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Den of obliquity
/.

The oblique adverb in the form f/.y applies f along the oblique lines on the angle (/) of an array. The most obvious application for this adverb is the summing of the oblique lines of the times table of two lists representing polynomial coefficient. For example, if p=.1 2 1 and q=.1 3 3 1 , then the times table

   ]t=.p*/q
1 3 3 1
2 6 6 2
1 3 3 1

may be summed along the oblique by

   +//.t
1 5 10 10 5 1

The obliques are 1, 3 2, 3 6 1, 1 6 3, 2 3, 1 . Two further uses of oblique are given in the following:

   b=.+//.@,:~ NB. sum obliquely self-laminated argument
   q=.,1
   b q
1 1
   b b q
1 2 1
   ]w=.b^:(i.8)q
1 0  0  0  0  0 0 0
1 1  0  0  0  0 0 0
1 2  1  0  0  0 0 0
1 3  3  1  0  0 0 0
1 4  6  4  1  0 0 0
1 5 10 10  5  1 0 0
1 6 15 20 15  6 1 0
1 7 21 35 35 21 7 1

You may know that the row sums are powers of 2 , but what are the oblique sums? (Only the first 8 are complete).

   8{.+//.w
1 1 2 3 5 8 13 21

This suggests the following Fibonacci number verbs:

   FibNo=.(+/ .!|.)@i."0 NB. Never-before-seen inner product
   FibNo i.13
0 1 1 2 3 5 8 13 21 34 55 89 144