Calculando o valor Numérico do Polinomio de Interpolação de Lagrange no ponto [;x;]:

def Lagrange_Factor(i,xs,x):
    #Calculates Lagrange factor no i (x-x_0) ... (x-x_i-1) (x-x_i+1) ... (x-x_n)
    #i index
    #xs abscissas (list)
    #x abscissa (float)

    product=1.0
    for j in range( len(xs) ):
        if (i!=j): product*=(x-xs[j])
    
    return product

def Lagrange_H(i,xs,x):
    #Calculates value of Lagrange Polynomials no i in point x
    #i index
    #xs abscissas (list)
    #x abscissa (float)
    
    return Lagrange_Factor(i,xs,x)/Lagrange_Factor(i,xs,xs[i])

def Lagrange_Y(xs,ys,x):
    #Calculates value of Lagrange Interpolation Polynomial in point x
    #xs abscissas (list)
    #x abscissa (float)

    sum=0.0
    for i in range( len(xs) ):
        sum+=ys[i]*Lagrange_H(i,xs,x)
        
    return sum