BB.BBasis
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Computes the border basis of a zero-dimensional ideal.
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BB.BorderDivAlg
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Applies the border division algorithm.
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BB.LiftASViaServer
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Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
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BB.LiftNDViaServer
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Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors.
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BB.TransformBBIntoGB
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Transforms a border basis into a Groebner basis.
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BB.TransformGBIntoBB
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Transforms a Groebner basis into a border basis.
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Bertini.BCMSolve
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Solves a zero dimensional non-homogeneous polynomial system of equations using multi-homogenization and user configurations.
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Bertini.BMSolve
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Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations.
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Bertini.BPCSolve
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Computes numerical irreducible decomposition by finding witness point supersets of a positive dimensional homogeneous or non-homogeneous polynomial systems of equations.
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Bertini.BPCSSolve
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Sampling a component for a positive dimensional homogeneous or non-homogeneous polynomial system.
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Bertini.BPMCSolve
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Membership testing for a positive dimensional homogeneous or non-homogeneous polynomial system.
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Bertini.BSolve
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Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations with default configurations.
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Bertini.BUHSolve
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Solves a zero dimensional non-homogeneous polynomial system of equations by user defined homotopy.
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Bertini.BZCSolve
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Solves a zero dimensional homogeneous or non-homogeneous polynomial system of equations using configurations provided by the user.
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CharP.GBasisF1024
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Computing a Groebner basis of a given ideal in F_1024.
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CharP.GBasisF128
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Computing a Groebner Basis of a given ideal in F_128.
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CharP.GBasisF16
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Computing a Groebner Basis of a given ideal in F_16.
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CharP.GBasisF2
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Computing a Groebner Basis of a given ideal in F_2.
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CharP.GBasisF2048
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Computing a Groebner Basis of a given ideal in F_2048.
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CharP.GBasisF256
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Computing a Groebner Basis of a given ideal in F_256.
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CharP.GBasisF32
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Computing a Groebner Basis of a given ideal in F_32.
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CharP.GBasisF4
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Computing a Groebner Basis of a given ideal in F_4.
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CharP.GBasisF512
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Computing a Groebner Basis of a given ideal in F_512.
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CharP.GBasisF64
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Computing a Groebner Basis of a given ideal in F_64.
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CharP.GBasisF8
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Computing a Groebner Basis of a given ideal in F_8.
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CharP.GBasisModSquares
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Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.
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CharP.IMNLASolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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CharP.IMXLSolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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CharP.MNLASolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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CharP.MXLSolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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CharP.NLASolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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CharP.XLSolve
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Computes the unique F_2-rational zero of a given polynomial system over F_2.
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FGLM.FGLM
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Performs a FGLM Groebner Basis conversion using ApCoCoAServer.
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GLPK.BPMax
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Solving binary programmes by maximizing the objective function.
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GLPK.BPMin
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Solving mixed integer linear programmes by minimizing the objective function.
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GLPK.L01PSolve
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Solve a system of polynomial equations over F_2 for one solution in F_2^n.
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GLPK.LPMax
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Solving linear programmes by maximizing the objective function.
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GLPK.LPMax
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Solving mixed integer linear programmes by maximizing the objective function.
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GLPK.LPMin
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Solving linear programmes by minimizing the objective function.
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GLPK.LPMin
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Solving mixed integer linear programmes by minimizing the objective function.
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GLPK.LPSolve
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Solving linear programmes.
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GLPK.MIPSolve
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Solving linear programmes.
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Hom.HSolve
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Solves a zero dimensional square homogeneous or non-homogeneous polynomial system of equations.
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Hom.LRSolve
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Solves a non-square zero dimensional homogeneous or non-homogeneous polynomial system of equations.
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Hom.SRSolve
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Solves a non-square zero dimensional homogeneous or non-homogeneous polynomial system of equations.
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IML.REF
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Compute a row echelon form of a matrix.
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IML.Solve
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Solves a system of linear equations.
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Latte.Count
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Counts the lattice points of a polyhedral given by a number of linear constraints.
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Latte.Ehrhart
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Computes the ehrhart series as a rational function for a polyhedral P given by a number of linear constraints.
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Latte.Maximize
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Maximizes the objective function over a polyhedral P given by a number of linear constraints.
