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D.7.1.21 primary_charp_random
Procedure from library finvar.lib (see finvar_lib).
- Usage:
- primary_charp_random(REY,ringname,r[,v]);
REY: a <matrix> representing the Reynolds operator, ringname: a
<string> giving the name of a ring where the Molien series is stored,
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 and
ringname gives the name of a ring of characteristic 0 that has been
created by molien 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
- 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);
string newring="alskdfj";
molien(L[2..size(L)],newring);
matrix P=primary_charp_random(L[1],newring,1);
kill Finvar::`newring`;
print(P);
==> z2,x2+y2,x4+y4-z4
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