32 citations · 58 across the 12 of their papers we have counts for
13 papers
Relative position of a parabola or a hyperbola and an ellipse without computing intersection points
Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti +1
Efficient methods to determine the relative position of two conics are of great interest for applications in robotics, computer animation, CAGD, computational physics, and other ar…
Cyclotomic polynomials without using the zeros of
Gema M. Diaz-Toca, Henri Lombardi, Claude Quitté
This note aims to construct an ``intrinsic'' splitting field for the polynomial over the rational field , in a way that Gauss, Kummer, Kronecker and Bishop would hav…
Tools for analyzing the intersection curve between a torus and a quadric through projection and lifting
Laureano Gonzalez-Vega, Jorge Caravantes, Gema M. Diaz-Toca +1
This article introduces efficient and user-friendly tools for analyzing the intersection curve between a ringed torus and an irreducible quadric surface. Without loose of generalit…
Closed formulae for multiple roots of univariate polynomials through subresultants
Jorge Caravantes, Gema M. Diaz-Toca, Laureano Gonzalez-Vega
The computation of the topology of a real algebraic plane curve is greatly simplified if there are no more than one critical point in each vertical line: the general position condi…
The Berlekamp-Massey Algorithm revisited
Nadia Ben Atti, Gema M. Diaz--Toca, Henri Lombardi
We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to expla…
Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid
Gema M. Diaz-Toca, Leandro Marin, Ioana Necula
This paper presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxia…
Computing the topology of a planar or space hyperelliptic curve
Juan Gerardo Alcázar, Jorge Caravantes, Gema M. Diaz-Toca +1
We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image o…
On the square-freeness of the offset equation to a rational planar curve
Juan Gerardo Alcázar, Jorge Caravantes, Gema M. Diaz-Toca
It is well known that an implicit equation of the offset to a rational planar curve can be computed by removing the extraneous components of the resultant of two certain polynomial…
On the Problem of Detecting When Two Implicit Plane Algebraic Curves Are Similar
Juan Gerardo Alcázar, Gema M. Diaz-Toca, Carlos Hermosa
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similari…
A new method to compute the singularities of offsets to rational plane curves
Juan Gerardo Alcázar, Jorge Caravantes, Gema M. Diaz-Toca
Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real…
The null space of the Bezout matrix in any basis and gcd's
Gema M. Diaz-Toca, Mario Fioravanti
This manuscript presents a generalization of the structure of the null space of the Bezout matrix in the monomial basis, see [G. Heinig and K. Rost, Algebraic methods for toeplitz-…
On the Shape of Curves that are Rational in Polar Coordinates
J. G. Alcázar, G. M. Díaz-Toca
In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization (r(t),θ(t)) w…
Topology of 2D and 3D Rational Curves
Juan Gerardo Alcazar, Gema Maria Diaz-Toca
In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the pa…