In ancient Rome a numeric system was used based on Roman numerals for the representation of integers. This numeric system is not a positional system, but an additive system in which the value of the integer is determined as the total sum of the digits used in the representation. The numbers one to ten can be expressed as Roman numerals as follows: I, II, III, IV, V, VI, VII, VIII, IX and X. Negative numbers and the zero value cannot be represented in the Roman numeric system. The Roman numeric system has largely become in disuse since the fourteenth century, in favor of the decimal numeric system that is based on Arab digits. However, Roman numeral are still in common use today in some applications, such as in numbering kings having the same name (e.g. Louis XIV of France), in numbering annual events and in numbering centuries in some countries (e.g. XIXe siècle).
In the Roman numeric system, integers are represented using symbols, the actual digits, where each symbol has a certain value independent of the position where it occurs in the integer representation. The symbols used in the Roman numeric system are:
| symbol | value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
The order of the Roman digits in the integer representation is not random. The values of the individual digits are added, except if a symbol with a lower value is immediately followed by a symbol with a higher value: in that case, the lower value is subtracted instead of being added. The rules for representing integers using Roman numerals has been very loose in Ancient times. As such, in its credits the BBC used the typographically more elegant representation MIM for the year 1999, instead of MCMXCIX.
PEP 3131 was a proposal to extend the Python programming language with support for the representation of Roman numerals as a literal data type. This proposal was rejected by Guido Van Rossum, who created the Python language and is nicknamed the Benevolent Dictator for Life (BDFL). However, since it is possible to extend Python by defining new data types, it is possible that we create or own data type to represent Roman numerals in Python. In order to do so, you proceed as follows:
Write a function roman2arab that converts a given string that only contains Roman digits (upper case or lower case) into the integer representation of the same number.
Write a function arab2roman that converts a given
integer into the string representation of the same number using Roman
digits (upper case only). This representation should be determined by
traversing the following table from left to right. As long as the
remaining integer value is larger then or equal to the current value
from the table, the corresponding combination of Roman digits is
appended to the Roman numeral. The current value is then subtracted
from the integer value. As soon as the current value is lower then the
remaining integer value, we traverse to the next position in the
table.
| M | CM | D | CD | C | XC | L | XL | X | IX | V | IV | I |
| 1000 | 900 | 500 | 400 | 100 | 90 | 50 | 40 | 10 | 9 | 5 | 4 | 1 |
Define a class Roman that can be used to represent Roman numerals in Python. New objects of this class can be initialized either by an integer value $$i$$ (where $$1 \leq i < 4000$$) or by a string $$s$$ that only contains Roman digits (upper case and/or lower case). All other values passed while initializing an object of the class should result in an AssertionError being thrown with the message invalid roman numeral. The conversion of a Roman numeral to a string — obtained using the built-in functions str() and repr() — should give the integer value represented in Roman digits (upper case, as generated by the function arab2roman) and the converstion to an integer — obtained using the built-in function int() — should give the integer value in Arab digits. Make sure that the sum, difference and product of two Roman numerals can be computed using the operators +, - and *. The evaluation of these operations should result in a new Roman numeral.
>>> roman2arab('MDCCCCX')
1910
>>> arab2roman(1910)
'MCMX'
>>> int(Roman('MDCCCCX'))
1910
>>> int(Roman('MCMLIV'))
1954
>>> int(Roman('MCMXC'))
1990
>>> rsum = Roman('MDCCCCX') + Roman('MCMXC')
>>> isinstance(rsum, Roman)
True
>>> print(rsum)
MMMCM
>>> difference = Roman('MCMXC') - Roman('MDCCCCX')
>>> isinstance(difference, Roman)
True
>>> str(difference)
'LXXX'
>>> product = Roman('CMX') * Roman('III')
>>> isinstance(product, Roman)
True
>>> product
MMDCCXXX
>>> print(Roman('mdccccx'))
MCMX
>>> Roman(1234)
MCCXXXIV
>>> Roman(4321)
Traceback (most recent call last):
AssertionError: invalid roman numeral
>>> Roman('ABCDEF')
Traceback (most recent call last):
AssertionError: invalid roman numeral
>>> Roman(3.14)
Traceback (most recent call last):
AssertionError: invalid roman numeral