Well, On second thought, I DO want the full set to be included in the subsets (Is THAT the universal set?) So the previous example, the set 1 2 2 3 3 should be in the output sets, but not the null set (though it is easy to get rid of the null set, if eliminating it in the function makes it too complex).
Skip Skip Cave Cave Consulting LLC On Sun, May 8, 2016 at 12:59 AM, Skip Cave <[email protected]> wrote: > Roger, Robert, Nollaig, > > Power Set! So THAT's what it is called! My Electrical Engineering math > courses in the '60s stopped at calculus and matrix algebra, and barely > touched on set theory, so I never knew that all the subsets of a set > had a name. > > In any case, I don't need the function to include the null set or the > universal set, so Nollaig's function looks like it would be what I > want. > > psm =. ((] # 2:) #: >:@i.@(_2: + 2: ^ ])) #L:0"1 <@i. > psmm=: (psm @#){ L:0 <@] > > psmm 1 2 2 3 3 > > > ┌─┬─┬───┬─┬───┬───┬─────┬─┬───┬───┬─────┬───┬─────┬─────┬───────┬─┬───┬───┬─────┬───┬─────┬─────┬───────┬───┬─────┬─────┬───────┬─────┬───────┬───────┐ > > │3│3│3 3│2│2 3│2 3│2 3 3│2│2 3│2 3│2 3 3│2 2│2 2 3│2 2 3│2 2 3 3│1│1 > 3│1 3│1 3 3│1 2│1 2 3│1 2 3│1 2 3 3│1 2│1 2 3│1 2 3│1 2 3 3│1 2 2│1 2 > 2 3│1 2 2 3│ > > └─┴─┴───┴─┴───┴───┴─────┴─┴───┴───┴─────┴───┴─────┴─────┴───────┴─┴───┴───┴─────┴───┴─────┴─────┴───────┴───┴─────┴─────┴───────┴─────┴───────┴───────┘ > > Looks right! > > Now how to I find the products of each subset? > > prod psmm 1 2 2 3 3 > > 3 3 9 2 6 6 18 2 6 6 18 4 12 ....... > > Skip > Skip Cave > Cave Consulting LLC > > > On Sun, May 8, 2016 at 12:35 AM, Nollaig MacKenzie > <[email protected]> wrote: >> My terminal has garbled much of the output, so I >> drop the previous content. >> >> I use >> >> psmn >> ((] # 2:) #: >:@i.@(_2: + 2: ^ ])) #L:0"1 <@i. >> >> which gives the power set without the null set >> and the relative universal set. >> >> Then psmm=: (psm @#){ L:0 <@] >> >> would give what SC wanted (except for the null >> and universal). >> >> Wouldn't be fast, I think. >> >> On 2016.05.08 00:18:40, you, >> the extraordinary Skip Cave, spake thus: >> >>> Nice! However, I realized that I didn't specify my problem in quite >>> enough detail. I need to keep duplicated integers in the final >>> sub-sets: >> >> -- >> Nollaig MacKenzie >> ftp://ftp.nollaig.ca/pub/pap/ >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
