Square Root: Difference between revisions

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{{Built-in|Square Root|√}} (<source lang=j inline>%:</syntaxhighlight> in [[J]]) is a [[monadic]] [[scalar function]] that returns the [[wikipedia:square root|square root]] of its [[argument]], that is, a number whose square is the argument. As there are two such numbers for any non-zero argument (negating one possible result gives another), the result returned is taken to have either a positive real part, or, if the real part is zero, a non-negative imaginary part; in particular, if the result is real then it will be zero or greater. Square Root may also be defined in terms of the [[Power]] function, by raising the argument to the power one-half. It is considered a case of the [[dyadic]] function [[Root]] (which uses the same [[glyph]]), with a default left argument of 2. Square Root is defined in [[J]], [[NARS2000]], [[dzaima/APL]], and [[Extended Dyalog APL]].
{{Built-in|Square Root|√}} (<syntaxhighlight lang=j inline>%:</syntaxhighlight> in [[J]]) is a [[monadic]] [[scalar function]] that returns the [[wikipedia:square root|square root]] of its [[argument]], that is, a number whose square is the argument. As there are two such numbers for any non-zero argument (negating one possible result gives another), the result returned is taken to have either a positive real part, or, if the real part is zero, a non-negative imaginary part; in particular, if the result is real then it will be zero or greater. Square Root may also be defined in terms of the [[Power]] function, by raising the argument to the power one-half. It is considered a case of the [[dyadic]] function [[Root]] (which uses the same [[glyph]]), with a default left argument of 2. Square Root is defined in [[J]], [[NARS2000]], [[dzaima/APL]], and [[Extended Dyalog APL]].


== History ==
== History ==
The radical symbol for the square root has been used in mathematics for centuries, and was suggested early in APL's development by [[Eugene McDonnell]], who stated that "when I designed the APL printer trains for the IBM 1403 printer, I included the radical symbol √ on the train, in the expectation that one day this function would be added to APL."<ref>[[Eugene McDonnell]]. [https://doi.org/10.1145/22415.22050 "A perfect square root routine"] ([https://www.jsoftware.com/papers/eem/sqrt.htm web]) at [[APL86]].</ref> It was featured in [[J]] following McDonnell's design but written with the ASCII bigraph <source lang=j inline>%:</syntaxhighlight>, and was introduced with the radical symbol by [[NARS2000]]. More recently, it was added first to [[Extended Dyalog APL]] and then to [[dzaima/APL]] in 2018.
The radical symbol for the square root has been used in mathematics for centuries, and was suggested early in APL's development by [[Eugene McDonnell]], who stated that "when I designed the APL printer trains for the IBM 1403 printer, I included the radical symbol √ on the train, in the expectation that one day this function would be added to APL."<ref>[[Eugene McDonnell]]. [https://doi.org/10.1145/22415.22050 "A perfect square root routine"] ([https://www.jsoftware.com/papers/eem/sqrt.htm web]) at [[APL86]].</ref> It was featured in [[J]] following McDonnell's design but written with the ASCII bigraph <syntaxhighlight lang=j inline>%:</syntaxhighlight>, and was introduced with the radical symbol by [[NARS2000]]. More recently, it was added first to [[Extended Dyalog APL]] and then to [[dzaima/APL]] in 2018.


== See also ==
== See also ==

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