Many of the inverse were motivated by f&.g .  See
http://www.jsoftware.com/jwiki/Essays/Under .

​When I first learned APL decades ago I found it amusing to find novel
inner products (e.g. not-equal dot equal, used in finding leap years).  Now
I am amused by finding neat duals.  My favorite:  If x ack y is f&.(3&+) y,
then (x+1) ack y is f^:(1+y)&.(3&+) 1, where ack is the Ackermann function.

​

On Fri, May 31, 2013 at 7:00 PM, elton wang <[email protected]> wrote:

> I guess this may deserve a new thread:
> for the inverse of m&|: like
>  3&|: b._1
> (] |:~ 3 C.^:_1 i.@#@$) :.(3&|:)
>
> How does J find this inverse? is this explicitly coded in J or J
> automatically figures this out by some rules? Either way, this is amazing.
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