{"id":7647,"date":"2021-12-31T13:44:16","date_gmt":"2021-12-31T12:44:16","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=7647"},"modified":"2021-12-31T13:44:16","modified_gmt":"2021-12-31T12:44:16","slug":"resena-windmills-of-the-minds-an-algorithm-for-fermats-two-squares-theorem","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-windmills-of-the-minds-an-algorithm-for-fermats-two-squares-theorem\/","title":{"rendered":"Rese\u00f1a: Windmills of the minds: an algorithm for Fermat&#8217;s two squares theorem"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en <a href=\"https:\/\/hol-theorem-prover.org\/\">HOL4<\/a> sobre teor\u00eda de n\u00fameros titulado <a href=\"https:\/\/arxiv.org\/pdf\/2112.02556.pdf\">Windmills of the minds: an algorithm for Fermat&#8217;s two squares theorem<\/a>.<\/p>\n<p>Sus autor es <a href=\"https:\/\/dblp.org\/pid\/121\/0258.html\">Hing Lun Chan<\/a> (de la <a href=\"https:\/\/www.anu.edu.au\/\">Australian National University<\/a> en Canberra, Australia).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Fermat%27s_theorem_on_sums_of_two_squares\">two squares theorem of Fermat<\/a> is a gem in number theory, with a spectacular one-sentence &#8220;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Proofs_from_THE_BOOK\">proof from the Book<\/a>&#8220;. Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves involutions on a finite set, especially the parity of the number of fixed points in the involutions. Starting as an existence proof that is non-constructive, there is an ingenious way to turn it into a constructive one. This gives an algorithm to compute the two squares by iterating the two involutions alternatively from a known fixed point.<\/p><\/blockquote>\n<p>El trabajo se presentar\u00e1 en el <a href=\"https:\/\/popl22.sigplan.org\/home\/CPP-2022\">Certified Programs and Proofs (CPP) 2022<\/a> el 18 de enero de 2022.<\/p>\n<p>El c\u00f3digo de las correspondientes teor\u00edas se encuentra <a href=\"https:\/\/bitbucket.org\/jhlchan\/project\/src\/master\/fermat\/twosq\/\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en HOL4 sobre teor\u00eda de n\u00fameros titulado Windmills of the minds: an algorithm for Fermat&#8217;s two squares theorem. Sus autor es Hing Lun Chan (de la Australian National University en Canberra, Australia). Su resumen es The two squares theorem of Fermat is a gem in number theory,&#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":[166,199,285],"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\/7647"}],"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=7647"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7647\/revisions"}],"predecessor-version":[{"id":7648,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/7647\/revisions\/7648"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=7647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=7647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=7647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}