To enforce monadic use of a verb you can use verb : [:
see Common Uses under http://www.jsoftware.com/jwiki/Vocabulary/squarelfco On Thursday, July 24, 2014, greg heil <[email protected]> wrote: > >i suppose it is obvious, but to get the decimal places before and after > the decimal point one can extend tdig to > > tdig=:1 :0 > : > NB. b: m, p: x, q: y > q=. y%x+.y > (>.m^.(<.x%y)),(>.m^.q)%0=#q-.&q:m > ) > > eg > 12(3 tdig)3 > 2 0 > > >i am still hoping there is less of a circumlocution for getting a verb`s > monadic case than ([: verb [) > > greg > ~krsnadas.org > > -- > > from: Raul Miller <[email protected] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > date: 23 July 2014 16:12 > subject: Re: [Jchat] Repeating decimals > > Sure... (hopefully I've copied this correctly...): > > tdig=:1 :0 > : > NB. b: m, p: x, q: y > q=. y%x+.y > (>.m^.q)%0=#q-.&q:m > ) > > For example, > 12 (10 tdig) 150 > > -- > Raul > > Thanks, > > -- > > from: greg heil <[email protected] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > date: 23 July 2014 08:25 > subject: Re: [Jchat] Repeating decimals > > 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] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > reply-to: [email protected] <javascript:;> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > to: Chat forum <[email protected] <javascript:;>> > 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] <javascript:;>> > to: [email protected] <javascript:;> > 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 > -- Sent from Gmail Mobile ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
