Click above to see sets!
]set=:<1;2;3
┌───────┐
│┌─┬─┬─┐│
││1│2│3││
│└─┴─┴─┘│
└───────┘
This match my idea of sets and subsets. The subsets are “names” for the
subsets.
psla=: 13 :'<"0<"0 <"1 |:((>:i.#y)*/"0 |:(|:|.|:(#y)#2)#:i.2^#y){A=:''
'',":10#.>>y'
psla 1;2;3
┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│┌─────┐│┌─────┐│┌─────┐│┌─────┐│┌─────┐│┌─────┐│┌─────┐│┌─────┐│
││┌───┐│││┌───┐│││┌───┐│││┌───┐│││┌───┐│││┌───┐│││┌───┐│││┌───┐││
│││ │││││ 3│││││ 2 │││││ 23│││││1 │││││1 3│││││12 │││││123│││
││└───┘│││└───┘│││└───┘│││└───┘│││└───┘│││└───┘│││└───┘│││└───┘││
│└─────┘│└─────┘│└─────┘│└─────┘│└─────┘│└─────┘│└─────┘│└─────┘│
└───────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
A
123
$A
4
I can’t explain how this happens! Any ideas?
psla set
┌─────┬─────┐
│┌───┐│┌───┐│
││┌─┐│││┌─┐││
│││ │││││1│││
││└─┘│││└─┘││
│└───┘│└───┘│
└─────┴─────┘
A
123
$A
4
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of km
Sent: Sunday, November 17, 2013 1:03 AM
To: [email protected]
Subject: Re: [Jprogramming] Sets
You are getting closer. I start with
set 1;2;3
+-------+
|+-+-+-+|
||1|2|3||
|+-+-+-+|
+-------+
and end with
ps set 1;2;3
+--------------------------------------------------------+
|+--+-----+-------+---------+-------+-----+-------+-----+|
||++|+---+|+-----+|+-------+|+-----+|+---+|+-----+|+---+||
||||||+-+|||+-+-+|||+-+-+-+|||+-+-+|||+-+|||+-+-+|||+-+|||
||++|||1|||||1|2|||||1|2|3|||||1|3|||||2|||||2|3|||||3||||
|| ||+-+|||+-+-+|||+-+-+-+|||+-+-+|||+-+|||+-+-+|||+-+|||
|| |+---+|+-----+|+-------+|+-----+|+---+|+-----+|+---+||
|+--+-----+-------+---------+-------+-----+-------+-----+|
+--------------------------------------------------------+
The result looks exactly the same if you start with
set '1';'2';'3'
+-------+
|+-+-+-+|
||1|2|3||
|+-+-+-+|
+-------+
"A set is box enclosing a list of boxes. Each box in the enclosed list
contains an element of the set."
--Kip
Sent from my iPad
> On Nov 16, 2013, at 6:46 PM, "Linda Alvord" <[email protected]> wrote:
>
> This looks more like your result:
>
> f=: 13 :'<"0<"0 <"1 |:((>:i.#y)*/"0 |:(|:|.|:(#y)#2)#:i.2^#y){'' '',y'
>
> f '123'
> --------T-------T-------T-------T-------T-------T-------T-------┐
> │------┐│------┐│------┐│------┐│------┐│------┐│------┐│------┐│
> ││----┐│││----┐│││----┐│││----┐│││----┐│││----┐│││----┐│││----┐││
> │││ │││││ 3│││││ 2 │││││ 23│││││1 │││││1 3│││││12 │││││123│││
> ││L----│││L----│││L----│││L----│││L----│││L----│││L----│││L----││
> │L------│L------│L------│L------│L------│L------│L------│L------│
> L-------+-------+-------+-------+-------+-------+-------+--------
>
> Linda
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of km
> Sent: Saturday, November 16, 2013 2:13 AM
> To: [email protected]
> Subject: [Jprogramming] Sets
>
> The following script for doing sets in J is a big improvement over
> what I proposed several years ago. You can save it and then do a
> loadd. I would like to make it a J Wiki page, but it will take a
> while to relearn how to do that. Near the end is my verb ps for
> creating power sets and another cp for creating the Cartesian product
> of two sets. --Kip Murray
>
> NB. A set is a box with a sorted list of boxes inside.
> NB. An element is the contents of a box in the sorted list.
> NB. A -: B tests whether set A is set B.
>
> set =: [: < [: /:~ ~. NB. create set from a box or list of boxes
>
> isset =: -: [: set > NB. test whether y is a set
>
>
> set 'a';i.2 2 NB. elements are 'a' and i. 2 2
>
> set <'a' NB. sole element is 'a'
>
> ]Empty =: set '' NB. the empty set, same as Ace a:
>
> isset Empty
>
>
> sf =: [: > ({ >) NB. From { for sets: retrieve xth element of y, a
> set
>
> sn =: ([: # >) : ([: < (# >)) NB. Number # for sets
>
> eo =: <@[ e. >@] NB. test whether x is an element of y
>
> un =: [: set ,&> NB. union of x and y
>
> mn =: [: < -.&> NB. "minus" -- create set with the elements of x that
> are not in y
>
> sd =: mn un mn~ NB. symmetric difference
>
> nt =: un mn sd NB. intersection
>
> so =: un -: ] NB. test whether x is a subset of y
>
> cp =: [: set [: , ({@(,&<))&> NB. Cartesian product, adapted from CP
> in Vocabulary's "Catalog {"
>
> ps =: [: set [: <"0 ([: #: [: i. 2 ^ #@>) <@#"1 > NB. ps y is the
> power set of y
>
> NB. ps y is the set whose elements are all the subsets of y . There
> are 2^#>y of them.
>
> dv =: [: < [: ,. > NB. dv y displays the set y vertically, useful for
> power sets!
>
>
> (set 1;2;3;3) -: set 3;1;2 NB. On each side the elements are 1 and 2
> and 3 .
>
> ]A =: set 2;'b';1;'a'
>
> ]B =: set 'b';'a';4;3;'a'
>
> A un B
>
> A sd B
>
> A nt B
>
> (set 1;2) cp set 'a';'b';'c'
>
> ps set 0;1;2
>
>
> Sent from my iPad
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