maths.primelib

Created on Thu Oct 5 16:44:23 2017

@author: Christian Bender

This Python library contains some useful functions to deal with prime numbers and whole numbers.

Overview:

is_prime(number) sieve_er(N) get_prime_numbers(N) prime_factorization(number) greatest_prime_factor(number) smallest_prime_factor(number) get_prime(n) get_primes_between(pNumber1, pNumber2)

---

is_even(number) is_odd(number) kg_v(number1, number2) // least common multiple get_divisors(number) // all divisors of ‘number’ inclusive 1, number is_perfect_number(number)

NEW-FUNCTIONS

simplify_fraction(numerator, denominator) factorial (n) // n! fib (n) // calculate the n-th fibonacci term.

---

goldbach(number) // Goldbach’s assumption

Functions

factorial(n)	input: positive integer 'n'
fib(→ int)	input: positive integer 'n'
get_divisors(n)	input: positive integer 'n' >= 1
get_prime(n)	Gets the n-th prime number.
get_prime_numbers(n)	input: positive integer 'N' > 2
get_primes_between(p_number_1, p_number_2)	input: prime numbers 'pNumber1' and 'pNumber2'
goldbach(number)	Goldbach's assumption
greatest_prime_factor(number)	input: positive integer 'number' >= 0
is_even(number)	input: integer 'number'
is_odd(number)	input: integer 'number'
is_perfect_number(number)	input: positive integer 'number' > 1
is_prime(→ bool)	input: positive integer 'number'
kg_v(number1, number2)	Least common multiple
prime_factorization(number)	input: positive integer 'number'
sieve_er(n)	input: positive integer 'N' > 2
simplify_fraction(numerator, denominator)	input: two integer 'numerator' and 'denominator'
smallest_prime_factor(number)	input: integer 'number' >= 0

Module Contents

maths.primelib.factorial(n)

input: positive integer ‘n’ returns the factorial of ‘n’ (n!)

>>> factorial(0)
1
>>> factorial(20)
2432902008176640000
>>> factorial(-1)
Traceback (most recent call last):
    ...
AssertionError: 'n' must been a int and >= 0
>>> factorial("test")
Traceback (most recent call last):
    ...
AssertionError: 'n' must been a int and >= 0

maths.primelib.fib(n: int) → int

input: positive integer ‘n’ returns the n-th fibonacci term , indexing by 0

>>> fib(0)
1
>>> fib(5)
8
>>> fib(20)
10946
>>> fib(99)
354224848179261915075
>>> fib(-1)
Traceback (most recent call last):
...
AssertionError: 'n' must been an int and >= 0
>>> fib("test")
Traceback (most recent call last):
...
AssertionError: 'n' must been an int and >= 0

maths.primelib.get_divisors(n)

input: positive integer ‘n’ >= 1 returns all divisors of n (inclusive 1 and ‘n’)

>>> get_divisors(8)
[1, 2, 4, 8]
>>> get_divisors(824)
[1, 2, 4, 8, 103, 206, 412, 824]
>>> get_divisors(-1)
Traceback (most recent call last):
    ...
AssertionError: 'n' must been int and >= 1
>>> get_divisors("test")
Traceback (most recent call last):
    ...
AssertionError: 'n' must been int and >= 1

maths.primelib.get_prime(n)

Gets the n-th prime number. input: positive integer ‘n’ >= 0 returns the n-th prime number, beginning at index 0

>>> get_prime(0)
2
>>> get_prime(8)
23
>>> get_prime(824)
6337
>>> get_prime(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been a positive int
>>> get_prime("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been a positive int

maths.primelib.get_prime_numbers(n)

input: positive integer ‘N’ > 2 returns a list of prime numbers from 2 up to N (inclusive) This function is more efficient as function ‘sieveEr(…)’

>>> get_prime_numbers(8)
[2, 3, 5, 7]
>>> get_prime_numbers(-1)
Traceback (most recent call last):
    ...
AssertionError: 'N' must been an int and > 2
>>> get_prime_numbers("test")
Traceback (most recent call last):
    ...
AssertionError: 'N' must been an int and > 2

maths.primelib.get_primes_between(p_number_1, p_number_2)

input: prime numbers ‘pNumber1’ and ‘pNumber2’

pNumber1 < pNumber2

returns a list of all prime numbers between ‘pNumber1’ (exclusive)

and ‘pNumber2’ (exclusive)

