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Floor: Difference between revisions
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→Complex floor
(Created page with "{{Built-in|Floor|⌊}} is a monadic scalar function which gives the floor of a real number, i.e. the greatest integer not exc...") |
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:''Main article: [[Complex Floor]]'' | :''Main article: [[Complex Floor]]'' | ||
[[Eugene McDonnell]] designed the domain extension of Floor to [[complex number|complex numbers]].<ref>McDonnell, Eugene. [https://www.jsoftware.com/papers/eem/complexfloor.htm "Complex Floor"].</ref> Complex floor maps every complex number to a [[wikipedia:Gaussian integer|Gaussian integer]]. It has an important property that the [[magnitude]] of [[subtract|difference]] between any complex number Z and its floor is [[less than]] 1. This extension is currently implemented in [[Dyalog APL]], [[J]], and [[NARS2000]]. | [[Eugene McDonnell]] designed the domain extension of Floor to [[complex number|complex numbers]].<ref>McDonnell, Eugene. [https://www.jsoftware.com/papers/eem/complexfloor.htm "Complex Floor"].</ref> Complex floor maps every complex number to a [[wikipedia:Gaussian integer|Gaussian integer]], a complex number whose real and imaginary parts are integers. It has an important property that the [[magnitude]] of [[subtract|difference]] between any complex number Z and its floor is [[less than]] 1. This extension is currently implemented in [[Dyalog APL]], [[J]], and [[NARS2000]], and is internally used to implement complex [[ceiling]], [[residue]], and [[GCD]]. | ||
<source lang=apl> | <source lang=apl> | ||