring R=3,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
list L=group_reynolds(A);
list l=primary_charp_no_molien_random(L[1],1);
print(l[1]);
==> z2,x2+y2,x4+y4-z4
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