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Latte.Minimize
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Minimizes the objective function over a polyhedral P given by a number of linear constraints.
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LinAlg.CharPoly
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Computes the characteristic polynomial of a matrix.
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LinAlg.Det
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Computes the determinant of a matrix.
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LinAlg.EF
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Computes a row echelon form of a matrix over F_2 with record keeping.
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LinAlg.REF
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Computes a row echelon form of a matrix.
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LinAlg.Solve
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Solves a system of linear equations.
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LinBox.CharPoly
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Computes the characteristic polynomial of a matrix.
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LinBox.Det
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Computes the determinant of a matrix.
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LinBox.REF
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Computes a row echelon form of a matrix.
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LinBox.Solve
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Solves a system of linear equations.
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LinSyz.BettyNumber
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Computes the N-th Betty number of a module generated by linear forms.
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LinSyz.BettyNumbers
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Computes all Betty numbers of a module generated by linear forms.
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LinSyz.Resolution
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Computes syzygy modules of a module generated by linear forms.
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NC.Add
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Addition of two polynomials over a free associative K-algebra.
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NC.Deg
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(Standard) degree of a polynomial over a free associative K-algebra.
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NC.FindPolynomials
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Find polynomials with specified alphabet (indeterminates) from a list of polynomials.
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NC.GAdd
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Addition of two polynomials in a free group ring over F2.
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NC.GB
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(Partial) Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra.
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NC.GDeg
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(Standard) degree of a polynomial of a polynomial in a free group ring over F2.
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NC.GGB
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(Partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
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NC.GHF
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Hilbert function of F2/(Gb).
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NC.GIsGB
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Checks whether a list of polynomials in a free group ring over F2 is a Groebner basis of the ideal generated by polynomials.
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NC.GLC
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Leading coefficient of a polynomial in a free group ring over F2.
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NC.GLT
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Leading term of a polynomial in a free group ring over F2.
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NC.GMultiply
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Multiplication of two polynomials in a free group ring over F2.
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NC.GNR
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Normal remainder polynomial with respect to a list of polynomials in a free group ring over F2.
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NC.GReducedGB
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Reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
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NC.GSubtract
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Subtraction of two polynomials in a free group ring over F2.
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NC.HF
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Hilbert function of K-algebra.
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NC.Intersection
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(Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a free associative K-algebra.
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NC.IsGB
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Checks whether a list of polynomials over a free associative K-algebra is a Groebner basis of the ideal generated by polynomials.
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NC.KernelOfHomomorphism
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(Partial) (two-sided) leading-term ideal of the kernel of a K-algebra homomorphism.
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NC.LC
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Leading coefficient of a polynomial over a free associative K-algebra.
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NC.LT
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Leading term of a polynomial over a free associative K-algebra.
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NC.LTIdeal
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(Partial) (two-sided) leading-term ideal of a finitely generated ideal over a free associative K-algebra.
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NC.MinimalPolynomial
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Minimal polynomial of a quotient ring element over a free associative K-algebra.
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NC.MRAdd
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Addition of two polynomials over a finitely presented monoid ring.
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NC.MRDeg
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(Standard) degree of a polynomial over a finitely presented monoid ring.
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NC.MRGB
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(Partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
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NC.MRHF
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Hilbert function of K-algebra.
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NC.MRIntersection
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(Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a finitely presented monoid ring.
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NC.MRIsGB
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Checks whether a list of polynomials over a finitely presented monoid ring is a Groebner basis of the ideal generated by polynomials.
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NC.MRKernelOfHomomorphism
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(Partial) Groebner basis of the kernel of a K-algebra homomorphism.
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NC.MRLC
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Leading coefficient of a polynomial over a finitely presented monoid ring.
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NC.MRLT
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Leading term of a polynomial over a finitely presented monoid ring.
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NC.MRLTIdeal
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(Partial) (two-sided) leading-term ideal of a finitely generated ideal over a finitely presented monoid ring.
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NC.MRMinimalPolynomial
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Minimal polynomials of a quotient ring element over a finitely presented monoid ring.
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NC.MRMultiply
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Multiplication of two polynomials over a finitely presented monoid ring.
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NC.MRNR
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Normal remainder of a polynomial with respect to a list of polynomials over a finitely presented monoid ring.
