D.6.1.14 primary_charp

Procedure from library finvar.lib (see finvar_lib).

Usage:

primary_charp(REY,ringname[,v]);
REY: a <matrix> representing the Reynolds operator, ringname: a <string> giving the name of a ring where the Molien series is stored, 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 program if v does not equal 0

Return:

primary invariants (type <matrix>) of the invariant ring

Theory:

Bases of homogeneous invariants are generated successively and those are chosen as primary invariants that lower the dimension of the ideal generated by the previously found invariants (see paper "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(L[1],newring);
if(system("with","Namespaces")) { kill Top::`newring`; }
kill `newring`;
print(P);
→ z2,x2+y2,x2y2