213 research outputs found
Matrix representations for toric parametrizations
In this paper we show that a surface in P^3 parametrized over a 2-dimensional
toric variety T can be represented by a matrix of linear syzygies if the base
points are finite in number and form locally a complete intersection. This
constitutes a direct generalization of the corresponding result over P^2
established in [BJ03] and [BC05]. Exploiting the sparse structure of the
parametrization, we obtain significantly smaller matrices than in the
homogeneous case and the method becomes applicable to parametrizations for
which it previously failed. We also treat the important case T = P^1 x P^1 in
detail and give numerous examples.Comment: 20 page
Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies
We show that the implicit equation of a surface in 3-dimensional projective
space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a
given positive integer d, can be represented and computed from the linear
syzygies of its parametrization if the base points are isolated and form
locally a complete intersection
Resultant of an equivariant polynomial system with respect to the symmetric group
Given a system of n homogeneous polynomials in n variables which is
equivariant with respect to the canonical actions of the symmetric group of n
symbols on the variables and on the polynomials, it is proved that its
resultant can be decomposed into a product of several smaller resultants that
are given in terms of some divided differences. As an application, we obtain a
decomposition formula for the discriminant of a multivariate homogeneous
symmetric polynomial
On the irreducibility of multivariate subresultants
Let be generic homogeneous polynomials in variables of
degrees respectively. We prove that if is an integer
satisfying then all multivariate
subresultants associated to the family in degree are
irreducible. We show that the lower bound is sharp. As a byproduct, we get a
formula for computing the residual resultant of
smooth isolated points in \PP^{n-1}.Comment: Updated version, 4 pages, to appear in CRA
Extraction of cylinders and cones from minimal point sets
We propose new algebraic methods for extracting cylinders and cones from
minimal point sets, including oriented points. More precisely, we are
interested in computing efficiently cylinders through a set of three points,
one of them being oriented, or through a set of five simple points. We are also
interested in computing efficiently cones through a set of two oriented points,
through a set of four points, one of them being oriented, or through a set of
six points. For these different interpolation problems, we give optimal bounds
on the number of solutions. Moreover, we describe algebraic methods targeted to
solve these problems efficiently
Elimination and nonlinear equations of Rees algebra
A new approach is established to computing the image of a rational map,
whereby the use of approximation complexes is complemented with a detailed
analysis of the torsion of the symmetric algebra in certain degrees. In the
case the map is everywhere defined this analysis provides free resolutions of
graded parts of the Rees algebra of the base ideal in degrees where it does not
coincide with the corresponding symmetric algebra. A surprising fact is that
the torsion in those degrees only contributes to the first free module in the
resolution of the symmetric algebra modulo torsion. An additional point is that
this contribution -- which of course corresponds to non linear equations of the
Rees algebra -- can be described in these degrees in terms of non Koszul
syzygies via certain upgrading maps in the vein of the ones introduced earlier
by J. Herzog, the third named author and W. Vasconcelos. As a measure of the
reach of this torsion analysis we could say that, in the case of a general
everywhere defined map, half of the degrees where the torsion does not vanish
are understood
An Interview with Hendrik Ehlers of MgM
Hendrik Ehlers discusses the challenges facing demining in Africa, research and development, and mechanical clearance used by his company. His candid replies offer insight into the world of demining and managing a multifaceted organization
THE COMPACT 230 MINECAT, J. Barry Middlesmass Lockwood Beck LTD.
J. Barry Middlemass, Managing Director of Lockwood Beck Limited, has considerable experience in the field of mechanical mine clearance and mine clearance equipment. Before embarking on a career in mine clearance, He served in the military, including reserves, for a total of twenty-nine years, specializing in mines, explosives and improvised explosive devices. When he resigned his commission, he devoted himself fulltime to mechanical demining. As a director of Aardvark for ten years, he had a key role and made a significant contribution to the company\u27s success. Currently, JBM runs his own consulting company, Lockwood Beck, advising a variety of clients on mechanical mine equipment. One of the projects he has been recently involved with is the development of the COMPACT 230 MINECAT
Résultant univarié et courbes algébriques planes
MasterLe premier chapitre traite du résultant de Sylvester qui constitue l'outil essentiel de ce cours. Le deuxième chapitre propose une étude effective du problème de l'intersection de deux courbes algébriques planes: théorème de Bézout, notion de multiplicité d'intersection et calcul de points d'intersection par valeurs et vecteurs propres. Le troisième chapitre aborde la manipulation des courbes algébriques planes rationnelles: degré d'une paramétrisation, problèmes d'implicitation et d'inversion d'une paramétrisation. Enfin, quelques compléments sont donnés sous forme d'exercices dans le dernier chapitre
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