Thanks Raul. I was interested in Skip's example: So, given the full parution set of say 3 par 4
]a =. 3 par 4 ┌───┬───┬───┐ │0 1│2 │3 │ ├───┼───┼───┤ │0 2│1 │3 │ ├───┼───┼───┤ │0 │1 2│3 │ ├───┼───┼───┤ │0 3│1 │2 │ ├───┼───┼───┤ │0 │1 3│2 │ ├───┼───┼───┤ │0 │1 │2 3│ └───┴───┴───┘ I didn't find the definition in the Wiki page. Linda -----Original Message----- From: Programming [mailto:[email protected]] On Behalf Of Raul Miller Sent: Saturday, November 4, 2017 6:50 PM To: Programming forum <[email protected]> Subject: Re: [Jprogramming] Partitions Use parRuskeyE for par - defined in http://www.jsoftware.com/pipermail/programming/2017-November/049493.html Thanks, -- Raul On Sat, Nov 4, 2017 at 4:25 PM, Linda Alvord <[email protected]> wrote: > This thread has gotten very long. I tried to find 'par' but didn't find it. > Any chance you could post it again? Linda > > -----Original Message----- > From: Programming [mailto:[email protected]] On Behalf > Of 'Skip Cave' via Programming > Sent: Saturday, November 4, 2017 4:12 PM > To: [email protected] > Subject: Re: [Jprogramming] Partitions > > Raul > > The purpose of the partitions verb is to find all the n ways to group the > prime factors > 1 of an integer p Then we can */ each partition in each row > to find all the prime *and/or non-prime except 1 factors* that when > multiplied together equals p. > > */ f1, f2, f3, f4, .... fn = p > > Skip > > Skip Cave > Cave Consulting LLC > > On Sat, Nov 4, 2017 at 12:06 PM, Raul Miller <[email protected]> wrote: > >> sel=: {each < >> >> Note also though: >> >> q: 75600 >> 2 2 2 2 3 3 3 5 5 7 >> # q: 75600 >> 10 >> $N=:5 parRuskeyE 10 >> 42525 5 >> $~. /:"1~ */@> N sel q:75600 >> 798 5 >> >> The number of factorizations using factors s greater than 1 of an >> integer will often be different than the number of partitions as we >> had defined them here. >> >> FYI, >> >> -- >> Raul >> >> >> On Sat, Nov 4, 2017 at 1:00 PM, 'Skip Cave' via Programming >> <[email protected]> wrote: >> > So, given the full parution set of say 3 par 4 >> > >> > ]a =. 3 par 4 >> > >> > ┌───┬───┬───┐ >> > >> > │0 1│2 │3 │ >> > >> > ├───┼───┼───┤ >> > >> > │0 2│1 │3 │ >> > >> > ├───┼───┼───┤ >> > >> > │0 │1 2│3 │ >> > >> > ├───┼───┼───┤ >> > >> > │0 3│1 │2 │ >> > >> > ├───┼───┼───┤ >> > >> > │0 │1 3│2 │ >> > >> > ├───┼───┼───┤ >> > >> > │0 │1 │2 3│ >> > >> > └───┴───┴───┘ >> > >> > >> > What would the verb 'sel' look like that would use those indices to >> select >> > from a different set of objects >> > >> > >> > a sel 'abcd' >> > >> > ┌───┬───┬───┐ >> > >> > │a b│c │d │ >> > >> > ├───┼───┼───┤ >> > >> > │a c│b │d │ >> > >> > ├───┼───┼───┤ >> > >> > │a │b c│d │ >> > >> > ├───┼───┼───┤ >> > >> > │a d│b │c │ >> > >> > ├───┼───┼───┤ >> > >> > │a │b d│c │ >> > >> > ├───┼───┼───┤ >> > >> > │a │b │c d│ >> > >> > └───┴───┴───┘ >> > >> > >> > Skip >> > >> > >> > >> > Skip Cave >> > Cave Consulting LLC >> > >> > On Sat, Nov 4, 2017 at 11:09 AM, Skip Cave <[email protected]> >> wrote: >> > >> >> Raul, >> >> Yes, the original Quora question specified positive factors only, >> >> but i forgot to include that in the specification. >> >> >> >> Skip >> >> >> >> Skip Cave >> >> Cave Consulting LLC >> >> >> >> On Sat, Nov 4, 2017 at 3:52 AM, Raul Miller <[email protected]> >> wrote: >> >> >> >>> Well, ok, though that was not a part of your re-specification this >> time. >> >>> >> >>> Actually, though, re-reading your spec, i left out a factor of 16 >> >>> of the solutions: integers can be negative and as long as we >> >>> include an even number of negatives