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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