> What was cute was that since X already meant ten, I decided it
> would be nice to write all numbers as polynomials in X, with coefficients
> I through IX, and use what was familiar as polynomial multiplication to
> get ordinary products, later replacing X^2 by C, etc.
I haven't bothered to join this thread before now, but I've always
been puzzled by the supposed difficulty of calculating with Roman Numerals,
since they differ from the Hindu-Arabic ones only by a simple translation,
namely 1 2 3 4 5 6 7 8 9
become I II III IV V VI VII VIII IX in the units place,
X XX XXX XL L LX LXX LXXX XC in the tens place,
C CC CCC CD D DC DCC DCCC CM in the hundreds place.
Any arithmetician would surely know the rule for multiplying by X,
namely I -> X -> C -> M and V -> L -> D , and so if (s)he knew
the multiplication table up to IX by IX, could obviously multiply
just the way we do.
So any difficulty could only have been due to the fact that
the typical arithmetician DIDN'T know the multiplication table
that far. However, my guess is that they probably DID know it
up to V by V, which permits an only slightly more complicated
method, which is presumably roughly what the abacists used.
John Conway