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 <[email protected]>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: [email protected] [mailto:programming- > [email protected]] On Behalf Of Raul Miller > Sent: Friday, February 01, 2013 9:20 AM > To: [email protected] > 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 <[email protected]> > 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: [email protected] > > [mailto:[email protected]] 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 > > <[email protected]>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 > > <[email protected]>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 > >>> > >> > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
