{"id":8331,"date":"2023-11-09T06:00:30","date_gmt":"2023-11-09T04:00:30","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8331"},"modified":"2024-05-17T18:44:38","modified_gmt":"2024-05-17T16:44:38","slug":"09-nov-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/09-nov-23\/","title":{"rendered":"Funciones inversas por el m\u00e9todo de Newton"},"content":{"rendered":"

Definir, usando puntoCero, la funci\u00f3n<\/p>\n

\n   inversa :: (Double -> Double) -> Double -> Double\n<\/pre>\n
tal que inversa g x<\/code> es el valor de la inversa de g<\/code> en x<\/code>. Por ejemplo,<\/p>\n
\n   inversa (^2) 9  ==  3.000000002941184\n<\/pre>\n
Definir, usando inversa, las funciones raizCuadrada, raizCubica, arcoseno y arcocoseno que calculen la ra\u00edz cuadrada, la ra\u00edz c\u00fabica, el arco seno y el arco coseno, respectivamente. Por ejemplo,<\/p>\n
\n   raizCuadrada 9  ==  3.000000002941184\n   raizCubica 27   ==  3.0000000000196048\n   arcoseno 1      ==  1.5665489428306574\n   arcocoseno 0    ==  1.5707963267949576\n<\/pre>\n
<\/p>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\nmodule Funciones_inversas_por_el_metodo_de_Newton where\n\nimport Metodo_de_Newton_para_calcular_raices (puntoCero)\nimport Test.Hspec (Spec, hspec, it, shouldBe)\n\ninversa :: (Double -> Double) -> Double -> Double\ninversa g a = puntoCero f\n  where f x = g x - a\n\nraizCuadrada, raizCubica, arcoseno, arcocoseno :: Double -> Double\nraizCuadrada = inversa (^2)\nraizCubica   = inversa (^3)\narcoseno     = inversa sin\narcocoseno   = inversa cos\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspec :: Spec\nspec = do\n  it \"e1\" $\n    inversa (^2) 9  `shouldBe`  3.000000002941184\n  it \"e2\" $\n    raizCuadrada 9  `shouldBe`  3.000000002941184\n  it \"e3\" $\n    raizCubica 27   `shouldBe`  3.0000000000196048\n  it \"e4\" $\n    arcoseno 1      `shouldBe`  1.5665489428306574\n  it \"e5\" $\n    arcocoseno 0    `shouldBe`  1.5707963267949576\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    e1\n--    e2\n--    e3\n--    e4\n--    e5\n--\n--    Finished in 0.0006 seconds\n--    5 examples, 0 failures\n<\/pre>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom math import cos, sin\nfrom typing import Callable\n\nfrom src.Metodo_de_Newton_para_calcular_raices import puntoCero\n\n\ndef inversa(g: Callable[[float],float], a: float) -> float:\n    def f(x: float) -> float:\n        return g(x) - a\n    return puntoCero(f)\n\ndef raizCuadrada(x: float) -> float:\n    return inversa(lambda y: y**2, x)\n\ndef raizCubica(x: float) -> float:\n    return inversa(lambda y: y**3, x)\n\ndef arcoseno(x: float) -> float:\n    return inversa(sin, x)\n\ndef arcocoseno(x: float) -> float:\n    return inversa(cos, x)\n\n# Verificaci\u00f3n\n# ============\n\ndef test_inversa() -> None:\n    assert inversa(lambda x: x**2, 9) == 3.000000002941184\n    assert raizCuadrada(9) == 3.000000002941184\n    assert raizCubica(27) == 3.0000000000196048\n    assert arcoseno(1) == 1.5665489428306574\n    assert arcocoseno(0) == 1.5707963267949576\n    print(\"Verificado\")\n\n# La comprobaci\u00f3n es\n#    >>> test_inversa()\n#    Verificado\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Definir, usando puntoCero, la funci\u00f3n inversa :: (Double -> Double) -> Double -> Double tal que inversa g x es el valor de la inversa de g en x. Por ejemplo, inversa (^2) 9 == 3.000000002941184 Definir, usando inversa, las funciones raizCuadrada, raizCubica, arcoseno y arcocoseno que calculen la ra\u00edz cuadrada, la ra\u00edz c\u00fabica, el…<\/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":"default","_kad_post_title":"default","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"default","_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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8331"}],"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=8331"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8331\/revisions"}],"predecessor-version":[{"id":8574,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8331\/revisions\/8574"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}