Some remarks.
1. A set is not required to be sorted, so I would propose (set=: <@~. ) .
2. Why not (Empty=: a:) ?
3. sf=: >@{S:1 NB. retrieve element from
4. eo=: e.S:0 NB. Is element of
5. un=: set@; NB. Union; also for a list of sets
6. your mn can be shorter: (mn=: -.&.>) or nicer (mn=: -.L:1) NB. minus
7. nt=: [ mn mn NB. Intersection; or
nt=: mn/ NB. Intersection for a list of sets
9. dv=: ,.L:1 NB. Display vertically
10. eq=: mn -: mn~ NB. Equality; important since sets are not sorted
R.E. Boss
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> -----Original Message-----
> From: [email protected] [mailto:programming-
> [email protected]] On Behalf Of km
> Sent: zaterdag 16 november 2013 8:13
> 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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