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6.1.9 Package gbmr
The following are commands and functions within the package gbmr:
NCo.Add Addition of two polynomials in a free monoid ring.
NCo.BAdd Addition of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.
NCo.BDeg The standard degree of a polynomial in a free monoid ring over the binary field F_{2}={0,1}.
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.BInterreduction Interreduce a LIST of polynomials in a free monoid ring over the binary field.
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.BLC The leading coefficient of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}.
NCo.BLW The leading word (or term) of a non-zero polynomial in a free monoid ring over the binary field F_{2}={0,1}.
NCo.BMB Enumerate a Macauley's basis of a finitely generated algebra over the binary field F_{2}={0,1}.
NCo.BMultiply Multiplication of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.
NCo.BNR The normal remainder of a polynomial with respect to a LIST of polynomials in a free monoid ring 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.BSubtract Subtraction of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.
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.Deg The standard degree of a polynomial in a free monoid ring.
NCo.FindPolynomials Find polynomials with specified alphabet (set of indeterminates) from a LIST of non-commutative polynomials.
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.IsHomog Check whether a polynomial or a list of polynomials is homogeneous in a free monoid ring.
NCo.KernelOfHomomorphism The kernel of an algebra homomorphism.
NCo.LC The leading coefficient of a non-zero polynomial in a free monoid ring.
NCo.LW The leading word (or term) of a non-zero polynomial in a free monoid ring.
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.MRAdd Addition of two polynomials in a finitely presented monoid ring.
NCo.MRDeg The standard degree of a polynomial in a finitely presented monoid ring.
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.MRInterreduction Interreduce a LIST of polynomials in a finitely presented monoid ring.
NCo.MRIsGB Check whether a finite LIST of non-zero polynomials in a finitely presented monoid ring is a Groebner basis.
NCo.MRLC The leading coefficient of a polynomial in a finitely presented monoid ring.
NCo.MRLW The leading word (or term) of a polynomial in a finitely presented monoid ring.
NCo.MRMB Enumerate a Macaulay's basis of a finitely generated K-algebra.
NCo.MRMultiply Multiplication of two polynomials in a finitely presented monoid ring.
NCo.MRNR The normal remainder of a polynomial with respect to a LIST of polynomials in a finitely presented monoid ring.
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.MRSubtract Subtraction of two polynomials in a finitely presented monoid ring.
NCo.Multiply Multiplication of two polynomials in a free monoid ring.
NCo.NR The normal remainder of a polynomial with respect to a LIST of polynomials in a free monoid ring.
NCo.PrefixGB Compute a prefix Groebner basis of a finitely generated right ideal in a finitely presented monoid ring.
NCo.PrefixInterreduction Prefix interreduction of a LIST of polynomials in a finitely presented monoid ring.
NCo.PrefixNR The prefix normal remainder of a polynomial with respect to a LIST of polynomials 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.SetFp Set coefficient field to a finite field.
NCo.SetOrdering Set a word ordering on .
NCo.SetRelations Set relations for a finitely presented monoid ring.
NCo.SetX Set alphabet (set of indeterminates) for a free monoid ring.
NCo.Subtract Subtraction of two polynomials 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.
NCo.UnsetFp Set coefficient field to the default coefficient field Q, i.e. RAT in CoCoAL.
NCo.UnsetRelations Set relations to the empty set.




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