Just for fun, a fully tacit version of your expression
(+/@((_1^ -) * !~ * 2^2^]) i.@>:)@>:@i. 7x NB. Use of Hook to provide left
argument and @ keeps rank of 0
2 10 218 64594 4294642034 18446744047940725978
340282366920938463334247399005993378250
1000 timespacex '(+/@((_1^ -) * !~ * 2^2^]) i.@>:)@>:@i. 7x'
0.000102337 20416
(](4 : ('+/(_1^(x-y)) * (y!x) * 2^2^y')) i.@>:)"0 >:i.7x
2 10 218 64594 4294642034 18446744047940725978
340282366920938463334247399005993378250
1000 timespacex '(](4 : (''+/(_1^(x-y)) * (y!x) * 2^2^y'')) i.@>:)"0 >:i.7x'
0.000104449 28032
Differences in space taken become significant as the size of the argument grows
timespacex '(+/@((_1^ -) * !~ * 2^2^]) i.@>:)@>:@i. 20x'
34.3555 1.15352e7
timespacex '(](4 : (''+/(_1^(x-y)) * (y!x) * 2^2^y'')) i.@>:)"0 >:i.20x'
34.3393 1.68177e7
Cheers, bob
> On Aug 22, 2019, at 9:33 AM, R.E. Boss <[email protected]> wrote:
>
> @ Nollaig MacKenzie
>
> Well I think I can answer your question: there is no need to submit the
> sequence, since it already known.
> First I had to fiddle out what a (non)degenerate truth table was and was
> enlightened on this subject by Wittgenstein himself!
> Then I found out what the formula was to generate the numbers of
> non-degenerate truth tables, it appeared to be
>
> (](4 : ('+/(_1^(x-y)) * (y!x) * 2^2^y')) i.@>:)"0 >:i.8x
> 2 10 218 64594 4294642034 18446744047940725978
> 340282366920938463334247399005993378250
>
> which coincides with A000371, from which the second line reads " Number of
> nondegenerate Boolean functions of n variables."
>
> I still don't grasp what your concept of self-duality is.
>
>
> R.E. Boss
>
>
>> -----Oorspronkelijk bericht-----
>> Van: Chat <[email protected]> Namens Nollaig
>> MacKenzie
>> Verzonden: dinsdag 20 augustus 2019 06:17
>> Aan: [email protected]
>> Onderwerp: Re: [Jchat] Number of self-dual arrays of rank N; OEIS
>>
>> It is a simple slip. T is, in the NOTE:
>>
>> 0 0
>> 0 1
>>
>> 0 1
>> 1 1
>>
>> And (let us call it Tlocs):
>>
>> ]Tlocs=:Gloc L:0 (0;1)=L:0 T
>> ┌─────┬─────┐
>> │0 0 0│0 1 1│
>> │0 0 1│1 0 1│
>> │0 1 0│1 1 0│
>> │1 0 0│1 1 1│
>> └─────┴─────┘
>>
>> If you then do the |. on the second item of Tlocs:
>>
>> (0{Tlocs),|.L:0 (1{Tlocs)
>> ┌─────┬─────┐
>> │0 0 0│1 1 1│
>> │0 0 1│1 1 0│
>> │0 1 0│1 0 1│
>> │1 0 0│0 1 1│
>> └─────┴─────┘
>>
>> You have the result you want.
>>
>> (I should mention that Gloc is meant to apply to arrays of 0 and 1. I should
>> really have defined it as, perhaps, ($ #: I.@,)@:*
>>
>> Best wishes, N.
>>
>> On 2019.08.19 09:52:02, you,
>> the extraordinary R.E. Boss, spake thus:
>>
>>> I tried to understand what you wrote and am left with questions.
>>>
>>> Take
>>> [T=:(0 1 1, 1 0 1, 1 1 0,:1 1 1);0 0 0,0 0 1,0 1 0,:1 0 0
>>> +-----+-----+
>>> |0 1 1|0 0 0|
>>> |1 0 1|0 0 1|
>>> |1 1 0|0 1 0|
>>> |1 1 1|1 0 0|
>>> +-----+-----+
>>>
>>> With Gloc=: $ #: I.@, from the Journal of J, I get
>>> Gloc L:0 (0;1)=L:0 T
>>> +---+---+
>>> |0 0|1 2|
>>> |1 1|2 1|
>>> |2 2|3 0|
>>> +---+---+
>>> From this I get
>>> (, (>:@$|"1 -.)L:0,:~-.L:0)Gloc L:0 (0;1)=L:0 T
>>> +-----+-----+
>>> |0 0 |1 2 |
>>> |1 1 |2 1 |
>>> |2 2 |3 0 |
>>> +-----+-----+
>>> | 1 1| 0 _1|
>>> | 0 0|_1 0|
>>> |_1 _1|_2 1|
>>> +-----+-----+
>>> |1 1 |0 2 |
>>> |0 0 |3 0 |
>>> |3 2 |2 1 |
>>> +-----+-----+
>>> Which are the original locations of 0 and 1 respectively, there negations
>>> (-.),
>> and these converted to locations.
>>> Being selfdual we should have the first and the reversed latest row to be
>> equal, however
>>> (-: [:|. (>:@$|"1 -.)L:0)Gloc L:0 (0;1)=L:0 T
>>> 0
>>>
>>> What do I do wrong?
>>>
>>>
>>> R.E. Boss
>> ----------------------------------------------------------------------
>> 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
