Singular Manual: sagbiHilbControlled

| #### D.15.19.3 sagbiHilbControlled Procedure from library `sagbiNormaliz.lib` (see sagbiNormaliz_lib). 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 computatiojn is controlled by the Hilbert series given by the numerator and the denominator. If sorting is set, the compouted elements are degrevlex sorted before a round of the algorithm. The optional parameter verb sets the terminal output. Fefault is 1 = on. The component 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. Example:
    LIB "sagbiNormaliz.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

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