{"id":8146,"date":"2023-05-22T06:00:14","date_gmt":"2023-05-22T04:00:14","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8146"},"modified":"2023-05-22T16:45:28","modified_gmt":"2023-05-22T14:45:28","slug":"22-may-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/22-may-23\/","title":{"rendered":"TAD de los polinomios: Factorizaci\u00f3n 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   factorizacion :: Polinomio Int -> [Polinomio Int]\n<\/pre>\n<p>tal que <code>factorizacion p<\/code> es la lista de la descomposici\u00f3n del polinomio <code>p<\/code> en factores obtenida mediante el regla de Ruffini. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPol1 = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero))\n   \u03bb> ejPol1\n   x^5 + 5*x^2 + 4*x\n   \u03bb> factorizacion ejPol1\n   [1*x,1*x + 1,x^3 + -1*x^2 + 1*x + 4]\n   \u03bb> ejPol2 = consPol 3 1 (consPol 2 2 (consPol 1 (-1) (consPol 0 (-2) polCero)))\n   \u03bb> ejPol2\n   x^3 + 2*x^2 + -1*x + -2\n   \u03bb> factorizacion ejPol2\n   [1*x + -1,1*x + 1,1*x + 2,1]\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\">\nmodule Pol_Factorizacion_de_un_polinomio where\n\nimport TAD.Polinomio (Polinomio, consPol, polCero, esPolCero)\nimport Pol_Termino_independiente_de_un_polinomio (terminoIndep)\nimport Pol_Raices_enteras_de_un_polinomio (divisores)\nimport Pol_Regla_de_Ruffini (cocienteRuffini)\nimport Pol_Reconocimiento_de_raices_por_la_regla_de_Ruffini (esRaizRuffini)\nimport Pol_Transformaciones_polinomios_densas (densaApolinomio)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\nfactorizacion :: Polinomio Int -> [Polinomio Int]\nfactorizacion p\n  | esPolCero p = [p]\n  | otherwise   = aux (0 : divisores (terminoIndep p))\n  where\n    aux [] = [p]\n    aux (r:rs)\n        | esRaizRuffini r p =\n            densaApolinomio [1,-r] : factorizacion (cocienteRuffini r p)\n        | otherwise = aux rs\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    map show (factorizacion ejPol1)\n      `shouldBe` [\"1*x\",\"1*x + 1\",\"x^3 + -1*x^2 + 1*x + 4\"]\n  it \"e2\" $\n    map show (factorizacion ejPol2)\n      `shouldBe` [\"1*x + -1\",\"1*x + 1\",\"1*x + 2\",\"1\"]\n  where\n    ejPol1 = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero))\n    ejPol2 = consPol 3 1 (consPol 2 2 (consPol 1 (-1) (consPol 0 (-2) polCero)))\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--\n--    Finished in 0.0015 seconds\n--    2 examples, 0 failures\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom src.Pol_Raices_enteras_de_un_polinomio import divisores\nfrom src.Pol_Reconocimiento_de_raices_por_la_regla_de_Ruffini import \\\n    esRaizRuffini\nfrom src.Pol_Regla_de_Ruffini import cocienteRuffini\nfrom src.Pol_Termino_independiente_de_un_polinomio import terminoIndep\nfrom src.Pol_Transformaciones_polinomios_densas import densaApolinomio\nfrom src.TAD.Polinomio import Polinomio, consPol, esPolCero, polCero\n\n\ndef factorizacion(p: Polinomio[int]) -> list[Polinomio[int]]:\n    def aux(xs: list[int]) -> list[Polinomio[int]]:\n        if not xs:\n            return [p]\n        r, *rs = xs\n        if esRaizRuffini(r, p):\n            return [densaApolinomio([1, -r])] + factorizacion(cocienteRuffini(r, p))\n        return aux(rs)\n\n    if esPolCero(p):\n        return [p]\n    return aux([0] + divisores(terminoIndep(p)))\n\n# Verificaci\u00f3n\n# ============\n\ndef test_factorizacion() -> None:\n    ejPol1 = consPol(5, 1, consPol(2, 5, consPol(1, 4, polCero())))\n    assert list(map(str, factorizacion(ejPol1))) \\\n        == [\"1*x\", \"1*x + 1\", \"x^3 + -1*x^2 + 1*x + 4\"]\n    ejPol2 = consPol(3, 1, consPol(2, 2, consPol(1, -1, consPol(0, -2, polCero()))))\n    assert list(map(str, factorizacion(ejPol2))) \\\n        == [\"1*x + -1\", \"1*x + 1\", \"1*x + 2\", \"1\"]\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_factorizacion()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de los polinomios, definir la funci\u00f3n factorizacion :: Polinomio Int -> [Polinomio Int] tal que factorizacion p es la lista de la descomposici\u00f3n del polinomio p en factores obtenida mediante el regla de Ruffini. Por ejemplo, \u03bb> ejPol1 = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero)) \u03bb> ejPol1&#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\/8146"}],"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=8146"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8146\/revisions"}],"predecessor-version":[{"id":8169,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8146\/revisions\/8169"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}