up previous next
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.
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.
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.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.
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/(Gb).
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.Subtract Subtraction of two polynomials over a free associative K-algebra.
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.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.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.
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.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.




For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").