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Aditya Balotra
df4a6528c5
* Add binomial_expansion function building on binomial_coefficient - Computes (a + b)^n for both positive and negative integer exponents - Uses existing binomial_coefficient function for term computation - Raises ZeroDivisionError when base is 0 and exponent is negative - Includes doctests and example cases * add URL
56 lines
1.4 KiB
Python
56 lines
1.4 KiB
Python
from maths.binomial_coefficient import binomial_coefficient
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def binomial_expansion(a: float, b: float, n: int) -> int | float:
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"""
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Compute the value of (a + b)^n using the Binomial Theorem.
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This function works for both positive and negative integer exponents.
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It raises a ZeroDivisionError if the base (a + b) is 0 and n is negative.
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Args:
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a: First term (int or float).
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b: Second term (int or float).
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n: Exponent (must be integer).
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Returns:
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The result of the binomial expansion (a + b)^n.
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Raises:
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ZeroDivisionError: If a + b == 0 and n < 0.
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See Also:
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https://en.wikipedia.org/wiki/Binomial_theorem
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Examples:
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>>> binomial_expansion(2, 3, 2)
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25
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>>> binomial_expansion(100, -4, 3)
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884736
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>>> binomial_expansion(2, 2, -2)
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0.0625
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>>> binomial_expansion(0, 0, 3)
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0
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>>> binomial_expansion(-2, 2, -1)
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Traceback (most recent call last):
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...
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ZeroDivisionError: Cannot raise 0 to the negative power
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"""
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total = a + b
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if total == 0 and n < 0:
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raise ZeroDivisionError("Cannot raise 0 to the negative power")
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abs_n = abs(n)
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value = sum(
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binomial_coefficient(abs_n, i) * (a ** (abs_n - i)) * (b**i)
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for i in range(abs_n + 1)
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)
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return value if n >= 0 else 1 / value
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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