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6.2.14 ApCoCoAServer
The following are the functions using ApCoCoAServer :
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.




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