Procedure from library finvar.lib (see finvar_lib).
Usage:
secondary_and_irreducibles_no_molien(P,REY[,v]);
P: a 1xn <matrix> with primary invariants, REY: a gxn <matrix>
representing the Reynolds operator, v: an optional <int>
Assume:
n is the number of variables of the basering, g the size of the group,
REY is the 1st return value of group_reynolds(), reynolds_molien() or
the second one of primary_invariants()
Return:
secondary invariants of the invariant ring (type <matrix>) and
irreducible secondary invariants (type <matrix>)
Display:
information if v does not equal 0
Theory:
Secondary invariants are calculated by finding a basis (in terms of
monomials) of the basering modulo primary invariants, mapping those to
invariants with the Reynolds operator and using these images or their
power products such that they are linearly independent modulo the
primary invariants (see paper "Some Algorithms in Invariant Theory of
Finite Groups" by Kemper and Steel (1997)).
Example:
LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
list L=primary_invariants(A,intvec(1,1,0));
matrix S,IS=secondary_and_irreducibles_no_molien(L[1..2]);
print(S);
→ 1,xyz,x2z-y2z,x3y-xy3
print(IS);
→ xyz,x2z-y2z,x3y-xy3
User manual for Singular version 2-0-4, October 2002,
generated by texi2html.