* Signum - Times

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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 0.6j0.8

The 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| | | | |
+---+---+--+--+-----+-----+

Signum is useful in effecting selections. For example:

 * 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| | |
+---------+----------+----------+-----------+-----------+

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