Polynomial parser and calculator using Horner's rule

polynomial.py

import re

from collections import namedtuple

def split_equation(equation):
	match = re.match(r'^\s*\w+\((\w+)\)\s*=\s*(.*)$', equation)
	return match.groups()


def find_terms(equation, var='x'):
	pattern = re.compile(r'(-?\s*\d+)?' 			 # coefficient
						 r'\s*\*?\s*(' + var + r')'	 # variable
						 r'(?:\s*\^\s*\(?(\d+)\)?)?' # exponent
						 r'|(-?\s*\d+)')			 # constant

	Term = namedtuple('Term', ['coef', 'exp'])
	terms = []

	match = pattern.search(equation)
	while match:
		coef, var, exp, const = match.groups()
		coef = coef if coef else const if const else '1'
		exp = int(exp) if exp else 1 if var else 0
		terms.append(Term(float(coef.replace(' ', '')), int(exp)))
		match = pattern.search(equation, match.end())
	return terms

def calculate(equation, value):
	var, polynomial = split_equation(equation)
	terms = find_terms(polynomial, var)
	if not terms:
		raise RuntimeError("Equation is ill-formed!")
	terms.sort(key=lambda t: t.exp)
	y = 0
	n = max(terms, key=lambda t: t.exp).exp
	j = len(terms) - 1
	for i in range(n, -1, -1):
		if j >= 0 and terms[j].exp == i:
			y = float(terms[j].coef) + value * y
			j -= 1
		else:
			y *= value
	return y

def main():
	equation = "f(t) = 5t^2 + 3 t^10 - 5 * t + 2"
	result = calculate(equation, 2)
	print(result)

if __name__ == '__main__':
	main()