Looks better. UN=:+./&.([:q:^:_1 p:)
IS=:*./&.([:q:^:_1 p:) 1 2 3 3 3 UN 3 3 3 3 3 4 5 6 3 3 3 1 2 3 3 3 IS 3 3 3 3 3 4 5 6 1 2 3 3 3 3 3 4 5 6 On Tue, Oct 30, 2018 at 7:56 AM Don Guinn <[email protected]> wrote: > You're right. The trick is to make them prime numbers. But it's not pretty. > > IS=:(_1 p:[:q:+.&([:*/[:p:]))/ > > UN=:(_1 p:[:q:*.&([:*/[:p:]))/ > > 1 2 3 3 3 UN 3 3 3 3 3 4 5 6 > > 1 2 3 3 3 3 3 4 5 6 > > 1 2 3 3 3 IS 3 3 3 3 3 4 5 6 > 3 3 3 > > On Tue, Oct 30, 2018 at 4:58 AM 'Bo Jacoby' via Programming < > [email protected]> wrote: > >> >> IS=.+.&.(*/) >> >> UN=.*.&.(*/) >> >> >> This still works for multisets of prime numbers. >> Den tirsdag den 30. oktober 2018 11.55.04 CET skrev 'Bo Jacoby' via >> Programming <[email protected]>: >> >> >> IS=.[:q:+.&(*/) >> >> UN=.[:q:*.&(*/) >> 2 3 3 5 IS 3 5 5 5 >> 3 5 >> 2 3 3 5 UN 3 5 5 5 >> 2 3 3 5 5 5 >> This works for multisets of PRIME numbers only. >> >> >> Den tirsdag den 30. oktober 2018 10.46.17 CET skrev R.E. Boss < >> [email protected]>: >> >> IMO we should interpret the intersection and the union of two >> (multi)sets (sets X with X >:&# ~.X) in the same way as is done by the GCD >> and the LCM of two numbers. >> So for two numbers N and M with (multi)sets of primefactors A and B, we >> should have (N +. M) = */(A IS B) and (N *. M) = */ (A UN B), with >> IS=intersection and UN = union of the (multi)sets A and B. >> Obviously we require (A IS B) =&(/:~) B IS A and also (A UN B) =&(/:~) B >> UN A for all (multi)sets A and B. >> E.g. >> 1 2 3 3 3 IS 3 3 3 3 3 4 5 6 >> 3 3 3 >> 1 2 3 3 3 UN 3 3 3 3 3 4 5 6 >> 1 2 3 3 3 3 3 4 5 6 >> >> What are elegant and efficient J-definitions for IS and UN? >> >> >> I have constructed >> UN_reb=: ([:(~.@{.#~ {. >.//.{:) |:@,&(({.,#)/.~)) >> and >> IS_reb=: ([:(~.@{.#~ {. <.//.{:) ([|:@, ],~ 0,.~ -.~&:({."1), >> -.&:({."1))&(({. , #)/.~)) >> >> 1 2 3 3 3 UN_reb 3 3 3 3 3 4 5 6 >> 1 2 3 3 3 3 3 4 5 6 >> 1 2 3 3 3 IS_reb 3 3 3 3 3 4 5 6 >> 3 3 3 >> 1 2 3 3 3 UN_reb~ 3 3 3 3 3 4 5 6 >> 3 3 3 3 3 4 5 6 1 2 >> 1 2 3 3 3 IS_reb~ 3 3 3 3 3 4 5 6 >> 3 3 3 >> >> a=: 1e7?.@#1e6 >> ts'a UN_reb a+499999' >> 0.76631908 4.6996013e8 >> #a UN_reb a+49999 >> 12186812 >> ts'a IS_reb a+499999' >> 0.76073743 3.3554592e8 >> #a IS_reb a+49999 >> 7813188 >> >> >> R.E. Boss >> ---------------------------------------------------------------------- >> 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
