Kip, Here are two thoughts:
This uses [: only rather than both [: and @
%~ can be "read" as "into" (it makes a prettier tree!)
a =:0 { ]
b =:1 { ]
c =:2 { ]
roots2=:(2*a)%~([:-b)(+,-)[:%:([:*:b)-4*a*c
roots2 1 3 2
_1 _2
roots2 1 0 4
0j2 0j_2
5!:4 <'roots2'
┌─ 2
┌─────┼─ *
│ └─ a
│
├─ ~ ─── %
│ ┌─ [:
──┤ ┌───┼─ -
│ │ └─ b
│ │
│ │ ┌─ +
│ ├───┼─ ,
└─────┤ └─ -
│
│ ┌─ [:
│ ├─ %:
│ │ ┌─ [:
└───┤ ┌───┼─ *:
│ │ └─ b
│ ├─ -
└────┤ ┌─ 4
│ ├─ *
└───┤ ┌─ a
└────┼─ *
└─ c
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Roger Hui
Sent: Wednesday, December 12, 2012 2:23 AM
To: Programming forum
Subject: Re: [Jprogramming] Cool roots
Cool.
On Tue, Dec 11, 2012 at 7:54 PM, km < <mailto:[email protected]>
[email protected]> wrote:
> Apologies:
>
> a =: 0 { ]
> b =: 1 { ]
> c =: 2 { ]
> roots =: ( (-@b) (+ , -) [: %: *:@b - 4 * a * c ) % 2 * a
> roots 1 3 2
> _1 _2
> roots 1 0 1
> 0j1 0j_1
> roots 1 2 1
> _1 _1
>
> Kip Murray
>
> Sent from my iPad
>
>
> On Dec 11, 2012, at 5:29 PM, Roger Hui < <mailto:[email protected]>
> [email protected]> wrote:
>
> > There are some cheeky (or is it cheesy?) versions:
> >
> > (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c NB. Kip Murray
> > (2*a) %~ - b (+,-) %: (b^2) - 4*a*c
> > (+:a) %~ - b (+,-) %: (*:b) - 4*a*c
> > -: a %~ - b (+,-) %: (*:b) - 4*a*c
> >
> >
> >
> > On Tue, Dec 11, 2012 at 11:37 AM, km < <mailto:[email protected]>
> > [email protected]> wrote:
> >
> >> It appears this could be translated into J as the rather cool
> >>
> >> (2*a) %~ (-b) (+,-) %: (b^2) - 4*a*c
> >>
> >> Sent from my iPad
> >>
> >>
> >> On Dec 11, 2012, at 12:59 PM, Roger Hui <
> >> <mailto:[email protected]> [email protected]>
> wrote:
> >>
> >>> Example from the Iverson and McDonnell *Phrasal
> >>> Forms*< <http://www.jsoftware.com/papers/fork.htm>
> >>> http://www.jsoftware.com/papers/fork.htm>paper (which
> >>> introduced fork):
> >>>
> >>> (-b)(+,-)√((b*2)-4×a×c)÷2×a
> >>>
> >>> √ is a postulated APL primitive, spelled %: in J.
> >>>
> >>>
> >>>
> >>>
> >>> On Tue, Dec 11, 2012 at 10:49 AM, km < <mailto:[email protected]>
> >>> [email protected]> wrote:
> >>>
> >>>> What is the coolest way of programming the quadratic formula in
> >>>> J? We
> >> are
> >>>> finding the roots of polynomial c + x*(b + x*a) without using p.
> >>>> . I
> >> offer
> >>>>
> >>>> roots
> >>>> 3 : 0
> >>>> 'a b c' =. y
> >>>> q =. %: (b^2) - 4*a*c
> >>>> (2*a) %~ (-b) + q,-q
> >>>> )
> >>>> roots 1 3 2
> >>>> _1 _2
> >>>> roots 1 0 1
> >>>> 0j1 0j_1
> >>>> roots 1 _2 1
> >>>> 1 1
> >>>>
> >>>> partly as problem definition. I am looking for cool roots verbs!
> >>>>
> >>>> Kip Murray
> >>>>
> >>>> Sent from my iPad
> >>>>
> >>>> -----------------------------------------------------------------
> >>>> ----- For information about J forums see
> <http://www.jsoftware.com/forums.htm> http://www.jsoftware.com/forums.htm
> >>> ------------------------------------------------------------------
> >>> ---- For information about J forums see
> >>> <http://www.jsoftware.com/forums.htm> http://www.jsoftware.com/forums.htm
> >> -------------------------------------------------------------------
> >> --- For information about J forums see
> >> <http://www.jsoftware.com/forums.htm> http://www.jsoftware.com/forums.htm
> > --------------------------------------------------------------------
> > -- For information about J forums see
> > <http://www.jsoftware.com/forums.htm> http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see <http://www.jsoftware.com/forums.htm>
> http://www.jsoftware.com/forums.htm
>
----------------------------------------------------------------------
For information about J forums see <http://www.jsoftware.com/forums.htm>
http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
