Definir la funci\u00f3n<\/p>\n
\n soluciones :: [(Integer,Integer,Integer)]\n<\/pre>\ntal que sus elementos son las ternas (x,y,k) de soluciones del sistema x\u00b2 = y\u00b3 = k. Por ejemplo,<\/p>\n
\n \u03bb> take 6 soluciones\n [(0,0,0),(-1,1,1),(1,1,1),(-8,4,64),(8,4,64),(-27,9,729)]\n \u03bb> soluciones !! (6*10^5+6) \n (27000810008100027,90001800009,729043741093514580109350437400729)\n<\/pre>\nSoluciones<\/h4>\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsoluciones :: [(Integer,Integer,Integer)]\nsoluciones = [(n^3, n^2, n^6) | n <- enteros]\n\n-- enteros es la lista ordenada de los n\u00fameros enteros. Por ejemplo,\n-- \u03bb> take 20 enteros\n-- [0,-1,1,-2,2,-3,3,-4,4,-5,5,-6,6,-7,7,-8,8,-9,9,-10]\nenteros :: [Integer]\nenteros = 0 : concat [[-x,x] | x <- [1..]]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsoluciones2 :: [(Integer,Integer,Integer)]\nsoluciones2 = [(x^3,x^2,x^6) | x <- 0 : aux 1]\n where aux n = -n : n : aux (n+1)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsoluciones3 :: [(Integer,Integer,Integer)]\nsoluciones3 =\n (0,0,0) : [(x,y,k) | k <- [n^6 | n <- [1..]] \n , let Just x' = raiz 2 k\n , let Just y = raiz 3 k\n , x <- [-x',x']]\n\n-- (raiz n x) es es justo la ra\u00edz n-\u00e9sima del n\u00famero natural x, si x es\n-- una potencia n-\u00e9sima y Nothing en caso contrario. Por ejemplo,\n-- raiz 2 16 == Just 4\n-- raiz 3 216 == Just 6\n-- raiz 5 216 == Nothing\nraiz :: Int -> Integer -> Maybe Integer \nraiz _ 1 = Just 1\nraiz n x = aux (0,x)\n where aux (a,b) | d == x = Just c\n | c == a = Nothing\n | d < x = aux (c,b)\n | otherwise = aux (a,c) \n where c = (a+b) `div` 2\n d = c^n\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- \u03bb> soluciones !! (6*10^5+6)\n-- (27000810008100027,90001800009,729043741093514580109350437400729)\n-- (1.87 secs, 247,352,728 bytes)\n-- \u03bb> soluciones2 !! (6*10^5+6)\n-- (27000810008100027,90001800009,729043741093514580109350437400729)\n-- (1.44 secs, 243,012,936 bytes)\n-- \u03bb> soluciones3 !! (6*10^5+6)\n-- (27000810008100027,90001800009,729043741093514580109350437400729)\n-- (0.84 secs, 199,599,664 bytes)\n<\/pre>\nPensamiento<\/h4>\n\nLeyendo a Cervantes me parece comprenderlo todo.<\/p>\n
Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n soluciones :: [(Integer,Integer,Integer)] tal que sus elementos son las ternas (x,y,k) de soluciones del sistema x\u00b2 = y\u00b3 = k. Por ejemplo, \u03bb> take 6 soluciones [(0,0,0),(-1,1,1),(1,1,1),(-8,4,64),(8,4,64),(-27,9,729)] \u03bb> soluciones !! (6*10^5+6) (27000810008100027,90001800009,729043741093514580109350437400729) Soluciones — 1\u00aa soluci\u00f3n — =========== soluciones :: [(Integer,Integer,Integer)] soluciones = [(n^3, n^2, n^6) | n take 20 enteros –…<\/p>\n","protected":false},"author":1,"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":[4],"tags":[8,30,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4611"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=4611"}],"version-history":[{"count":7,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4611\/revisions"}],"predecessor-version":[{"id":4667,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4611\/revisions\/4667"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4611"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4611"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}