FilesExpand file tree

master

/

basic_maths.py

Copy path

Blame

More file actions

Blame

More file actions

Latest commit

 

History

History

History

109 lines (98 loc) · 2.67 KB

master

/

basic_maths.py

Copy path

Top

File metadata and controls

• Code
• Blame

109 lines (98 loc) · 2.67 KB

Raw

Copy raw file

Download raw file

Open symbols panel

Edit and raw actions

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

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

import math

def prime_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

"""

if n <= 0:

raise ValueError("Only positive integers have prime factors")

pf = []

while n % 2 == 0:

pf.append(2)

n = int(n / 2)

for i in range(3, int(math.sqrt(n)) + 1, 2):

while n % i == 0:

pf.append(i)

n = int(n / i)

if n > 2:

pf.append(n)

return pf

def number_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

"""

if n <= 0:

raise ValueError("Only positive numbers are accepted")

div = 1

temp = 1

while n % 2 == 0:

temp += 1

n = int(n / 2)

div *= temp

for i in range(3, int(math.sqrt(n)) + 1, 2):

temp = 1

while n % i == 0:

temp += 1

n = int(n / i)

div *= temp

return div

def sum_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

"""

if n <= 0:

raise ValueError("Only positive numbers are accepted")

s = 1

temp = 1

while n % 2 == 0:

temp += 1

n = int(n / 2)

if temp > 1:

s *= (2**temp - 1) / (2 - 1)

for i in range(3, int(math.sqrt(n)) + 1, 2):

temp = 1

while n % i == 0:

temp += 1

n = int(n / i)

if temp > 1:

s *= (i**temp - 1) / (i - 1)

return int(s)

def euler_phi(n: int) -> int:

"""Calculate Euler's Phi Function.

>>> euler_phi(100)

40

"""

s = n

for x in set(prime_factors(n)):

s *= (x - 1) / x

return int(s)

if __name__ == "__main__":

import doctest

doctest.testmod()