**Si está interesado en alguno de nuestros trabajos, no dude en contactarme.**

**If you are interested in any paper, please, do not hesitate to contact me.
**

**S'il vous plaît, ne hésitez pas à me contacter si vous êtes intéressé par un papier.**


























====== BOOKS ======

o	//Modules sur les anneaux commutatifs. Cours et exercices.// Claude Quitté (Auteur), Henri Lombardi (Auteur), Gema Maria Diaz Toca (Auteur). Calvage et Mounet (October 2014). See the report on [[http://www.zentralblatt-math.org/MIRROR/zmath/en/search/?q=an:06374397&type=pdf&format=complete|Zentralblatt]].


====== Preprints ======

o	//Closed formulae for multiple roots of univariate polynomials through subresultants.// Jorge Caravantes, Gema M. Diaz-Toca and Laureano Gonzalez-Vega. {{ :generalpositionlowdegree_mars23.pdf |Preprint}} 






























====== PAPERS ======

  * Jorge Caravantes, Gema M. Diaz-Toca, and Laureano Gonzalez-Vega.// Avoiding the General Position Condition When Computing the Topology of a Real Algebraic Plane Curve Defined Implicitly.//  Geometric Science of Information: 6th International Conference, GSI 2023, St. Malo, France, August 30-September 1, Proceedings, Part I. Lecture Notes in Computer Science (LNCS) 14071, Springer.

   * Juan Gerardo Alcázar, Gema M. Diaz-Toca. //Computing the topology of the image of a parametric planar curve under a birational transformation.// Computer Aided Geometric Design, 102, May 2023, 102189. https://doi.org/10.1016/j.cagd.2023.102189 
{{ :parambir.txt.zip |code}}


  * Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti and Laureano Gonzalez-Vega.// Solving the interference problem for ellipses and ellipsoids: New formulae.//  Journal of Computational and Applied Mathematics, Volume 407, 2022, 114072, https://doi.org/10.1016/j.cam.2021.114072 . https://authors.elsevier.com/c/1eQ2y1LkiPSsBS

  * Jorge Caravantes, Gema M. Diaz-Toca, Mario Fioravanti and Laureano Gonzalez-Vega.// On the Implicit Equation of Conics and Quadrics Offsets.// Mathematics 2021, 9(15), 1784; Jul 2021, https://doi.org/10.3390/math9151784 

  * G.M. Diaz-Toca, L. Marin and I. Necula.// Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid.// Computers and Geosciences, Volume 142, September 2020. https://doi.org/10.1016/j.cageo.2020.104551

  * J.G. Alcázar, J. Caravantes, G.M. Diaz-Toca , E. Tsigaridas. //Computing the topology of a planar or space hyperelliptic curve.// Computer Aided Geometric Design, Volume 78, March 2020,  {{{progred.txt|code}}} .https://doi.org/10.1016/j.cagd.2020.101830

  * Gema M. Diaz-Toca et Henri Lombardi. //Calcul matriciel généralisé sur les domaines de Prüfer.// Bulletin des Sciences Mathématiques 159, 2020.//
https://authors.elsevier.com/a/1a64g1iQ5tsBh //https://doi.org/10.1016/j.bulsci.2019.102808

  * Jorge Caravantes, Mario Fioravanti, Laureano Gonzalez-Vega, Gema Diaz-Toca. //Offsets to conics and quadrics: a new determinantal representation for their implicit equation.// ACM Commun. Comput. Algebra, 52, 3, 2018. [[https://dl.acm.org/citation.cfm?doid=3313880.3313890| doi>10.1145/3313880.3313890]]

  * J.G. Alcázar, G.M. Diaz-Toca and C. Hermoso. //On the Problem of Detecting When Two Implicit Plane Algebraic Curves Are Similar//.{{semejanza_code.txt|code}}[[http://arxiv.org/abs/1505.06095|ArXiv]] International Journal of Algebra and Computation. Volume No.29, Issue No. 05. Pages 775-793, 2019. https://doi.org/10.1142/S0218196719500279

