Of course, after I sent the message I noticed that gray11 and solution 6 ( gray6=. (22 b. (_1: 33 b. ]))@:(2 i.@:^ ]) ) are almost identical. Yet, I get these results,
100 st'gray8 19' ┌────────┬──────────┐ │13108864│0.00762324│ └────────┴──────────┘ 100 st'gray6 19' ┌────────┬──────────┐ │12583808│0.00637481│ └────────┴──────────┘ 100 st'gray11 19' ┌────────┬─────────┐ │12583936│0.0062754│ └────────┴─────────┘ Maybe the implementation is different now? On Tue, Nov 19, 2013 at 3:10 PM, Jose Mario Quintana < [email protected]> wrote: > That is a nice shift! Gray3 is certainly an improvement over Gray, > > > > o=. @: > > st=. 7!:2@:] ; 6!:2 > > > > ( xor=. 22 b. ) ( shift=. 33 b. ) > > 22 b. 33 b. > > > > ( Gray=. #: o (xor <. o -: ) f. ) > > #:@:(22 b. <.@:-:) > > ( gray3=. #: o (xor _1&shift) f. ) > > #:@:(22 b. _1&(33 b.)) > > > > (Gray -: gray3) i.524288 > > 1 > > 10 st'Gray i.524288' > > ┌────────┬─────────┐ > > │25166784│0.0399368│ > > └────────┴─────────┘ > > 10 st'gray3 i.524288' > > ┌────────┬─────────┐ > > │25166848│0.0194468│ > > └────────┴─────────┘ > > > > According to the jwiki discussion, solution8 > http://www.jsoftware.com/jwiki/Puzzles/Gray%20Code#soln8 holds the crown, > > > > gray8=. [:>[:(({. * #@]) ,@:+ ($ (,: |.)))&.>/ (<0 1) ,~ 2: <@^ ]((($~ > *)@- +:@{:) , |.@]) i.@<.&.(2&^.) > > gray8 4 > > 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 > > > > One can rewrite grey3 to a compatible form (which turns out to be the > original "Grey" but with the crucial shift instead), > > > > ( gray11=. (xor _1&shift) o i. o (2&^) f. ) > > (22 b. _1&(33 b.))@:i.@:(2&^) > > gray11 4 > > 0 1 3 2 6 7 5 4 12 13 15 14 10 11 9 8 > > > > So, > > > > ( gray8 -: gray11 ) 19 > > 1 > > > > 100 st'gray8 19' > > ┌────────┬─────────┐ > > │13108864│0.0076141│ > > └────────┴─────────┘ > > 100 st'gray11 19' > > ┌────────┬──────────┐ > > │12583936│0.00616758│ > > └────────┴──────────┘ > > > The king is dead, long live the king? > > > > On Mon, Nov 18, 2013 at 5:33 AM, Henry Rich <[email protected]> wrote: > >> Or: >> gray2 =. [: (~: (_1 |.!.0"1 ])) 2&#.^:_1 >> >> >> gray3 =: #:@(22 b. _1&(33 b.)) >> >> >> Henry Rich >> >> >> On 11/18/2013 5:10 AM, R.E. Boss wrote: >> >>> Replace gray by >>> gray=. [: -. [: (= (_1 |.!.0"1 ])) 2&#.^:_1 >>> to allow large(r) Gray codes. >>> >>> See solution 10 on http://www.jsoftware.com/jwiki/Puzzles/Gray%20Code >>> >>> ('0.4';'c12.0') (8!:2) ts' Gray i.524288' NB. 54288=2^19 >>> 0.0247 33,556,352 >>> >>> ('0.4';'c12.0') (8!:2) ts' gray i.524288' NB. 54288=2^19 >>> 0.4365 293,615,616 >>> >>> ('0.4';'c12.0') (8!:2) ts' #:([: ({: (({. * #@]) ,@:+ ($ (,: |.))) >>> ((* #) ,@:+ # $ (,: |.))^:({.`(0: , 1:))) ] (] , 2: ^ (- 2&^)) >>> <.@(2&^.)@<:) 19' >>> 0.0182 26,231,168 >>> >>> (gray i.524288)-: #:([: ({: (({. * #@]) ,@:+ ($ (,: |.))) ((* #) >>> ,@:+ # $ (,: |.))^:({.`(0: , 1:))) ] (] , 2: ^ (- 2&^)) <.