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
