up previous next
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.
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.
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.WNormalForm Computes the Normal form of a Weyl polynomial.
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.




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