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from typing import Sequence
def evaluate_poly(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial f(x) at specified point x and return the value.
Arguments:
poly -- the coeffiecients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
return sum(c * (x ** i) for i, c in enumerate(poly))
def horner(poly: Sequence[float], x: float) -> float:
"""Evaluate a polynomial at specified point using Horner's method.
In terms of computational complexity, Horner's method is an efficient method
of evaluating a polynomial. It avoids the use of expensive exponentiation,
and instead uses only multiplication and addition to evaluate the polynomial
in O(n), where n is the degree of the polynomial.
https://en.wikipedia.org/wiki/Horner's_method
Arguments:
poly -- the coeffiecients of a polynomial as an iterable in order of
ascending degree
x -- the point at which to evaluate the polynomial
>>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
79800.0
"""
result = 0.0
for coeff in reversed(poly):
result = result * x + coeff
return result
if __name__ == "__main__":
"""
Example:
>>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2
>>> x = -13.0
>>> print(evaluate_poly(poly, x)) # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
180339.9
"""
poly = (0.0, 0.0, 5.0, 9.3, 7.0)
x = 10.0
print(evaluate_poly(poly, x))
print(horner(poly, x))