{"id":5477,"date":"2016-08-12T11:00:09","date_gmt":"2016-08-12T09:00:09","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=5477"},"modified":"2016-08-12T11:01:24","modified_gmt":"2016-08-12T09:01:24","slug":"resena-a-decision-procedure-for-univariate-real-polynomials-in-isabellehol","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-a-decision-procedure-for-univariate-real-polynomials-in-isabellehol\/","title":{"rendered":"Rese\u00f1a: A decision procedure for univariate real polynomials in Isabelle\/HOL"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle sobre \u00e1lgebra titulado <a href=\"http:\/\/home.in.tum.de\/~eberlm\/sturm_paper.pdf\">A decision procedure for univariate real polynomials in Isabelle\/HOL<\/a>.<\/p>\n<p>Su autor es <a href=\"http:\/\/home.in.tum.de\/~eberlm\">Manuel Eberl<\/a> (de la <em>Technische Universit\u00e4t M\u00fcnchen<\/em>, Alemania).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\n  <a href=\"https:\/\/en.wikipedia.org\/wiki\/Sturm%27s_theorem\">Sturm sequences<\/a> are a method for computing the number of real roots of a univariate real polynomial inside a given interval efficiently. In this paper, this fact and a number of methods to construct Sturm sequences efficiently have been formalised with the interactive theorem prover Isabelle\/HOL. Building upon this, an Isabelle\/HOL proof method was then implemented to prove interesting statements about the number of real roots of a univariate real polynomial and related properties such as non-negativity and monotonicity.\n<\/p><\/blockquote>\n<p>El trabajo se ha presentado en la <a href=\"http:\/\/cpp2015.inria.fr\/program.html\">CPP 2015<\/a> (<em>The 4th ACM-SIGPLAN Conference on Certified Programs and Proofs<\/em>).<\/p>\n<p>El c\u00f3digo de las correspondientes teor\u00edas en Isabelle\/HOL se encuentra <a href=\"https:\/\/www.isa-afp.org\/entries\/Sturm_Sequences.shtml\">aqu\u00ed<\/a>.<\/p>\n<p>Este art\u00edculo puede servir de lectura complementaria en los cursos de <a href=\"http:\/\/www.cs.us.es\/~jalonso\/cursos\/m-ra\">Razonamiento autom\u00e1tico<\/a>, <a href=\"http:\/\/www.cs.us.es\/cursos\/rac\/\">Razonamiento asistido por ordenador<\/a> y <a href=\"http:\/\/www.cs.us.es\/~mjoseh\/LCyTM-15\">L\u00f3gica computacional y teor\u00eda de modelos<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle sobre \u00e1lgebra titulado A decision procedure for univariate real polynomials in Isabelle\/HOL. Su autor es Manuel Eberl (de la Technische Universit\u00e4t M\u00fcnchen, Alemania). Su resumen es Sturm sequences are a method for computing the number of real roots of a univariate real polynomial inside a&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[144,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5477"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=5477"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5477\/revisions"}],"predecessor-version":[{"id":5480,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/5477\/revisions\/5480"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=5477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=5477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=5477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}