; roman.lsp
; Sam Cox December 8, 2003
;
; LM 2003/12/12: took out type checking of n
;                 
;
; This function constructs a roman numeral representation from its positive
; integer argument, N.  For example,
;
;     (roman 1988) --> MCMLXXXVIII
;
; The Roman method of writing numbers uses two kinds of symbols: the basic
; symbols are I=1, X=10, C=100 and M=1000; the auxiliary symbols are V=5,
; L=50 and D=500. A rule prescribes that the symbol for the larger number
; always stands to the left of that for the smaller number. An exception
; is motivated by the desire to use as few symbols as possible. For
; example, the number nine can be represented as VIIII (5+4) or IX (10-1);
; the latter is preferred.  Therefore, if the symbol of a smaller number
; stands at the left, the corresponding number has to be subtracted, not
; added.  It is not permitted to place several basic symbols or an
; auxiliary symbol in front.  For example, use CML for 950 instead of LM.
; ---
; The VNR Encyclopedia of Mathematics, W. Gellert, H. Kustner, M. Hellwich,
; and H. Kastner, eds., Van Nostrand Reinhold Company, New York, 1975.  

(define (roman n)
        (roman-aux "" n (first *ROMAN*) (rest *ROMAN*)))

(define (roman-aux result n pair remaining)
    (roman-aux-2 result n (first pair) (second pair) remaining)) 

(define (roman-aux-2 result n val rep remaining)
    (if
        (= n 0)
            result
        (< n val)
            (roman-aux result n (first remaining) (rest remaining))
        ;else
            (roman-aux-2 (append result rep) (- n val) val rep remaining))) 

(define (second x) (nth 1 x)) 

(setq *ROMAN*
         '(( 1000  "M" )
           (  999 "IM" )
           (  990 "XM" )
           (  900 "CM" )
           (  500  "D" )
           (  499 "ID" )
           (  490 "XD" )
           (  400 "CD" )
           (  100  "C" )
           (   99 "IC" )
           (   90 "XC" )
           (   50  "L" )
           (   49 "IL" )
           (   40 "XL" )
           (   10  "X" )
           (    9 "IX" )
           (    5  "V" )
           (    4 "IV" )
           (    1  "I" ))) 

; end of file