  * J.G. Alcázar, J. Caravantes and G.M. Diaz-Toca. //On the square-freeness of the offset equation to a rational planar curve.// International Journal of Algebra and Computation, Volume No.28, Issue No. 03, Pages 395-409, 2018. https://doi.org/10.1142/S0218196718500194

  * Jorge Caravantes, Gema M Diaz-Toca, Mario Fioravanti, Laureano Gonzalez-Vega y Ioana Necula. //An algebraic framework for computing the topology of offsets to rational curves.// Computer Aided Geometric Design. Volume 52-53, Pages 28-47, 2017. http://dx.doi.org/10.1016/j.cagd.2017.03.007

  * G.M. Diaz–Toca, S. Belhaj.// Blind image deconvolution through Bezoutians.// Journal of Computational and Applied Mathematics. 
Volume 315,1, May 2017, Pages 98–106. http://dx.doi.org/10.1016/j.cam.2016.10.021

  * F. Crespo, G. Díaz–Toca , S. Ferrer , M. Lara.// Poisson and symplectic reductions of 4−DOF isotropic oscillators. The van der Waals system as benchmark.// Applied Mathematics and Nonlinear Sciences 1(2) (2016) 473–492. http://dx.doi.org/10.21042/AMNS.2016.2.00038

  * J. Caravantes, J.G. Alcázar and G.M. Díaz-Toca. //A new method to compute the singularities of offsets to rational plane curves//. Journal of Computational and Applied Mathematics 290, 385--402, December 2015. See the {{thecode.txt|code}}. http://dx.doi.org/10.1016/j.cam.2015.06.001

  * D. Aruliah, R. Corless, G.M. Díaz-Toca, L. González-Vega and A. Shakoori.// The Bézout Matrix for Hermite Interpolants//. See the
{{hermite_prog.txt|code}}. Linear Algebra and its Applications, Vol. 474, 12--29, June 2015. http://dx.doi.org/10.1016/j.laa.2015.02.001


  * Gema M Diaz-Toca y Ioana Necula. //Direct symbolic transformation from 3D cartesian into hyperboloidal coordinates//. Applied Mathematics and Computation 228, 349--365, 2014. http://dx.doi.org/10.1016/j.amc.2013.11.099 


  * R. M. Corless, G. M. Diaz-Toca, M. Fiovanati, L. Gonzalez--Vega, I.F. Rua and A. Shakoori. //
	 Computing the topology of a real algebraic plane curve whose defining equations are available only "by values".// Computer Aided Geometric Design, Vol 30, 675-706, Issue 7, 2013. http://dx.doi.org/10.1016/j.cagd.2013.04.003

  * G. M. Diaz--Toca and M. Fioravanti and L. Gonzalez--Vega and A. Shakoori.//
Using implicit equations of parametric curves and surfaces without computing them: polynomial algebra by values.// Computer Aided Geometric Design. Vol 30, Issue 1, 116-139, 2013. http://dx.doi.org/10.1016/j.cagd.2012.06.006 

  * Juan Gerardo Alcázar y Gema M Diaz-Toca. //On the Shape of Curves that are Rational in Polar Coordinates.//  Computer Aided Geometric Design. Vol. 29, 665-675, 2012.  http://dx.doi.org/10.1016/j.cagd.2012.09.001  

  * Gema M Diaz-Toca y Henri Lombardi. A polynomial bound on the number of comaximal localizations needed in order to make free a projective module. Linear Algebra and Its Applications, Volume 435, Issue 2, 354-360, 2011.

  * Gema M Diaz-Toca y Henri Lombardi. //Dynamic Galois Theory//. Journal of Symbolic Computation, Vol  45, 12, 1316-1329, 2010.

  * Juan Gerardo Alcázar y Gema M Diaz-Toca. //Topology of 2D and 3D Rational Curves.// Computer Aided Geometric Design, Volume 27, Issue 7, Pages 483-502, 2010.

