D.15.22.3 sagbiHilbControlled

Usage:

agbiHilbControlled(ideal Q, intvec HS_num_algebra, intvec HS_denom_algebra, int Sagbi_degree_bound [,int finalChweck, int sorting, int verb]);

Return:

An ideal whose generators form the Sagbi basis of the algebra generated by the polynomials inin degrwees <= Sagbi_degree_bound. The computation is controlled by the Hilbert series given by the numerator and the denominator.

If sorting is set, the computed elements are degrevlex sorted before a round of the algorithm. The optional parameter verb sets the terminal output. Default is 1 = on.

The return value has a second integer component. Its possible values are: 0, if the full Sagbi basis has not been reached, 1 if this is unknown, and 2 if the full Sagbi basis has been computed.

LIB "sagbiNormaliz0.lib";
ring R = 0, (x,y,z),dp;
ideal P = x^6+y^6+z^6, x^7+y^7+z^7, x^8+y^8+z^8;
ideal Q;
intvec HS_num = 1;
intvec HS_denom = 6,7,8;
int success;
// degree bound 40, final check, ,no sorting, no terminal output
(Q,success) = sagbiHilbControlled(P,HS_num, HS_denom,40, 1,0,0);
lead(Q);
==> _[1]=x6
==> _[2]=x7
==> _[3]=x8
==> _[4]=x8y6
==> _[5]=x18y6
==> _[6]=x23y7
==> _[7]=x25y7
"Note: success = 0 <==> Sagbi basis incomplete";
==> Note: success = 0 <==> Sagbi basis incomplete
"success",success;
==> success 0