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55 lines
1.9 KiB
Python
55 lines
1.9 KiB
Python
# Imports de bibliothèques standard
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from math import factorial
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# Imports de bibliothèques tierces
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import pytest
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from numpy.polynomial import Polynomial
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def compute_legendre_polynomial_coefficients(n: int) -> [float]:
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"""
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Compute the coefficients of the nth Legendre polynomial.
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The Legendre polynomials are solutions to Legendre's differential equation
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and are widely used in physics and engineering.
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Parameters:
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n (int): The order of the Legendre polynomial.
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Returns:
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list[float]: Coefficients of the polynomial in ascending order of powers.
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"""
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legendre_polynomial = (1 / (factorial(n) * (2**n))) * (Polynomial([-1, 0, 1]) ** n)
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return legendre_polynomial.deriv(n).coef.tolist()
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def test_legendre_polynomial_degree_0() -> None:
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"""Test the 0th Legendre polynomial."""
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assert compute_legendre_polynomial_coefficients(0) == [1.0], "The 0th Legendre polynomial should be [1.0]"
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def test_legendre_polynomial_degree_1() -> None:
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"""Test the 1st Legendre polynomial."""
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assert compute_legendre_polynomial_coefficients(1) == [0.0, 1.0], "The 1st Legendre polynomial should be [0.0, 1.0]"
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def test_legendre_polynomial_degree_2() -> None:
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"""Test the 2nd Legendre polynomial."""
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assert compute_legendre_polynomial_coefficients(2) == [-0.5, 0.0, 1.5],
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"The 2nd Legendre polynomial should be [-0.5, 0.0, 1.5]"
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def test_legendre_polynomial_degree_3() -> None:
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"""Test the 3rd Legendre polynomial."""
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assert compute_legendre_polynomial_coefficients(3) == [0.0, -1.5, 0.0, 2.5], "The 3rd Legendre polynomial should be [0.0, -1.5, 0.0, 2.5]"
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def test_legendre_polynomial_degree_4() -> None:
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"""Test the 4th Legendre polynomial."""
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assert compute_legendre_polynomial_coefficients(4) == pytest.approx([0.375, 0.0, -3.75, 0.0, 4.375])
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"The 4th Legendre polynomial should be [0.375, 0.0, -3.75, 0.0, 4.375]"
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if __name__ == "__main__":
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pytest.main()
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