up previous next
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 Enumerate (partial) Groebner bases of finitely generated two-sided ideals in a non-commutative polynomial ring via the Buchberger procedure.
NC.HF Enumerate the values of the Hilbert-Dehn function of a finitely generated K-algebra.
NC.Intersection Intersection of two finitely generated two-sided ideals in a non-commutative polynomial ring.
NC.IsGB Check whether a LIST of non-zero polynomials is a Groebner basis in a non-commutative polynomial ring.
NC.KernelOfHomomorphism The kernel of an algebra homomorphism.
NC.LWIdeal Leading word ideal of a finitely generated two-sided ideal in a non-commutative polynomial ring.
NC.MB Enumerate a Macaulay's basis of a finitely generated K-algebra.
NC.RedGB Enumerate reduced (partial) Groebner bases of finitely generated two-sided ideals in a non-commutative polynomial ring.
NC.TruncatedGB Compute truncated Groebner bases of finitely generated homogeneous two-sided ideals in a non-commutative polynomial ring.
NCo.BGB Enumerate a (partial) Groebner basis of a finitely generated two-sided ideal in a free monoid ring over the binary field F_{2}={0,1} via the Buchberger procedure.
NCo.BHF Enumerate values of the Hilbert function of a finitely generated algebra over the binary field F_{2}={0,1}.
NCo.BIsGB Check whether a finite LIST of non-zero polynomials in a free monoid ring over the binary field F_{2}={0,1} is a Groebner basis.
NCo.BMB Enumerate a Macauley's basis of a finitely generated algebra over the binary field F_{2}={0,1}.
NCo.BReducedGB Enumerate a (partial) Groebner basis of a finitely generated two-sided ideal in a free monoid ring over the binary field F_{2}={0,1} via the Buchberger procedure.
NCo.BTruncatedGB Compute a truncated Groebner basis of a finitely generated homogeneous two-sided ideal in a free monoid ring over the binary field F_{2}={0,1}.
NCo.GB Enumerate a (partial) Groebner basis of a finitely generated two-sided ideal in a free monoid ring (using the Buchberger procedure).
NCo.HF Enumerate values of the Hilbert function of a finitely generated K-algebra.
NCo.Interreduction Interreduce a LIST of polynomials in a free monoid ring.
NCo.Intersection Intersection of two finitely generated two-sided ideals in a free monoid ring.
NCo.IsFinite Check whether the K-dimension dim(K/) is finite, where is an monoid ideal generated by a finite set M of words.
NCo.IsGB Check whether a finite LIST of non-zero polynomials in a free monoid ring is a Groebner basis.
NCo.LWIdeal Leading word ideal of a finitely generated two-sided ideal in a free monoid ring.
NCo.MB Enumerate a Macaulay's basis of a finitely generated K-algebra.
NCo.MRGB Enumerate a (partial) Groebner basis of a finitely generated two-sided ideal in a finitely presented monoid ring via the Buchberger procedure.
NCo.MRHF Enumerate values of the Hilbert function of a finitely generated K-algebra.
NCo.MRIsGB Check whether a finite LIST of non-zero polynomials in a finitely presented monoid ring is a Groebner basis.
NCo.MRMB Enumerate a Macaulay's basis of a finitely generated K-algebra.
NCo.MRReducedGB Enumerate a reduced (partial) Groebner basis of a finitely generated two-sided ideal in a finitely presented monoid ring via the Buchberger procedure.
NCo.PrefixGB Compute a prefix Groebner basis of a finitely generated right ideal in a finitely presented monoid ring.
NCo.PrefixReducedGB Compute a prefix reduced Groebner basis of a finitely generated right ideal in a finitely presented monoid ring.
NCo.PrefixSaturation Compute a prefix saturation of a polynomial in a finitely presented monoid ring.
NCo.ReducedGB Enumerate a reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free monoid ring.
NCo.TruncatedGB Compute a truncated Groebner basis of a finitely generated homogeneous two-sided ideal in a free monoid ring.
PGBC.ParallelGBC Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.
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").