Another take on the Quet problem

[Eugene McDonnell]

While eating supper I toyed with a simpler solution to the Quet problem 
than the one I posted earlier today, first in pseudo Mathematica:

Index Insert AI PermutationIndex Integers 7

Where the only new thing is Index, defined as
    x Index y
is the items of array y selected by indexes x

Which, being translated into J is
    { / AI A. i. 7

Where AI is the list of required reversing indexes:
    AI
5039 719 3294 23 1560 1

And AI A. i. 7 are the six rows in the permutation table of order 7 
selected by AI.

Finally, { / AI A. i. 7 is the result of indexing my way through these 
rows from the bottom up.
    { / AI A. i. 7
5 0 1 2 4 3 6

Eugene McDonnell