You are omitting some subsets, for example set 3;4;'b' . There should be sixteen sets in your power set. --Kip Murray
dv =: [: < [: ,. > NB. dv set displays set vertically dv ;@(<@(<\.)\S:1) set 'b';'a';4;3;'a' +---------+ |+-+-+-+-+| ||3| | | || |+-+-+-+-+| ||3|4| | || |+-+-+-+-+| ||4| | | || |+-+-+-+-+| ||3|4|a| || |+-+-+-+-+| ||4|a| | || |+-+-+-+-+| ||a| | | || |+-+-+-+-+| ||3|4|a|b|| |+-+-+-+-+| ||4|a|b| || |+-+-+-+-+| ||a|b| | || |+-+-+-+-+| ||b| | | || |+-+-+-+-+| +---------+ dv ps set 'b';'a';4;3;'a' +-----------+ |+---------+| || || |+---------+| ||+-+ || |||3| || ||+-+ || |+---------+| ||+-+-+ || |||3|4| || ||+-+-+ || |+---------+| ||+-+-+-+ || |||3|4|a| || ||+-+-+-+ || |+---------+| ||+-+-+-+-+|| |||3|4|a|b||| ||+-+-+-+-+|| |+---------+| ||+-+-+-+ || |||3|4|b| || ||+-+-+-+ || |+---------+| ||+-+-+ || |||3|a| || ||+-+-+ || |+---------+| ||+-+-+-+ || |||3|a|b| || ||+-+-+-+ || |+---------+| ||+-+-+ || |||3|b| || ||+-+-+ || |+---------+| ||+-+ || |||4| || ||+-+ || |+---------+| ||+-+-+ || |||4|a| || ||+-+-+ || |+---------+| ||+-+-+-+ || |||4|a|b| || ||+-+-+-+ || |+---------+| ||+-+-+ || |||4|b| || ||+-+-+ || |+---------+| ||+-+ || |||a| || ||+-+ || |+---------+| ||+-+-+ || |||a|b| || ||+-+-+ || |+---------+| ||+-+ || |||b| || ||+-+ || |+---------+| +-----------+ Sent from my iPad > On Nov 14, 2013, at 3:24 PM, "R.E. Boss" <[email protected]> wrote: > > Powerset is given by ;@(<@(<\.)\S:1) > > ;@(<@(<\.)\S:1) set 'b';'a';4;3;'a' > +---+-----+---+-------+-----+---+---------+-------+-----+---+ > |+-+|+-+-+|+-+|+-+-+-+|+-+-+|+-+|+-+-+-+-+|+-+-+-+|+-+-+|+-+| > ||3|||3|4|||4|||3|4|a|||4|a|||a|||3|4|a|b|||4|a|b|||a|b|||b|| > |+-+|+-+-+|+-+|+-+-+-+|+-+-+|+-+|+-+-+-+-+|+-+-+-+|+-+-+|+-+| > +---+-----+---+-------+-----+---+---------+-------+-----+---+ > > > 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: donderdag 14 november 2013 21:18 >> To: [email protected] >> Subject: [Jprogramming] Sets >> >> Here is my latest attempt at sets in J. Would anyone care to write a verb > ps >> (power set) such that ps y is the set of all subsets of set y? It's > called the >> power set in part because when a set has n elements its power set has 2^n >> elements. --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 list. >> NB. A -: B tests whether set A is set B. >> >> set =: [: < [: /:~ ~. NB. create set from list of boxes >> >> NB. The list may have duplicates but the set has none. >> >> EE =: <$0 NB. empty set, same as Ace a: >> >> eo =: <@[ e. >@] NB. test whether x is an element of y >> >> uu =: [: set ,&> NB. union >> >> mm =: [: < -.&> NB. minus >> >> sd =: mm uu mm~ NB. symmetric difference >> >> cp =: uu mm sd NB. common part (intersection) >> >> ss =: uu -: ] NB. test whether x is a subset of y >> >> (set 1;2;3;3) -: set 3;1;2 >> 1 >> >> ]A =: set 2;'b';1;'a' >> +---------+ >> |+-+-+-+-+| >> ||1|2|a|b|| >> |+-+-+-+-+| >> +---------+ >> >> ]B =: set 'b';'a';4;3;'a' >> +---------+ >> |+-+-+-+-+| >> ||3|4|a|b|| >> |+-+-+-+-+| >> +---------+ >> >> A uu B >> +-------------+ >> |+-+-+-+-+-+-+| >> ||1|2|3|4|a|b|| >> |+-+-+-+-+-+-+| >> +-------------+ >> >> A sd B >> +---------+ >> |+-+-+-+-+| >> ||1|2|3|4|| >> |+-+-+-+-+| >> +---------+ >> >> A cp B >> +-----+ >> |+-+-+| >> ||a|b|| >> |+-+-+| >> +-----+ >> >> NB. Below is the set of all subsets of set 0;1 >> >> set EE;(set <0);(set <1);<set 0;1 >> +------------------------+ >> |+--+-----+-------+-----+| >> ||++|+---+|+-----+|+---+|| >> ||||||+-+|||+-+-+|||+-+||| >> ||++|||0|||||0|1|||||1|||| >> || ||+-+|||+-+-+|||+-+||| >> || |+---+|+-----+|+---+|| >> |+--+-----+-------+-----+| >> +------------------------+ >> >> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
