Conference rusure::math

The same book also contains some other clever algorithms for things like
generating permutations.  It's well worth having a look at - although
you have to know at least some SNOBOL to make any sense of some of the
details.
							-- Jerry

    How does .0 work?  Is there nothing to distinguish the times-fives
    from the times-twos?  (I-to-V vs. V-to-X.)
    
    Are there accepted rules on Roman numerals?  VIII vs. IIX?  XCV
    vs. VC?  Is IMM legal?  Is CIM?
    
    John

    ...and what is (are) the legitimate Roman representation(s) for 1990?
    
    John

    Re:                       <<< Note 12.3 by ESCROW::MUNZER >>>

>    ...and what is (are) the legitimate Roman representation(s) for 1990?
    
    There are really two questions here:
    
    	What Roman numerals can be read as 1990?
    
    	How would a typical writer of Roman numerals represent 1990?
    
    The title of this note offers another answer to the first question.
    
    As I remember, the subtractive convention (IX for VIIII) was introduced
    some time after the fall of the Roman Empire, so no citizen of the
    empire would have used it.
    
    MDCCCCLXXXX is, I think, how a such a citizen would have represented
    1990, assuming the subject came up.
    
    But if you allow more recent writers of Roman numerals, then you have
    to guess at their conventions.  I know MCM=1900 is quite common, and I
    have never seen MLM=1950.  So I suspect that the title above is not a
    valid answer to the second question.

    The "rule" which was added post-classically was something like this:
    
    		(1) V' I' I' I' I' -> I' X'
    		(2) I' I' I' I' -> I' V'
    
    where I', V', X' equals
    
    		I, V, X  or
    		X, L, C  or ... etc
    
    If the first subrule applies the second cannot be used.
    
    					Topher

re .-1
Ok, start with the classical version:

	MDCCCCLXXXX

applying rule 1) to the "DCCCC" part gives
	MCMLXXXX

applying rule 1) to the "LXXXX" part gives
	MCMXC
No further simplification is possible using those rules.  I don't see
how you can claim that "MXM" is correct using the rules you've given.

You just don't see these kind of arguments for Arabic numerals, do you?

RE: .7
    
    Sorry, my title to .6 lead to a misunderstanding -- I meant that the
    *body* of .5, which claimed that the *title* of .5 was illegal, was
    correct, i.e., that MXM is not an allowed combination.
    
    					Topher

See also note 2143 of MEIS::ASKENET.

-Mike

        Would Mary Tyler Moore write it as MTM? :-)
        
        Dan

    
    	Does anyone have a DCL, BASIC or C program that will convert a
    	number to a roman numeral?
    
    	Or a program that will scan a file and convert ALL numbers to
    	roman numerals?
    
    	Thanks for any info.
    

Why would such be needed ?  

        Roman numeral output is built into VAX LISP.
        
        Dan

    The idea is to work the number left-to-right, replacing 
    
    		I,V,X,L,C with X,L,C,D,M
    
    respectively, and tacking on the next digit.
    
    Take 1492:
    
    (1a) Start with nothing
    (1b) tack on I from the 1
    (2a) I to X via replace
    (2b) tack on IV from the 4, "XIV" or 14
    (3a) XIV becomes CXL via replace
    (3b) tack on IX from the 9 for "CXLIX" or 149
    (4a) CXLIX becomes MCDXC
    (4b) tack on II from the 2 for "MCDXCII", 1492
    
    I never loearned Roman Numerals > 5000
    
      John

>    
>    I never loearned Roman Numerals > 5000
> 

	what's 5000 ?  Is there a letter ?  Or just MMMMM.


/Eric

    re .14
    
    That's fine if for some reason you require strictly sequential access
    to the input data.
    
    It seems better though to buffer the entire input number so that we
    know that the weight of the first digit is 1000 and then treat 1492 as
    1000,400,90,2 and then just substitute appropriate Roman numeral
    strings for each viz. M,CD,XC,II. (This would require a 10*4
    translation table but it's conceptually simple.)

>    It seems better though to buffer the entire input number so that we
>    know that the weight of the first digit is 1000 and then treat 1492 as
>    1000,400,90,2 and then just substitute appropriate Roman numeral
>    strings for each viz. M,CD,XC,II. (This would require a 10*4
>    translation table but it's conceptually simple.)
    
    "Better" in what sense? I could just as easily argue it is "better" to
     define a 4999-entry table of strings, and do a lookup.
    
      John

    re .17
    
    Not a mathematical concept I admit.
    
    Better = ill-defined compromise between efficiency of execution, time
    to code correctly, ease of comprehension by maintenance programmer,
    ease of modification, weighted according to your priorities. Choice of
    language will of course impact these factors.
    
    A 4999 entry lookup table could be reasonable if it were program
    generated and memory wasn't tight.

