from pylab import *

a = 0
b = 8
m = (a+b)/2

x = linspace(a, b, 101)

l0 = (x-m)/(a-m)*(x-b)/(a-b)
l1 = (x-a)/(m-a)*(x-b)/(m-b)
l2 = (x-a)/(b-a)*(x-m)/(b-m)

plot([a,m,b],zeros(3),"s") # position des valeurs 0
plot([a,m,b],ones(3), "o")  # position des valeurs 1
plot(x,l0, label="l0")
plot(x,l1, label="l1")
plot(x,l2, label="l2")

title("Polynomes de Lagrange")
xlim(-1,9)
ylim(-1,2)
text(a,-0.1,"(a,0)",ha="center",va="top")
text(m,-0.1,"(m,0)",ha="center",va="top")
text(b,-0.1,"(b,0)",ha="center",va="top")
text(a,1.05,"(a,1)",ha="center",va="bottom")
text(m,1.05,"(m,1)",ha="center",va="bottom")
text(b,1.05,"(b,1)",ha="center",va="bottom")
legend()
grid()

show()