In an expression like +./&.:(1p1&*)12 30 6
we should note that 12 and 30 are both [small] integers (and, thus, exact). Also, 1p1 is a value close to pi, and while it's true that it's not exactly pi, it's a common factor in this context. So it comes through in the gcd result. Basically it's just an arbitrary value which has an exact representation (which is all that matters in this context). Thanks, -- Raul On Sat, May 16, 2020 at 8:24 AM 'Bo Jacoby' via Programming <programm...@jsoftware.com> wrote: > > Raul, note that this works: > > (+.&.(*&1p1))/2 3 > > 1 > > > > even though the numbers > > 0j16":(*&1p1)2 3 > > 6.2831853071795862 9.4247779607693793 > > do not satisfy your demands of being exactly represented. > Thanks! > Bo > > > > > Den lørdag den 16. maj 2020 13.03.21 CEST skrev Hauke Rehr > <hauke.r...@uni-jena.de>: > > The answer 3j2 looks sane. > 3j2 * 0j1 0j_1 > and the only one in the first quadrant. > Nice! > > Am 16.05.20 um 12:32 schrieb Raul Miller: > > Oh, I see -- or, I think I see what you were trying to illustrate now. > > > > That said, this is kind of interesting: > > +./(,-)2j_3 > > 3j2 > > > > But I also noticed that +/(,-) seems to bring back associativity (we > > already had commutativity with +.): > > > > (i.6) A."0 1]4.57 4.34 4.44 > > 4.57 4.34 4.44 > > 4.57 4.44 4.34 > > 4.34 4.57 4.44 > > 4.34 4.44 4.57 > > 4.44 4.57 4.34 > > 4.44 4.34 4.57 > > +./@(,-)"1 (i.6) A."0 1]4.57 4.34 4.44 > > 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 8.88178e_16 > > > > Thanks, > > > > > > -- > > Raul > > > > On Sat, May 16, 2020 at 5:51 AM Hauke Rehr <hauke.r...@uni-jena.de> wrote: > >> > >> sorry, I was not sufficiently precise about my example > >> I meant to talk about atomic a only > >> > >> if $ a is empty, then > >> +./ (, -) a > >> will work > >> > >> Thanks for pointing out the lack of precision. > >> > >> Am 16.05.20 um 11:46 schrieb Raul Miller: > >>> I was talking about the implementation. > >>> > >>> These are different results: > >>> > >>> +./@(,-)4.57 4.34 4.44 > >>> 8.88178e_16 > >>> +./@(,-)&.x:4.57 4.34 4.44 > >>> 0.01 > >>> +./@(,-)&.:(*&1p1)4.57 4.34 4.44 > >>> 5.65432e_16 > >>> > >>> The reason is that binary floating point cannot represent 5^_1 nor > >>> 5^_2 accurately. > >>> > >>> Thanks, > >>> > >> > >> -- > >> ---------------------- > >> mail written using NEO > >> neo-layout.org > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > ---------------------- > mail written using NEO > neo-layout.org > ---------------------------------------------------------------------- > 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
