Vocabulary/percentco
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%: y Square Root
Rank 0 -- operates on individual atoms of y, producing a result of the same shape -- WHY IS THIS IMPORTANT?
The square root of y .
%: 49 7
Common Uses
Can lead to neater tacit expressions than using (y^0.5).
More Information
Related Primitives
Double (+: y), Square (*: y), Halve (-: y)
x %: y Root
Rank 0 0 -- operates on individual atoms of x and y, producing a result of the same shape -- WHY IS THIS IMPORTANT?
The x-th root of y .
2 %: 49 NB. square-root 7 3 %: 49 NB. cube-root 3.65931
Common Uses
Can lead to neater tacit expressions than using (y^%x).
Details
1. %: y and x %: y return the principal value of the root, which is defined as ^ (^. y) % x
The logarithm (^.) is in turn defined to use the angle in the range: (-π, π]
A consequence of this definition is that all roots of negative numbers are complex, even cube roots:
3 %: _1 0.5j0.866025
2. Taking an integer root of an extended integer by an integer (extended or not) produces an extended integer if the quotient is an integer, or floating-point otherwise.