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6.1.18 Package numerical
The following are commands and functions within the package numerical:
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.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.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.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.




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