[Jprogramming] inverse oblique

[Don Guinn]

In a first algebra class the teacher gave us some expressions to
"simplify". Most were pretty obvious. But a few had more than one
expression that was the "simplest". They really bothered me because if I
didn't choose the one the teacher thought was the "simplest" she would mark
it wrong.

On Sat, Feb 2, 2013 at 12:00 AM, Linda Alvord <lindaalvord at verizon.net>wrote:

> I remember fondly how Ken loved to read the unabridged dictionary. Richness
> of the language and the derivations of the words was a joyous experience
> for him.  The J language has this same richness.
>
> For students coming to the language with years of mathematical background
> in abstract algebra, calculus, differential equations and the like, they
> are ready t o jump easily to abstract combinations.
>
> I keep thinking in terms of the long time it takes high school students to
> master functional notation like  f(x)  and  g(x).
>
>
> To get from  t1 to t2 requires and "idiom"  x u&v y ↔ (v x) u (v y)
>
> t1=: 13 :'(2{.x)$(;y)/:;</.i.x'
> t2=: 13 :'(2{.x)$y/:&;</.i.x'
>
> So although t1 is longer than t2,  t2 is more condensed and compex.  This
> is why I say easier:
>
>     t1
> (2 {. [) $ ([: ; ]) /: [: ; [: </. [: i. [
>     t2
> (2 {. [) $ ] /:&; [: </. [: i. [
>
> The condensed spacing of  /:&;  gives away the increased complexity of the
> second tacit version.
>
> My guess is that you would spend less time reading the dictionary to master
> t1 than t2.
>
> Linda
>
> -----Original Message----- wo
> From: programming-bounces at forums.jsoftware.com [mailto:programming-
> bounces at forums.jsoftware.com] On Behalf Of Raul Miller
> Sent: Friday, February 01, 2013 9:20 AM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] inverse oblique
>
> How do you define "easier"?
>
> In my opinion, it's easier to go from simple (fewer tokens) to complex
> (more tokens), but also someone has to write the code to do the
> transformation and until that's been done even this concept of "easier" can
> be indistinguishable from "can't be done".
>
> --
> Raul
>
> On Fri, Feb 1, 2013 at 5:05 AM, Linda Alvord <lindaalvord at verizon.net>
> wrote:
> >  If t1 is easy tacit and t2 is advanced tacit, wouldn't it be easier
> > for  J to figure  t2  from  t1  than it is for me?
> >
> >     t=: 5 7 2 ?@$ 1e6
> >     s=: $t
> >     x=: </.t
> >    t1=: 13 :'(2{.x)$(;y)/:;</.i.x'
> >    t-:s f x
> > 1
> >    t2=: 13 :'(2{.x)$y/:&;</.i.x'
> >    t-:s g x
> > 1
> >    t1
> > (2 {. [) $ ([: ; ]) /: [: ; [: </. [: i. [
> >    t2
> > (2 {. [) $ ] /:&; [: </. [: i. [
> >
> > Or is that just wishful thinking?
> >
> > Linda
> >
> >
> > -----Original Message-----
> > From: programming-bounces at forums.jsoftware.com
> > [mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Roger
> > Hui
> > Sent: Thursday, January 31, 2013 1:49 PM
> >  To: Programming forum
> > Subject: Re: [Jprogramming] inverse oblique
> >
> >    t -: (2{.s) $ x /:&; </.i.s
> > 1
> >
> >
> >
> > On Thu, Jan 31, 2013 at 10:47 AM, Roger Hui
> > <rogerhui.canada at gmail.com>wrote:
> >
> >>    t=: 5 7 2 ?@$ 1e6
> >>    s=: $t
> >>    x=: </.t
> >>
> >>    t -: (2{.s) $ (;x)/:;</.i.s
> >> 1
> >>
> >>
> >>
> >> On Thu, Jan 31, 2013 at 10:28 AM, Raul Miller
> > <rauldmiller at gmail.com>wrote:
> >>
> >>> Let's start with an arbitrary array:
> >>>
> >>>    A=: i. 2 3
> >>>
> >>> We can box oblique lines from this array:
> >>>
> >>>    </. A
> >>> +-+---+---+-+
> >>> |0|1 3|2 4|5|
> >>> +-+---+---+-+
> >>>
> >>> However, the interpreter does not currently provide us with an
> >>> inverse for this operation:
> >>>
> >>>    </.inv </. A
> >>> |domain error
> >>>
> >>> One problem is that you cannot uniquely determine the first two
> >>> elements of the shape of the original array by inspecting </.'s
> >>> result:
> >>>
> >>>    (</. 5 7$0) -: </.7 5$0
> >>> 1
> >>>
> >>> If its shape is provided, how might we reconstruct the original array?
> >>>
> >>> [For the sake of simple code, it's ok to focus on numeric, rank 2
> >>> arrays.]
> >>>
> >>> --
> >>> Raul
> >>> --------------------------------------------------------------------
> >>> -
> >>> - For information about J forums see
> >>> http://www.jsoftware.com/forums.htm
> >>>
> >>
> >>
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