Oblique | m/. u/. _ _ _ | Key |
u/.y applies u to each of the oblique lines
of a table y . For example:i.3 4 0 1 2 3 4 5 6 7 8 9 10 11 </. i.3 4 +-+---+-----+-----+----+--+ |0|1 4|2 5 8|3 6 9|7 10|11| +-+---+-----+-----+----+--+In general, u/.y is the result of applying u to the oblique lines of _2-cells of y . If the rank of y is less than two, y is treated as the table ,.y . m/.y applies successive verbs from the gerund m to the oblique lines of _2-cells of y, extending m cyclically as required. Thus: <`(<@|.) /. i.3 4 +-+---+-----+-----+----+--+ |0|4 1|2 5 8|9 6 3|7 10|11| +-+---+-----+-----+----+--+ |
x u/.y ↔ (=x) u@# y , that is, items of x
specify keys for corresponding items of y and u
is applied to each collection of y having identical keys.
For example:1 2 3 1 3 2 1 </. 'abcdefg' +---+--+--+ |adg|bf|ce| +---+--+--+x m/.y applies successive verbs from the gerund m to the collections of y, extending m cyclically as required. |
t=: p */ q [ p=: 1 2 1 [ q=: 1 3 3 1 t ; (+//.t) ; 1 1 &(+//.@(*/)) ^: (i.6) 1 +-------+-------------+-------------+ |1 3 3 1|1 5 10 10 5 1|1 0 0 0 0 0| |2 6 6 2| |1 1 0 0 0 0| |1 3 3 1| |1 2 1 0 0 0| | | |1 3 3 1 0 0| | | |1 4 6 4 1 0| | | |1 5 10 10 5 1| +-------+-------------+-------------+ ((10#.p)*10#.q), 10 #. +//. p */ q 161051 161051
Unlike polynomial coefficients, the diagonal sums of a multiplication table of digits should be “normalized” if any equal or exceed the radix.