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.
Char2.GBasisF1024 Computing a Groebner basis of a given ideal in F_1024.
Char2.GBasisF128 Computing a Groebner Basis of a given ideal in F_128.
Char2.GBasisF16 Computing a Groebner Basis of a given ideal in F_16.
Char2.GBasisF2 Computing a Groebner Basis of a given ideal in F_2.
Char2.GBasisF2048 Computing a Groebner Basis of a given ideal in F_2048.
Char2.GBasisF256 Computing a Groebner Basis of a given ideal in F_256.
Char2.GBasisF32 Computing a Groebner Basis of a given ideal in F_32.
Char2.GBasisF4 Computing a Groebner Basis of a given ideal in F_4.
Char2.GBasisF512 Computing a Groebner Basis of a given ideal in F_512.
Char2.GBasisF64 Computing a Groebner Basis of a given ideal in F_64.
Char2.GBasisF8 Computing a Groebner Basis of a given ideal in F_8.
Char2.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.Add Addition of two polynomials over a free associative K-algebra.
NC.BP Computes (partial) two-sided Groebner basis of finitely generated ideal using Buchberger's procedure over a monoid ring.
NC.Deg (Standard) degree of a polynomial over a free associative K-algebra.
NC.FindPolynomials Find polynomials with specified alphabet (indeterminates) from a list of polynomials.
NC.GB Computes a (partial) two-sided Groebner basis of finitely generated ideal (using Buchberger's procedure) over a free associative K-algebra.
NC.Intersection Computes the intersection of two finitely generated two-sided ideals over a free associative K-algebra.
NC.IsGB Checks whether a list of polynomials is a Groebner basis over a free associative K-algebra.
NC.KernelOfHomomorphism Computes a (partial) Groebner basis of the kernel of a K-algebra homomorphism.
NC.LC Leading coefficient of a polynomial over a free associative K-algebra.
NC.LT Leading term of a polynomial over a free associative K-algebra.
NC.LTIdeal Computes the (partial) two-sided leading-term ideal of a finitely generated ideal over a free associative K-algebra.
NC.MinimalPolynomial Computes the minimal polynomial of a quotient ring element over a free associative K-algebra.
NC.MRAdd Addition of two polynomials over a monoid ring.
NC.MRBP Buchberger procedure for computing a (partial) Groebner basis of a finitely generated two-sided ideal over a monoid ring.
NC.MRIntersection Computes a (partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a monoid ring.
NC.MRKernelOfHomomorphism Computes a Groebner basis of the kernel of a k-algebra homomorphism.
NC.MRMinimalPolynomials Computes the minimal polynomials of a quotient ring element over a monoid ring.
NC.MRMultiply Computes multiplication of two polynomials over a monoid ring.
NC.MRReducedBP Buchberger procedure for computing reduced (partial) Groebner basis of a finitely generated two-sided ideal.
NC.MRSubtract Computes the subtraction of two polynomials over a monoid ring.
NC.Multiply Multiplication of two polynomials over a free associative K-algebra.
NC.NR Normal remainder polynomial with respect to a list of polynomials over a free associative K-algebra.
NC.ReducedBP Computes the reduced (partial) two-sided Groebner basis of a finitely generated ideal using Buchberger's procedure over a monoid ring.
NC.ReducedGB Computes the reduced (partial) two-sided Groebner basis of a finitely generated ideal (using Buchberger's procedure) over a free associative K-algebra.
NC.SetFp Set coefficient to a finite field.
NC.SetOrdering Sets an (admissible) ordering.
NC.SetRelations Sets the relations for a monoid ring.
NC.SetRules Sets the (rewriting) rules over a monoid ring.
NC.SetX Sets the alphabet (indeterminates).
NC.Subtract Subtraction of two polynomials over a free associative K-algebra.
NC.UnsetFp Set coefficient field to default coefficient field Q. Note that default coefficient field is the set of rational numbers Q, i.e. RAT in CoCoAL.
NC.UnsetOrdering Sets the current admissible ordering to default ordering LLEX (length-lexicographic ordering).
NC.UnsetRelations Sets the relations of a rewriting system to an empty set, i.e. changes the current monoid ring to a free associative K-algebra.
NC.UnsetRules Sets the rewriting rules to empty set.
NC.UnsetX Sets the alpbabet (inderminates) to an empty string.
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.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").