up previous next
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 (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.GReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.HF Hilbert function of K-algebra.
NC.Intersection (Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a free associative K-algebra.
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.KernelOfHomomorphism (Partial) (two-sided) leading-term ideal of the kernel of a K-algebra homomorphism.
NC.LTIdeal (Partial) (two-sided) leading-term ideal of a finitely generated ideal over a free associative K-algebra.
NC.MRGB (Partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
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.MRKernelOfHomomorphism (Partial) Groebner basis of the kernel of a K-algebra homomorphism.
NC.MRLTIdeal (Partial) (two-sided) leading-term ideal of a finitely generated ideal over a finitely presented monoid ring.
NC.MRReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal over 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.
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.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").