Function to convert a number to any base leq to 10

from math import log, floor

def to_base(num, base):
    if num == 0:
        return '0'
    largest_power = floor(log(num, base))
    current_power = largest_power
    digits = []
    while current_power >= 0:
        base_to_power = base ** current_power  # Used in multiple calculations. this makes it simpler.

# For each number that we could have to multiply by at this power, going down and including zero:
        for scalar in range(base - 1, -1, -1):
            if num >= scalar * base_to_power:
                digits.append(str(scalar))  # Append a string version of the scalar.
                num = num - scalar * base_to_power
                break  # Break out of the loop when we find the biggest number that works.
                # This loop includes zero, and the number is always >= 0 * base_to_power.
        current_power = current_power - 1
    return ''.join(digits)

to_trinary = lambda x: to_base(x, 3)

def test():
    for base in range(2, 11):
        for num in range(0, 10):
            assert (num == int(to_base(num, base), base))

test()

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