Alphabetical list of commands |
BCDFGHILNRSW |
BB.ASgens -- Computes the generators of the vanishing ideal of a border basis scheme.
BB.ASneighbors -- Computes a list of across-the-street neighbors. BB.BBasis -- Computes the border basis of a zero-dimensional ideal. BB.BBasisForMP -- Computes the border basis of a zero-dimensional ideal generated by marked polynomials. BB.BBasisForOI -- Computes the border basis of an ideal w.r.t. a given order ideal. BB.BBscheme -- Computes the defining equations of a border basis scheme. BB.Border -- Computes the border of an order ideal. BB.BorderDivAlg -- Applies the border division algorithm. BB.Box -- Computes a box order ideal. BB.CoeffOfBB -- Computes the coefficient matrix of a border basis. BB.GenericBB -- Computes a generic border basis. BB.GenericHomBB -- Computes a generic homogeneous border basis. BB.GenHomMultMat -- Computes a generic homogeneous multiplication matrix. BB.GenMultMat -- Computes a generic multiplication matrix. BB.HomASgens -- Computes the generators of the vanishing ideal of a homogeneous border basis scheme. BB.HomBBscheme -- Computes the defining equations of a homogeneous border basis scheme. BB.HomNDgens -- Computes the generators of the vanishing ideal of a homogeneous border basis scheme. BB.LiftAS -- Computes the border basis scheme ideal generators obtained from lifting of AS neighbours. BB.LiftASViaServer -- Computes the border basis scheme ideal generators obtained from lifting of AS neighbours. BB.LiftHomAS -- Computes the homogeneous border basis scheme generators obtained from lifting of AS neighbours. BB.LiftHomND -- Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors. BB.LiftND -- Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours. BB.LiftNDViaServer -- Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors. BB.MultMat -- Computes the i-th multiplication matrix associated to a border basis. BB.NDgens -- Computes the generators of the vanishing ideal of a border basis scheme. BB.NDneighbors -- Computes a list of next-door neighbors. BB.TransformBBIntoGB -- Transforms a border basis into a Groebner basis. BB.TransformGBIntoBB -- Transforms a Groebner basis into a border basis. BBF.Cancel -- Cancels the current border basis computation. BBF.Explanation of BBF variables and structures -- Explanation of the variables and structures used in the Border Basis Framework. BBF.Finish -- Finishes a border basis computation. BBF.Init -- Initializes a border basis computation. BBF.Quit -- Terminates the ApCoCoABBFServer. BBF.RetrieveBorderBasis -- Retrieves a computed border basis. BBF.RetrieveBorderBasisLTs -- Retrieves leading terms of a computed border basis. BBF.RetrieveBorderBasisPolyByLT -- Retrieves a computed border basis polynomial. BBF.RetrieveOGenerators -- Retrieves generators of the order ideal. BBF.RetrieveUGenerators -- Retrieves generators of the order ideal. BBF.RetrieveV -- Retrieves polynomials from V. BBF.RetrieveVLTs -- Retrieve leading terms of polynomials of V. BBF.RetrieveVPolysWithTermInSupport -- Retrieves polynomials with specific support term from V. BBF.RetrieveWPrime -- Retrieves polynomials from W'. BBF.RetrieveWPrimeLTs -- Retrieves leading terms of polynomials of W'. BBF.Status -- Retrieves status information from ApCoCoABBFServer. BBF.Steps -- Executes border basis computation steps. BBF.SwitchPort -- Changes the ApCoCoABBFServer communication port. Bertini.BCMSolve -- Solves a zero dimensional non-homogeneous polynomial system of equations using multi-homogenization and user configurations. Bertini.BMSolve -- Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations. Bertini.BPCSolve -- Computes numerical irreducible decomposition by finding witness point supersets of a positive dimensional homogeneous or non-homogeneous polynomial systems of equations. Bertini.BPCSSolve -- Sampling a component for a positive dimensional homogeneous or non-homogeneous polynomial system. Bertini.BPMCSolve -- Membership testing for a positive dimensional homogeneous or non-homogeneous polynomial system. Bertini.BSolve -- Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations. Bertini.BUHSolve -- Solves a zero dimensional non-homogeneous polynomial system of equations by user defined homotopy. Bertini.BZCSolve -- Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations using configurations provided by the user. |
CharP.GBasisF1024 -- Computing a Groebner basis of a given ideal in F_1024.
