{"id":35388,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/algoritmos-eficientes-en-geometria-algebraica-real-formulas-para-la-resolucion-de-sistemas-de-ecuaciones-algebraicas\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"algoritmos-eficientes-en-geometria-algebraica-real-formulas-para-la-resolucion-de-sistemas-de-ecuaciones-algebraicas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/algoritmos-eficientes-en-geometria-algebraica-real-formulas-para-la-resolucion-de-sistemas-de-ecuaciones-algebraicas\/","title":{"rendered":"Algoritmos eficientes en geometria algebraica real. formulas para la resolucion de sistemas de ecuaciones algebraicas."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Guadalupe Trujillo Perez <\/strong><\/h2>\n<p>La memoria est\u00e1 dedicada al desarrollo y estudio de nuevos algoritmos eficientes dirigidos al an\u00e1lisis del conjunto de soluciones de un sistema de ecuaciones algebraicas. Para ello, se distinguen siete cap\u00edtulos, distribuidos en tres bloques, as\u00ed como tres ap\u00e9ndices. El primer y segundo bloques analizan el caso cero-dimensional desde dos puntos de vista distintos. El bloque primero utiliza m\u00e9todos directos, mientras que el segundo bloque enfoca el problema mediante la reducci\u00f3n del mismo al caso univariado. En los cap\u00edtulos 1 y 2 se muestra como el problema se puede reducir al \u00e1mbito del \u00e1lgebra lineal, utilizando la asignatura y el rango de la matriz de la traza; bien directamente con el m\u00e9todo de hermite, o con la generalizaci\u00f3n del concepto de bezoutiano al caso multivariable. En los cap\u00edtulos 3 y 4 la idea b\u00e1sica consiste en determinar un polinomio univariable cuyas ra\u00edces est\u00e9n en correspondencia con las soluciones del sistema de ecuaciones algebraicas cero-dimensional. El tercer bloque est\u00e1 dedicado al caso de dimensi\u00f3n positiva. En este contexto, se presenta la noci\u00f3n de grado topol\u00f3gico y se muestra su aplicaci\u00f3n al estudio del conjunto de soluciones reales, de un sistema de ecuaciones algebraicas, en el interior de un regi\u00f3n dada.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Algoritmos eficientes en geometria algebraica real. formulas para la resolucion de sistemas de ecuaciones algebraicas.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Algoritmos eficientes en geometria algebraica real. formulas para la resolucion de sistemas de ecuaciones algebraicas. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Guadalupe Trujillo Perez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Cantabria<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>vega Gonzalez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jaime Puig-pey Echebeste <\/li>\n<li>Dominique Duval (vocal)<\/li>\n<li>Hans Stetter (vocal)<\/li>\n<li>Mar\u00eda no Gasca (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Guadalupe Trujillo Perez La memoria est\u00e1 dedicada al desarrollo y estudio de nuevos algoritmos eficientes dirigidos al [&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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