My initial goal was to find all the divisors of a number, eg 100:
Get the prime factors:
q:100
2 2 5 5
Get all combinations of those prime factors (the power set)
ps0 =: #:@i.@(2&^)@#<@#"1 _]
ps0 q:100
┌┬─┬─┬───┬─┬───┬───┬─────┬─┬───┬───┬─────┬───┬─────┬─────┬───────┐
││5│5│5 5│2│2 5│2 5│2 5 5│2│2 5│2 5│2 5 5│2 2│2 2 5│2 2 5│2 2 5 5│
└┴─┴─┴───┴─┴───┴───┴─────┴─┴───┴───┴─────┴───┴─────┴─────┴───────┘
Get the products of each box:
*/ each ps0 q: 100
┌─┬─┬─┬──┬─┬──┬──┬──┬─┬──┬──┬──┬─┬──┬──┬───┐
│1│5│5│25│2│10│10│50│2│10│10│50│4│20│20│100│
└─┴─┴─┴──┴─┴──┴──┴──┴─┴──┴──┴──┴─┴──┴──┴───┘
Get the unique set of divisors and sort them:
/:~ ~.>*/ each ps0 q:100
1 2 4 5 10 20 25 50 100
Now thanks to everyone's help, I can find all the divisors of any number:
f=.3 :'/:~ ~.>*/ each ps0 q:y'
f 110
1 2 5 10 11 22 55 110
f 43
1 43
f 444
1 2 3 4 6 12 37 74 111 148 222 444
Skip
Skip Cave
Cave Consulting LLC
On Mon, Oct 2, 2017 at 2:40 PM, Raul Miller <[email protected]> wrote:
> Perhaps this is closer to what you want?
>
> F=:1 :', u@> { (~. (u@#"0~ i.@>:)&.> #/.~) y'
> f=: /F
>
> *f 2 2 5 7
> 1 7 5 35 2 14 10 70 4 28 20 140
> +f 2 2 5 7
> 0 7 5 12 2 9 7 14 4 11 9 16
>
> I probably should just merge the two definitions together, but I think
> this works?
>
> (Note that I have sort of assumed that the verb argument to f is an
> associative verb. If you're doing something where that is not the
> case... well... I guess I would need more specification.)
>
> Thanks,
>
> --
> Raul
>
>
> On Mon, Oct 2, 2017 at 3:17 PM, Skip Cave <[email protected]> wrote:
> > Sorry about the wrong terminology. What i meant was:
> >
> > Given a vector of random integers (there may be duplicates), what is the
> > most concise and or efficient way to
> > generate a list of the numbers along with the sum of all combinations of
> > the numbers in a single vector? How about the products of all
> > combinations?
> >
> > Skip Cave
> > Cave Consulting LLC
> >
> > On Mon, Oct 2, 2017 at 1:51 PM, Raul Miller <[email protected]>
> wrote:
> >
> >> Prime factors of an integer are not, in the general case, a set. And
> >> you really should be careful to avoid specifying a set when what you
> >> want is not a set.
> >>
> >> You might be interested in
> >> https://rosettacode.org/wiki/Factors_of_an_integer#J ?
> >>
> >> That said, refinement is an important part of the specification
> >> process, so - since it seems you were looking for something different
> >> - maybe it's worth redoing the specification?
> >>
> >> Thanks,
> >>
> >> --
> >> Raul
> >>
> >>
> >> On Mon, Oct 2, 2017 at 2:09 PM, Skip Cave <[email protected]>
> wrote:
> >> > My original approach was even more naive than Marc's:
> >> >
> >> > NB. from Roger Hui's Combinations essay on the J website:
> >> > https://goo.gl/WL4nXn
> >> >
> >> > c=: ((= +/"1) |.@:I.@# ]) #:@i.@(2&^) NB. Roger called this
> >> 'comb2'
> >> >
> >> > NB. I used this definition because I could cut & paste one line, and
> not
> >> > require an editor
> >> >
> >> > a =. 2 2 5 5
> >> >
> >> > ~.(*/"1(4 c 4){a),(*/"1(3 c 4){a),(*/"1(2 c 4){a),, |:(1 c 4){a
> >> >
> >> > 100 20 50 4 10 25 2 5
> >> >
> >> >
> >> > I like to sort it:
> >> >
> >> > /:~~.(*/"1(4 c 4){a),(*/"1(3 c 4){a),(*/"1(2 c 4){a),, |:(1 c
> 4){a
> >> >
> >> > 2 4 5 10 20 25 50 100
> >> >
> >> >
> >> > The final goal of this exercise was to find all the divisors of an
> >> integer
> >> > (not just the prime divisors).
> >> >
> >> >
> >> > So you need to find the prime factors of the integer, for example 100:
> >> >
> >> >
> >> > ]a =. q:100
> >> >
> >> > 2 2 5 5
> >> >
> >> > /:~~.(*/"1(4 c 4){a),(*/"1(3 c 4){a),(*/"1(2 c 4){a),,
> |:(1 c
> >> 4){a
> >> >
> >> > 2 4 5 10 20 25 50 100
> >> >
> >> >
> >> > So these are all the divisors of 100.
> >> >
> >> >
> >> > To use Raul's verb, it needs some mods. I can't do the unique until
> the
> >> > end, because prime factors of an integer are often duplicated.