CharP.GBasisF128 -- Computing a Groebner Basis of a given ideal in F_128. CharP.GBasisF16 -- Computing a Groebner Basis of a given ideal in F_16. CharP.GBasisF2 -- Computing a Groebner Basis of a given ideal in F_2. CharP.GBasisF2048 -- Computing a Groebner Basis of a given ideal in F_2048. CharP.GBasisF256 -- Computing a Groebner Basis of a given ideal in F_256. CharP.GBasisF32 -- Computing a Groebner Basis of a given ideal in F_32. CharP.GBasisF4 -- Computing a Groebner Basis of a given ideal in F_4. CharP.GBasisF512 -- Computing a Groebner Basis of a given ideal in F_512. CharP.GBasisF64 -- Computing a Groebner Basis of a given ideal in F_64. CharP.GBasisF8 -- Computing a Groebner Basis of a given ideal in F_8. CharP.GBasisModSquares -- Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x. CharP.IMNLASolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.IMXLSolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.MNLASolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.MXLSolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.NLASolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.XLSolve -- Computes the unique F_2-rational zero of a given polynomial system over F_2. |
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.DiffTO -- Matrix corresponding to predefined differential term orderings. 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. |
FGLM.FGLM -- Performs a FGLM Groebner Basis conversion using ApCoCoAServer.
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GetApCoCoAServerLogLevel -- Retrieve current log level used by ApCoCoAServer.
GLPK.BPMax -- Solving binary programmes by maximizing the objective function. GLPK.BPMin -- Solving mixed integer linear programmes by minimizing the objective function. GLPK.L01PSolve -- Solve a system of polynomial equations over F_2 for one solution in F_2^n. GLPK.LPMax -- Solving linear programmes by maximizing the objective function. GLPK.LPMax -- Solving mixed integer linear programmes by maximizing the objective function. GLPK.LPMin -- Solving linear programmes by minimizing the objective function. GLPK.LPMin -- Solving mixed integer linear programmes by minimizing the objective function. GLPK.LPSolve -- Solving linear programmes. GLPK.MIPSolve -- Solving linear programmes. GnuPlot.Plot -- Tries to plot the given data by using Gnu Plot. |
Hom.HSolve -- Solves a zero dimensional square homogeneous or non-homogeneous polynomial system of equations.
Hom.LRSolve -- Solves a non-square zero dimensional homogeneous or non-homogeneous polynomial system of equations. Hom.SRSolve -- Solves a non-square zero dimensional homogeneous or non-homogeneous polynomial system of equations. |
IML.REF -- Compute a row echelon form of a matrix.
IML.Solve -- Solves a system of linear equations. |
Latte.Count -- Counts the lattice points of a polyhedral given by a number of linear constraints.
Latte.Ehrhart -- Computes the ehrhart series as a rational function for a polyhedral P given by a number of linear constraints. Latte.Maximize -- Maximizes the objective function over a polyhedral P given by a number of linear constraints. Latte.Minimize -- Minimizes the objective function over a polyhedral P given by a number of linear constraints. LinAlg.CharPoly -- Computes the characteristic polynomial of a matrix. LinAlg.Det -- Computes the determinant of a matrix. LinAlg.EF -- Computes a row echelon form of a matrix over F_2 with record keeping. LinAlg.REF -- Computes a row echelon form of a matrix. LinAlg.Solve -- Solves a system of linear equations. LinBox.CharPoly -- Computes the characteristic polynomial of a matrix. LinBox.Det -- Computes the determinant of a matrix. LinBox.REF -- Computes a row echelon form of a matrix. LinBox.Solve -- Solves a system of linear equations. LinSyz.BettyNumber -- Computes the N-th Betty number of a module generated by linear forms. LinSyz.BettyNumbers -- Computes all Betty numbers of a module generated by linear forms. LinSyz.Resolution -- Computes syzygy modules of a module generated by linear forms. |
