Power | u^:n _ _ _ |
Two cases occur: a numeric integer n, and a
gerund n .
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(] ; +/\ ; +/\^:2 ; +/\^:0 1 2 3 _1 _2 _3 _4) 1 2 3 4 5 +---------+-----------+------------+-------------+ |1 2 3 4 5|1 3 6 10 15|1 4 10 20 35|1 2 3 4 5| | | | |1 3 6 10 15| | | | |1 4 10 20 35| | | | |1 5 15 35 70| | | | |1 1 1 1 1| | | | |1 0 0 0 0| | | | |1 _1 0 0 0| | | | |1 _2 1 0 0| +---------+-----------+------------+-------------+An infinite power n produces the limit of the application of u . For example, if x=:2 and y=:1, then x o.^:_ y is 0.73908, the solution of the equation y=Cos y . If n is negative, the obverse u^:_1 is applied |n times. The obverse (which is normally the inverse) is specified for six cases:
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p:^:_1 n gives the number of primes less than n,
denoted by π(n) in math | |
q:^:_1 is */ | |
b^:_1 where b is a boolean list is "Expand"
(whose fill atom f can be specified by
fit, b&#^:_1!.f) | |
a.^:_1 produces the base-a representation | |
!^:_1 and !&n^:_1 and !&n&^:_1
produce the appropriate results |
x u^:(v0`v1`v2)y ↔ (x v0 y)u^:(x v1 y) (x v2 y) x u^:( v1`v2)y ↔ x u^:([` v1`v2) y u^:( v1`v2)y ↔ u^:(v1 y) (v2 y)