Alphabetical list of commands |
BCDFGHILNPRSWB |
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.BBasisMutantStrategyF2 -- Computes a Border Basis of a given ideal over F_2.
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.IMBBasis -- Computes a Border Basis of a given ideal over F_2. 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.LAAlgorithm -- Computes the unique F_2-rational zero of a given polynomial system over F_2. CharP.MBBasis -- Computes a Border Basis of a given ideal 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.
Fn.ArcCos -- Returns the arccosine of a given value. Fn.ArcCosN -- Returns the arccosine of a given value with a given accuracy. Fn.ArcSin -- Returns the arcsine of a given value. Fn.ArcSinN -- Returns the arcsine of a given value with a given accuracy. Fn.ArcTan -- Returns the arctangent of a given value. Fn.ArcTanN -- Returns the arctangent of a given value with a given accuracy. Fn.Cos -- Returns the cosine of a given value. Fn.CosN -- Returns the cosine of a given value with a given accuracy. Fn.E -- Returns Euler's number e rounded to the current global accuracy. Fn.EN -- Returns Eulers' number e rounded to accuracy Acc. Fn.Exp -- Returns the exponential of a given value. Fn.ExpN -- Returns the exponential of a given value with a given accuracy. Fn.GetAccuracy -- Get the currently used accuracy. Fn.Ln -- Returns the natural logarithm of a given value. Fn.Ln2 -- Returns the natural logarithm of 2 rounded to the current global accuracy. Fn.Ln2N -- Returns the natural logarithm of 2 rounded to accuracy Acc. Fn.LnN -- Returns the natural logarithm of a given value with a given accuracy. Fn.Log -- Returns the logarithm to a given base. Fn.LogN -- Returns the logarithm to a given base with a given accuracy. Fn.Pi -- Returns the constant pi rounded to the current global accuracy. Fn.PiN -- Returns the constant pi rounded to accuracy N. Fn.Pow -- Returns Base to the power of Exponent. Fn.PowN -- Returns Base to the power of Exponent with a given accuracy. Fn.ReduceModLn2 -- Reduces a given value modulo the natural logarithm of 2. Fn.ReduceModPi -- Reduces a given value modulo 2*pi to the interval between -pi and pi. Fn.Root -- Returns the N-th root of a given value. Fn.RootN -- Returns the N-th root of a given value with a given accuracy. Fn.Round -- Round a number. Fn.RoundN -- Round a number to a desired accuracy. Fn.SetAccuracy -- Set the default accuracy. Fn.Sin -- Returns the sine of a given value. Fn.SinN -- Returns the sine of a given value with a given accuracy. Fn.Sqrt -- Returns the square root of a given value. Fn.SqrtN -- Returns the square root of a give value with a given accuracy. Fn.Tan -- Returns the tangent of a given value. Fn.TanN -- Returns the tangent of a given value with a given accuracy. |
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.IPCSolve -- Solves a system of polynomial equations over F_2 for one solution in F_2^n. 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. GLPK.RIPCSolve -- Solves a system of polynomial equations over F_2 for one solution in F_2^n. GLPK.RPCSolve -- Solves a system of polynomial equations over F_2 for one solution in F_2^n. GLPK.RRPCSolve -- Solves a system of polynomial equations over F_2 for one solution in F_2^n. 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 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 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. 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.CEXTABM -- Computes the border basis of an almost vanishing ideal for a set of points. 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.NumericalDerivative -- Compute numerical derivatives of arbitrarily spaced data using local polynomial regression. 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.SavGol -- Compute numerical derivatives of equally spaced data using local polynomial regression. Num.SimDiag -- Computes an approximate diagonalization of a set of matrices. Num.SingularValues -- Computes the singular values of a matrix. 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. |
PGBC.ParallelGBC -- Computes a Gröbner Bases over a prime field using the degree reverse lexicographic term ordering in parallel.
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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.TwoWGB -- Computes the reduced two-sided Groebner basis of a two-sided ideal I in the Weyl algebra A_n over the field of positive characteristic. 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.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. Weyl.WStandardForm -- Computes the Standard form of a Weyl polynomial. |
BBSGen.BBFinder -- Let LF be a list of indeterminates from the ring K[t[k,l,i,j] that is the subset of the ring XX:=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]] . This function finds the defining equations of border basis scheme and their degrees that correspond to the elements of the list LF.
BBSGen.JacobiFull -- Let R:=K[x_1,...,x_N]. This function computes the entries of the Jacobi identity matrix J^klm [ A_m[A_k,A_l]]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ], where m,k,l is from {1...N}. BBSGen.JacobiLin -- This function computes the K[c]-linear polynomial entries of the Jacobi identity matrix [ A_m[A_k,A_l ] ]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ] where m,k,l is from {1,...,N}. BBSGen.JacobiStep -- Let R:=K[x_1,...,x_N] and let OO be an order ideal. This function computes the entry in the position (I,J) of the Jacobi identity matrix J^klm [ A_m[A_k,A_l ] ]+[ A_k[ A_l,A_m]] +[ A_l[A_m,A_k ] ] where m,k,l is from {1,...,N} and I,J in {1,...,Len(OO)}. BBSGen.LinIndepGen -- Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list. BBSGen.NonStand -- This function computes the non-standard indeterminates from K[c] with respect to the arrow grading. BBSGen.NonStandPoly -- This function computes the non-standard polynomial generators of the vanishing ideal of border basis scheme with respect to the arrow grading. BBSGen.NonTriv -- This function computes the non-trivial polynomials of the generating set of the vanishing ideal of a border basis scheme. BBSGen.PolDeg -- This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see BBSGen.WMat). BBSGen.PurPow -- This function finds the pure power indeterminates in the ring K[c]. BBSGen.TraceSyzFull -- This function computes the trace polynomials. BBSGen.TraceSyzLin -- : This function computes the K[c]-linear summand of trace polynomials.(see BBSGen.TraceSyzFull) BBSGen.TraceSyzLinStep -- This function computes the K[c]-linear summand of the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull) BBSGen.TraceSyzStep -- This function computes the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull) BBSGen.WMat -- This function computes the Weight Matrix with respect to the arrow grading. |