 # Lagrange interpolating polynomials

Here is the Lagrange interpolating polynomial equation:  You can find a python code hosted in GitHub here: https://github.com/Eddy-Barraud/Lagrange-interpolating-polynomials

It calculates the polynomial that passes through points given interactively.

And it plots a graph like these ones :

Code :

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 from functools import reduce from sympy import Symbol X = Symbol('X') def Lagrange(points): P=[reduce((lambda x,y: x*y),[(X-points[j])/(points[i] - points[j]) for j in range(len(points)) if i != j])*points[i] 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 == : 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] for i in range(len(points))], [points[i] for i in range(len(points))], 'ro') plt.title('P(X)=' + str(P)) xmin=min([points[i] for i in range(len(points))])-1 xmax=max([points[i] 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)