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D.7.1.14 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 shoud 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
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