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# RE: st: RE: Change roman to Arabic numerals

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: RE: Change roman to Arabic numerals Date Tue, 21 Dec 2010 18:08:51 +0000

```I added a regex check to the code which improves matters.

Nick
n.j.cox@durham.ac.uk

Lachenbruch, Peter

To me, an obvious out on this one would be to trap such "non-roman-numbers"

Nick Cox

Sergiy is commenting on the code I posted last Friday and not the expanded code I posted on Monday. But his main points remain correct.

My code indulges many numerals that might be considered improper. It doesn't have much error checking. This raises a practical question of whether that matters to any particular user and a question of principle of whether it's worth adding a constraint on improper numerals, e.g. by some kind of regular expression definition.

My interest was piqued by this problem because it seemed an amusing little programming problem.

However, my interest peaked when I ran into the kind of fuzziness that Sergiy also encountered, e.g. would IL be allowed as 49? Once you find that authorities disagree, or do not provide rigorous definitions, there is no longer an absolutely precise problem to be solved.

When made public, my code and help file could serve as stepping-stones for anyone else who wanted to take the problem further.

Peter writes that his Colleague had to deal only with Roman numbers in
the range I-X. For that situation another code (one
line) can be suggested:
generate byte arabic =
strpos("=====I====II===III==IV===V====VI===VII==VIII=IX===X====","="+roman+"=")/5
if !missing(roman)
Below is a demo. Obviously the code is not easily extended to the
larger ranges, or to include dual notation for 4: "IV" and "IIII".

Nick's code is doing a great job of converting the numbers both small
and large, however it appears to be too robust,
converting even misspelled Roman numerals, such as: IM (999), or IL
(49). Both notations may occur in practice (depends
on the source of data). Wikipedia denotes them as "would not be
generally accepted". I think it would be great to modify the
code to either report them as erroneous (misspelled Roman numeral), or
convert based on the possible intuition of the
respondents (999 and 49 correspondingly), but not to incorrect values
(1001 and 51 correspondingly) as the current version
does.
Numbers like "IIIIIIIIIIIIIIIIIIIII" are converted correctly, but
perhaps it's better to report an argument error in such a case.

Similarly, not used, characters are currently not reported as errors
(e.g. "K" in "XK", although one could encounter "K" in
exotic medieval Roman numerals...). This wouldn't be a problem if the
program handled all symbols of the Roman numerals,
but e.g. "S" (half) is not handled (again see Wikipedia for reference).

[...]

On Fri, Dec 17, 2010 at 2:38 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> I think anyone tempted to write this would be best advised to extract the subtraction parts of the syntax first, i.e. CM etc.
>
> (Also, from what I recall IIII is sometimes allowed as a non-standard variant of IV.)
>
> Here is one stab. This is a Mata function that works on a string vector of Roman numerals in upper case.
>
> Example first:
>
> . mata
>
> : stuff = ("IV", "MCMIV")
>
> : roman_to_arabic(stuff)
>          1      2
>    +---------------+
>  1 |     4   1904  |
>    +---------------+
>
> : roman_to_arabic(stuff')
>          1
>    +--------+
>  1 |     4  |
>  2 |  1904  |
>    +--------+
>
> : end
>
> Code second:
>
> mata :
>
> real roman_to_arabic(string vector roman) {
>
>        numeric vector ro
>        string vector work
>        ro = J(rows(roman), cols(roman), 0)
>        work = roman
>
>        ro = ro + 900 * (strpos(work, "CM") :> 0)
>        work = subinstr(work, "CM", "", .)
>        ro = ro + 400 * (strpos(work, "CD") :> 0)
>        work = subinstr(work, "CD", "", .)
>        ro = ro + 90 * (strpos(work, "XC") :> 0)
>        work = subinstr(work, "XC", "", .)
>        ro = ro + 40 * (strpos(work, "XL") :> 0)
>        work = subinstr(work, "XL", "", .)
>        ro = ro + 9 * (strpos(work, "IX") :> 0)
>        work = subinstr(work, "IX", "", .)
>        ro = ro + 4 * (strpos(work, "IV") :> 0)
>        work = subinstr(work, "IV", "", .)
>
>        while (sum(strpos(work, "M"))) {
>                ro = ro + 1000 * (strpos(work, "M") :> 0)
>                work = subinstr(work, "M", "", 1)
>        }
>
>        while (sum(strpos(work, "D"))) {
>                ro = ro + 500 * (strpos(work, "D") :> 0)
>                work = subinstr(work, "D", "", 1)
>        }
>
>        while (sum(strpos(work, "C"))) {
>                ro = ro + 100 * (strpos(work, "C") :> 0)
>                work = subinstr(work, "C", "", 1)
>        }
>
>        while (sum(strpos(work, "L"))) {
>                ro = ro + 50 * (strpos(work, "L") :> 0)
>                work = subinstr(work, "L", "", 1)
>        }
>
>        while (sum(strpos(work, "X"))) {
>                ro = ro + 10 * (strpos(work, "X") :> 0)
>                work = subinstr(work, "X", "", 1)
>        }
>
>        while (sum(strpos(work, "V"))) {
>                ro = ro + 5 * (strpos(work, "V") :> 0)
>                work = subinstr(work, "V", "", 1)
>        }
>
>        while (sum(strpos(work, "I"))) {
>                ro = ro + (strpos(work, "I") :> 0)
>                work = subinstr(work, "I", "", 1)
>        }
>
>        return(ro)
> }
>
> end

Lachenbruch, Peter

> A colleague wants to generate Arabic numbers from Roman numerals and I was = wondering if anyone has written a routine for this.  She only has I to X so=  I suggested Gen numb=(rom=="I")+2*(rom=="2")+3*(rom=="3")+4*(rom=="4"=
> )  etc.
> This is OK for this application, but not if we have many numbers.  Of course the ordering  gets messed up - I, II, III, IV, IX, V, VI, VII, VIII, X so=  encode won't work  and gen numb=3Dreal(rom) won't do either.

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