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6.1.8 Package gbmr
The following are commands and functions within the package gbmr:
NC.Add Addition of two polynomials over a free associative K-algebra.
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.GAdd Addition of two polynomials in a free group ring over F2.
NC.GB (Partial) Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra.
NC.GDeg (Standard) degree of a polynomial of a polynomial in a free group ring over F2.
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.GInterreduction Interreduces a LIST of polynomials in a free group ring over F2.
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.GLC Leading coefficient of a polynomial in a free group ring over F2.
NC.GLT Leading term of a polynomial in a free group ring over F2.
NC.GMB Macauley basis of F2/(Gb) with respect to Ordering.
NC.GMultiply Multiplication of two polynomials in a free group ring over F2.
NC.GNR Normal remainder polynomial with respect to a list of polynomials in a free group ring over F2.
NC.GReducedGB Reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.GSubtract Subtraction of two polynomials in a free group ring over F2.
NC.GTruncatedGB Degree truncated Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
NC.HF Hilbert function of K-algebra.
NC.Interreduction Interreduces a LIST of polynomials over a free associative K-algebra.
NC.Intersection (Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a free associative K-algebra.
NC.IsFinite Checks whether K-vector space K/ is finitely generated.
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.IsHomog Checks whether a polynomial of a list of polynomials is homogeneous over a free associative K-algebra.
NC.KernelOfHomomorphism (Partial) (two-sided) leading-term ideal 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 (Partial) (two-sided) leading-term ideal of a finitely generated ideal over a free associative K-algebra.
NC.MB Macaulay basis of K-algebra with respect to Ordering.
NC.MinimalPolynomial Minimal polynomial of a quotient ring element over a free associative K-algebra.
NC.MRAdd Addition of two polynomials over a finitely presented monoid ring.
NC.MRDeg (Standard) degree of a polynomial over a finitely presented monoid ring.
NC.MRGB (Partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
NC.MRHF Hilbert function of K-algebra.
NC.MRInterreduction Interreduces a list of polynomials 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.MRIsHomog Checks whether a polynomial or a set (LIST) of polynomials is homogeneous over a finitely presented monoid ring.
NC.MRKernelOfHomomorphism (Partial) Groebner basis of the kernel of a K-algebra homomorphism.
NC.MRLC Leading coefficient of a polynomial over a finitely presented monoid ring.
NC.MRLT Leading term of a polynomial over a finitely presented monoid ring.
NC.MRLTIdeal (Partial) (two-sided) leading-term ideal of a finitely generated ideal over a finitely presented monoid ring.
NC.MRMB Macaulay basis of K-algebra with respect to Ordering.
NC.MRMinimalPolynomial Minimal polynomials of a quotient ring element over a finitely presented monoid ring.
NC.MRMultiply Multiplication of two polynomials over a finitely presented monoid ring.
NC.MRNR Normal remainder of a polynomial with respect to a list of polynomials 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.MRSubtract Subtraction of two polynomials over a finitely presented 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.PrefixGB Prefix Groebner basis of a finitely generated (right) ideal in a finitely presented monoid ring.
NC.PrefixInterreduction Prefix interreduction of a list of polynomials in a finitely presented monoid ring.
NC.PrefixNR Prefix normal remainder of a polynomial with respect to a list of polynomials in a finitely presented monoid ring.
NC.PrefixReducedGB Prefix reduced Groebner basis of a finitely generated (right) ideal in a finitely presented monoid ring.
NC.PrefixSaturation Prefix saturation of a polynomial in 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.
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.TruncatedGB Degree truncated Groebner basis of a finitely generated two-sided ideal in 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.




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