from pylab import *

a = 0
b = 8
m = (a+b)/2
# valeurs de la fonction en a, m, et b
ya = 4
ym = 8
yb = -6

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)
P = ya*l0 + ym*l1 + yb*l2

plot([a,m,b],zeros(3),"s") # position des valeurs 0
plot([a,m,b],[ya,ym,yb], "o")  # position des valeurs de f
plot(x,P)

title("Interpolation de Lagrange")
xlim(-1,9)
ylim(-8,10)
text(a,-0.5,"(a,0)",ha="center",va="top")
text(m,-0.5,"(m,0)",ha="center",va="top")
text(b,-0.5,"(b,0)",ha="center",va="top")
text(a,ya+0.05,"(a,f(a))",ha="right",va="bottom")
text(m,ym+0.2,"(m,f(m))",ha="left",va="bottom")
text(b,yb-0.4,"(b,f(b))",ha="left",va="top")
grid()

show()