$!
$!	Convert decimal number to roman numberals for
$!	busy busy Slabounty. (currently limited to 1 - 3999)
$!
$!	Usage:
$!
$!		@roman n
$!
$!	Author:  Eric Osman 14-Jun-1995
$!
$ one = "I"
$ five = "V"
$ ten = "X"
$ fifty = "L"
$ hundred = "C"
$ fivehundred = "D"
$ thousand = "M"
$ units = "one,five,ten"
$ tens = "ten,fifty,hundred"
$ hundreds = "hundred,fivehundred,thousand"
$ thousands = "thousand,unknown,unknown"
$ groups = "thousands,hundreds,tens,units"
$ quans = "1000,100,10,1"
$ forms = " !AS:n1 !AS!AS:n1,n1 !AS!AS!AS:n1,n1,n1 !AS!AS:n1,n2 !AS:n2" + -
	" !AS!AS:n2,n1 !AS!AS!AS:n2,n1,n1 !AS!AS!AS!AS:n2,n1,n1,n1 !AS!AS:n1,n3"
$ set = "set" ! use usual definition of "set"
$ set symbol/scope=(nolocal,noglobal) ! use usual definition of all others
$ on warning then exit ! stop as soon as something goes wrong
$ unknown = ""
$ n = p1
$ i = 0
$ if n .gt. 3999 .or. n .lt. 1
$ then
$	write sys$output "Not converting ", n
$	exit
$ endif
$ roman = ""
$ lup:
$ quan = f$int(f$ele(i,",",quans))
$ digit = n/quan
$ n = n - digit*quan
$ if digit .eq. 0 then goto next_i
$ form = f$ele(digit," ",forms)
$ group = 'f$ele(i,",",groups)'
$ n1 = 'f$ele(0,",",group)'
$ n2 = 'f$ele(1,",",group)'
$ n3 = 'f$ele(2,",",group)'
$ roman = roman + f$fao (f$ele(0,":",form), 'f$ele(1,":",form)')
$ next_i: i = i + 1
$ if i .lt. 4 then goto lup
$ write sys$output roman

    
    A request for assistance (cross posted in Brain Bogglers...)
    
       <<< ROBTOB::ROBTOB$DKA300:[BRAIN_BOGGLERS]BRAIN_BOGGLERS.NOTE;4 >>>
                              -< Brain Bogglers >-
================================================================================
Note 409.10                      Roman numerals                         10 of 12
MROA::BERGART "Jeff-the-ref"                         23 lines  31-OCT-1995 17:06
              -< So why are the Roman Numerals what they are??? >-
--------------------------------------------------------------------------------
    I'll be teaching Roman Numerals very soon to a 6th grade class.
    The question is: Why are the roman numerals what they are?
    Your insights and/or inputs to the lesson plan are most welcome....
    
    I = 1		I looks like a single finger.
    V = 5		The shape of the thumb and first finger of a whole
    				hand (i.e. five fingers)?
    X = 10		Two V's connected bottom to bottom?
    L = 50
    C = 100
    D = 500
    M = 1000
    
    	And what examples can I use showing how these now impact our lives?
    
    I = 1	"I"  meaning me, a single person
    V = 5		
    X = 10	Deci/Deca means ten (e.g. decade) so why X, why is 500 a "D"?
    L = 50
    C = 100	"Cent" (1/100th of a dollar), "Century" (100 years)
    D = 500
    M = 1000	"Milli" (1/1000th of something)  "Millenium" (1000 yrs)
    

    re .20
    
    You may have it round the wrong way regarding the impact of C and M on
    our lives i.e. C and M may have been used as abbreviations for the
    corresponding Latin words (and it would then be anyone's guess as to
    the origins of the words).
    
    See topic 1776 and specifically 1776.7 in the COMMAND_PROCEDURES
    conference (currently on the move) for more information on Roman
    numerals.
    
    You might want to mention some places where we still use them today
    viz. year of production for TV and film, page numbering in books before
    we get to page 1, numbering olympiads, size of a cricket team�.
    
�But you may then have to explain what cricket is since I suspect that you
are US based. Maybe a more familiar sport also does this.

    	The real place to enquire about this is SMURF::SPQR, where all the
    staggeringly knowledgeable classical whizzes live. They can give you
    the total story.
    
    Cheers,
    Andy.

> are US based. Maybe a more familiar sport also does this.
    
    Was that a set-up? In the States we number Super Bowls thusly.
    THE big TV event of the year, except for the occasional verdict or
    other surprise event.
    
      John C. Hallyburton II

re .23
    
>    Was that a set-up?
    
    Nope.
    
>    In the States we number Super Bowls thusly.
    
    I find bowls a somewhat boring game to watch. (-:
    
    
    But seriously, yes, that should give an example that the target
    audience can relate to.

I missed the first IX episodes, but Malcolm X was a pretty good movie.

/Eric