{"id":8107,"date":"2023-05-04T06:00:17","date_gmt":"2023-05-04T04:00:17","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8107"},"modified":"2023-04-27T17:44:45","modified_gmt":"2023-04-27T15:44:45","slug":"04-may-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/04-may-23\/","title":{"rendered":"TAD de los polinomios: Potencia 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   potencia :: (Num a, Eq a) => Polinomio a -> Int -> Polinomio a\n<\/pre>\n<p>tal que <code>potencia p n<\/code> es la potencia <code>n<\/code>-\u00e9sima del polinomio <code>p<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPol = consPol 1 2 (consPol 0 3 polCero)\n   \u03bb> ejPol\n   2*x + 3\n   \u03bb> potencia ejPol 2\n   4*x^2 + 12*x + 9\n   \u03bb> potencia ejPol 3\n   8*x^3 + 36*x^2 + 54*x + 27\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)\nimport Pol_Producto_polinomios (multPol)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\npotencia :: (Num a, Eq a) => Polinomio a -> Int -> Polinomio a\npotencia _ 0 = polUnidad\npotencia p n = multPol p (potencia p (n-1))\n\npolUnidad :: (Num a, Eq a) => Polinomio a\npolUnidad = consPol 0 1 polCero\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\npotencia2 :: (Num a, Eq a) => Polinomio a -> Int -> Polinomio a\npotencia2 _ 0 = polUnidad\npotencia2 p n\n  | even n    = potencia2 (multPol p p) (n `div` 2)\n  | otherwise = multPol p (potencia2 (multPol p p) ((n-1) `div` 2))\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_potencia :: Polinomio Int -> NonNegative Int -> Bool\nprop_potencia p (NonNegative n) =\n  potencia p n == potencia2 p n\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_potencia\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> import TAD.Polinomio (grado)\n--    \u03bb> ejPol = consPol 1 2 (consPol 0 3 polCero)\n--    \u03bb> grado (potencia ejPol 1000)\n--    1000\n--    (4.57 secs, 2,409,900,720 bytes)\n--    \u03bb> grado (potencia2 ejPol 1000)\n--    1000\n--    (2.78 secs, 1,439,596,632 bytes)\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom sys import setrecursionlimit\nfrom timeit import Timer, default_timer\nfrom typing import TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nfrom src.Pol_Producto_polinomios import multPol\nfrom src.TAD.Polinomio import Polinomio, consPol, polCero, polinomioAleatorio\n\nsetrecursionlimit(10**6)\n\nA = TypeVar('A', int, float, complex)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef potencia(p: Polinomio[A], n: int) -> Polinomio[A]:\n    if n == 0:\n        return consPol(0, 1, polCero())\n    return multPol(p, potencia(p, n - 1))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef potencia2(p: Polinomio[A], n: int) -> Polinomio[A]:\n    if n == 0:\n        return consPol(0, 1, polCero())\n    if n % 2 == 0:\n        return potencia2(multPol(p, p), n \/\/ 2)\n    return multPol(p, potencia2(multPol(p, p), (n - 1) \/\/ 2))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef potencia3(p: Polinomio[A], n: int) -> Polinomio[A]:\n    r: Polinomio[A] = consPol(0, 1, polCero())\n    for _ in range(0, n):\n        r = multPol(p, r)\n    return r\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(p=polinomioAleatorio(),\n       n=st.integers(min_value=1, max_value=10))\ndef test_potencia(p: Polinomio[int], n: int) -> None:\n    r = potencia(p, n)\n    assert potencia2(p, n) == r\n    assert potencia3(p, n) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q Pol_Potencia_de_un_polinomio.py\n#    1 passed in 0.89s\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e: str) -> None:\n    \"\"\"Tiempo (en segundos) de evaluar la expresi\u00f3n e.\"\"\"\n    t = Timer(e, \"\", default_timer, globals()).timeit(1)\n    print(f\"{t:0.2f} segundos\")\n\n# La comparaci\u00f3n es\n#    >>> from src.TAD.Polinomio import grado\n#    >>> ejPol = consPol(1, 2, consPol(0, 3, polCero()))\n#    >>> tiempo('grado(potencia(ejPol, 1000))')\n#    8.58 segundos\n#    >>> tiempo('grado(potencia2(ejPol, 1000))')\n#    8.75 segundos\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo abstracto de los polinomios, definir la funci\u00f3n potencia :: (Num a, Eq a) => Polinomio a -> Int -> Polinomio a tal que potencia p n es la potencia n-\u00e9sima del polinomio p. Por ejemplo, \u03bb> ejPol = consPol 1 2 (consPol 0 3 polCero) \u03bb> ejPol 2*x + 3 \u03bb> potencia&#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\/8107"}],"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=8107"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8107\/revisions"}],"predecessor-version":[{"id":8108,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8107\/revisions\/8108"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}