up previous next
Numerical.HBasisOfPointsInIdeal5

Macaulay basis of a almost vanishing sub ideal for a set of points and ideal
Syntax

$numerical.HBasisOfPointsInIdeal5(Points, Epsilon, GetO,GBasis):Object


Description
This function is implemented in ApCoCoALib (requires an active CoCoAServer).

Warning: This function does not yet work!

This command computes H border basis of an almost vanishing sub-ideal for a set of points and ideal using the algorithm described in the paper

D. Heldt, M. Kreuzer, H. Poulisse: Computing Approximate Vanishing Ideals (Work in progress)

The current ring has to be a ring over the rationals with a standard-degree compatible term-ordering. The matrix Points contains the points: each point is a row in the matrix, so the number of columns must equal the number of indeterminates in the current ring. Epsilon is a rational >0, describing which singular values should be treated as 0 (smaller values for epsilon lead to bigger errors of the polynomials evaluated at the point set). Epsilon should be in the interval (0,1). As a rule of thumb, Epsilon is the expected percentage of error on the input points. GetO must be either True or False. If it is true, the command returns a list of two values: the first contains the H basis, the second one a vector space basis of P/I comprising those power products lying outside the leading term ideal of I. If GetO is false, the function returns only the H basis (not in a list). GBasis has to be a homogeneous Groebner Basis in the current ring. This basis defines the ideal we compute the approximate vanishing ideal's basis in. Warning: for efficiency, the validity of GBasis is not checked.

Example
-- NOT YET WORKING --


See Also