ps=: a:,[:(],[,,L:1)/ <L:0@> ,.L:1 ps B
+-+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | |+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+| | ||3|||4|||4|||a|||a|||a|||a|||b|||b|||b|||b|||b|||b|||b|||b|| | |+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+|+-+| | | | ||3|| ||3|||4|||4|| ||3|||4|||4|||a|||a|||a|||a|| | | | |+-+| |+-+|+-+|+-+| |+-+|+-+|+-+|+-+|+-+|+-+|+-+| | | | | | | | ||3|| | | ||3|| ||3|||4|||4|| | | | | | | | |+-+| | | |+-+| |+-+|+-+|+-+| | | | | | | | | | | | | | | | ||3|| | | | | | | | | | | | | | | | |+-+| +-+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ R.E. Boss (Add your info to http://www.jsoftware.com/jwiki/Community/Demographics ) > -----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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
