{"id":8073,"date":"2023-04-26T06:00:06","date_gmt":"2023-04-26T04:00:06","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8073"},"modified":"2023-04-19T12:10:02","modified_gmt":"2023-04-19T10:10:02","slug":"26-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/26-abr-23\/","title":{"rendered":"TAD de los polinomios: Suma de polinomios"},"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   sumaPol :: (Num a, Eq a) => Polinomio a -> Polinomio a -> Polinomio a\n<\/pre>\n<p>tal que (sumaPol p q) es la suma de los polinomios p y q. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPol1 = consPol 4 3 (consPol 2 (-5) (consPol 0 3 polCero))\n   \u03bb> ejPol2 = consPol 5 1 (consPol 2 5 (consPol 1 4 polCero))\n   \u03bb> ejPol1\n   3*x^4 + -5*x^2 + 3\n   \u03bb> ejPol2\n   x^5 + 5*x^2 + 4*x\n   \u03bb> sumaPol ejPol1 ejPol2\n   x^5 + 3*x^4 + 4*x + 3\n<\/pre>\n<p>Comprobar con QuickCheck las siguientes propiedades:<\/p>\n<ul>\n<li><code>polCero<\/code> es el elemento neutro de la suma.<\/li>\n<li>la suma es conmutativa.<\/li>\n<\/ul>\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, esPolCero, consPol, grado,\n                      coefLider, restoPol)\nimport Test.QuickCheck\n\nsumaPol :: (Num a, Eq a) => Polinomio a -> Polinomio a -> Polinomio a\nsumaPol p q\n  | esPolCero p = q\n  | esPolCero q = p\n  | n1 > n2      = consPol n1 a1 (sumaPol r1 q)\n  | n1 < n2      = consPol n2 a2 (sumaPol p r2)\n  | otherwise    = consPol n1 (a1+a2) (sumaPol r1 r2)\n  where (n1, a1, r1) = (grado p, coefLider p, restoPol p)\n        (n2, a2, r2) = (grado q, coefLider q, restoPol q)\n\n-- Propiedad. El polinomio cero es el elemento neutro de la suma.\nprop_neutroSumaPol :: Polinomio Int -> Bool\nprop_neutroSumaPol p =\n  sumaPol polCero p == p\n\n-- Comprobaci\u00f3n con QuickCheck.\n--    \u03bb> quickCheck prop_neutroSumaPol\n--    OK, passed 100 tests.\n\n-- Propiedad. La suma es conmutativa.\nprop_conmutativaSuma :: Polinomio Int -> Polinomio Int -> Bool\nprop_conmutativaSuma p q =\n  sumaPol p q == sumaPol q p\n\n-- Comprobaci\u00f3n:\n--    \u03bb> quickCheck prop_conmutativaSuma\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.TAD.Polinomio import (Polinomio, coefLider, consPol, esPolCero, grado,\n                               polCero, polinomioAleatorio, restoPol)\n\nA = TypeVar('A', int, float, complex)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef sumaPol(p: Polinomio[A], q: Polinomio[A]) -> Polinomio[A]:\n    if esPolCero(p):\n        return q\n    if esPolCero(q):\n        return p\n    n1, a1, r1 = grado(p), coefLider(p), restoPol(p)\n    n2, a2, r2 = grado(q), coefLider(q), restoPol(q)\n    if n1 > n2:\n        return consPol(n1, a1, sumaPol(r1, q))\n    if n1 < n2:\n        return consPol(n2, a2, sumaPol(p, r2))\n    return consPol(n1, a1 + a2, sumaPol(r1, r2))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef sumaPol2(p: Polinomio[A], q: Polinomio[A]) -> Polinomio[A]:\n    if p.esPolCero():\n        return q\n    if q.esPolCero():\n        return p\n    n1, a1, r1 = p.grado(), p.coefLider(), p.restoPol()\n    n2, a2, r2 = q.grado(), q.coefLider(), q.restoPol()\n    if n1 > n2:\n        return sumaPol(r1, q).consPol(n1, a1)\n    if n1 < n2:\n        return sumaPol(p, r2).consPol(n2, a2)\n    return sumaPol(r1, r2).consPol(n1, a1 + a2)\n\n# Equivalencia de las definiciones\n# ================================\n\n# La propiedad es\n@given(p=polinomioAleatorio(), q=polinomioAleatorio())\ndef test_sumaPol(p: Polinomio[int], q: Polinomio[int]) -> None:\n    assert sumaPol(p, q) == sumaPol2(p,q)\n\n# Propiedad. El polinomio cero es el elemento neutro de la suma.\n@given(p=polinomioAleatorio())\ndef test_neutroSumaPol(p: Polinomio[int]) -> None:\n    assert sumaPol(polCero(), p) == p\n    assert sumaPol(p, polCero()) == p\n\n# -- Propiedad. La suma es conmutativa.\n@given(p=polinomioAleatorio(), q=polinomioAleatorio())\ndef test_conmutativaSuma(p: Polinomio[int], q: Polinomio[int]) -> None:\n    assert sumaPol(p, q) == sumaPol(q, p)\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -v Pol_Suma_de_polinomios.py\n#    test_sumaPol PASSED\n#    test_neutroSumaPol PASSED\n#    test_conmutativaSuma PASSED\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de los polinomios, definir la funci\u00f3n sumaPol :: (Num a, Eq a) => Polinomio a -> Polinomio a -> Polinomio a tal que (sumaPol p q) es la suma de los polinomios p y q. Por ejemplo, \u03bb> ejPol1 = consPol 4 3 (consPol 2 (-5) (consPol 0 3 polCero)) \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\/8073"}],"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=8073"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8073\/revisions"}],"predecessor-version":[{"id":8074,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8073\/revisions\/8074"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}