BB.ASgens
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Computes the generators of the vanishing ideal of a border basis scheme.
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BB.ASneighbors
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Computes a list of across-the-street neighbors.
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BB.BBasis
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Computes the border basis of a zero-dimensional ideal.
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BB.BBasisForMP
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Computes the border basis of a zero-dimensional ideal generated by marked polynomials.
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BB.BBasisForOI
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Computes the border basis of an ideal w.r.t. a given order ideal.
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BB.BBscheme
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Computes the defining equations of a border basis scheme.
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BB.Border
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Computes the border of an order ideal.
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BB.BorderDivAlg
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Applies the border division algorithm.
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BB.Box
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Computes a box order ideal.
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BB.CoeffOfBB
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Computes the coefficient matrix of a border basis.
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BB.GenericBB
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Computes a generic border basis.
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BB.GenericHomBB
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Computes a generic homogeneous border basis.
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BB.GenHomMultMat
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Computes a generic homogeneous multiplication matrix.
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BB.GenMultMat
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Computes a generic multiplication matrix.
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BB.HomASgens
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Computes the generators of the vanishing ideal of a homogeneous border basis scheme.
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BB.HomBBscheme
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Computes the defining equations of a homogeneous border basis scheme.
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BB.HomNDgens
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Computes the generators of the vanishing ideal of a homogeneous border basis scheme.
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BB.LiftAS
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Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
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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.LiftHomAS
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Computes the homogeneous border basis scheme generators obtained from lifting of AS neighbours.
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BB.LiftHomND
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Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.
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BB.LiftND
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Computes the border basis scheme ideal generators obtained from lifting of next-door 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.MultMat
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Computes the i-th multiplication matrix associated to a border basis.
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BB.NDgens
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Computes the generators of the vanishing ideal of a border basis scheme.
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BB.NDneighbors
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Computes a list 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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BBF.Cancel
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Cancels the current border basis computation.
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BBF.Finish
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Finishes a border basis computation.
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BBF.Init
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Initializes a border basis computation.
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BBF.Quit
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Terminates the ApCoCoABBFServer.
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BBF.RetrieveBorderBasis
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Retrieves a computed border basis.
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BBF.RetrieveBorderBasisLTs
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Retrieves leading terms of a computed border basis.
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BBF.RetrieveBorderBasisPolyByLT
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Retrieves a computed border basis polynomial.
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BBF.RetrieveOGenerators
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Retrieves generators of the order ideal.
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BBF.RetrieveUGenerators
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Retrieves generators of the order ideal.
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BBF.RetrieveV
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Retrieves polynomials from V.
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BBF.RetrieveVLTs
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Retrieve leading terms of polynomials of V.
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BBF.RetrieveVPolysWithTermInSupport
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Retrieves polynomials with specific support term from V.
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BBF.RetrieveWPrime
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Retrieves polynomials from W'.
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BBF.RetrieveWPrimeLTs
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Retrieves leading terms of polynomials of W'.
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BBF.Status
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Retrieves status information from ApCoCoABBFServer.
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BBF.Steps
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Executes border basis computation steps.
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BBF.SwitchPort
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Changes the ApCoCoABBFServer communication port.
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BBSGen.BBFinder
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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.
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BBSGen.LinIndepGen
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Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list.
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BBSGen.NonStand
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This function computes the non-standard indeterminates from K[c] with respect to the arrow grading.
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BBSGen.NonStandPoly
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This function computes the non-standard polynomial generators of the vanishing ideal of border basis
scheme with respect to the arrow grading.
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BBSGen.NonTriv
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This function computes the non-trivial polynomials of the generating set of the vanishing ideal of a border basis scheme.
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BBSGen.PolDeg
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This function computes the arrow degree of a given homogenous polynomial from the ring K[c](see BBSGen.WMat).
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BBSGen.PurPow
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This function finds the pure power indeterminates in the ring K[c].
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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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