{"id":8110,"date":"2023-05-05T06:00:41","date_gmt":"2023-05-05T04:00:41","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8110"},"modified":"2023-04-29T13:37:40","modified_gmt":"2023-04-29T11:37:40","slug":"05-may-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/05-may-23\/","title":{"rendered":"TAD de los polinomios: Integral de un polinomio"},"content":{"rendered":"<p>Usando el <a href=\"https:\/\/bit.ly\/3KwqXYu\">tipo abstracto de los polinomios<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   integral :: (Fractional a, Eq a) => Polinomio a -> Polinomio a\n<\/pre>\n<p>tal que <code>integral p<\/code> es la integral del polinomio <code>p<\/code> cuyos coefientes son n\u00fameros racionales. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPol = consPol 7 2 (consPol 4 5 (consPol 2 5 polCero))\n   \u03bb> ejPol\n   2*x^7 + 5*x^4 + 5*x^2\n   \u03bb> integral ejPol\n   0.25*x^8 + x^5 + 1.6666666666666667*x^3\n   \u03bb> integral ejPol :: Polinomio Rational\n   1 % 4*x^8 + x^5 + 5 % 3*x^3\n<\/pre>\n<p><b>Soluciones<\/b><\/p>\n<p>A continuaci\u00f3n se muestran las <a href=\"#haskell\">soluciones en Haskell<\/a> y las <a href=\"#python\">soluciones en Python<\/a>.<\/p>\n<p><a name=\"haskell\"><\/a><br \/>\n<b>Soluciones en Haskell<\/b><\/p>\n<pre lang=\"haskell\">\nimport TAD.Polinomio (Polinomio, polCero, consPol, esPolCero, grado,\n                      coefLider, restoPol)\nimport Data.Ratio\n\nintegral :: (Fractional a, Eq a) => Polinomio a -> Polinomio a\nintegral p\n  | esPolCero p = polCero\n  | otherwise   = consPol (n+1) (b \/ fromIntegral (n+1)) (integral r)\n  where n = grado p\n        b = coefLider p\n        r = restoPol p\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom src.TAD.Polinomio import (Polinomio, coefLider, consPol, esPolCero, grado,\n                               polCero, restoPol)\n\n\ndef integral(p: Polinomio[float]) -> Polinomio[float]:\n    if esPolCero(p):\n        return  polCero()\n    n = grado(p)\n    b = coefLider(p)\n    r = restoPol(p)\n    return consPol(n + 1, b \/ (n + 1), integral(r))\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de los polinomios, definir la funci\u00f3n integral :: (Fractional a, Eq a) => Polinomio a -> Polinomio a tal que integral p es la integral del polinomio p cuyos coefientes son n\u00fameros racionales. Por ejemplo, \u03bb> ejPol = consPol 7 2 (consPol 4 5 (consPol 2 5 polCero)) \u03bb> ejPol 2*x^7&#8230;<\/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":[581],"tags":[265],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8110"}],"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=8110"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8110\/revisions"}],"predecessor-version":[{"id":8111,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8110\/revisions\/8111"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}