Please move this thread from beta to chat, thanks.
On Thu, Nov 13, 2014 at 2:19 PM, Linda Alvord <[email protected]>
wrote:
> Here's what I have so far, but I can't seem to make a nice looking table of
> mixed numbers.
>
> load 'viewmat'
>
>
> GRB=:1 0 2{"1 (#:i.8){0 255
>
>
> T=:(i.11)*/i.11
> ]TT=:(i.11) * table i.11
> D=:(i.101)%/>:i.9x
> ]DD=:(i.101) % table >:i.9x
> ]W=:<.D
> ]R=:D-W
> (1|D) -: R NB. Thanks Roger
>
> GRB viewmat T
> GRB viewmat D
> GRB viewmat W
> GRB viewmat R
>
> ]CW=:<"1 ":"0 W
>
> $CW
>
> ]CR=:<"1 ":"0 R
>
> $CR
>
> CW,"2 CR
> $CW,."1 CR
> CW,."1 CR
>
> Linda
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of Roger Hui
> Sent: Thursday, November 13, 2014 4:53 PM
> To: Beta forum
> Subject: Re: [Jbeta] Odd Pattern of Rationals
>
> If you want arithmetic to work perfectly, stick with rational numbers and
> extended precision integers.
>
> The integer part of a ration number is <.x . The fractional part is 1|x.
> Thus:
>
> (<. , 1&|) 14r3
> 4 2r3
>
>
>
>
> On Thu, Nov 13, 2014 at 1:47 PM, Linda Alvord <[email protected]>
> wrote:
>
> > In Grade 3 in USA students learn multiplication of numbers from 0 to
> > 100, (I'm not sure what happenes to division by zero). However they
> > only deal with fractions of single digit denominators. So having
> > experiented a little with rationals, see my question at the end.
> >
> > N=:11 33333330575r99999991726
> > $N
> > 2
> > 6 2$N
> > 11 33333330575r99999991726
> > 11 33333330575r99999991726
> > 11 33333330575r99999991726
> > 11 33333330575r99999991726
> > 11 33333330575r99999991726
> > 11 33333330575r99999991726
> >
> > +/ 6 2$N
> > 66 99999991725r49999995863
> >
> > +/ +/ 6 2$N
> > 3399999718683r49999995863
> >
> > 3399999718683%49999995863
> > 68
> >
> > +/ 6#2r3
> > 4
> > +/ 7#2r3
> > 14r3
> >
> > In third grade the anser should be 4 2r3 or something like it. How
> > are rational fractions generally handled?
> >
> > Linda
> >
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf Of Roger Hui
> > Sent: Thursday, November 13, 2014 10:58 AM
> > To: Beta forum
> > Subject: Re: [Jbeta] Odd Pattern of Rationals
> >
> > And, most importantly,
> >
> > x: 1%3
> > 1r3
> >
> > x: is subject to tolerance. The implementation can possibly be
> > improved by using the ideas in
> >
> > https://en.wikipedia.org/wiki/Continued_fraction#Best_rational_approxi
> > mation
> > s
> >
> >
> >
> > On Thu, Nov 13, 2014 at 7:35 AM, Mike Day <[email protected]>
> > wrote:
> >
> > > FYI
> > > NB. enumerate x:0.333... for between 1 and 20 decimal places
> > > (>:i.20),.x:+/"1 (10^>:i.20)%~"1(3#~])"0>:i.q =. 20
> > >
> > > 1 3r10
> > >
> > > 2 33r100
> > >
> > > 3 333r1000
> > >
> > > 4 3333r10000
> > >
> > > 5 33333r100000
> > >
> > > 6 333333r1000000
> > >
> > > 7 3333333r10000000
> > >
> > > 8 1r3
> > >
> > > 9 166666671r500000014
> > >
> > > 10 3333333057r9999999173
> > >
> > > 11 33333330575r99999991726
> > >
> > > 12 1r3
> > >
> > > 13 1r3
> > >
> > > 14 1r3
> > >
> > > 15 1r3
> > >
> > > 16 1r3
> > >
> > > 17 1r3
> > >
> > > 18 1r3
> > >
> > > 19 1r3
> > >
> > > 20 1r3
> > >
> > >
> > > in Windows 8 - same in J32 & J64
> > >
> > >
> > > Mike
> > >
> > >
> > > On 13/11/2014 14:56, Ben Gorte - CITG wrote:
> > >
> > >> I guess that's why Linda asked: Should 0.33333333 really be 1r3 ?
> > >> Raul showed that it is.
> > >>
> > >> (I also don't get it)
> > >> ________________________________________
> > >> From: [email protected] [beta-bounces@forums.
> > >> jsoftware.com] on behalf of Dan Bron [[email protected]]
> > >> Sent: Thursday, November 13, 2014 15:39
> > >> To: [email protected]
> > >> Subject: Re: [Jbeta] Odd Pattern of Rationals
> > >>
> > >> Linda, exact numbers have to be exact from the get-go. If a number
> > >> starts out inexact, it will stay inexact forever, even if you later
> > apply
> > x:
> > >> (though then it will be quite exactly inexact :).
> > >>
> > >> Thus, to get 1r3 you must say 1r3. If you say 0.333 you'll get 0.333
> .
> > >> That's not 1r3 and never will be.
> > >>
> > >> -Dan
> > >>
> > >> ----- Original Message ---------------
> > >>
> > >> Subject: [Jbeta] Odd Pattern of Rationals
> > >> From: "Linda Alvord" <[email protected]>
> > >> Date: Wed, 12 Nov 2014 23:10:14 -0500
> > >> To: <[email protected]>
> > >>
> > >> Should 0.33333333 really be 1r3 ?
> > >>
> > >>
> > >>
> > >> x: 0.333333
> > >>
> > >> 333333r1000000
> > >>
> > >> x: 0.3333333
> > >>
> > >> 3333333r10000000
> > >>
> > >> x: 0.33333333
> > >>
> > >> 1r3
> > >>
> > >> x: 0.333333333
> > >>
> > >> 166666671r500000014
> > >>
> > >> x: 0.3333333333
> > >>
> > >> 3333333057r9999999173
> > >>
> > >>
> > >>
> > >> Linda
> > >>
> > >>
> > >
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