BB.BBasis
|
Computes the border basis of a zero-dimensional ideal.
|
BB.BorderDivAlg
|
Applies the border division algorithm.
|
BB.LiftASViaServer
|
Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
|
BB.LiftNDViaServer
|
Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors.
|
BB.TransformBBIntoGB
|
Transforms a border basis into a Groebner basis.
|
BB.TransformGBIntoBB
|
Transforms a Groebner basis into a border basis.
|
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.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.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.
|
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.
|
FGLM.FGLM
|
Performs a FGLM Groebner Basis conversion using 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.
|
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.AdMatrix
|
Construct an adjacency matrix of the Ufnarovski graph for a finite set of words 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.IsFinite
|
Check whether a K-algebra R/ has finite K-dimension.
|
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.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.AdMatrix
|
Construct an adjacency matrix of the Ufnarovski graph for a finite set of words.
|
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.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-Dehn 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/) is finite, where is an monoid ideal generated by a finite set M of words.
|
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.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.
|
Num.ABM
|
Computes the border basis of an almost vanishing ideal for a set of points using the ABM algorithm.
|
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.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.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.
|
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.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.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.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.
|