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6.2.13 Groebner-Type Computations
The following are the commands and functions for computations based on Groebner bases. In addition to these, there are many commands that provide finer control over the computations (see the next section: The Interactive Groebner Framework).
BB.TransformBBIntoGB Transforms a border basis into a Groebner basis.
BB.TransformGBIntoBB Transforms a Groebner basis into a border basis.
CharP.GBasisF1024 Computing a Groebner basis of a given ideal in F_1024.
CharP.GBasisF128 Computing a Groebner Basis of a given ideal in F_128.
CharP.GBasisF16 Computing a Groebner Basis of a given ideal in F_16.
CharP.GBasisF2 Computing a Groebner Basis of a given ideal in F_2.
CharP.GBasisF2048 Computing a Groebner Basis of a given ideal in F_2048.
CharP.GBasisF256 Computing a Groebner Basis of a given ideal in F_256.
CharP.GBasisF32 Computing a Groebner Basis of a given ideal in F_32.
CharP.GBasisF4 Computing a Groebner Basis of a given ideal in F_4.
CharP.GBasisF512 Computing a Groebner Basis of a given ideal in F_512.
CharP.GBasisF64 Computing a Groebner Basis of a given ideal in F_64.
CharP.GBasisF8 Computing a Groebner Basis of a given ideal in F_8.
CharP.GBasisModSquares Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.
DA.DiffGB Computes a differential Groebner basis.
FGLM.FGLM Performs a FGLM Groebner Basis conversion using ApCoCoAServer.
NC.GB (Partial) Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra.
NC.GGB (Partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.GHF Hilbert function of F2/(Gb).
NC.GIsGB Checks whether a list of polynomials in a free group ring over F2 is a Groebner basis of the ideal generated by polynomials.
NC.GMB Macauley basis of F2/(Gb) with respect to Ordering.
NC.GReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.GTruncatedGB Degree truncated Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.HF Hilbert function of K-algebra.
NC.Interreduction Interreduces a LIST of polynomials over a free associative K-algebra.
NC.Intersection (Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a free associative K-algebra.
NC.IsFinite Checks whether K-vector space K/ is finitely generated.
NC.IsGB Checks whether a list of polynomials over a free associative K-algebra is a Groebner basis of the ideal generated by polynomials.
NC.IsHomog Checks whether a polynomial of a list of polynomials is homogeneous over a free associative K-algebra.
NC.LTIdeal (Partial) (two-sided) leading-term ideal of a finitely generated ideal over a free associative K-algebra.
NC.MB Macaulay basis of K-algebra with respect to Ordering.
NC.MRGB (Partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
NC.MRHF Hilbert function of K-algebra.
NC.MRIntersection (Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a finitely presented monoid ring.
NC.MRIsGB Checks whether a list of polynomials over a finitely presented monoid ring is a Groebner basis of the ideal generated by polynomials.
NC.MRIsHomog Checks whether a polynomial or a set (LIST) of polynomials is homogeneous over a finitely presented monoid ring.
NC.MRMB Macaulay basis of K-algebra with respect to Ordering.
NC.MRReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
NC.PrefixGB Prefix Groebner basis of a finitely generated (right) ideal in a finitely presented monoid ring.
NC.PrefixReducedGB Prefix reduced Groebner basis of a finitely generated (right) ideal in a finitely presented monoid ring.
NC.PrefixSaturation Prefix saturation of a polynomial in a finitely presented monoid ring.
NC.ReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra. K-algebra.
NC.TruncatedGB Degree truncated Groebner basis of a finitely generated two-sided ideal in a free associative K-algebra.
Weyl.Inw Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).
Weyl.TwoWGB Computes the reduced two-sided Groebner basis of a two-sided ideal I in the Weyl algebra A_n over the field of positive characteristic.
Weyl.WGB Computes the Groebner basis of an ideal I in Weyl algebra A_n.
Weyl.WRedGB Computes reduced Groebner basis of a D-ideal in Weyl algebra A_n.
Weyl.WRGB Reduced Groebner basis of an ideal I in Weyl algebra A_n.
Weyl.WRGBS Convert a Groebner basis of an ideal in Weyl algebra A_n in to its reduced Groebner Basis using corresponding implementation in ApCoCoALib.


For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").