mathdatech/Python
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/Python.git synced 2025-04-25 15:13:38 +00:00
Code Issues Packages Projects Releases Wiki Activity

[pre-commit.ci] auto fixes from pre-commit.com hooks

Browse Source 
for more information, see https://pre-commit.ci
This commit is contained in:
pre-commit-ci[bot] 2024-10-23 19:44:15 +00:00
parent 25c5430b47
commit 273ee447bf
1 changed files with 19 additions and 16 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

35
maths/series/logarithmic_series.py
View File

@ -3,47 +3,50 @@ This is an implementation of logarithmic series in Python.
Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series Reference: https://math.stackexchange.com/questions/3973429/what-is-a-logarithmic-series
""" """
def logarithmic_series(x: float, n_terms: int = 5, expand: bool = False) -> list: def logarithmic_series(x: float, n_terms: int = 5, expand: bool = False) -> list:
""" """
Returns the logarithmic series for a number x (log x) upto n terms. Returns the logarithmic series for a number x (log x) upto n terms.
Parameters: Parameters:
x: a floating point number for log(x) x: a floating point number for log(x)
n_terms: number of terms to be computed n_terms: number of terms to be computed
expand: Set this flag to get the terms as real numbers, expand: Set this flag to get the terms as real numbers,
unset for unsolved expressions unset for unsolved expressions
Examples: Examples:
>>> logarithmic_series(3) >>> logarithmic_series(3)
['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5'] ['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5']
>>> logarithmic_series(-3) >>> logarithmic_series(-3)
['-(4^1)/1', '(4^2)/2', '-(4^3)/3', '(4^4)/4', '-(4^5)/5'] ['-(4^1)/1', '(4^2)/2', '-(4^3)/3', '(4^4)/4', '-(4^5)/5']
>>> logarithmic_series(3, 6) >>> logarithmic_series(3, 6)
['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6'] ['(2^1)/1', '-(2^2)/2', '(2^3)/3', '-(2^4)/4', '(2^5)/5', '-(2^6)/6']
>>> logarithmic_series(3, expand=True) >>> logarithmic_series(3, expand=True)
[2.0, -2.0, 2.6666666666666665, -4.0, 6.4] [2.0, -2.0, 2.6666666666666665, -4.0, 6.4]
""" """
n_times_x_minus_1: float = x-1 n_times_x_minus_1: float = x - 1
n: int = 1 n: int = 1
series: list = [] series: list = []
for _ in range(n_terms): for _ in range(n_terms):
if (expand): if expand:
series.append(((-1)**(n+1))*(n_times_x_minus_1/n)) series.append(((-1) ** (n + 1)) * (n_times_x_minus_1 / n))
n_times_x_minus_1 *= (x-1) n_times_x_minus_1 *= x - 1
else: else:
sign: str = '-' if (-1)**(n+1) == -1 else '' sign: str = "-" if (-1) ** (n + 1) == -1 else ""
term: str = sign+'('+str(x-1)+'^'+str(n)+')'+'/'+str(n) term: str = sign + "(" + str(x - 1) + "^" + str(n) + ")" + "/" + str(n)
if (term.startswith("-(-")): if term.startswith("-(-"):
term = '('+term[3::] term = "(" + term[3::]
elif (term.startswith("(-")): elif term.startswith("(-"):
term = "-("+term[2::] term = "-(" + term[2::]
series.append(term) series.append(term)
n += 1 n += 1
return series return series
if (__name__ == "__main__"):
if __name__ == "__main__":
import doctest import doctest
doctest.testmod() doctest.testmod()