{"id":76217,"date":"2018-03-09T23:21:35","date_gmt":"2018-03-09T23:21:35","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/varias-perspectivas-sobre-las-bases-de-gra%c2%b6bner-forma-normal-de-smith-algoritmo-de-berlekamp-y-algebras-de-leibniz\/"},"modified":"2018-03-09T23:21:35","modified_gmt":"2018-03-09T23:21:35","slug":"varias-perspectivas-sobre-las-bases-de-gra%c2%b6bner-forma-normal-de-smith-algoritmo-de-berlekamp-y-algebras-de-leibniz","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/varias-perspectivas-sobre-las-bases-de-gra%c2%b6bner-forma-normal-de-smith-algoritmo-de-berlekamp-y-algebras-de-leibniz\/","title":{"rendered":"Varias perspectivas sobre las bases de gr\u00c1\u00b6bner: forma normal de smith, algoritmo de berlekamp y \u00e1lgebras de leibniz."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Manuel Avelino Insua Hermo <\/strong><\/h2>\n<p>Resumen: la memoria se enmarca dentro de \u00e1lgebra computacional y tiene como hilo conductor las bases de gr\u00ed\u00b6bner en tres marcos diferentes de las matem\u00e1tica. La memoria consta de cuatro cap\u00edtulos. En el primer resumen: la memoria se enmarca dentro del \u00e1lgebra computacional y tiene como hilo conductor las bases de gr6bner en tres marcos diferentes de las matem\u00e1ticas. la memoria consta de cuatro cap\u00edtulos. En el primer cap\u00edtulos se plantea la obtenci\u00f3n de la forma normal de smith sobre un dominio de ideales principales utilizando bases de grobner sin cuestionarse la eficacia de dicho algoritmo. como aplicaci\u00f3n obtiene algoritmos para las formas can\u00f3nicas racional y de jordan de una matriz.  todos estos algoritmos son programados en el lenguaje mathematica, desarrollando un paquete que permite calcular la forma normal de smith y las matrices de paso con coeficientes en varios dominios de ideales principales, las formas can\u00f3nicas racional y de jordan, as\u00ed como sus respectivas matrices de paso en los cuerpos de los n\u00fameros racionales, reales, complejos o n\u00fameros finitos y los generadores de los m\u00f3dulos crclicos en los que se descompone un m\u00f3dulo finita mente generado sobre el anillo de polinomios en una variable con coeficientes en un cuerpo. Finaliza el primer capitulo dando aplicaciones de dichos algoritmos en la clasificaci\u00f3n de grupos abelianos finita mente generados y en la resoluci\u00f3n de sistemas de ecuaciones diferenciales lineales y sistemas de ecuaciones diof\u00e1nticas.  en el capitulo segundo, el autor plantea una versi\u00f3n del algoritmo de berlekamp, para factorizar polinomios en una variable sobre un cuerpo finito, con bases de grobner. La justificaci\u00f3n de dicho planteamiento se debe a que en mathematica no tiene ning\u00fan paquete que permita dicha factorizaci\u00f3n y que el autor necesita para poder implementar algunos algoritmos sobre formas can\u00f3nicas de matrices del primer capitulo.  en el tercer cap\u00edtulo, se plant<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Varias perspectivas sobre las bases de gr\u00c1\u00b6bner: forma normal de smith, algoritmo de berlekamp y \u00e1lgebras de leibniz.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Varias perspectivas sobre las bases de gr\u00c1\u00b6bner: forma normal de smith, algoritmo de berlekamp y \u00e1lgebras de leibniz. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Manuel Avelino Insua Hermo <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 19\/09\/2005<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Manuel Ladra Gonz\u00e1lez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  G\u00f3mez pardo Jos\u00e9 Luis <\/li>\n<li>tomas Recio mu\u00f1iz (vocal)<\/li>\n<li> Barja p\u00e9rez Jos\u00e9 Mar\u00eda (vocal)<\/li>\n<li>Francisco Jes\u00fas Castro jim\u00e9nez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Manuel Avelino Insua Hermo Resumen: la memoria se enmarca dentro de \u00e1lgebra computacional y tiene como hilo [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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