@(2&^.)@<:) 19 >>> 1 >>> (Gray i.524288)-: #:([: ({: (({. * #@]) ,@:+ ($ (,: |.))) ((* #) >>> ,@:+ # $ (,: |.))^:({.`(0: , 1:))) ] (] , 2: ^ (- 2&^)) <.@(2&^.)@<:) 19 >>> 1 >>> >>> >>> 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 Jose Mario Quintana >>>> Sent: zondag 17 november 2013 22:28 >>>> To: Programming forum >>>> Subject: Re: [Jprogramming] Sets >>>> >>>> "Grey" and gray are related but they take different arguments and >>>> produce >>>> different results. However, we can compare Gray (derived from Grey) and >>>> gray. Gray is shorter than gray, >>>> >>>> ( gray=. [: -. [: (= (_1 |.!.0"1 ])) bin f. ) NB. Fixed >>>> [: -. [: (= (_1 |.!.0"1 ])) 2 2 2 2&#: >>>> >>>> ( Gray=. #: @: (22 b. <.@:-:) ) NB. Fixed >>>> #:@:(22 b. <.@:-:) >>>> >>>> Gray and gray produce the same result for the given argument, >>>> >>>> (Gray -: gray) i.16 >>>> 1 >>>> >>>> Gray is more efficient than gray, >>>> >>>> 100 st'gray i.16' >>>> ┌────┬─────────────┐ >>>> │2112│4.55809702e_6│ >>>> └────┴─────────────┘ >>>> 100 st'Gray i.16' >>>> ┌────┬─────────────┐ >>>> │1408│3.12123995e_6│ >>>> └────┴─────────────┘ >>>> >>>> and it is more general, >>>> >>>> (Gray ; gray) i.32 >>>> ┌─────────┬───────┐ >>>> │0 0 0 0 0│0 0 0 0│ >>>> │0 0 0 0 1│0 0 0 1│ >>>> │0 0 0 1 1│0 0 1 1│ >>>> │0 0 0 1 0│0 0 1 0│ >>>> │0 0 1 1 0│0 1 1 0│ >>>> │0 0 1 1 1│0 1 1 1│ >>>> │0 0 1 0 1│0 1 0 1│ >>>> │0 0 1 0 0│0 1 0 0│ >>>> │0 1 1 0 0│1 1 0 0│ >>>> │0 1 1 0 1│1 1 0 1│ >>>> │0 1 1 1 1│1 1 1 1│ >>>> │0 1 1 1 0│1 1 1 0│ >>>> │0 1 0 1 0│1 0 1 0│ >>>> │0 1 0 1 1│1 0 1 1│ >>>> │0 1 0 0 1│1 0 0 1│ >>>> │0 1 0 0 0│1 0 0 0│ >>>> │1 1 0 0 0│0 0 0 0│ >>>> │1 1 0 0 1│0 0 0 1│ >>>> │1 1 0 1 1│0 0 1 1│ >>>> │1 1 0 1 0│0 0 1 0│ >>>> │1 1 1 1 0│0 1 1 0│ >>>> │1 1 1 1 1│0 1 1 1│ >>>> │1 1 1 0 1│0 1 0 1│ >>>> │1 1 1 0 0│0 1 0 0│ >>>> │1 0 1 0 0│1 1 0 0│ >>>> │1 0 1 0 1│1 1 0 1│ >>>> │1 0 1 1 1│1 1 1 1│ >>>> │1 0 1 1 0│1 1 1 0│ >>>> │1 0 0 1 0│1 0 1 0│ >>>> │1 0 0 1 1│1 0 1 1│ >>>> │1 0 0 0 1│1 0 0 1│ >>>> │1 0 0 0 0│1 0 0 0│ >>>> └─────────┴───────┘ >>>> >>>> >>>> On Sun, Nov 17, 2013 at 2:53 PM, Bo Jacoby <[email protected]> wrote: >>>> >>>> This program for graycode may be simpler? >>>>> >>>>> bin=.2 2 2 2&#: >>>>> gray=.[:-.[:(=_1|.!.0"1])bin >>>>> bin i.16 >>>>> 0 0 0 0 >>>>> 0 0 0 1 >>>>> 0 0 1 0 >>>>> 0 0 1 1 >>>>> 0 1 0 0 >>>>> 0 1 0 1 >>>>> 0 1 1 0 >>>>> 0 1 1 1 >>>>> 1 0 0 0 >>>>> 1 0 0 1 >>>>> 1 0 1 0 >>>>> 1 0 1 1 >>>>> 1 1 0 0 >>>>> 1 1 0 1 >>>>> 1 1 1 0 >>>>> 1 1 1 1 >>>>> gray i.16 >>>>> 0 0 0 0 >>>>> 0 0 0 1 >>>>> 0 0 1 1 >>>>> 0 0 1 0 >>>>> 0 1 1 0 >>>>> 0 1 1 1 >>>>> 0 1 0 1 >>>>> 0 1 0 0 >>>>> 1 1 0 0 >>>>> 1 1 0 1 >>>>> 1 1 1 1 >>>>> 1 1 1 0 >>>>> 1 0 1 0 >>>>> 1 0 1 1 >>>>> 1 0 0 1 >>>>> 1 0 0 0 >>>>> >>>>> >>>>> >>>>> >>>>> Den 19:40 søndag den 17. november 2013 skrev Jose Mario Quintana < >>>>> [email protected]>: >>>>> >>>>> Thanks for the assertion and the