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Based on the computation of a superset of the implicit support,
implicitization of a parametrically given hyper-surface is reduced to computing
the nullspace of a numeric matrix. Our approach exploits the sparseness of the
given parametric equations and of the implicit polynomial. In this work, we
study how this interpolation matrix can be used to...
Contexts in source publication
Context 1
... Figure 1 for an example of applying Definition 9 to the folium of Descartes curve defined by y 3 − 3xy + x 3 = 0. ...
Context 2
... test if point (1, 0) lies on the curve, function membtest builds a 15 × 15 matrix M ((1, 0)), whose rank is 14, equal to the rank of matrix M hence membtest informs us that point (1, 0) lies on the curve. ...
Context 3
... ResPol we obtain the implicit polytope's vertices (0, 0, 1, 1), (1, 0, 0, 1), (0, 1, 0, 0), (0, 0, 1, 0), (1, 0, 0, 2), (0, 1, 0, 1); this polytope contains 6 lattice points. In order to determine if the point (1, 1, 1, 1) belongs to the surface we build a 5 × 6 membership matrix M ; it has rank 5 and nullity 1. The 6 x 6 matrix M q, constructed by adding to M a row of monomials evaluated at query point, has nullity 1, therefore the point (1, 1, 1, 1) lies on the hypersurface. ...
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