>>> get_primes_between(3, 67)
[5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61]
>>> get_primes_between(0)
Traceback (most recent call last):
    ...
TypeError: get_primes_between() missing 1 required positional argument: 'p_number_2'
>>> get_primes_between(0, 1)
Traceback (most recent call last):
    ...
AssertionError: The arguments must been prime numbers and 'pNumber1' < 'pNumber2'
>>> get_primes_between(-1, 3)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and positive
>>> get_primes_between("test","test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and positive

maths.primelib.goldbach(number)

Goldbach’s assumption input: a even positive integer ‘number’ > 2 returns a list of two prime numbers whose sum is equal to ‘number’

>>> goldbach(8)
[3, 5]
>>> goldbach(824)
[3, 821]
>>> goldbach(0)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int, even and > 2
>>> goldbach(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int, even and > 2
>>> goldbach("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int, even and > 2

maths.primelib.greatest_prime_factor(number)

input: positive integer ‘number’ >= 0 returns the greatest prime number factor of ‘number’

>>> greatest_prime_factor(0)
0
>>> greatest_prime_factor(8)
2
>>> greatest_prime_factor(287)
41
>>> greatest_prime_factor(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0
>>> greatest_prime_factor("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0

maths.primelib.is_even(number)

input: integer ‘number’ returns true if ‘number’ is even, otherwise false.

>>> is_even(0)
True
>>> is_even(8)
True
>>> is_even(287)
False
>>> is_even(-1)
False
>>> is_even("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int

maths.primelib.is_odd(number)

input: integer ‘number’ returns true if ‘number’ is odd, otherwise false.

>>> is_odd(0)
False
>>> is_odd(8)
False
>>> is_odd(287)
True
>>> is_odd(-1)
True
>>> is_odd("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int

maths.primelib.is_perfect_number(number)

input: positive integer ‘number’ > 1 returns true if ‘number’ is a perfect number otherwise false.

>>> is_perfect_number(28)
True
>>> is_perfect_number(824)
False
>>> is_perfect_number(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 1
>>> is_perfect_number("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 1

maths.primelib.is_prime(number: int) → bool

input: positive integer ‘number’ returns true if ‘number’ is prime otherwise false.

>>> is_prime(3)
True
>>> is_prime(10)
False
>>> is_prime(97)
True
>>> is_prime(9991)
False
>>> is_prime(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and positive
>>> is_prime("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and positive

maths.primelib.kg_v(number1, number2)

Least common multiple input: two positive integer ‘number1’ and ‘number2’ returns the least common multiple of ‘number1’ and ‘number2’

>>> kg_v(8,10)
40
>>> kg_v(824,67)
55208
>>> kg_v(1, 10)
10
>>> kg_v(0)
Traceback (most recent call last):
    ...
TypeError: kg_v() missing 1 required positional argument: 'number2'
>>> kg_v(10,-1)
Traceback (most recent call last):
    ...
AssertionError: 'number1' and 'number2' must been positive integer.
>>> kg_v("test","test2")
Traceback (most recent call last):
    ...
AssertionError: 'number1' and 'number2' must been positive integer.

maths.primelib.prime_factorization(number)

input: positive integer ‘number’ returns a list of the prime number factors of ‘number’

>>> prime_factorization(0)
[0]
>>> prime_factorization(8)
[2, 2, 2]
>>> prime_factorization(287)
[7, 41]
>>> prime_factorization(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0
>>> prime_factorization("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0

maths.primelib.sieve_er(n)

input: positive integer ‘N’ > 2 returns a list of prime numbers from 2 up to N.

This function implements the algorithm called sieve of erathostenes.

>>> sieve_er(8)
[2, 3, 5, 7]
>>> sieve_er(-1)
Traceback (most recent call last):
    ...
AssertionError: 'N' must been an int and > 2
>>> sieve_er("test")
Traceback (most recent call last):
    ...
AssertionError: 'N' must been an int and > 2

maths.primelib.simplify_fraction(numerator, denominator)

input: two integer ‘numerator’ and ‘denominator’ assumes: ‘denominator’ != 0 returns: a tuple with simplify numerator and denominator.

>>> simplify_fraction(10, 20)
(1, 2)
>>> simplify_fraction(10, -1)
(10, -1)
>>> simplify_fraction("test","test")
Traceback (most recent call last):
    ...
AssertionError: The arguments must been from type int and 'denominator' != 0

maths.primelib.smallest_prime_factor(number)

input: integer ‘number’ >= 0 returns the smallest prime number factor of ‘number’

>>> smallest_prime_factor(0)
0
>>> smallest_prime_factor(8)
2
>>> smallest_prime_factor(287)
7
>>> smallest_prime_factor(-1)
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0
>>> smallest_prime_factor("test")
Traceback (most recent call last):
    ...
AssertionError: 'number' must been an int and >= 0