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6.2.21 Non Commutative Computations
The following are commands and functions for Non Commutative Computations:
NC.Add Addition of two polynomials in a non-commutative polynomial ring.
NC.CoCoALToC Convert a polynomial in a non-commutative polynomial ring from the CoCoAL format to the C format.
NC.CToCoCoAL Convert a polynomial in a non-commutative polynomial ring from the C format to the CoCoAL format.
NC.Deg The standard degree of a polynomial in a non-commutative polynomial ring.
NC.FindPolys Find polynomials with specified indeterminates from a LIST of non-commutative polynomials.
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.Interreduction Interreduction of a LIST of polynomials in a non-commutative polynomial ring.
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.IsHomog Check whether a polynomial or a LIST of polynomials is homogeneous in a non-commutative polynomial ring.
NC.KernelOfHomomorphism The kernel of an algebra homomorphism.
NC.LC Leading coefficient of a non-zero polynomial in a non-commutative polynomial ring.
NC.LW The leading word (or term) of a non-zero polynomial in a non-commutative polynomial ring.
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.Mul Multiplication of two polynomials in a non-commutative polynomial ring.
NC.NR Normal remainder of a polynomial with respect to a LIST of polynomials in a non-commutative polynomial ring.
NC.RedGB Enumerate reduced (partial) Groebner bases of finitely generated two-sided ideals in a non-commutative polynomial ring.
NC.SetOrdering Set a word ordering on the monoid of all words in a non-commutative polynomial ring.
NC.Sub Subtraction of two polynomials 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.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.




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