bidule<\/em>.<\/p>\n\n\n\nAinsi, si je souhaite afficher lisiblement mon objet, je dois formater cet affichage.<\/p>\n\n\n\n
def __str__(self):\n c, r = self.simp()[0], self.simp()[1]\n if r == 1:\n return c.__str__()\n elif c == 1:\n return f'\u221a({self.simp()[1]})'\n else:\n return f'({c})\u221a({r})'<\/pre>\n\n\n\n\u00c0 ce stade de l’impl\u00e9mentation, on a:<\/p>\n\n\n\n
>>> a = Rc(1,150)\n>>> print( a )\n(5)\u221a(6)<\/code><\/pre>\n\n\n\nL\u2019apparence du r\u00e9sultat est un choix artistique personnel… Libre \u00e0 vous de l’adapter \u00e0 votre convenance. Il m’a juste paru plus clair de mettre les nombres entre parenth\u00e8ses dans le cas o\u00f9 on manipulerait des fractions:<\/p>\n\n\n\n
>>> a = Rc(1,Fraction(150,9072))\n>>> print( a )\n(5\/6)\u221a(1\/42)<\/code><\/pre>\n\n\n\n<\/p>\n\n\n\n
On peut alors bien lire:$$\\sqrt{\\frac{150}{9072}}=\\frac{5}{6}\\sqrt{\\frac{1}{42}}.$$<\/p>\n\n\n\n
<\/span>Une alternative<\/span><\/h4>\n\n\n\nSi ce formatage ne vous convient pas, ce que je peux ais\u00e9ment concevoir, et si vous pr\u00e9f\u00e9rez le formatage conventionnel \\(k\\sqrt{n}\\), on peut utiliser la m\u00e9thode l\u00e9g\u00e8rement modifi\u00e9e:<\/p>\n\n\n\n
def __str__(self):\n c, r = self.simp()[0], self.simp()[1]\n \n if r.denominator != 1:\n c, r = Fraction(c.numerator,c.denominator*r.denominator), Fraction(r.denominator,1)\n \n if r == 1:\n return c.__str__()\n elif c == 1:\n return f'\u221a({self.simp()[1]})'\n else:\n return f'({c})\u221a({r})'<\/pre>\n\n\n\n>>> a = Rc(1,Fraction(150,9072))\n>>> print(a)\n(5\/252)\u221a(42)<\/code><\/pre>\n\n\n\nIl est vrai que l’on pr\u00e9f\u00e8re \u00e9crire les r\u00e9sultats de sorte qu’il n’y ait pas de radical au d\u00e9nominateur d’une fraction!<\/p>\n\n\n\n
<\/span>M\u00e9thode de multiplication<\/span><\/h3>\n\n\n\n def __mul__(self, other):\n c,r = other.coef, other.radicand\n return Rc( self.coef * c , self.radicand * r)<\/pre>\n\n\n\n>>> a, b = Rc(1,150), Rc(1,9072)\n>>> print( a*b )\n(180)\u221a(42)<\/code><\/pre>\n\n\n\nLe produit est ici consid\u00e9r\u00e9 comme une racine carr\u00e9e, donc comme un objet de la m\u00eame nature que ceux qui sont multipli\u00e9s entre eux.<\/p>\n\n\n\n
<\/span>La m\u00e9thode de soustraction<\/span><\/h3>\n\n\n\n def __sub__(self, other):\n return self.__add__(Rc(-other.coef,other.radicand))<\/pre>\n\n\n\nRien de plus simple quand on sait qu’une diff\u00e9rence n’est qu’une somme dans le corps des nombres r\u00e9els…<\/p>\n\n\n\n
<\/span>La m\u00e9thode de division<\/span><\/h3>\n\n\n\n def __truediv__(self, other):\n return self.__mul__( Rc(1\/other.coef,1\/other.radicand) )<\/pre>\n\n\n\nRien de plus simple quand on sait qu’une division n’est qu’une multiplication dans le corps des nombres r\u00e9els…<\/p>\n\n\n\n
<\/span>La m\u00e9thode d’exponentiation<\/span><\/h3>\n\n\n\n def __pow__(self,n):\n r = Rc(1,1)\n for _ in range(n):\n r *= self\n \n return r<\/pre>\n\n\n\nRien de plus simple quand on sait que l’exponentiation est une suite de multiplications \ud83d\ude42<\/p>\n\n\n\n
>>> a = Rc(1,150)\n>>> print( a**6 )\n3375000\n>>> print( a**7 )\n(16875000)\u221a(6)<\/code><\/pre>\n\n\n\n<\/span>L’impl\u00e9mentation compl\u00e8te<\/span><\/h2>\n\n\n\nAllez, c’est cadeau mon coco, voici le tout:<\/p>\n\n\n\n
from fractions import Fraction\n\ndef decomp(n):\n D = dict() # dictionnaire vide\n \n k = 2\n \n while n > 1:\n exposant = 0\n while n%k == 0:\n exposant = exposant + 1\n n = n\/k\n if exposant != 0:\n D[k] = exposant\n k = k+1\n j = 2\n while k%j == 0:\n k = k + 1 \n \n return D\n\nclass Rc:\n def __init__(self,a,b):\n self.coef = Fraction(a)\n self.radicand = Fraction(b)\n \n def simp(self):\n x = self.radicand\n numer = decomp(x.numerator)\n denom = decomp(x.denominator)\n coef_num, radicand_num = 1, 1\n for facteur, exposant in numer.items():\n coef_num *= facteur**(exposant\/\/2)\n if exposant%2 == 1:\n radicand_num *= facteur\n \n coef_denom, radicand_denom = 1, 1\n for facteur, exposant in denom.items():\n coef_denom *= facteur**(exposant\/\/2)\n if exposant%2 == 1:\n radicand_denom *= facteur\n \n return Fraction(coef_num,coef_denom)*self.coef, Fraction(radicand_num,radicand_denom)\n \n def __str__(self):\n c, r = self.simp()[0], self.simp()[1]\n \n if r.denominator != 1:\n c, r = Fraction(c.numerator,c.denominator*r.denominator), Fraction(r.denominator,1)\n \n if r == 1:\n return c.__str__()\n elif c == 1:\n return f'\u221a({self.simp()[1]})'\n else:\n return f'({c})\u221a({r})'\n \n def __mul__(self, other):\n c,r = other.coef, other.radicand\n return Rc( self.coef * c , self.radicand * r)#.__str__()\n \n def __add__(self, other):\n c,r = other.coef, other.radicand\n s1, s2 = self.simp(), Rc(c,r).simp()\n if s1[1] == s2[1]:\n result = Rc(s1[0]+s2[0] , s1[1])\n return result.__str__()\n else:\n return self.__str__() + ' + ' + other.__str__()\n \n def __sub__(self, other):\n return self.__add__(Rc(-other.coef,other.radicand))\n \n def __truediv__(self, other):\n return self.__mul__( Rc(1\/other.coef,1\/other.radicand) )\n \n def __pow__(self,n):\n r = Rc(1,1)\n for _ in range(n):\n r *= self\n \n return r<\/pre>\n","protected":false},"excerpt":{"rendered":"Simplifier une racine carr\u00e9e en Python peut s’av\u00e9rer un peu compliqu\u00e9. C’est pourquoi j’ai cr\u00e9\u00e9 une classe pour cela.<\/p>\n","protected":false},"author":1,"featured_media":9347,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[125,403,222],"class_list":["post-9342","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","tag-decomposistion","tag-facteurs-premiers","tag-racines-carrees"],"yoast_head":"\n
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