Here are some patterns which guarantee use of the monadic definition of verb v (and let's say that u is some other verb):
(u v) u&v v@ u v@] Thanks, -- Raul On Jul 24, 2014 5:48 PM, "Kip Murray" <[email protected]> wrote: > 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
