Python/maths/mobius_function.py

44 lines
977 B
Python
Raw Normal View History

"""
References: https://en.wikipedia.org/wiki/M%C3%B6bius_function
References: wikipedia:square free number
python/black : True
flake8 : True
"""
from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors
def mobius(n: int) -> int:
"""
Mobius function
>>> mobius(24)
0
>>> mobius(-1)
1
>>> mobius('asd')
Traceback (most recent call last):
...
TypeError: '<=' not supported between instances of 'int' and 'str'
>>> mobius(10**400)
0
>>> mobius(10**-400)
1
>>> mobius(-1424)
1
>>> mobius([1, '2', 2.0])
Traceback (most recent call last):
...
TypeError: '<=' not supported between instances of 'int' and 'list'
"""
factors = prime_factors(n)
if is_square_free(factors):
return -1 if len(factors) % 2 else 1
return 0
if __name__ == "__main__":
import doctest
doctest.testmod()