D.6.1.12 invariant_basis_reynolds

Procedure from library finvar.lib (see finvar_lib).

Usage:

invariant_basis_reynolds(REY,d[,flags]);
REY: a <matrix> representing the Reynolds operator, d: an <int> indicating of which degree (>0) the homogeneous basis should be, flags: an optional <intvec> with two entries: its first component gives the dimension of the space (default <0 meaning unknown) and its second component is used as the number of polynomials that should be mapped to invariants during one call of evaluate_reynolds if the dimension of the space is unknown or the number such that number x dimension polynomials are mapped to invariants during one call of evaluate_reynolds

Assume:

REY is the first return value of group_reynolds() or reynolds_molien() and flags[1] given by partial_molien

Return:

the basis (type <ideal>) of the space of invariants of degree d

Theory:

Monomials of degree d are mapped to invariants with the Reynolds operator. A linearly independent set is generated with the help of minbase.

Example:

LIB "finvar.lib";
ring R=0,(x,y,z),dp;
matrix A[3][3]=0,1,0,-1,0,0,0,0,-1;
intvec flags=0,1,0;
matrix REY,M=reynolds_molien(A,flags);
flags=8,6;
print(invariant_basis_reynolds(REY,6,flags));
→ z6,
→ x2z4+y2z4,
→ x2y2z2,
→ x3yz2-xy3z2,
→ x4z2+y4z2,
→ x4y2+x2y4,
→ x5y-xy5,
→ x6+y6