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Numerical.HBasisOfPoints5
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almost vanishing ideal's Macaulay basis for a set of points
$numerical.HBasisOfPoints5(Points, Epsilon, GetO):Object
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WARNING: This function does not yet work!
This command computes a H basis of an almost vanishing ideal for a set of points using the algorithm described in the paper
D. Heldt, M. Kreuzer, H. Poulisse, S.Pokutta:
Approximate Computation
of Zero-Dimensional Ideals Submitted: August 2006
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).