  * Gema M Diaz-Toca, Juan Egea, Sebastián Ferrer, Jan Cees van der Meer y Juan Antonio Vera. //Relative equilibria and bifurcations in the generalized van der Waals 4-D oscillator//. Physica D: Nonlinear Phenomena, 2010, Vol 239, 16, 1610-1625.

  * Nadia Ben Atti y Gema M Diaz-Toca. //LU Equivalence and Signatures of Bezoutians and Hankel matrices.// Contribuciones científicas en honor de Mirian Andrés Gómez, 2010.[[http://dialnet.unirioja.es/servlet/extart?codigo=3217821|descargar]]

  * Jounaidi Abdeljaoued, Gema M Diaz-Toca y Laureano González Vega. //Bezout matrices, Subresultant polynomials and parameters.// Applied Mathematics and Computation, 2009, Vol/Pg 214, 588–594. 

  * Nadia Ben Atti y Gema M Diaz-Toca. //Block LU factorization of Hankel and Bezout matrices and Euclidean algorithm.// Int J. Computer Math., 2009,  Vol/Pg 135-149.

  * Gema M Diaz-Toca , Laureano González Vega, Claude Quitté y Henri Lombardi. //Modules projectifs de type fini, applications lineaires croisees et inverses generalises.// Journal of Algebra, 2006, Vol/Pg 303, 450 - 475.

  * Nadia Ben Atti , Gema M Diaz-Toca y Henri Lombardi. //The Berlekamp-Massey Algorithm revisited.// Applicable Algebra in Engineering, Communication and Computing (AAECC) 2006, Vol/Pg 17, nº1, 75 - 82.

  * Gema M Diaz-Toca y Laureano Gonzalez-Vega. //Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases.// Linear Algebra and its Applications (LAA). 2006, Vol/Pg 412, 222-246.

  * Nadia Ben Atti y Gema M Diaz-Toca. //Block diagonalization and LU- equivalence of Hankel matrices.// Linear Algebra and its Applications, 2006, Vol/Pg 412, 247-269.

  * Gema M Diaz-Toca. //Galois Theory, Splitting fields and Computer Algebra.// Journal of Symbolic Computation, Vol. 41, Nº 11, 2006 , págs. 1174-1186, (2006)

  * Gema M Diaz-Toca, Laureano Gonzalez-Vega y Henri Lombardi.// Generalizing Cramer’s Rule : Solving Uniformly linear systems of Equations.// SIAM Journal of Matrix Analysis and Applications, 2005, Vol/Pg 27, 621-637

  * Gema M Diaz-Toca y Laureano Gonzalez-Vega. //Various New Expressions for Subresultants and Their Appplications.// Applicable Algebra in Engineering, Communication and Computing (AAECC), 2004, Vol/Pg 15, 3-4, 233 – 266 

  * Jounaidi Abdeljaoued, Gema M Diaz-Toca y Laureano Gonzalez-Vega. //Minors of Bezout matrices, Subresultants and the parameterization of the degree of the polynomial greatest common divisor.// Int. Journal of Computer Mathematics, 2004, Vol/Pg 81, 10, 1223-1238

  * Gema M Diaz-Toca y Laureano Gonzalez-Vega. //Barnett's theorems about the greatest common divisor of several univariate polynomials through Bezout-like matrices.// Journal of Symbolic Computation, 2002 ,Vol/Pg 34, 1, 59-81.

  * Gema M Diaz-Toca y Laureano Gonzalez-Vega. //Squarefree decomposition of univariate polynomials depending on a parameter.// Application to the integration of parametric rational functions. Journal of Symbolic Computation. 2001 Vol/Pg 32 , nº 3, 191-209
 

  * Gema M Diaz-Toca y Laureano Gonzalez-Vega. //An explicit description for the triangular decomposition of a zero-dimensional ideal through trace computations.// Symbolic computation: solving equations in algebra, geometry, and engineering. Contemporary Mathematics. AMS. 2001 Vol/Pg 286, 21-35