useOn 2019.08.20 12:01:34, you,
the extraordinary Raul Miller, spake thus:
> Ok... so here's a routine which gives us all the truth valued arrays
> with n axes:
> rntt=: (#2:) $"1 [: #:@i. 2>. 2^2*]
I think you want: rntt=: (#2:) $"1 [: #:@i. 2>. 2^2^]
(the number of arrays for 0,1,2,3 axes = 2 4 16 256
>
> And, here's a test to see if an n-dimensional truth table is degenerate:
> degenerate=: 1 e. (1 ]\. i.@#@$) -:/@|: ]
I will have to puzzle out 'degenerate' - it seems faster than
the brute force routine I use.
> (Use with "_1 cn a result from rntt)
>
A quick way to get the dual of some N-axis array is:
nudu=: $ $ -.@:|.@,
nudu 2 2$0 0 0 1 (and)
0 1
1 1 (or)
selfdual=: -: nudu
If we have a string, deldegen, with 0s for the degenerate
2-axis arrays:
0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0
then
selfdual"_1 deldegen#rntt 2
0 0 0 0 0 0 0 0 0 0
> But I don't understand what a dual would be for an arbitrary truth
> valued array with an arbitrary number axes, so I'm not quite sure how
> I would write that test.
>
> For example, if I implement:
>
> Glock=: $ #: I.@,
> dual=: (-:&(/:~) -.)&Glock
> selfdual=: dual~
>
> I find four self-dual arrays of rank 2:
> (#~ selfdual"_1) rntt 2
> 0 0
> 0 0
>
> 0 1
> 1 0
>
> 1 0
> 0 1
>
> 1 1
> 1 1
>
> What's a dual of a truth table array with arbitrary axes?
>
> Thanks,
>
> --
> Raul
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