In the case of "i:", the connection is arbitrary - it's more of a convenience than anything else. Monadic "i: N" returns the integers from _N to N. As this is equivalent to "i:Nj0", the complex argument case of "i:NjP" returning P+1 results does not in fact hold. The case where P~:0 appears to be simply a convenience - I can't fathom a logical relation here.
This could have been implemented as "i: N P" acting like "i:NjP" but "i:" already gives a result for a vector argument. On Tue, Jan 15, 2013 at 3:00 PM, Linda Alvord <[email protected]>wrote: > I am considering the structure of mathematics education. A domain of > numbers > from _2 to 2 in steps of one half could be understood and developed in > elementary school even in J. It is not really sensible until square root > is > mastered. After that an imaginary numbers might show up. So %:_1 becomes > 0j1 in J. It will take a while to master numbers like 2j8 and other > imaginaries. The leap to an idiom which uses 2j8 in a totally different > way is counterproductive until much later. > > How can you explain the connection to imaginary numbers in this expression: > > i:2j8 > _2 _1.5 _1 _0.5 0 0.5 1 1.5 2 > > Linda > > -----Original Message----- > Froch: [email protected] > [mailto:[email protected]] On Behalf Of Raul Miller > Sent: Tuesday, January 15, 2013 11:35 AM > Tr o: [email protected] > Subject: Re: [Jprogramming] atop continues to puzzle me > > I am uncomfortable with this reasoning, because: > > *) i:9j3 is related to complex arithmetic only by notation. > > *) class becomes boring when its pace is set for someine else (when it does > not match the student's needs). > > *) simplicity is good, but so are different perspectives. > > Waiting to introduce imaginary numbers before introducing this notation > seems analogous to waiting to introduce polynomials before introducing > decimal numbers. > > Anyways, I this notation can be optional, but if I were stuck teaching a > class using J (rather than providing guidance, pacing and structure to a > group of students who had been taught how to learn and who were being > responsible for their own education) I think I'd introduce this as an > optional notation about the same time I introduced i: > > -- > Raul > > On Tuesday, January 15, 2013, Linda Alvord <[email protected]> > wrote: > > Devon, Since I think of everything going forward from kindergarten > > (maybe someday we'll do more with prenatal education) I would use Y=: > > _2 + 0.5 * i.9" until the middle of the second year of algebra. > > > > I really like your solution! It would be a great next step when > > teaching imaginary numbers. > > > > Linda > > > > -----Original Message----- > > From: [email protected] > > [mailto:[email protected]] On Behalf Of Devon > > McCormick > > Sent: Monday, January 14, 2013 2:58 PM > > To: J-programming forum > > Subject: Re: [Jprogramming] atop continues to puzzle me > > > > Linda - > > > > a nice short cut for your expression "Y=: _2 + 0.5 * i.9" is "Y=: i:2j8". > > In general, providing the complex argument PjN to i: gives you N+1 > > points from -P to P. > > > > Regards, > > > > Devon > > > > > > On Mon, Jan 14, 2013 at 12:24 PM, Jose Mario Quintana < > > [email protected]> wrote: > > > >> To Henry: > >> > >> My apologies, the worst part is that I noticed the misspelling but I > >> neglected to correct it; I guess watching the playoffs and writing to > >> the forum do not mix very well. > >> > >> To Linda: > >> > >> That is a nice feature; thanks for sharing it. One refreshing thing > >> about J is that one never seems to stop learning it. Moreover, if one > >> follows the forums and this one in particular one is shown (or > >> reminded) how capable the J system really is. > >> > >> On Mon, Jan 14, 2013 at 3:10 AM, Linda Alvord > >> <[email protected]> > >> wrote: > >> > Jose, Here's a simper version. Using the aspect ratio helps make > >> > the derivative more obvious. I use Chrome and I don't know how > >> > this will > >> look > >> > elsewhere. > >> > > >> > Load 'plot' > >> > u=: -: > >> > v=: *: > >> > Y=:_2 + 0.5 * i.9 > >> > f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' > >> > f > >> > plot f Y > >> > 'aspect 1'plot f Y > >> > > >> > Linda > >> > > >> > -----Original Message----- > >> > From: [email protected] > >> > [mailto:[email protected]] On Behalf Of > >> > Linda > >> Alvord > >> > Sent: Sunday, January 13, 2013 9:21 PM > >> > To: [email protected] > >> > Subject: Re: [Jprogramming] atop continues to puzzle me > >> > > >> > load'plot' > >> > > >> > u=: -: > >> > v=: *: > >> > Y=: _2 + 0.01 * i.401 > >> > f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' > >> > f > >> > ] ; [: |: u@v d._2 _1 0 1 2 > >> > plot f Y > >> > > >> > If this is in a jijs and then run, it will shw the graph you > >> > expect bu > >> t > >> > it will provide a long J error message in a separate window. I > >> > don't > >> know > >> > how to prevent it. > >> > > >> > Also, maybe when u@v can be replaced by ([:u v)"v that will > >> > work > >> also. > >> > > >> > Linda > >> > > >> > > >> > -----Original Message----- > >> > From: [email protected] > >> > [mailto:[email protected]] On Behalf Of Jose > >> Mario > >> > Quintana > >> > Sent: Sunday, January 13, 2013 5:17 PM > >> > To: [email protected] > >> > Subject: Re: [Jprogramming] atop continues to puzzle me > >> > > >> > To Raul: > >> > > >> >> I have no idea what "works reasonably well" means. > >> > > >> > That is a very subjective statement, apparently one can make use of > >> > (@) and (@:) within the scope of (d.) but, of course, that depends > >> > on > >> one's > >> > point of view. > >> > > >> >> But consider also: > >> >> > >> >> AT=: 2 :0 > >> >> u@v"v > >> >> ) > >> >> > >> >> +:AT*: d. 1 > >> >> 0 4x&p."0 0 0 > >> >> +:@*: d. 1 > >> >> 0 4x&p. > >> > > >> > Th> >> --- 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 > >> > > > > > > > > -- > > Devon McCormick, CFA > > ^me^ at acm. > > org is my > > preferred e-mail > > ---------------------------------------------------------------------- > > 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 > -- Devon McCormick, CFA ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
