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From: rjnoe@ihlts.UUCP (Roger Noe @ 41:48:31 N, 88:07:13 W)
Newsgroups: net.math
Subject: Re: Rules for Roman Numerals?
Message-ID: <303@ihlts.UUCP>
Date: Fri, 6-Jan-84 12:39:21 EST
Article-I.D.: ihlts.303
Posted: Fri Jan  6 12:39:21 1984
Date-Received: Sat, 7-Jan-84 03:07:34 EST
References: <465@ihuxq.UUCP>
Organization: AT&T Bell Labs, Naperville, IL
Lines: 28

CHOMP THIS

>Does anyone know any definitive rules for computing Roman
>numeral values for numbers? . . . How general is this [the subtraction]
>feature? . . . Is there a definitive, exhaustive character set?

Roman numerals are typically used to demonstrate the decimal nature of a
number.  Thus the only way the "subtraction feature" is generally used is
when a 4 or 9 occurs in the decimal (Arabic notation) of a number.  In
these events, a Roman numeral with a value which is a power of ten (e.g.
I=10^0, X=10^1, C=10^2, etc.) is followed immediately by a numeral which
has a value five or ten times it.  For example, IV=4, IX=9, XL=40, XC=90,
CD=400, CM=900, and so forth.  The definitive character set is I=1, V=5,
X=10, L=50, C=100, D=500, M=1000, and putting a bar over any of these
(except I) multiplies its value by 1000.  M-bar, or 10^6, is the largest
authentic Roman numeral.  Apparently the Romans did not have much need
to count any higher than a few million.  Now there's no reason you can't
decide to write IM for 999 rather than CMXCIX, the canonical way to do it.
[Yes, in 1999, films and buildings will have MCMXCIX on them, almost
certainly not MIM.]  It's pretty clear that IM has one interpretation.
But what about IVX?  Does it have any meaning?  Some would say it is
the same as IV, because -1-5+10=4.  It's usually best to stick with the
widely-accepted, commonly-used and well-understood definition which only
allows the combinations mentioned above.  I have a C program which does
just this which I'll send to anyone interested.  I've also a closely
related program which takes Roman numerals of a much more general nature
(e.g. MIM and IVX) and gives the Arabic notation version.
	Roger Noe		...ihnp4!ihlts!rjnoe