6.2.9 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 free monoid ring. |
NC.Deg | (Standard) degree of a polynomial in a free monoid ring. |
NC.FindPolynomials | Find polynomials with specified alphabet (set of indeterminates) from a list of polynomials in monoid rings. |
NC.GAdd | Addition of two polynomials in a free group ring over F2. |
NC.GDeg | (Standard) degree of a polynomial in a free monoid ring over F2. |
NC.GInterreduction |
Interreduce a list (set) of polynomials in a free monoid ring over F2.
Note that, given an admissible ordering Ordering, a set of non-zero polynomial G is called interreduced w.r.t. Ordering if no element of Supp(g) is contained in LT(G\{g}) for all g in G. |
NC.GLC | Leading coefficient of a polynomial in a free monoid ring over F2. |
NC.GLT | Leading term of a polynomial in a free monoid ring over F2. |
NC.GMultiply | Multiplication of two polynomials in a free monoid ring over F2. |
NC.GNR | Normal remainder of polynomial with respect to a list of polynomials in a free monoid ring over F2. |
NC.GSubtract | Subtraction of two polynomials in a free monoid ring over F2. |
NC.LC | Leading coefficient of a polynomial in a free monoid ring. |
NC.LT | Leading term of a polynomial in a free monoid ring. |
NC.MinimalPolynomial | Compute a minimal polynomial of an element over the quotient of a free monoid ring if it exists. |
NC.MRAdd | Addition of two polynomials in a finitely presented monoid ring. |
NC.MRDeg | (Standard) degree of a polynomial in a finitely presented monoid ring. |
NC.MRInterreduction |
Interreduce a list (set) of polynomials in a finitely presented monoid ring.
Given an admissible ordering Ordering, a set of non-zero polynomial G is called interreduced w.r.t. Ordering if no element of Supp(g) is contained in LT(G\{g}) for all g in G. |
NC.MRLC | Leading coefficient of a polynomial in a finitely presented monoid ring. |
NC.MRLT | Leading term of a polynomial in a finitely presented monoid ring. |
NC.MRMinimalPolynomial | Compute a minimal polynomial of an element over the quotient of a finitely presented monoid ring if it exists. |
NC.MRMultiply | Multiplication of two polynomials in a finitely presented monoid ring. |
NC.MRNR | Normal remainder of a polynomial with respect to a list of polynomials in a finitely presented monoid ring. |
NC.MRSubtract | Subtraction of two polynomials in a finitely presented monoid ring. |
NC.Multiply | Multiplication of two polynomials in a free monoid ring. |
NC.NR | Normal remainder of polynomial with respect to a list of polynomials in a free 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.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. |