In the case of i: it is not really complex numbers but a convenient way to pair two numbers into a scalar. This is done with # as well.
1 2j1 1j2 1#'ABCD' ABB C D On Tue, Jan 15, 2013 at 8:43 PM, Linda Alvord <[email protected]>wrote: > How can i:2j8 have two different results. One is correct using the rules > of > J mentally and the other different result the computer provides. > > Linda > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Raul Miller > Sent: Tuesday, January 15, 2013 7:58 PM > To: [email protected] > Subject: Re: [Jprogramming] atop continues to puzzle me > > And this is indeed a correct model. > > But note that it's entirely possible to have a different thought process > about what's happening here. > > As long as there are not too many spaces (you can have spaces after the > colon but the rest of this phrase does not tolerate spaces), it's just a > recipe which can work without a deeper understanding of the design. > > -- > Raul > > On Tue, Jan 15, 2013 at 5:50 PM, Linda Alvord <[email protected]> > wrote: > > I'm not sure who you are asking this question. My answer would be > > that I read from right to left and you come to 2j8 first. This is a > > complex number to my way of thinking. Thus I get i: applied to a > > single number. In this case you get something like: > > > > i:4 > > _4 _3 _2 _1 0 1 2 3 4 > > > > The sit of complex numbers are unordered so this is meaningless. > > > > Linda > > > > -----Original Message----- > > From: [email protected] > > [mailto:[email protected]] On Behalf Of Raul > > Miller > > Sent: Tuesday, January 15, 2013 3:17 PM > > To: [email protected] > > Subject: Re: [Jprograming] atop continues to puzzle me > > > > Why is the j in i:2j8 more important than the i? wa > > > > -- > > Raul > > > > 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 > > ---------------------------------------------------------------------- > > 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
