a. The monad { computes a generalized Cartesian
product. For example:
{0 1 2;3 4 5 6
+---+---+---+---+
|0 3|0 4|0 5|0 6|
+---+---+---+---+
|1 3|1 4|1 5|1 6|
+---+---+---+---+
|2 3|2 4|2 5|2 6|
+---+---+---+---+
b. When using the dyad u/ to compute a function
table, it can be helpful to apply <"_2 to the
result. For example:
t=: 2 2&$"1 #: i.16 NB. all 2-by-2 boolean matrices
det=: -/ .* NB. determinant
$t
16 2 2
t=: (0~:det t)#t NB. non-singular 2-by-2 boolean matrices
$t
6 2 2
t=: t /: (,:=0 1) i. t NB. put identity matrix first
<"2 t
+---+---+---+---+---+---+
|1 0|0 1|0 1|1 0|1 1|1 1|
|0 1|1 0|1 1|1 1|0 1|1 0|
+---+---+---+---+---+---+
$ ~:/ .*"2/~ t
6 6 2 2
<"_2 ~:/ .*"2/~ t NB. group table
+---+---+---+---+---+---+
|1 0|1 1|1 1|0 1|1 0|0 1|
|0 1|0 1|1 0|1 1|1 1|1 0|
+---+---+---+---+---+---+
|1 0|1 1|1 1|0 1|1 0|0 1|
|1 1|1 0|0 1|1 0|0 1|1 1|
+---+---+---+---+---+---+
|0 1|0 1|1 0|1 1|1 1|1 0|
|1 1|1 0|0 1|1 0|0 1|1 1|
+---+---+---+---+---+---+
|1 1|1 0|0 1|1 0|0 1|1 1|
|1 0|1 1|1 1|0 1|1 0|0 1|
+---+---+---+---+---+---+
|1 1|1 0|0 1|1 0|0 1|1 1|
|0 1|0 1|1 0|1 1|1 1|1 0|
+---+---+---+---+---+---+
|0 1|0 1|1 0|1 1|1 1|1 0|
|1 0|1 1|1 1|0 1|1 0|0 1|
+---+---+---+---+---+---+
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