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Numerical.HBasisOfPointsInIdeal5
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Macaulay basis of a almost vanishing sub ideal for a set of points and ideal
$numerical.HBasisOfPointsInIdeal5(Points, Epsilon, GetO,GBasis):Object
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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.