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StableBBasis5 --
Stable Border Basis of ideal of points
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StableBBasis5(Pts: LIST, Toler: LIST): RECORD
StableBBasis5(Pts: LIST, Toler: LIST, Gamma: RAT): RECORD |
***** NOT YET IMPLEMENTED *****
See
ApproxPointsNBM
This function returns a record containing a
stable order ideal of
the ideal of points, and a list of
almost vanishing polynomials.
If the cardinality of the order ideal is equal to the number of points,
it is in fact a
quotient basis, and in this case a
stable border basis founded on it is also returned. The boolean field
StableBBasisFound is set to
true if a stable border basis was found,
otherwise
false.
The first argument is a list of points in k-dimensional space, and the
second argument is list of k positive tolerances (one for each dimension).
The function builds the stable order ideal stepwise by testing, from a
numerical point of view, the linear dependence of a set of vectors.
So that the answer can be represented, the current ring must have at
least k indeterminates; the term ordering is ignored as it plays no role
in determining the border basis.
There is a third, optional argument: it is a real non negative number
Gamma which is used for scaling the threshold on the
admissible perturbation of the points.
A value of
Gamma << 1 should be used.
If no value is specified then by default
Gamma = 0.1
For a full description of the algorithms we refer to the paper
J.Abbott, C.Fassino, L.Torrente
Stable Border Bases for Ideals of Points (to appear in JSC
or arXiv:07062316).
***** NOT YET IMPLEMENTED ***** See ApproxPointsNBM
Pts := [[0.1,-1],[1,1],[2,3]];
Toler := [0.1,0.1];
StableBBasis5(Pts, Toler);
record[
AlmostVanishing := [ (...) ],
BBasis := [
-3602879701896397/288230376151711744y^2 + x -
32425917317067571/72057594037927936y -
154923827181545063/288230376151711744,
xy - 140512308373959475/288230376151711744y^2 -
39631676720860365/72057594037927936y +
10808639105689191/288230376151711744,
y^3 - 3y^2 - y + 3,
xy^2 - 580063632005319885/288230376151711744y^2 -
32425917317067571/72057594037927936y +
421536925121878425/288230376151711744],
SOI := [1, y, y^2],
StableBBasisFound := true]
-------------------------------
Toler := [0.6, 0.6]:
StableBBasis5(Pts, Toler);
record[AlmostVanishing := [.....], SOI := [1, y], StableBBasisFound := false]
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