{"id":7356,"date":"2022-09-12T06:00:03","date_gmt":"2022-09-12T04:00:03","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7356"},"modified":"2022-12-14T14:33:24","modified_gmt":"2022-12-14T12:33:24","slug":"raices-de-la-ecuacion-de-segundo-grado","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/raices-de-la-ecuacion-de-segundo-grado\/","title":{"rendered":"Ra\u00edces de la ecuaci\u00f3n de segundo grado"},"content":{"rendered":"

Definir la funci\u00f3n<\/p>\n

\n   raices :: Double -> Double -> Double -> [Double]\n<\/pre>\n
tal que (raices a b c)<\/code> es la lista de las ra\u00edces reales de la ecuaci\u00f3n \"ax^2. Por ejemplo,<\/p>\n
\n   raices 1 3 2    ==  [-1.0,-2.0]\n   raices 1 (-2) 1 ==  [1.0,1.0]\n   raices 1 0 1    ==  []\n<\/pre>\n
Comprobar con QuickCheck que la suma de las ra\u00edces de la ecuaci\u00f3n \"ax^2 (con \"a\" no nulo) es \"\dfrac{-b}{a}\" y su  producto es \"\dfrac{c}{a}\".<\/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
\nimport Test.QuickCheck\n\nraices :: Double -> Double -> Double -> [Double]\nraices a b c\n    | d >= 0    = [(-b+e)\/t,(-b-e)\/t]\n    | otherwise = []\n    where d = b^2 - 4*a*c\n          e = sqrt d\n          t = 2*a\n\n-- Para comprobar la propiedad se usar\u00e1 el operador\n--    (~=) :: (Fractional a, Ord a) => a -> a -> Bool\n-- tal que (x ~= y) se verifica si x e y son casi iguales; es decir si\n-- el valor absoluto de su diferencia es menor que una mil\u00e9sima. Por\n-- ejemplo,\n--    12.3457 ~= 12.3459  ==  True\n--    12.3457 ~= 12.3479  ==  False\n(~=) :: (Fractional a, Ord a) => a -> a -> Bool\nx ~= y  = abs (x-y) < 0.001\n\n-- La propiedad es\nprop_raices :: Double -> Double -> Double -> Property\nprop_raices a b c =\n    a \/= 0 && not (null xs) ==> sum xs ~= (-b\/a) && product xs ~= (c\/a)\n    where xs = raices a b c\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_raices\n--    +++ OK, passed 100 tests.\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom math import sqrt\nfrom hypothesis import given, assume, strategies as st\n\ndef raices(a: float, b: float, c: float) -> list[float]:\n    d = b**2 - 4*a*c\n    if d >= 0:\n        e = sqrt(d)\n        t = 2*a\n        return [(-b+e)\/t, (-b-e)\/t]\n    return []\n\n# Para comprobar la propiedad se usar\u00e1 la funci\u00f3n\n#    casiIguales : (float, float) -> bool\n# tal que casiIguales(x, y) se verifica si x e y son casi iguales; es\n# decir si el valor absoluto de su diferencia es menor que una\n# mil\u00e9sima. Por  ejemplo,\n#    casiIguales(12.3457, 12.3459)  ==  True\n#    casiIguales(12.3457, 12.3479)  ==  False\ndef casiIguales(x: float, y: float) -> bool:\n    return abs(x - y) < 0.001\n\n# La propiedad es\n@given(st.floats(min_value=-100, max_value=100),\n       st.floats(min_value=-100, max_value=100),\n       st.floats(min_value=-100, max_value=100))\ndef test_prop_raices(a, b, c):\n    assume(abs(a) > 0.1)\n    xs = raices(a, b, c)\n    assume(xs)\n    [x1, x2] = xs\n    assert casiIguales(x1 + x2, -b \/ a)\n    assert casiIguales(x1 * x2, c \/ a)\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q raices_de_la_ecuacion_de_segundo_grado.py\n#    1 passed in 0.35s\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n raices :: Double -> Double -> Double -> [Double] tal que (raices a b c) es la lista de las ra\u00edces reales de la ecuaci\u00f3n . Por ejemplo, raices 1 3 2 == [-1.0,-2.0] raices 1 (-2) 1 == [1.0,1.0] raices 1 0 1 == [] Comprobar con QuickCheck que la suma…<\/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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7356"}],"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=7356"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7356\/revisions"}],"predecessor-version":[{"id":7694,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7356\/revisions\/7694"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}