Ponencias (Álgebra)
URI permanente para esta colecciónhttps://hdl.handle.net/11441/10806
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Ponencia On reduction curves and Garside properties of braids(ArXiv, 2010-06-11) González-Meneses, Juan; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y HomotopíaIn this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a cyclic sliding (which is a particular kind of conjugation) affects the normal form of a braid with respect to the normal forms of its components. Finally, using the above methods, we provide the example of a family of braids whose sets of sliding circuits (hence ultra summit sets) have exponential size with respect to the number of strands and also with respect to the canonical length.Ponencia A computacional approach to the D-module of Meromorphic functions(Universidad de Valladolid, 2002-04-12) Castro Jiménez, Francisco Jesús; Ucha, J.M.; Álgebra; Giménez, Philippe; FQM333: Algebra Computacional en Anillos no Conmutativos y AplicacionesLet be a divisor in . We present methods to compare the -module of the meromorphic functions to some natural approximations. We show how the analytic case can be treated with computations in the Weyl algebra.Ponencia Galois Representations and the Tame Inverse Galois Problem(AMS, 2011-04-14) Arias de Reyna Domínguez, Sara; Vila, Nuria; Álgebra; Cojocaru, Alina-Carmen; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y HomotopíaIn this paper we will focus on a variant of the Inverse Galois Problem over the rationals, emphasizing the progress made through the analysis of the Galois representations arising from arithmetic-geometric objects. The study of the Inverse Galois Problem explores the finite quotients of the absolute Galois group GQ = Gal(Q=Q), and sheds light on its structure.Ponencia Resolution of the Frobenius Problem with an Adiabatic Quantum Computer(Springer, 2021-07-13) Ossorio Castillo, Joaquín; Tornero Sánchez, José María; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y HomotopíaThe (Diophantine) Frobenius problem is a well-known NPhard problem (also called the stamp problem or the chicken nugget problem) whose origins lie in the realm of combinatorial number theory. In this paper we present an algorithm which solves it, via a translation into a QUBO problem of the so-called Ap´ery set of a numerical semigroup. This algorithm was specifically designed to run in an adiabatic quantum computer (a D-Wave 2X machine), and the performance problems for this precise setting are also discussed.Ponencia Generating partial Hadamard matrices as solutions to a Constraint Satisfaction Problem characterizing cliques(2017-07) Álvarez Solano, Víctor; Armario Sampalo, José Andrés; Falcón Ganfornina, Raúl Manuel; Frau García, María Dolores; Gudiel Rodríguez, Félix; Güemes Alzaga, María Belén; Osuna Lucena, Amparo; Matemática Aplicada I; Álgebra; Junta de AndalucíaA procedure is described looking for partial Hadamard matrices, as cliques of a particular subgraph Gt of Ito’s Hadamard Graph Δ(4t) [9]. The key idea is translating the problem of extending a given clique Cm to a larger clique of size m+ 1 in Gt, into a constraint satisfaction problem, and look for a solution to this problem by means of Minion [6]. Iteration of this process usually ends with a large partial Hadamard matrix.Ponencia Invariance properties for coefficients of symmetric functions(2016) Briand, Emmanuel; Orellana, Rosa C.; Rosas Celis, Mercedes Helena; Álgebra; FQM333: Álgebra Computacional en Anillos no Conmutativos y AplicacionesWe show that several of the main structural constants for symmetric functions (Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients, and the Kostka-Foulkes polynomials) share invariance properties related to the operations of taking complements with respect to rectangles and adding rectangles.Ponencia Lógicas polivalentes y bases de Gröbner(1987) Alonso Jiménez, José Antonio; Ciencias de la Computación e Inteligencia Artificial; Álgebra; TIC137: Lógica, Computación e Ingeniería del Conocimiento; FQM366: Álgebras de Semigrupos, Computación y AplicacionesEl objetivo de la comunicación es presentar una aplicación de las bases de Gröbner a la demostración automática en lógicas proposicionales polivalentes. La estructura de la comunicación es la siguiente: En la sección 1, recordamos conceptos sintácticos y semánticos de las lógicas polivalentes. A continuación, reducimos el problema de la validez en lógicas polivalentes al de pertenencia a un ideal (sección 2) y al de cálculo de una base de Gröbner (sección 3). Finalmente, en la sección 4 damos algoritmos para resolver los anteriores problemas.Ponencia Preuve automatique dans le calcul propositionnel et les logiques trivalentes(1987) Alonso Jiménez, José Antonio; Briales Morales, Emilio; Ciencias de la Computación e Inteligencia Artificial; Álgebra; TIC137: Lógica, Computación e Ingeniería del Conocimiento; FQM366: Álgebras de Semigrupos, Computación y AplicacionesNous présentons une application des bases de Gröbner (bases standard) d’idéaux de polynômes la vérification des tautologies dans le Calcul Propositionnel et dans trois types de logiques trivalentes. L’idée base est de transformer les formules en polynômes, et de trouver l’´equivalent algèbrique de la déduction: nous verons des théorèmes faisant la liaison entre déduction et crièeres de réduction algèbrique.Ponencia The Chemist's Cabinet Puzzle: a polynomial approach(Universidad de Granada. Departamento de Álgebra, 2008-09) Gago Vargas, Manuel Jesús; Hartillo Hermoso, Isabel; Ucha Enríquez, José María; Álgebra; Cortadellas Izquierdo, Ó. A.Realizamos un análisis del juego conocido por el herbolario. Se modeliza su solución mediante un sistema polinómico, y deducimos el número de soluciones a partir de herramientas de Álgebra Conmutativa.