> From: [email protected]
> 
> Taking that last description literally, you can (once again) let J
> figure out how to de-itemize, given that itemize (monadic ,:) 
> and inverse are easily at hand:
> 
>          inv =. ^: _1
>          ,: inv i. 2 3 4
>       0 1  2  3
>       4 5  6  7
>       8 9 10 11
>          $ ,: inv i. 2 3 4
>       3 4

Additionally you can ask J what the inverse for ,: is:

   ,: b. _1
{.
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