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The case of ^: with a verb right argument is
defined in terms of the noun right argument
case (u ^: n) as follows:
x u ^: v y « x u^:(x v y) y
u ^: v y « u^:(v y) y
|
For example:
x=: 1 3 3 1
y=: 0 1 2 3 4 5 6
x p. y
1 8 27 64 125 216 343
x p. ^: (]>3:)"1 0 y
0 1 2 3 125 216 343
a=: _3 _2 _1 0 1 2 3
%: a
0j1.73205 0j1.41421 0j1 0 1 1.41421 1.73205
* a
_1 _1 _1 0 1 1 1
%: ^: * " 0 a
9 4 1 0 1 1.41421 1.73205
*: a
9 4 1 0 1 4 9
The following monads are equivalent. (See the example of ^ T. _
in the definition of the Taylor Approximation T. .)
g=: u ^: p ^: _
h=: 3 : 't=. y. while. p t do. t=. u t end.'
u=: -&3 [. p=: 0&<
(g"0 ; h"0) i. 10
+-------------------------+-------------------------+
|0 _2 _1 0 _2 _1 0 _2 _1 0|0 _2 _1 0 _2 _1 0 _2 _1 0|
+-------------------------+-------------------------+
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