Math, in arbitrary bases! Even irrational ones!

arbitary_base.py

import re
from math import log, ceil

DIGITS = '0123456789abcdefghijklmnopqrtstuvwxyz'
    
def to_number(
    base,
    string_or_digits,
    decimal_digits=None,
    assert_base=True,
):
    '''
    Turn a string into a number using this base.

    If assert_base is True, verifies that digits are below the base.
    '''
    if isinstance(string_or_digits, str):
        a = string_or_digits.lower()
        if '.' in a:
            a, b = a.split('.', 1)
        else:
            b = ''
        digits = [DIGITS.index(c) for c in a[::-1]]
        decimal_digits = [DIGITS.index(c) for c in b]
    else:
        digits = string_or_digits
        decimal_digits = decimal_digits or []

    if assert_base:
        for d in digits[::-1] + decimal_digits:
            if d >= abs(base):
                raise ValueError(f'Cannot have digit {d} with base {base}.')

    value = 0
    for i, d in enumerate(digits):
        value += d * base ** i
    for i, d in enumerate(decimal_digits):
        value += d * base ** (-i-1)
    return value

def to_digits(base, number, delta=1e-10):
    if number == 0:
        return [0], []
    pos_digits = ceil(log(number, base))
    digits = []
    i = pos_digits - 1

    # this avoids trailing .9999 or equivalent
    if number > 1:
        number += delta
        
    while number > delta:
        digit = int(number // (base ** i))
        digits.append(digit)
        number -= digit * base ** i
        i -= 1    

    return digits[:pos_digits][::-1], digits[pos_digits:]

def digits_to_string(digits, decimal_digits=None):
    string = ''.join(DIGITS[i] for i in digits[::-1])
    if decimal_digits:
        string += '.' + ''.join(DIGITS[i] for i in decimal_digits)
    return string

def to_string(base, number):
    return digits_to_string(*to_digits(base, number))

if __name__ == '__main__':
    def print_integers(N, base):
        print(f'Integers in base {base}:')
        for i in range(1, N+1):
            d = to_string(base, i)
            print(f'{i:>5} {d}')

    phi = (1 + 5**0.5)/2
    from math import pi

    print_integers(20, phi)
    print_integers(20, pi)