Lagrange interpolating polynomials

Here is the Lagrange interpolating polynomial equation:

$L_i(X)=\prod_{j=0\atop j \ne i}^n\frac{(X-a_j)}{(a_i-a_j)}$

$\boxed{P=\sum_{i=0}^nP(a_i)L_i(X)}$

It calculates the polynomial that passes through points given interactively.

And it plots a graph like these ones :

Code :

	from functools import reduce
	from sympy import Symbol
	X = Symbol('X')

	def Lagrange(points):

	P=[reduce((lambda x,y: xy),[(X-points[j][0])/(points[i][0] - points[j][0]) for j in range(len(points)) if i != j])points[i][1] for i in range(len(points))]

	return sum(P)

	print("Enter every points in this format : x y \nStop the list by entering 0")

	p1=0
	points=[]
	while True:
	p1 = [int(x) for x in input("Enter point coord: ").split()]
	if p1 == [0]:
	break
	points+=[p1]
	print(points)
	P=Lagrange(points)
	print("\nLagrange equation :\n")
	print(P)

	import matplotlib.pyplot as plt
	from numpy import arange

	def graph(P,points):
	plt.plot([points[i][0] for i in range(len(points))], [points[i][1] for i in range(len(points))], 'ro')
	plt.title('P(X)=' + str(P))

	xmin=min([points[i][0] for i in range(len(points))])-1
	xmax=max([points[i][0] for i in range(len(points))])+1

	t1 = arange(xmin, xmax, 0.02)

	def f(t):
	t2 = []
	for i in t :
	t2 += [P.subs(X,i)]
	return t2

	plt.plot(t1,f(t1),'r--')
	plt.show()

	graph(P,points)

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