> >> >
> >> >
> >> > F1=:1 :'u@#~ #:@i.@(2^#)' NB. Here's Raul's verb minus
> the
> >> initial
> >> > unique
> >> >
> >> > */F1 q:100 NB. we take the product
> >> >
> >> > 1 5 5 25 2 10 10 50 2 10 10 50 4 20 20 100
> >> >
> >> > ~.*/F1 q:100 NB. Now we take the unique
> >> >
> >> > 1 5 25 2 10 50 4 20 100
> >> >
> >> > /:~~.*/F1 q:100 NB. Sort it to make it pretty
> >> >
> >> > 1 2 4 5 10 20 25 50 100
> >> >
> >> >
> >> > Didn't really need the 1, but Raul likes the empty combination.
> >> >
> >> >
> >> > Now we put it all in one verb:
> >> >
> >> >
> >> > F2=. /:~~.*/F1 q:
> >> >
> >> > F2 100
> >> >
> >> > |length error: F2
> >> >
> >> > | F2 100
> >> >
> >> > F2=. /:~~.*/F1 q:]
> >> >
> >> > F2 100
> >> >
> >> > |domain error: F2
> >> >
> >> > | F2 100
> >> >
> >> >
> >> > So this is above my pay grade. I'll have to stick with my inline code:
> >> >
> >> >
> >> > /:~~.*/F1 q:110
> >> >
> >> > 1 2 5 10 11 22 55 110
> >> >
> >> > /:~~.*/F1 q:43
> >> >
> >> > 1 43
> >> >
> >> > /:~~.*/F1 q:45
> >> >
> >> > 1 3 5 9 15 45
> >> >
> >> > /:~~.*/F1 q:444
> >> >
> >> > 1 2 3 4 6 12 37 74 111 148 222 444
> >> >
> >> >
> >> > So I can find all the divisors of an integer.
> >> >
> >> >
> >> > Skip
> >> >
> >> >
> >> >
> >> >
> >> >
> >> >
> >> > Skip Cave
> >> > Cave Consulting LLC
> >> >
> >> > On Mon, Oct 2, 2017 at 12:15 PM, Marc Simpson <[email protected]>
> wrote:
> >> >
> >> >> More naive than Raul's approach, first pass using the 'stats' lib:
> >> >>
> >> >> a=.2 5 7
> >> >> require'stats'
> >> >> combv=: ] {~ (comb #@])
> >> >> 3 combv a
> >> >> 2 5 7
> >> >> 2 combv a
> >> >> 2 5
> >> >> 2 7
> >> >> 5 7
> >> >> 1 combv a
> >> >> 2
> >> >> 5
> >> >> 7
> >> >> combos=: (1 + i.@#) <@combv"0 1 ]
> >> >> combos a
> >> >> ┌─┬───┬─────┐
> >> >> │2│2 5│2 5 7│
> >> >> │5│2 7│ │
> >> >> │7│5 7│ │
> >> >> └─┴───┴─────┘
> >> >> f=: 1 : ';u/"1 each combos y'
> >> >> +f a
> >> >> 2 5 7 7 9 12 14
> >> >> *f a
> >> >> 2 5 7 10 14 35 70
> >> >>
> >> >> /M
> >> >>
> >> >> On Mon, Oct 2, 2017 at 10:06 AM, Raul Miller <[email protected]>
> >> >> wrote:
> >> >> > For a first effort, I would go with
> >> >> >
> >> >> > F=:1 :'(u@#~ #:@i.@(2^#))@~.'
> >> >> > f=: /F
> >> >> >
> >> >> > Hopefully that makes the issues obvious - the specification here
> calls
> >> >> > for a result which grows exponentially with the size of the
> argument
> >> >> > set.
> >> >> >
> >> >> > Also:
> >> >> >
> >> >> > The ~. might be extra work, but for typical cases the effort of
> >> >> > ensuring that the argument is a set is trivial compared to the
> effort
> >> >> > of constructing the result.
> >> >> >
> >> >> > You did not include the empty combination in your example results,
> but
> >> >> > given your specification my initial inclination is to treat that
> as an
> >> >> > oversight.
> >> >> >
> >> >> > I defined F instead of going straight for f because for testing
> >> >> > purposes I want to be able to do (<F a), and perhaps similar
> things.
> >> >> >
> >> >> > Thanks,
> >> >> >
> >> >> > --
> >> >> > Raul
> >> >> >
> >> >> >
> >> >> > On Mon, Oct 2, 2017 at 12:49 PM, Skip Cave <
> [email protected]>
> >> >> wrote:
> >> >> >> Given a set of integers, what is the most concise and or efficient
> >> way
> >> >> to
> >> >> >> list the numbers along with the sum of all combinations of the
> >> numbers?
> >> >> the
> >> >> >> products of all combinations?
> >> >> >>
> >> >> >> for example:
> >> >> >>
> >> >> >> a =. 2 5 7
> >> >> >> + f a NB. 2, 5, 7, (2+5), (2+7), (5+7), (2+5+7)
> >> >> >> 2 5 7 7 9 12 14
> >> >> >>
> >> >> >> * f a NB. 2, 5, 7, (2*5), (2*7), (5*7), (2*5*7)
> >> >> >> 2 5 7 10 14 35 70
> >> >> >>
> >> >> >> The function 'f' should work for any verb and any size right
> argument
> >> >> noun
> >> >> >> vector.
> >> >> >>
> >> >> >> Skip
> >> >> >>
> >> >> >> Skip Cave
> >> >> >> Cave Consulting LLC
> >> >> >> ------------------------------------------------------------
> >> ----------
> >> >> >> 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
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> >>
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