correction. I knew it was named >>>>> after a >>>>> >>>>>> person, hence the upper case G, but I am one of those that reads and >>>>>> >>>>> writes >>>>> >>>>>> phonetically (if you know what I mean) and I could not see (hear) the >>>>>> difference between Gray and grey. >>>>>> >>>>>> On Sun, Nov 17, 2013 at 12:06 PM, Henry Rich <[email protected]> >>>>>> >>>>> wrote: >>>>> >>>>>> >>>>>> Oh - and it's Gray code, not Grey. It's named not because you don't >>>>>>> >>>>>> have >>>>> >>>>>> black-to-white transitions on more than one bit at a time; it's named >>>>>>> >>>>>> for >>>>> >>>>>> Frank Gray. >>>>>>> >>>>>>> >>>>>>> Henry Rich >>>>>>> >>>>>>> On 11/17/2013 11:24 AM, Jose Mario Quintana wrote: >>>>>>> >>>>>>> My understanding is that Grey codes encode numbers in such a way >>>>>>>> >>>>>>> that >>>> >>>>> the >>>>> >>>>>> binary representation of consecutive numbers (including the last and >>>>>>>> >>>>>>> first >>>>> >>>>>> couple) in the sequence can be produced, one from the other, by >>>>>>>> >>>>>>> flipping >>>>> >>>>>> only one bit. >>>>>>>> For example, the binary representation of a four bit Grey sequence, >>>>>>>> of >>>>>>>> >>>>>>> 2^4 >>>>> >>>>>> numbers, and the flipping bit to produce the next number follows, >>>>>>>> >>>>>>>> o=. @: >>>>>>>> ( Grey=. (xor f. <. o -:) o i. o (2&^)) ( xor=. 22 b. ) >>>>>>>> (22 b. <.@:-:)@:i.@:(2&^) 22 b. >>>>>>>> >>>>>>>> (#: ; (2 #: o (xor/\) ]) o (, {.)) o Grey 4 >>>>>>>> ┌───────┬───────┐ >>>>>>>> │0 0 0 0│0 0 0 1│ >>>>>>>> │0 0 0 1│0 0 1 0│ >>>>>>>> │0 0 1 1│0 0 0 1│ >>>>>>>> │0 0 1 0│0 1 0 0│ >>>>>>>> │0 1 1 0│0 0 0 1│ >>>>>>>> │0 1 1 1│0 0 1 0│ >>>>>>>> │0 1 0 1│0 0 0 1│ >>>>>>>> │0 1 0 0│1 0 0 0│ >>>>>>>> │1 1 0 0│0 0 0 1│ >>>>>>>> │1 1 0 1│0 0 1 0│ >>>>>>>> │1 1 1 1│0 0 0 1│ >>>>>>>> │1 1 1 0│0 1 0 0│ >>>>>>>> │1 0 1 0│0 0 0 1│ >>>>>>>> │1 0 1 1│0 0 1 0│ >>>>>>>> │1 0 0 1│0 0 0 1│ >>>>>>>> │1 0 0 0│1 0 0 0│ >>>>>>>> └───────┴───────┘ >>>>>>>> >>>>>>>> However, flipping as many as three bits are sometimes required for >>>>>>>> >>>>>>> the >>>> >>>>> referred sequence, >>>>>>>> >>>>>>>> T=. 0 8 12 14 15 13 10 11 9 4 6 7 5 2 3 1 >>>>>>>> >>>>>>>> (#: ; (2 #: o (xor/\) ]) o (, {.)) T >>>>>>>> ┌───────┬───────┐ >>>>>>>> │0 0 0 0│1 0 0 0│ >>>>>>>> │1 0 0 0│0 1 0 0│ >>>>>>>> │1 1 0 0│0 0 1 0│ >>>>>>>> │1 1 1 0│0 0 0 1│ >>>>>>>> │1 1 1 1│0 0 1 0│ >>>>>>>> │1 1 0 1│0 1 1 1│ >>>>>>>> │1 0 1 0│0 0 0 1│ >>>>>>>> │1 0 1 1│0 0 1 0│ >>>>>>>> │1 0 0 1│1 1 0 1│ >>>>>>>> │0 1 0 0│0 0 1 0│ >>>>>>>> │0 1 1 0│0 0 0 1│ >>>>>>>> │0 1 1 1│0 0 1 0│ >>>>>>>> │0 1 0 1│0 1 1 1│ >>>>>>>> │0 0 1 0│0 0 0 1│ >>>>>>>> │0 0 1 1│0 0 1 0│ >>>>>>>> │0 0 0 1│0 0 0 1│ >>>>>>>> └───────┴───────┘ >>>>>>>> >>>>>>>> Am I missing something? >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Fri, Nov 15, 2013 at 2:07 PM, R.E. Boss <[email protected]> >>>>>>>> wrote: >>>>>>>> >>>>>>>> Actually, it IS a (4D binary