Alphabetical list of commands

BCDFGHILNRSW

B

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.

Back to the top --- Back to the alphabet

C

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.

Back to the top --- Back to the alphabet

D

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.

Back to the top --- Back to the alphabet

F

FGLM.FGLM -- Performs a FGLM Groebner Basis conversion using ApCoCoAServer.

Back to the top --- Back to the alphabet

G

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.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.
GnuPlot.Plot -- Tries to plot the given data by using Gnu Plot.

Back to the top --- Back to the alphabet

H

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.

Back to the top --- Back to the alphabet

I

IML.REF -- Compute a row echelon form of a matrix.
IML.Solve -- Solves a system of linear equations.

Back to the top --- Back to the alphabet

L

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.

Back to the top --- Back to the alphabet

N

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.SetFp -- Set coefficient to a finite field.
NC.SetOrdering -- Sets an (admissible) ordering.
NC.SetRelations -- Sets the relations for a monoid ring.
NC.SetRules -- Sets the (rewriting) rules over a monoid ring.
NC.SetX -- Sets the alphabet (indeterminates).
NC.Subtract -- Subtraction of two polynomials over a free associative K-algebra.
NC.UnsetFp -- Set coefficient field to default coefficient field Q. Note that default coefficient field is the set of rational numbers Q, i.e. RAT in CoCoAL.
NC.UnsetOrdering -- Sets the current admissible ordering to default ordering LLEX (length-lexicographic ordering).
NC.UnsetRelations -- Sets the relations of a rewriting system to an empty set, i.e. changes the current monoid ring to a free associative K-algebra.
NC.UnsetRules -- Sets the rewriting rules to empty set.
NC.UnsetX -- Sets the alpbabet (inderminates) to an empty string.
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.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.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.

Back to the top --- Back to the alphabet

R

Representation of finite fields --

Back to the top --- Back to the alphabet

S

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.

Back to the top --- Back to the alphabet

W

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.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.WNormalForm -- Computes the Normal form of a Weyl polynomial.
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.

Back to the top --- Back to the alphabet