{"id":8100,"date":"2023-05-02T06:00:58","date_gmt":"2023-05-02T04:00:58","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8100"},"modified":"2023-04-26T11:17:59","modified_gmt":"2023-04-26T09:17:59","slug":"02-may-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/02-may-23\/","title":{"rendered":"TAD de los polinomios: Derivada 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   derivada :: (Eq a, Num a) => Polinomio a -> Polinomio a\n<\/pre>\n<p>tal que <code>derivada p<\/code> es la derivada del polinomio <code>p<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPol = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero))\n   \u03bb> ejPol\n   x^5 + 5*x^2 + 4*x\n   \u03bb> derivada ejPol\n   5*x^4 + 10*x + 4\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, grado, coefLider,\n                      restoPol)\nimport Pol_Suma_de_polinomios (sumaPol)\nimport Test.QuickCheck\n\nderivada :: (Eq a, Num a) => Polinomio a -> Polinomio a\nderivada p\n  | n == 0     = polCero\n  | otherwise  = consPol (n-1) (b * fromIntegral n) (derivada r)\n  where n = grado p\n        b = coefLider p\n        r = restoPol p\n\n-- Propiedad. La derivada de la suma es la suma de las derivadas.\nprop_derivada :: Polinomio Int -> Polinomio Int -> Bool\nprop_derivada p q =\n  derivada (sumaPol p q) == sumaPol (derivada p) (derivada q)\n\n-- Comprobaci\u00f3n\n--    \u03bb> quickCheck prop_derivada\n--    OK, passed 100 tests.\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom typing import TypeVar\n\nfrom hypothesis import given\n\nfrom src.Pol_Suma_de_polinomios import sumaPol\nfrom src.TAD.Polinomio import (Polinomio, coefLider, consPol, grado, polCero,\n                               polinomioAleatorio, restoPol)\n\nA = TypeVar('A', int, float, complex)\n\n\ndef derivada(p: Polinomio[A]) -> Polinomio[A]:\n    n = grado(p)\n    if n == 0:\n        return polCero()\n    b = coefLider(p)\n    r = restoPol(p)\n    return consPol(n - 1, b * n, derivada(r))\n\n# Propiedad. La derivada de la suma es la suma de las derivadas.\n@given(p=polinomioAleatorio(), q=polinomioAleatorio())\ndef test_derivada(p: Polinomio[int], q: Polinomio[int]) -> None:\n    assert derivada(sumaPol(p, q)) == sumaPol(derivada(p), derivada(q))\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Pol_Derivada_de_un_polinomio.py\n#    1 passed in 0.46s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de los polinomios, definir la funci\u00f3n derivada :: (Eq a, Num a) => Polinomio a -> Polinomio a tal que derivada p es la derivada del polinomio p. Por ejemplo, \u03bb> ejPol = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero)) \u03bb> ejPol x^5 + 5*x^2 + 4*x \u03bb>&#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\/8100"}],"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=8100"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8100\/revisions"}],"predecessor-version":[{"id":8101,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8100\/revisions\/8101"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}