| Signum | * 0 0 0 | Times |
*y is _1 if y is negative, 0
if it is zero, 1 if it is positive; more generally, *y
is the intersection of the unit circle with the line from the origin
through the argument y in the complex plane. For example:*_3 0 5 3j4 _1 0 1 0.6j0.8The comparison with zero is tolerant, as defined by the phrase (y%|y)*t<:|y where t denotes the tolerance. The fit conjunction applies to signum, as in *!.t . |
* denotes multiplication, defined as in elementary mathematics
and extended to complex numbers as usual:t=:+.x,y [ x=:2j4 [ y=:5j3 r=:-/*/t [ i=:+/ . * t (x,:y);t;r;i;(r j. i);(x*y) +---+---+--+--+-----+-----+ |2j4|2 4|_2|26|_2j26|_2j26| |5j3|5 3| | | | | +---+---+--+--+-----+-----+ |
* y=: _4 0 4
_1 0 1
>:@* y
0 1 2
f=: %:
f ^: * " 0 y NB. Inverse of f, Identity, or f
16 0 2
(* y) { ;:'Yes No Maybe' NB. Select using Indexing ({)
+-----+---+--+
|Maybe|Yes|No|
+-----+---+--+
g=: <:`-:`+:@.*"0 NB. See Agenda (@.)
g y
_8 _1 2
The dyad * used on a list and a table illustrates the significance
of agreement, as discussed in
Section II B:m=: i. 3 4 [ v=: 3 2 1 m ; (v*m) ; (m*v) ; (+/ m*v) ; (v +/ . * m) +---------+----------+----------+-----------+-----------+ |0 1 2 3|0 3 6 9|0 3 6 9|16 22 28 34|16 22 28 34| |4 5 6 7|8 10 12 14|8 10 12 14| | | |8 9 10 11|8 9 10 11|8 9 10 11| | | +---------+----------+----------+-----------+-----------+