Nth root: Difference between revisions

=={{header|BQN}}==

There are two builtin methods to solve this problem(<code>√</code> and <code>⋆</code>), both give a result at the highest precision possible.

<code>Root2</code> is a translation of the [[Run BASIC]] implementation, which uses Newton's approximation method. It allows an optional argument for precision, and otherwise defaults to 10^¯5.

<code>_while_</code> is a [https://mlochbaum.github.io/bqncrate/ BQNcrate] idiom used for unbounded looping here.

<lang bqn>_while_ ← {𝔽⍟𝔾∘𝔽_𝕣_𝔾∘𝔽⍟𝔾𝕩}

Root ← √

Root1 ← ⋆⟜÷˜

Root2 ← {

n 𝕊 a‿prec:

1⊑{

p‿x:

⟨

x

((p × n - 1) + a ÷ p ⋆ n - 1) ÷ n

⟩

} _while_ {

p‿x:

prec ≤ | p - x

} ⟨a, ⌊a÷n⟩;

𝕨 𝕊 𝕩: 𝕨 𝕊 𝕩‿1E¯5

}

•Show 3 Root 5

•Show 3 Root1 5

•Show 3 Root2 5

•Show 3 Root2 5‿1E¯16</lang>

<lang>1.7099759466766968

1.7099759466766968

1.7099759641072136

1.709975946676697</lang>

[https://mlochbaum.github.io/BQN/try.html#code=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 Try It!]