Raul Yer right! One can take out the gcd with b bq q%p+.q
>The big thing for me though is the circumlocution apparently needed to force >the monadic case. Ie ([:q:[) has five characters devoted to just that!-( Don >Not yet ready to stand up to that challenge, though i would imagine once the >infinite case were filtered it would involve using #. . greg ~krsnadas.org -- from: Don Guinn <[email protected]> to: Chat forum <[email protected]> date: 23 July 2014 05:23 subject: Re: [Jchat] Repeating decimals >Why not extend the question a bit? Given p, q and b, how many digits of base b >will be required in the repeat? The answer could be an infinite number. -- from: Raul Miller <[email protected]> to: Chat forum <[email protected]> date: 23 July 2014 04:15 subject: Re: [Jchat] Repeating decimals >OK, rereading the original post, I guess I should assume that we are not only >interested in the decimal case. >That said, I'm not certain that it makes sense to assume that the least common >denominator has been factored out of p and q, either. --- Raul -- from: greg heil <[email protected]> to: Chat forum <[email protected]> date: 22 July 2014 22:28 subject: Re: [Jchat] Repeating decimals Raul >Well the way i read Dans query only q and b are important... so if bq=:([:q:])-.([:q:[) then a null result would be finite, eg 3 bq 3 10 bq 3 3 greg ~krsnadas.org -- from: Raul Miller <[email protected]> reply-to: [email protected] to: Chat forum <[email protected]> date: 22 July 2014 20:42 subject: Re: [Jchat] Repeating decimals That's an interesting point. >Nevertheless, given the subject line of this thread, I think that maybe the >base has already been determined. Thanks, --- Raul -- from: greg heil <[email protected]> to: Chat forum <[email protected]> date: 22 July 2014 19:42 subject: Re: [Jchat] Repeating decimals >What ever formula would also depend on b ... eg the division of 1 by 3 has a >finite representation in base 3 of 0.1. (although its representation in base >10 is infinite) greg ~krsnadas.org -- from: Raul Miller <[email protected]> to: Chat forum <[email protected]> date: 22 July 2014 10:18 subject: Re: [Jchat] Repeating decimals $p(2 5-.~[:q:]%+.)q 0 >Assuming p and q are rank 0, of course. (And this is a reasonable assumption, >since the problem statement suggests no use for dimensions). Thanks, --- Raul -- from: Dan Bron <[email protected]> to: [email protected] date: 22 July 2014 08:25 subject: [Jchat] Repeating decimals >Given 3 positive integers p,q and b, where p and q represent the numerator and >denominator of a rational number (respectively), and b a numerical base (or >radix), how can we know if p%q has a finite (or not) representation in b? >In other words, if p%q can be represented by a finite >(non-infinitely-repeating) decimal in base b, then what do we know about the >relationship of p to q or p%q to b ? >You may allow p to take on the value 0 if needed for generality, but q is >strictly > 0 (obviously) and b is strictly > 1 (probably?). -Dan ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
