# -*- coding:utf-8 -*-

__projet__ = "CoursS5"
__nom_fichier__ = "14_equation"
__author__ = "A-J. Tinet"
__date__ = "décembre 2022"

"""
========================================================================================================================

                                         Ex. 14 - RESOLUTION D'UNE EQUATION ALGEBRIQUE

========================================================================================================================
"""

# Définition de fonctions
def resolution(equation, x0, epsilon = 0.0000001):
    """
    :param equation: Coefficients de l'équation sous la forme d'une liste
    :param x0: Solution initiale
    :param epsilon: Précision
    :return: Solution approchée
    """

    xsol = x0
    x0 = xsol + 2*epsilon

    while abs(x0 - xsol) > epsilon:

        x0 = xsol
        xsol = 0
        for i in range(len(equation)):
            xsol -= equation[i]*(x0**i)

        xsol = xsol**(1/len(equation))

    return xsol

if __name__ == '__main__':
    equation = [0,0,3,0,-10]
    sol = resolution(equation,2)

    test = 0
    for i in range(len(equation)):
        test += equation[i] * sol**i

    test += sol**len(equation)

    print(sol, test)