Are there numerical algorithms for Roman numerals? In positional number systems there are algorithms for performing certain operations, like long division, to name one of the simplest. This works for positional systems, whatever base. I realize in number theory there are very advanced algorithms, typically for working with Very Long Numbers. (disclaimer: except for a Fourier transform I don't know any of them, I'm not a mathematician.)  

I was wondering how the Romans could do anything numerical with their odd Roman numerals. You can't divide MMDCCI by LXXIII using long division. So, question: are there numerical methods for Roman numerals, and if not, how did the Romans divide MMDCCI by LXXIII?
This web page has information about some possible approaches to doing arithmetic using Roman Numerals: http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/
Are there numerical algorithms for Roman numerals?

Yes there are, all the algorithms for our current numbers can work on Roman Numerals ( as far as the numbers can be represented in Roman Numeral Form). All you have to do is to represent each number in it's Roman Form, why would dividing , adding or any other operation on numbers depend on how the number is represented?

You can't divide MMDCCI by LXXIII using long division

Yes you can, Here is one way to divide MMDCCI by LXXIII : Convert them to their decimal ( arabic numeral ) equivalants, carry out the long division as usual, at the end substitute roman numerals in place of every number appearing in the division. But this does not answer the question of how Romans did it, just that it is possible to divided MMDCCI by LXXIII using long division and arabic numerals as we are used to, the algorihm is a composite of Long Division and Converting numbers between two different types of their representation.

how did the Romans divide MMDCCI by LXXIII?

How did the Romans actually divide MMDCCI by LXXIII? One simple way would have been by adding LXXIII as many times to LXXIII until the results was greater than MMDCCI, a truely long divison algorithm, it is a way that although maybe not acceptable by todays standards but at least in principal they could do it.
This is on how it could be done, pondering about idiotic system can look this up youtube.com/watch?v=5PxXpDH8-2A