Solving roots of negative numbers
As part of an assignment for college summer classes, I was tasked with writing a program that solves roots of negative numbers. I've ran it through the test cases I was provided and it computes correctly. I'm looking for any feedback, especially about the determine_factors function, which really should be renamed. It looks messy and I don't like it, but it's all I could come up with. I'll be tweaking it since it's not due for a while, but I wanted to get some experienced eyes on this.
"""
Helper tool for solving negative square roots.
@author Ben Antonellis
@date 06-08-2020
"""
from math import isqrt
from typing import List, Union, Tuple
def is_perfect(number: int) -> bool:
"""
Returns if a number is a perfect square.
"""
return number == isqrt(number) ** 2
def get_factors(number: int) -> List[List[int]]:
"""
Returns all the factors of a number.
"""
factors = [[x, number // x] for x in range(2, number + 1) if number % x == 0]
factors = factors[:len(factors) // 2] # Removes duplicates and any [1, x] pairs #
return factors
def determine_factors(factors: List[int], num: int) -> str:
"""
Determines what factors are left at the end of calculation.
"""
simplified, remainder = 0, 0
for number, times_in_number in factors:
if number == times_in_number:
return f"{number}i"
if get_factors(number) == [] and get_factors(times_in_number) == []:
return f"√({num})i"
if is_perfect(number):
simplified += isqrt(number)
if not is_perfect(times_in_number):
if get_factors(times_in_number) == [] or not any(is_perfect(x) or is_perfect(y) for [x, y] in get_factors(times_in_number)):
remainder += times_in_number
return f"{simplified}√({remainder})i"
elif is_perfect(times_in_number):
simplified += isqrt(times_in_number)
if not is_perfect(number):
if get_factors(number) == []:
remainder += number
return f"{simplified}√({remainder})i"
if not any(is_perfect(number) or is_perfect(times_in_number) for number, times_in_number in factors):
return f"√({num})i"
def solve(num: int) -> str:
"""
Solves a negative square root with the passed number.
"""
num = abs(num)
# Check for prime numbers #
if not any(num % i == 0 for i in range(2, num)):
return f"√({num})i"
# Find all factors #
factors = get_factors(num)
# Determine what factors to use and weed out perfect numbers #
return determine_factors(factors, num)
def main():
num = int(input("Enter negative inside square root: "))
result = solve(num)
print(result)
if __name__ == "__main__":
main()
Test cases are below
Input -> Output
---------------
-52 -> 2√(13)i
-20 -> 2√(5)i
-35 -> √(35)i
-36 -> 6i
-30 -> √(30)i
-18 -> 3√(2)i
-70 -> √(70)i
-90 -> 3√(10)i
-100 -> 10i
lang-py