import numpy as np
import matplotlib.pyplot as plt
import scipy as sp

def horner(P,x):
    """ P liste des coefficients par degre croissant (P[i]x**i est le polynome)"""
    n = len(P)-1
    v = P[n]
    for i in range(n-1,-1,-1):
        v = P[i] + x*v
    return v

def vaexp(x,n):
    v = 1
    for i in range(n,0,-1):
        v = 1 + v*x/i
    return(v)

def Euclide(a,b):
    a , b = max((a,b)) , min((a,b))
    if b == 0 :
        return a
    else :
        return(Euclide(b,a%b))