{"id":4697,"date":"2015-01-06T08:41:34","date_gmt":"2015-01-06T07:41:34","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=4697"},"modified":"2015-01-06T08:41:34","modified_gmt":"2015-01-06T07:41:34","slug":"resena-fibonacci-numbers-and-the-stern-brocot-tree-in-coq","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-fibonacci-numbers-and-the-stern-brocot-tree-in-coq\/","title":{"rendered":"Rese\u00f1a: Fibonacci numbers and the Stern-Brocot tree in Coq"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Coq titulado <a href=\"http:\/\/bit.ly\/1JZqPLC\">Fibonacci numbers and the Stern-Brocot tree in Coq<\/a>.<\/p>\n<p>Sus autor es <a href=\"http:\/\/www-sop.inria.fr\/members\/Jose.Grimm\">Jos\u00e9 Grimm<\/a> (del <a href=\"https:\/\/team.inria.fr\/marelle\/en\">Marelle Team<\/a> en el <em>Inria, Sophia-Antipolis M\u00e9diterran\u00e9e<\/em>).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\n  In this paper, we study the representation of a number by some other numbers. For instance, an integer may be represented uniquely as a sum of powers of two; if each power of two is allowed to appear at most twice, the number of representations is s(n), a sequence studied by Dijkstra, that has many nice properties proved here with the use of the proof assistant Coq. It happens that every rational number x is uniquely the quotient s(n)\/s(n+1) as noticed by Stern, and that the integer n is related to the continued fraction expansion of x. It happens that by reverting the bits on n, one gets a sequence of rational numbers with increasing denominators that goes from 1 to x and becomes nearer at each iteration; this was studied by Brocot, whence the name Stern-Brocot tree. An integer can also be represented as a sum of Fibonacci numbers; we study R(n) the number of such representations; there is uniqueness for the predecessors of Fibonacci numbers; there is also uniqueness under additional constraints (for instance, no two consecutive Fibonacci numbers can be used, or no two consecutive numbers can be omitted).\n<\/p><\/blockquote>\n<p>El c\u00f3digo de las correspondientes teor\u00edas en Coq se encuentra <a href=\"http:\/\/www-sop.inria.fr\/marelle\/gaia\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Coq titulado Fibonacci numbers and the Stern-Brocot tree in Coq. Sus autor es Jos\u00e9 Grimm (del Marelle Team en el Inria, Sophia-Antipolis M\u00e9diterran\u00e9e). Su resumen es In this paper, we study the representation of a number by some other numbers. For instance, an integer may be&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","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":[45,285],"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\/4697"}],"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=4697"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4697\/revisions"}],"predecessor-version":[{"id":4698,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4697\/revisions\/4698"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=4697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=4697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=4697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}