Python/maths/basic_maths.py at master · imanghotbi-python/Python · GitHub

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"""Implementation of Basic Math in Python."""
importmath


defprime_factors(n: int) ->list:
"""Find Prime Factors.
 >>> prime_factors(100)
 [2, 2, 5, 5]
 >>> prime_factors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 >>> prime_factors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive integers have prime factors
 """
ifn<=0:
raiseValueError("Only positive integers have prime factors")
pf= []
whilen%2==0:
pf.append(2)
n=int(n/2)
foriinrange(3, int(math.sqrt(n)) +1, 2):
whilen%i==0:
pf.append(i)
n=int(n/i)
ifn>2:
pf.append(n)
returnpf


defnumber_of_divisors(n: int) ->int:
"""Calculate Number of Divisors of an Integer.
 >>> number_of_divisors(100)
 9
 >>> number_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> number_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
ifn<=0:
raiseValueError("Only positive numbers are accepted")
div=1
temp=1
whilen%2==0:
temp+=1
n=int(n/2)
div*=temp
foriinrange(3, int(math.sqrt(n)) +1, 2):
temp=1
whilen%i==0:
temp+=1
n=int(n/i)
div*=temp
ifn>1:
div*=2
returndiv


defsum_of_divisors(n: int) ->int:
"""Calculate Sum of Divisors.
 >>> sum_of_divisors(100)
 217
 >>> sum_of_divisors(0)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 >>> sum_of_divisors(-10)
 Traceback (most recent call last):
 ...
 ValueError: Only positive numbers are accepted
 """
ifn<=0:
raiseValueError("Only positive numbers are accepted")
s=1
temp=1
whilen%2==0:
temp+=1
n=int(n/2)
iftemp>1:
s*= (2**temp-1) / (2-1)
foriinrange(3, int(math.sqrt(n)) +1, 2):
temp=1
whilen%i==0:
temp+=1
n=int(n/i)
iftemp>1:
s*= (i**temp-1) / (i-1)
returnint(s)


defeuler_phi(n: int) ->int:
"""Calculate Euler's Phi Function.
 >>> euler_phi(100)
 40
 """
s=n
forxinset(prime_factors(n)):
s*= (x-1) /x
returnint(s)


if__name__=="__main__":
importdoctest

doctest.testmod()