#### 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 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

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