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NC.MRReducedGB
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Reduced (partial) Groebner basis of a finitely generated two-sided ideal over a finitely presented monoid ring.
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NC.MRSubtract
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Subtraction of two polynomials over a finitely presented monoid ring.
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NC.Multiply
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Multiplication of two polynomials over a free associative K-algebra.
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NC.NR
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Normal remainder polynomial with respect to a list of polynomials over a free associative K-algebra.
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NC.ReducedGB
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Reduced (partial) Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra. K-algebra.
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NC.Subtract
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Subtraction of two polynomials over a free associative K-algebra.
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Num.ABM
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Computes the border basis of an almost vanishing ideal for a set of points using the ABM algorithm.
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Num.AVI
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Computes a border basis of an almost vanishing ideal for a set of points.
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Num.BBABM
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Computes the border basis of an almost vanishing ideal for a set of points using the BB ABM algorithm.
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Num.CABM
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Computes the border basis of an almost vanishing ideal for a set of complex points.
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Num.ContainsLinearRelations
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Checks if a given set of terms has some epsilon-linear dependencies with respect to a set of points.
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Num.DABM
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In a differential setting, computes the border basis of an almost vanishing ideal for a set of points using the ABM algorithm.
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Num.EigenValues
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Computes the eigenvalues of a matrix.
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Num.EigenValuesAndAllVectors
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Computes eigenvalues and left and right eigenvectors of a matrix.
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Num.EigenValuesAndVectors
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Computes the eigenvalues and eigenvectors of a matrix.
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Num.EXTABM
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Computes the border basis of an almost vanishing ideal for a set of points.
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Num.IsAppBB
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Checks if a given set of polynomials is an approximate border basis.
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Num.IsAVI
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Checks if a given set of polynomials vanishes at a given set of points.
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Num.LeastSquaresQR
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Computes the least squares solution of the linear system of equations Ax=b.
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Num.ProjectAVI
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Computes the least squares solution of the general problem Ax=b, where x are coefficients of an order ideal.
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Num.QR
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Computes the QR-decomposition of a matrix.
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Num.RatPoints
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Computes the zero set of an exact zero dimensional border basis. The zeros are computed approximately using the eigenvalues of the transposed multiplication matrices.
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Num.SimDiag
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Computes an approximate diagonalization of a set of matrices.
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Num.SubABM
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Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.ABM algorithm.
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Num.SubAVI
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Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.AVI algorithm.
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Num.SubBBABM
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Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.BBABM algorithm.
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Num.SubEXTABM
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Computes a border basis of an almost vanishing sub-ideal for a set of points and an ideal using the Num.EXTABM algorithm.
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Num.SVD
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Computes the singular value decomposition of a matrix.
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Slinalg.SEF
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Computes the row echelon form of a sparse matrix over F2.
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Slinalg.SGEF
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Performs specified steps of structured gaussian elimination on a sparse matrix over F2.
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Weyl.AnnFs
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Computes annihilating ideal of a polynomial F^s in Weyl algebra A_n.
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Weyl.BFs
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Computes B-function of a polynomial F in Weyl algebra A_n.
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Weyl.CharI
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Computes the characteristic ideal of a D-ideal I in Weyl algebra A_n.
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Weyl.InIw
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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).
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Weyl.Inw
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Computes the initial form of a polynomial in Weyl algebra A_n with respect to the weight vector W=(u_i,v_i).
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Weyl.IsHolonomic
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Checks whether an ideal in Weyl algebra A_n is holonomic or not.
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Weyl.WDim
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Computes the dimension of an ideal I in Weyl algebra A_n.
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Weyl.WGB
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Computes the Groebner basis of an ideal I in Weyl algebra A_n.
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Weyl.WLT
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Computes the leading term ideal of a D-ideal I in Weyl algebra A_n.
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Weyl.WNormalRemainder
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Computes the normal remainder of a Weyl polynomial F with respect
to a polynomial or a set of polynomials.
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Weyl.WNR
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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.
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Weyl.WRedGB
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Computes reduced Groebner basis of a D-ideal in Weyl algebra A_n.
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Weyl.WRGB
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Reduced Groebner basis of an ideal I in Weyl algebra A_n.
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Weyl.WRGBS
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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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