Papers by Gema M. Díaz Toca
Contribuciones Cientificas En Honor De Mirian Andres Gomez 2010 Isbn 978 84 96487 50 5 Pags 231 241, 2010
Dedicado a la memoria de Mirian Andrés Gómez Resumen. En este artículo introducimos una equivalen... more Dedicado a la memoria de Mirian Andrés Gómez Resumen. En este artículo introducimos una equivalencia LU de matrices de Bézout y de Hankel. La presentación de aplicaciones de esta equivalencia nos lleva a hacer una revisión del significado y el cálculo de la signatura de las matrices de Bézout y Hankel asociadas a dos polinomios de coeficientes reales. Concluimos el artículo discutiendo el caso que aparece cuando sus coeficientes dependen de parámetros reales.
International Journal of Algebra and Computation, 2019
We make use of the complex implicit representation in order to provide a deterministic algorithm ... more 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 similarity. The algorithm has been implemented in the computer algebra system Maple 2016. The implementation can be freely downloaded from the webpage of one of the authors. Examples and evidence of the good practical performance of the algorithm are given.
ACM Communications in Computer Algebra, 2015
Journal of Computational and Applied Mathematics, 2015
Given a planar curve defined by means of a real rational parametrization, we prove that the affin... more 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 roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Maple, showing the efficiency of the algorithm for moderate degrees.
Computer Aided Geometric Design, 2013
This paper is devoted to introducing a new approach for computing the topology of a real algebrai... more This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only "by values". This approach is based on the replacement of the usual algebraic manipulation of the polynomials (and their roots) appearing in the topology determination of the given curve with the computation of numerical matrices (and their eigenvalues). Such numerical matrices arise from a typical construction in Elimination Theory known as the Bézout matrix which in our case is specified by the values of the defining polynomial equations on several sample points.
Contemporary Mathematics, 2001
ABSTRACT
Computer Aided Geometric Design, 2010
In this paper we present algorithms for computing the topology of planar and space rational curve... more 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 parametrization of the curve, and do not require to compute or use the implicit equation of the curve (in the case of planar curves) or of any projection (in the case of space curves). Moreover, these algorithms have been implemented in Maple; the examples considered and the timings obtained show good performance skills.
Libro De Resumenes Del Xiii Encuentro De Algebra Computacional Y Aplicaciones Eaca2012 2012 Isbn 978 84 8138 770 4 Pags 35 38, 2012
Applied Mathematics and Computation, 2009
The main purpose of this paper is to analyze new determinantal expressions which define the subre... more The main purpose of this paper is to analyze new determinantal expressions which define the subresultant sequence of two polynomials, when the coefficients of such polynomials depend on parameters.
Uploads
Papers by Gema M. Díaz Toca