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 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.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.HF -- Hilbert function of K-algebra. NC.Intersection -- (Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a free associative K-algebra. 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.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.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.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.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.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.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.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. Num.ABM -- Computes the border basis of an almost vanishing ideal for a set of points using the ABM algorithm. Num.AppKer -- Calculates the approximate kernel of a matrix. Num.AVI -- Computes a border basis of an almost vanishing ideal for a set of points. Num.BBABM -- Computes the border basis of an almost vanishing ideal for a set of points using the BB ABM algorithm. Num.CABM -- Computes the border basis of an almost vanishing ideal for a set of complex points. Num.Ceil -- Maps a rational number to the next biggest integer. Num.ContainsLinearRelations -- Checks if a given set of terms has some epsilon-linear dependencies with respect to a set of points. Num.DABM -- In a differential setting, computes the border basis of an almost vanishing ideal for a set of points using the ABM algorithm. Num.EigenValues -- Computes the eigenvalues of a matrix. Num.EigenValuesAndAllVectors -- Computes eigenvalues and left and right eigenvectors of a matrix. Num.EigenValuesAndVectors -- Computes the eigenvalues and eigenvectors of a matrix. Num.EXTABM -- Computes the border basis of an almost vanishing ideal for a set of points. Num.Floor -- Maps a rational number to the next smallest integer. Num.FPart -- Returns the fractional part of a rational number. 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.LeastSquaresQR -- Computes the least squares solution of the linear system of equations Ax=b. Num.ProjectAVI -- Computes the least squares solution of the general problem Ax=b, where x are coefficients of an order ideal. Num.QR -- Computes the QR-decomposition of a matrix. 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. Num.SimDiag -- Computes an approximate diagonalization of a set of matrices. Num.SubABM -- Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.ABM algorithm. Num.SubAVI -- Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.AVI algorithm. Num.SubBBABM -- Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.BBABM algorithm. Num.SubEXTABM -- Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.EXTABM algorithm. Num.SVD -- Computes the singular value decomposition of a matrix. |
Representation of finite fields --
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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. SB.IsInSubalgebra -- Subalgebra membership test of a polynomial. SB.IsSagbi -- Checks if a set of polynomials is a SAGBI-basis. SB.IsSagbiOf -- Checks if a set of polynomials is a SAGBI-basis of a given subalgebra. SB.NFS -- Computes the subalgebra normal form of a polynomial with respect to subalgebra generators. SB.ReducedSagbi -- Computes the finite reduced SAGBI-basis of a subalgebra if existing. SB.Sagbi -- Computes a finite SAGBI-basis of a subalgebra if existing. SB.SubalgebraPoly -- Computes a subalgebra polynomial from a subalgebra representation. SB.TermRepr -- Computes a representation of a term in other terms if it exists. SetApCoCoAServerLogLevel -- Influences the amount of log output of ApCoCoAServer. Slinalg.SEF -- Computes the row echelon form of a sparse matrix over F2. Slinalg.SGEF -- Performs specified steps of structured gaussian elimination on a sparse matrix over F2. |
Weyl.AnnFs -- Computes annihilating ideal of a polynomial F^s in Weyl algebra A_n.
Weyl.BFs -- Computes B-function of a polynomial F in Weyl algebra A_n. Weyl.CharI -- Computes the characteristic ideal of a D-ideal I in Weyl algebra A_n. Weyl.InIw -- Computes the initial ideal of a D-ideal I in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i). Weyl.Inw -- Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i). Weyl.IsHolonomic -- Checks whether an ideal in Weyl algebra A_n is holonomic or not. Weyl.WDim -- Computes the dimension of an ideal I in Weyl algebra A_n. Weyl.WeylMul -- Computes the product F*G of two Weyl polynomials, F and G, in normal form. Weyl.WGB -- Computes the Groebner basis of an ideal I in Weyl algebra A_n. Weyl.WLT -- Computes the leading term ideal of a D-ideal I in Weyl algebra A_n. 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.WRedGB -- Computes reduced Groebner basis of a D-ideal in Weyl algebra A_n. Weyl.WRGB -- Reduced Groebner basis of an ideal I in Weyl algebra A_n. Weyl.WRGBS -- Convert a Groebner basis of an ideal in Weyl algebra A_n in to its reduced Groebner Basis using corresponding implementation in ApCoCoALib. Weyl.WSPoly -- Computes the S-polynomial of two Weyl polynomials. |