reflected) Gray code. >>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> 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 Devon McCormick >>>>>>>>>> Sent: vrijdag 15 november 2013 19:33 >>>>>>>>>> To: J-programming forum >>>>>>>>>> Subject: Re: [Jprogramming] Sets >>>>>>>>>> >>>>>>>>>> These look like Gray codes. >>>>>>>>>> >>>>>>>>>> On Nov 14, 2013 10:04 PM, "Raul Miller" <[email protected]> >>>>>>>>>> >>>>>>>>> wrote: >>>>> >>>>>> >>>>>>>>>> >>>>>>>>>>> Easy enough to add. >>>>>>>>>>> >>>>>>>>>>> It's an interesting progression though: >>>>>>>>>>> >>>>>>>>>>> #:/:&> (<@#~ 2 #:@i.@^ #)&.> set 2;'b';1;'a' >>>>>>>>>>> 0 0 0 0 >>>>>>>>>>> 1 0 0 0 >>>>>>>>>>> 1 1 0 0 >>>>>>>>>>> 1 1 1 0 >>>>>>>>>>> 1 1 1 1 >>>>>>>>>>> 1 1 0 1 >>>>>>>>>>> 1 0 1 0 >>>>>>>>>>> 1 0 1 1 >>>>>>>>>>> 1 0 0 1 >>>>>>>>>>> 0 1 0 0 >>>>>>>>>>> 0 1 1 0 >>>>>>>>>>> 0 1 1 1 >>>>>>>>>>> 0 1 0 1 >>>>>>>>>>> 0 0 1 0 >>>>>>>>>>> 0 0 1 1 >>>>>>>>>>> 0 0 0 1 >>>>>>>>>>> >>>>>>>>>>> -- >>>>>>>>>>> Raul >>>>>>>>>>> >>>>>>>>>>> On Thu, Nov 14, 2013 at 6:06 PM, km <[email protected]> wrote: >>>>>>>>>>> >>>>>>>>>>> Cool; needs a sort. --Kip >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> psr=: (<@#~ 2 #:@i.@^ #)&.> NB. Raul's >>>>>>>>>>>> psr set 0;1 >>>>>>>>>>>> +----------------+ >>>>>>>>>>>> |++---+---+-----+| >>>>>>>>>>>> |||+-+|+-+|+-+-+|| >>>>>>>>>>>> ||||1|||0|||0|1||| >>>>>>>>>>>> |||+-+|+-+|+-+-+|| >>>>>>>>>>>> |++---+---+-----+| >>>>>>>>>>>> +----------------+ >>>>>>>>>>>> ps set 0;1 NB. list inside box is sorted >>>>>>>>>>>> +----------------+ >>>>>>>>>>>> |++---+-----+---+| >>>>>>>>>>>> |||+-+|+-+-+|+-+|| >>>>>>>>>>>> ||||0|||0|1|||1||| >>>>>>>>>>>> |||+-+|+-+-+|+-+|| >>>>>>>>>>>> |++---+-----+---+| >>>>>>>>>>>> +----------------+ >>>>>>>>>>>> >>>>>>>>>>>> Sent from my iPad >>>>>>>>>>>> >>>>>>>>>>>> On Nov 14, 2013, at 3:17 PM, Raul Miller >>>>>>>>>>>> >>>>>>>>>>> <[email protected]> >>>> >>>>> >>>>>>>>>>>>> wrote: >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> Derived from ps at http://rosettacode.org/wiki/Power_set#J >>>>>>>>>>>>> >>>>>>>>>>>>> ps=: (<@#~ 2 #:@i.@^ #)&.> >>>>>>>>>>>>> >>>>>>>>>>>>> -- >>>>>>>>>>>>> Raul >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On Thu, Nov 14, 2013 at 3:17 PM, km <[email protected]> >>>>>>>>>>>>> >>>>>>>>>>>> wrote: >>>> >>>>> 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 >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> ------------------------------------------------------------ >>>>> ---------- >>>>> >>>>>> 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 >>>> >>>>> >>>>>>>> ------------------------------------------------------------ >>>>>>>> ---------- >>>>>>>> >>>>>>> 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 >>>> >>> >>> ---------------------------------------------------------------------- >>> 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
