Arabic numbers to Roman numerals and back

Question

I have decided to give python a try and have to start out at the very basics, so I chose this well-represented kata. The code aims to convert Arabic numbers between 1 and 3999 to Roman numerals and back. Here, Roman numerals are 'well-formed', that is, no 'XM' or similar, even though I know they were occasionally used.

I took some of the test values from the publicly available Dive into Python.

I'm very interested in everything you have to say, as from what I've heard Python has quite some guidelines and best practices! Also I'm not sure whether the data structures I use are appropriate/a good choice. But here goes the code:

roman.py

import re


class NumberOutOfRangeError(Exception):
    pass


class InvalidRomanNumeralError(Exception):
    pass


roman_numeral_validator = re.compile(
    '^M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$',
    re.IGNORECASE
)


base_conversions = {
    1: 'I',
    4: 'IV',
    5: 'V',
    9: 'IX',
    10: 'X',
    40: 'XL',
    50: 'L',
    90: 'XC',
    100: 'C',
    400: 'CD',
    500: 'D',
    900: 'CM',
    1000: 'M'
}


base_numerals = {v: k for k, v in base_conversions.items()}


base_numbers = sorted(base_conversions.keys(), reverse=True)


def to_roman(arabic_number):
    if arabic_number < 0:
        raise NumberOutOfRangeError('negative values are not allowed')
    elif arabic_number == 0:
        raise NumberOutOfRangeError('zero is not allowed')
    elif arabic_number > 3999:
        raise NumberOutOfRangeError('number is too big')

    resulting_numeral = ''
    for num in base_numbers:
        while arabic_number >= num:
            arabic_number -= num
            resulting_numeral += base_conversions[num]

    return resulting_numeral


def from_roman(roman_numeral):
    if not roman_numeral_validator.match(roman_numeral):
        raise InvalidRomanNumeralError('invalid roman numeral')

    resulting_number = 0
    i = 0
    while i < len(roman_numeral):
        current_letter = roman_numeral[i]

        if i + 1 < len(roman_numeral):
            potential_base_numeral = current_letter + roman_numeral[i + 1]
            if potential_base_numeral in base_numerals:
                resulting_number += base_numerals[potential_base_numeral]
                i += 2
                continue

        resulting_number += base_numerals[roman_numeral[i]]
        i += 1

    return resulting_number

test_roman.py

import pytest
import roman


single_digit_values = (
    (1, 'I'),
    (2, 'II'),
    (3, 'III'),
    (4, 'IV'),
    (5, 'V'),
    (6, 'VI'),
    (7, 'VII'),
    (8, 'VIII'),
    (9, 'IX')
)


extended_known_values = (
    (1, 'I'),
    (2, 'II'),
    (3, 'III'),
    (4, 'IV'),
    (5, 'V'),
    (6, 'VI'),
    (7, 'VII'),
    (8, 'VIII'),
    (9, 'IX'),
    (10, 'X'),
    (50, 'L'),
    (100, 'C'),
    (500, 'D'),
    (1000, 'M'),
    (31, 'XXXI'),
    (148, 'CXLVIII'),
    (294, 'CCXCIV'),
    (312, 'CCCXII'),
    (421, 'CDXXI'),
    (528, 'DXXVIII'),
    (621, 'DCXXI'),
    (782, 'DCCLXXXII'),
    (870, 'DCCCLXX'),
    (941, 'CMXLI'),
    (1043, 'MXLIII'),
    (1110, 'MCX'),
    (1226, 'MCCXXVI'),
    (1301, 'MCCCI'),
    (1485, 'MCDLXXXV'),
    (1509, 'MDIX'),
    (1607, 'MDCVII'),
    (1754, 'MDCCLIV'),
    (1832, 'MDCCCXXXII'),
    (1993, 'MCMXCIII'),
    (2074, 'MMLXXIV'),
    (2152, 'MMCLII'),
    (2212, 'MMCCXII'),
    (2343, 'MMCCCXLIII'),
    (2499, 'MMCDXCIX'),
    (2574, 'MMDLXXIV'),
    (2646, 'MMDCXLVI'),
    (2723, 'MMDCCXXIII'),
    (2892, 'MMDCCCXCII'),
    (2975, 'MMCMLXXV'),
    (3051, 'MMMLI'),
    (3185, 'MMMCLXXXV'),
    (3250, 'MMMCCL'),
    (3313, 'MMMCCCXIII'),
    (3408, 'MMMCDVIII'),
    (3501, 'MMMDI'),
    (3610, 'MMMDCX'),
    (3743, 'MMMDCCXLIII'),
    (3844, 'MMMDCCCXLIV'),
    (3888, 'MMMDCCCLXXXVIII'),
    (3940, 'MMMCMXL'),
    (3999, 'MMMCMXCIX')
)


def test_single_arabic_digits_are_converted_correctly():
    for digit, numeral in single_digit_values:
        assert roman.to_roman(digit) == numeral


def test_negative_number_raises_exception():
    with pytest.raises(roman.NumberOutOfRangeError):
        roman.to_roman(-2)


def test_zero_raises_exception():
    with pytest.raises(roman.NumberOutOfRangeError):
        roman.to_roman(0)


def test_number_greater_than_3999_raises_exception():
    with pytest.raises(roman.NumberOutOfRangeError):
        roman.to_roman(4000)


def test_numbers_are_converted_correctly():
    for digit, numeral in extended_known_values:
        assert roman.to_roman(digit) == numeral


def test_too_many_repeated_numeral_letters():
    for numeral in ('MMMM', 'DD', 'CCCC', 'LL', 'XXXX', 'VV', 'IIII'):
        with pytest.raises(roman.InvalidRomanNumeralError):
            roman.from_roman(numeral)


def test_numerals_are_converted_correctly():
    for digit, numeral in extended_known_values:
        assert roman.from_roman(numeral) == digit


def test_sanity_check_to_then_from_roman():
    for i in range(1, 3999):
        assert i == roman.from_roman(roman.to_roman(i))

Answer 1

Instead of building a dict, sorting the keys and using that sorted list of keys to get the right elements from the dict, why not use a collections.OrderedDict:

from collections import OrderedDict
...
base_conversions = OrderedDict(
    (1000, 'M'),
    ...
    (5, 'V'),
    (4, 'IV'),
    (1, 'I'))

Same for base_numerals.

In python it is considered more pythonic to iterate over the elements of a list. Consider the following implementation where I used zip to have both the current and the following numeral to compare:

def roman_to_int(roman_numeral):
    """Convert from Roman numerals to an integer. Number must be < 4000."""
    if not roman_numeral_validator.match(roman_numeral):
        raise InvalidRomanNumeralError('invalid roman numeral')

    numbers = [base_numerals[char] for char in roman_numeral]
    total = 0
    for current_n, next_n in zip(numbers, numbers[1:]):
        if current_n >= next_n:
            total += current_n
        else:
            total -= current_n
    return total + numbers[-1]

In addition, you should add a docstring to every function you write. This allows you to do e.g. help(roman_to_int), which will print Convert from Roman numerals to an integer. Number must be < 4000.