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53 lines
1.7 KiB
Python
53 lines
1.7 KiB
Python
"""
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This is an implementation of logarithmic series in Python.
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Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series
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"""
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def logarithmic_series(x_value: float, n_terms: int = 5, expand: bool = False) -> list:
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"""
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Returns the logarithmic series for a number x (log x) upto n terms.
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Parameters:
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x_value: a floating point number for log(x)
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n_terms: number of terms to be computed
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expand: Set this flag to get the terms as real numbers,
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unset for unsolved expressions
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Examples:
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>>> logarithmic_series(3)
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['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5']
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>>> logarithmic_series(-3)
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['-(4^1)/1', '(4^2)/2', '-(4^3)/3', '(4^4)/4', '-(4^5)/5']
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>>> logarithmic_series(3, 6)
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['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6']
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>>> logarithmic_series(3, expand=True)
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[2.0, -2.0, 2.6666666666666665, -4.0, 6.4]
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"""
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n_times_x_minus_1: float = x_value - 1
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n: int = 1
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series: list = []
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for _ in range(n_terms):
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if expand:
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series.append(((-1) ** (n + 1)) * (n_times_x_minus_1 / n))
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n_times_x_minus_1 *= x_value - 1
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else:
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sign: str = "-" if (-1) ** (n + 1) == -1 else ""
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term: str = sign + "(" + str(x_value - 1) + "^" + str(n) + ")" + "/" + str(n)
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if term.startswith("-(-"):
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term = "(" + term[3::]
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elif term.startswith("(-"):
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term = "-(" + term[2::]
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series.append(term)
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n += 1
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return series
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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