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
>>
>
>
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