That isn't what complex | does, or what it should do, I think. However, it is a consistent extension of "mod" to the complex numbers--we are just using a different subgroup of the complex numbers to mod out by. Note, however, that this approach adapts poorly to complex left arguments. It still works, by subtracting (real) integer multiples of x from y, but the resultant range is a weird bar in the complex plane. As you noted, it's easy to define your version in terms of real | .
Marshall On Sun, Jan 22, 2012 at 2:27 PM, Bo Jacoby <bojac...@yahoo.dk> wrote: > I wanted to take 'mod' of the real part and leave the imaginary part > untouched. > f=:(|9&o.)+j.&(11&o.)&] > 7 f 73j73+i.6 > 3j73 4j73 5j73 6j73 0j73 1j73 > Perhaps this is not done by a complex '|' ? > > > > > >________________________________ > > Fra: Marshall Lochbaum <mwlochb...@gmail.com> > >Til: Programming forum <programming@jsoftware.com> > >Sendt: 19:50 søndag den 22. januar 2012 > >Emne: Re: [Jprogramming] 5|0 1 2 3 4 is not equal to 5|0 1 2 3 4 j.0 > > > >It would be possible to change complex mod without changing floor. Floor > is > >consistent on reals and complex numbers, while complex mod is not, so it > >doesn't necessarily need to be fixed. > > > >The problem with complex mod is that for left argument b it that it > ensures > >that the result is in the box defined by corners -:(j./~ _0.5 0.5)*b . > That > >means that it subtracts the closest Gaussian integer multiple of b from > the > >right argument. This is inconsistent with mod for the reals, which > >subtracts the floor under division by b. > > > >Marshall > > > >On Sun, Jan 22, 2012 at 1:28 PM, Henry Rich <henryhr...@nc.rr.com> wrote: > > > >> Well, I know complex floor was something Gene McDonnell was proud of, > >> and I expect it's embedded in some applications. You'll need to produce > >> a compelling argument for changing it. > >> > >> Henry Rich > >> > >> On 1/22/2012 12:38 PM, Marshall Lochbaum wrote: > >> > I'm pretty sure I understand the definition, but I still don't get the > >> > rationale. Under my scheme the "obvious" complex floor would be (- > 1&|), > >> > which also has the properties of convexity, translatability, and > >> > compatibility listed in the dictionary. > >> > > >> > Marshall > >> > > >> > On Sun, Jan 22, 2012 at 12:08 PM, Henry Rich<henryhr...@nc.rr.com> > >> wrote: > >> > > >> >> As Don said, make sure you understand complex floor before you start > >> >> coding. > >> >> > >> >> Henry Rich > >> >> > >> >> On 1/22/2012 11:38 AM, Marshall Lochbaum wrote: > >> >>> The theory of moduli is based on the quotient group of the integers > by > >> a > >> >>> subgroup. For instance, the integers (mod 2) are produced by taking > all > >> >> the > >> >>> integers and identifying all the ones that are even, as well as all > the > >> >>> ones that are odd. Then we get a two-element group which we can > preform > >> >>> addition on: even+even=even, even+odd=odd, etc. > >> >>> > >> >>> To reduce a number in a particular modulus, we need to find a > canonical > >> >>> representation for that number. For positive numbers n the choice is > >> >> fairly > >> >>> simple: n|l gives the l' such that 0<=l'<n. In the complex plane, a > >> >> number > >> >>> generates a grid by taking its product with the Gaussian integers; > try > >> >>> 'dot; pensize 2' plot , 1j2 * j./~i:10 > >> >>> to see what I mean. Then what we want is a canonical form for what > >> >> happens > >> >>> when we identify all those points together. We're allowed to > "shift" by > >> >> any > >> >>> Gaussian integer times the modulus. > >> >>> > >> >>> Based on this, I think a good way to calculate the modulus is to get > >> the > >> >>> number into the square that lies counterclockwise of the modulus > >> number. > >> >>> Practically, this means we decompose a complex number y into (a > j.b)*x, > >> >> and > >> >>> then return (1|a)j.(1|b) . > >> >>> > >> >>> I'll see if I can get around to editing this. I have a working copy > of > >> >> the > >> >>> source, but I haven't made sense of it entirely. > >> >>> > >> >>> Marshall > >> >>> > >> >>> On Sun, Jan 22, 2012 at 10:45 AM, Raul Miller<rauldmil...@gmail.com > > > >> >> wrote: > >> >>> > >> >>>> Yes, this is a bug. > >> >>>> > >> >>>> Someone should fix it. > >> >>>> > >> >>>> J is open source. (Though distributed sources do not compile for > me, > >> >>>> and I keep getting sidetracked when I investigate forks that might > >> >>>> compile.) > >> >>>> > >> >>>> -- > >> >>>> 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 > > > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
