TaylorSeries.py

import sympy as sy
import numpy as np
from sympy.functions import sin,cos
import matplotlib.pyplot as plt
from sympy import E

plt.style.use("ggplot")

# Define the variable and the function to approximate
x = sy.Symbol('x')
f = sin(x)

# Factorial function
def factorial(n):
	if n <= 0:
		return 1
	else:
		return n*factorial(n-1)

# Taylor approximation at x0 of the function 'function'
# Since I'm still having difficulting getting this to work, I can just create individual functions for each equation (since I don't need the whole thing).
#Make sure you create a function estimating the upper bound error

def taylor(function,x0,n,a):
	i = 0
	p = 0
	while i <= n:
		p = p + (function.diff(x,i).subs(x,x0))/(factorial(i))*(x-x0)**i
		i += 1
	# u = (M / factorial(n + 1)) * (x - x0)**(n+1)
	return p
e = E.evalf()
print(taylor(e**x,0.5,5,1))
print("Break")
print(taylor(e**x, 0.05,5,0.1))
print("Break")
print(taylor(e**x,0.005,5,0.01))