'''

KIT103 Assignment 4: Fun with Numbers

Submission script

Name: Genemo Muhammed

ID: 539650

Enter your answers to each question below by completing each

function. After answering a question run this script and test

your implementation in the IPython console.

'''

sid = '539650' #Replace this with your student ID as a string

#%% Question 5: GCD from a prime factorisations

from collections import Counter

def prime_factor_gcd(a, b):

'''Returns gcd(a, b), calculated from their prime factorisations.'''

factors_a = Counter(factor_list(a))

factors_b = Counter(factor_list(b))

exp = factors_a & factors_b

gcd = 1

for p in exp:

gcd *= p ** exp[p]

return gcd

#%% Question 6: convert_base

import string

digits = string.digits + string.ascii_uppercase

# Q6a: Record your FOUR test cases here. Remember to replace the example one provided.

convert_base_test_cases = [

('42', 10, 10, '42'), # For each test case briefly explain why you chose it/what it's testing

(None, None, None, None), # Explanation...

(None, None, None, None), # Explanation...

(None, None, None, None) # Explanation...

]

# Q6b: Implement your solution

#Declare any additional helper function here

def convert_base(n, b1, b2):

'''

Converts n, a string representing a number in base b1, to a

string representing the same value in base b2. 2 <= b1, b2 <= 36.

'''

return None

#%% Question 7: Vigenere Cipher

from string import ascii_uppercase

ALPHABET = ascii_uppercase + ' '

'''

Q7a: Test cases

Briefly describe the test cases and why you chose them:

'''

encryption_tests = [

('', '', ALPHABET, ''), #use this structure

('', '', ALPHABET, ''), #replace ALPHABET if using different sequence of symbols

]

decryption_tests = [ #add test cases

]

def to_numbers(text, symbols=ALPHABET):

'''Returns a list of the positions of characters from ``text`` in ``symbols``.'''

return [ symbols.index(a) for a in text if a in symbols ]

def to_text(indices, symbols=ALPHABET):

'''Returns a string using the given ``indices`` into ``symbols``.'''

return ''.join(symbols[n] for n in indices)

def vencrypt(message, key, symbols=ALPHABET):

'''

Encrypts the ``message`` using a Vigenere cipher with the given ``key``.

Ignores any character not in ``symbols``.

'''

cipher = to_numbers(message, symbols)

shifts = to_numbers(key, symbols)

for i in range(len(cipher)):

cipher[i] = cipher[i] #<-- Q7b: You must replace this with the encryption expression

return to_text(cipher, symbols)

def vdecrypt(ciphertext, key, symbols=ALPHABET):

'''

Decrypts the ``ciphertext`` using a Vigenere cipher with the given ``key``.

'''

#Q7c: Implement this function

return None

# End of answers

#%% Provided functions for Question 5

from math import floor, sqrt

def primes(n):

'''Returns the set of primes between 2 and n, inclusive.'''

primes = set(range(2, n+1))

for k in range(2, floor(sqrt(n))+1):

if k in primes:

primes.difference_update(range(k**2, n+1, k))

return primes

def primes_list(n):

'''Returns a sorted list of primes between 2 and n, inclusive.'''

return sorted(primes(n))

def factors_for(n):

'''Returns the list of prime factors of n.'''

factors = []

iprimes = iter(primes_list(n))

while n > 1:

p = next(iprimes)

while n % p == 0:

n = n // p

factors.append(p)

return factors

# End of provided functions