* 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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