they cancel out in a product. >> >>> >> >>> Thanks, >> >>> >> >>> -- >> >>> Raul >> >>> >> >>> >> >>> On Sat, Nov 4, 2017 at 2:28 AM, 'Skip Cave' via Programming >> >>> <[email protected]> wrote: >> >>> > Raul, very nice! >> >>> > >> >>> > Actually I prefer the solution that doesn't allow 1 as a factor >> >>> > of >> p. Of >> >>> > course, that restricts the max number of partitions to the max >> number of >> >>> > prime factors of any p. That also greatly reduces the number of >> >>> partition >> >>> > instances that will be generated. Then: >> >>> > >> >>> > 5 par 358258 >> >>> > >> >>> > ┌─┬─┬──┬──┬───┐ >> >>> > >> >>> > │2│7│11│13│179│ >> >>> > >> >>> > └─┴─┴──┴──┴───┘ >> >>> > >> >>> > Skip >> >>> > >> >>> > Skip Cave >> >>> > Cave Consulting LLC >> >>> > >> >>> > On Fri, Nov 3, 2017 at 2:40 AM, Raul Miller >> >>> > <[email protected]> >> >>> wrote: >> >>> > >> >>> >> So... 358358 has five prime factors (32 integer factors). We >> >>> >> want to find all sorted sequences (not sets - values can >> >>> >> repeat) of five of those factors whose product is 358358. >> >>> >> >> >>> >> To restrict our search, we can investigate only those sorted >> sequences >> >>> >> of "number of prime factors represented in the variable" whose >> >>> >> sum >> is >> >>> >> five: >> >>> >> >> >>> >> ~./:~"1 (#~ 5=+/"1) 6 #.inv i.6^5 >> >>> >> 0 0 0 0 5 >> >>> >> 0 0 0 1 4 >> >>> >> 0 0 0 2 3 >> >>> >> 0 0 1 1 3 >> >>> >> 0 0 1 2 2 >> >>> >> 0 1 1 1 2 >> >>> >> 1 1 1 1 1 >> >>> >> >> >>> >> In other words, the results of these seven expressions (use >> >>> >> require'stats' first to get comb): >> >>> >> >> >>> >> 1 1 1 1 >> >>> >> >> >>> >> 358358 >> >>> >> (1 1 1,(358358%*/),*/)"1 (4 comb 5){q:358358 >> >>> >> /:~"1 (1 1 1,(358358%*/),*/)"1 (3 comb 5){q:358358 >> >>> >> /:~"1 (1 1,q:@(358358%*/),*/)"1 (3 comb 5){q:358358 >> >>> >> ~./:~"1 (1 1,({.,*/@}.)@q:@(358358%*/),*/)"1 (2 comb 5){q:358358 >> >>> >> /:~"1 (1,q:@(358358%*/),*/)"1 (2 comb 5){q:358358 >> >>> >> q:358358 >> >>> >> >> >>> >> That's 44 different solutions: >> >>> >> >> >>> >> 1 1 1 1 358358 >> >>> >> 1 1 1 179 2002 >> >>> >> 1 1 1 13 27566 >> >>> >> 1 1 1 11 32578 >> >>> >> 1 1 1 7 51194 >> >>> >> 1 1 1 2 179179 >> >>> >> 1 1 1 154 2327 >> >>> >> 1 1 1 182 1969 >> >>> >> 1 1 1 143 2506 >> >>> >> 1 1 1 286 1253 >> >>> >> 1 1 1 91 3938 >> >>> >> 1 1 1 77 4654 >> >>> >> 1 1 1 358 1001 >> >>> >> 1 1 1 26 13783 >> >>> >> 1 1 1 22 16289 >> >>> >> 1 1 1 14 25597 >> >>> >> 1 1 13 154 179 >> >>> >> 1 1 11 179 182 >> >>> >> 1 1 11 13 2506 >> >>> >> 1 1 7 179 286 >> >>> >> 1 1 7 13 3938 >> >>> >> 1 1 7 11 4654 >> >>> >> 1 1 2 179 1001 >> >>> >> 1 1 2 13 13783 >> >>> >> 1 1 2 11 16289 >> >>> >> 1 1 2 7 25597 >> >>> >> 1 1 11 14 2327 >> >>> >> 1 1 7 22 2327 >> >>> >> 1 1 7 26 1969 >> >>> >> 1 1 7 143 358 >> >>> >> 1 1 2 77 2327 >> >>> >> 1 1 2 91 1969 >> >>> >> 1 1 2 143 1253 >> >>> >> 1 11 13 14 179 >> >>> >> 1 7 13 22 179 >> >>> >> 1 7 11 26 179 >> >>> >> 1 7 11 13 358 >> >>> >> 1 2 13 77 179 >> >>> >> 1 2 11 91 179 >> >>> >> 1 2 11 13 1253 >> >>> >> 1 2 7 143 179 >> >>> >> 1 2 7 13 1969 >> >>> >> 1 2 7 11 2327 >> >>> >> 2 7 11 13 179 >> >>> >> >> >>> >> We could of course come up with a routine which does something >> similar >> >>> >> for other examples (but we will run into prohibitive resource >> >>> >> limitations if we allow large enough integers). >> >>> >> >> >>> >> So... just to confirm... this is the problem we are trying to solve? >> >>> >> >> >>> >> Thanks, >> >>> >> >> >>> >> -- >> >>> >> 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
