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6.2.9 Polynomials
The following are commands and functions for polynomials:
BB.BorderDivAlg Applies the border division algorithm.
BB.TransformBBIntoGB Transforms a border basis into a Groebner basis.
BB.TransformGBIntoBB Transforms a Groebner basis into a border basis.
BBF.RetrieveBorderBasisPolyByLT Retrieves a computed border basis polynomial.
BBF.RetrieveVPolysWithTermInSupport Retrieves polynomials with specific support term from V.
DA.Class Returns the class of a given derivative.
DA.DiffAutoReduce Computes a reduced list of differential polynomials.
DA.Differentiate Computes the derivation of a differential polynomial.
DA.DiffGB Computes a differential Groebner basis.
DA.DiffOrd Computes the differential order of a differential polynomial.
DA.DiffReduce Computes a differential normal form of a differential polynomial wrt. a list of differential polynomials.
DA.DiffSupp Computes the differential support of a differential polynomial.
DA.Initial Computes the initial of a differential polynomial.
DA.InitialOfDer Computes the initial wrt. a given derivative.
DA.LD Computes the leading derivative of a differential polynomial.
DA.LPot Computes the leading power of a differential polynomial.
DA.NthDerivation Computes the N-th derivation of a differential polynomial.
DA.PseudoAutoReduce Computes a pseudo reduced list of differential polynomials.
DA.PseudoReduce Computes a pseudo normal form of a differential polynomial.
DA.Sep Computes the separand of a differential polynomial.
DA.Weight Computes the weight of a differential polynomial.
Dec Pretty Printing of Objects.
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.Interreduction Interreduction of a LIST of polynomials 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.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.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.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.
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.BInterreduction Interreduce a LIST of polynomials in a free monoid ring over the binary field.
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.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.BSubtract Subtraction of two polynomials 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.IsHomog Check whether a polynomial or a list of polynomials is homogeneous in a free monoid ring.
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.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.MRInterreduction Interreduce a LIST of polynomials in a finitely presented monoid ring.
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.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.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.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.Subtract Subtraction of two polynomials in a free monoid ring.
Num.IsAppBB Checks if a given set of polynomials is an approximate border basis.
Num.IsAVI Checks if a given set of polynomials vanishes at a given set of points.
Num.RatPoints Computes the zero set of an exact zero dimensional border basis. The zeros are computed approximately using the eigenvalues of the transposed multiplication matrices.
PGBC.ParallelGBC Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.
SAT.ConvertToCNF Converts a given quadratic (cubic) system of polynomial equations (SPE) over GF(2) to CNF. Writes the CNF to the file sat.cnf
SAT.ConvertToXOR Converts a given quadratic (cubic) system of polynomial equations (SPE) over GF(2) to XOR-CNF. Writes the XOR-CNF to the file sat_xor.cnf.
SAT.FixBits Allows to fix chosen bits in advance within a SAT input file. The new input file is sat_fixed.cnf.
SAT.GetResult Looks up the configuration of the indeterminates in the file output produced by a SAT-Solver. The file output must be in the folder ApCoCoA-directory/sat/bin.
SAT.LaunchCryptoMiniSat Launches CryptoMiniSat via the ApCoCoAServer on a given input file located in ApCoCoA-directory/sat/bin. The result is written to the file output.
SAT.LaunchMiniSat Launches MiniSat via the ApCoCoAServer on a given input file located in ApCoCoA-directory/sat/bin. The result is written to the file output.
Weyl.WeylMul Computes the product F*G of two Weyl polynomials, F and G, in normal form.
Weyl.WMul Computes the product F*G of Weyl polynomial F and G in normal form.
Weyl.WMulByMonom Computes the product M*F of a Weyl monomial M and a Weyl polynomial F in normal form.
Weyl.WMult Computes the product F*G of two Weyl polynomials, F and G, in normal form using corresponding implementation in ApCoCoALib.
Weyl.WNormalRemainder Computes the normal remainder of a Weyl polynomial F with respect to a polynomial or a set of polynomials.
Weyl.WNR Computes the normal remainder of a Weyl polynomial F with respect to a polynomial or a list of Weyl polynomials using corresponding implementation in ApCoCoALib.
Weyl.WPower Computes the N-th power of a Weyl polynomial.
Weyl.WSPoly Computes the S-polynomial of two Weyl polynomials.
Weyl.WStandardForm Computes the Standard form of a Weyl polynomial.




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