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123 lines
3.0 KiB
Python
123 lines
3.0 KiB
Python
"""Implementation of Basic Math in Python."""
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import math
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def prime_factors(n: int) -> list:
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"""Find Prime Factors.
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>>> prime_factors(100)
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[2, 2, 5, 5]
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>>> prime_factors(0)
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Traceback (most recent call last):
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...
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ValueError: Only positive integers have prime factors
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>>> prime_factors(-10)
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Traceback (most recent call last):
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...
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ValueError: Only positive integers have prime factors
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"""
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if n <= 0:
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raise ValueError("Only positive integers have prime factors")
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pf = []
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while n % 2 == 0:
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pf.append(2)
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n = int(n / 2)
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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while n % i == 0:
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pf.append(i)
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n = int(n / i)
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if n > 2:
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pf.append(n)
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return pf
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def number_of_divisors(n: int) -> int:
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"""Calculate Number of Divisors of an Integer.
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>>> number_of_divisors(100)
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9
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>>> number_of_divisors(0)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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>>> number_of_divisors(-10)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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"""
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if n <= 0:
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raise ValueError("Only positive numbers are accepted")
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div = 1
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temp = 1
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while n % 2 == 0:
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temp += 1
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n = int(n / 2)
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div *= temp
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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temp = 1
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while n % i == 0:
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temp += 1
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n = int(n / i)
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div *= temp
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if n > 1:
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div *= 2
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return div
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def sum_of_divisors(n: int) -> int:
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"""Calculate Sum of Divisors.
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>>> sum_of_divisors(100)
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217
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>>> sum_of_divisors(0)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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>>> sum_of_divisors(-10)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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"""
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if n <= 0:
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raise ValueError("Only positive numbers are accepted")
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s = 1
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temp = 1
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while n % 2 == 0:
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temp += 1
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n = int(n / 2)
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if temp > 1:
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s *= (2**temp - 1) / (2 - 1)
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for i in range(3, int(math.sqrt(n)) + 1, 2):
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temp = 1
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while n % i == 0:
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temp += 1
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n = int(n / i)
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if temp > 1:
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s *= (i**temp - 1) / (i - 1)
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return int(s)
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def euler_phi(n: int) -> int:
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"""Calculate Euler's Phi Function.
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>>> euler_phi(100)
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40
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>>> euler_phi(0)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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>>> euler_phi(-10)
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Traceback (most recent call last):
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...
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ValueError: Only positive numbers are accepted
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"""
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if n <= 0:
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raise ValueError("Only positive numbers are accepted")
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s = n
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for x in set(prime_factors(n)):
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s *= (x - 1) / x
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return int(s)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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