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6.2.11 Ideals
The following are commands and functions for ideals:
BB.BBasis Computes the border basis of a zero-dimensional ideal.
BB.BBasisForMP Computes the border basis of a zero-dimensional ideal generated by marked polynomials.
BB.BBasisForOI Computes the border basis of an ideal w.r.t. a given order ideal.
BB.Border Computes the border of an order ideal.
BB.Box Computes a box order ideal.
BB.HomASgens Computes the generators of the vanishing ideal of a homogeneous border basis scheme.
BB.HomNDgens Computes the generators of the vanishing ideal of a homogeneous border basis scheme.
BB.LiftAS Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
BB.LiftASViaServer Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
BB.LiftND Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours.
BB.LiftNDViaServer Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors.
BB.NDgens Computes the generators of the vanishing ideal of a border basis scheme.
BBF.Init Initializes a border basis computation.
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.KernelOfHomomorphism The kernel of an algebra homomorphism.
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.
Num.SubABM Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.ABM algorithm.
Num.SubAVI Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.AVI algorithm.
Num.SubBBABM Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.BBABM algorithm.
Num.SubEXTABM Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.EXTABM algorithm.
Weyl.AnnFs Computes annihilating ideal of a polynomial F^s in Weyl algebra A_n.
Weyl.BFs Computes B-function of a polynomial F in Weyl algebra A_n.
Weyl.CharI Computes the characteristic ideal of a D-ideal I in Weyl algebra A_n.
Weyl.InIw Computes the initial ideal of a D-ideal I in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).
Weyl.IsHolonomic Checks whether an ideal in Weyl algebra A_n is holonomic or not.
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.WDim Computes the dimension of an ideal I in Weyl algebra A_n.
Weyl.WGB Computes the Groebner basis of an ideal I in Weyl algebra A_n.
Weyl.WLT Computes the leading term ideal of a D-ideal I in Weyl algebra A_n.




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