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{{Built-in|Circular|○}}, or '''Circle Function''', is a [[dyadic]] [[scalar function]], which is essentially a collection of related monadic functions. Circular encompasses [[wikipedia:trigonometric functions|trigonometric functions]], [[wikipedia:hyperbolic functions|hyperbolic functions]], and a few relationships between them. On some implementations with [[complex number|complex numbers]], Circular also includes functions to decompose and assemble a complex number. It shares the [[glyph]] <source lang=apl inline>○</source> with the monadic arithmetic function [[Pi Times]]. | {{Built-in|Circular|○}}, or '''Circle Function''', is a [[dyadic]] [[scalar function]], which is essentially a collection of related monadic functions. Circular encompasses [[wikipedia:trigonometric functions|trigonometric functions]], [[wikipedia:hyperbolic functions|hyperbolic functions]], and a few relationships between them. On some implementations with [[complex number|complex numbers]], Circular also includes functions to decompose and assemble a complex number. It shares the [[glyph]] <source lang=apl inline>○</source> with the [[monadic]] arithmetic function [[Pi Times]]. | ||
== Design == | |||
The Circular function, as found in today's APL implementations, was designed by [[Gene McDonnell]], based on three things:<ref>[[Gene McDonnell|McDonnell, Gene]]. [https://www.jsoftware.com/papers/eem/storyofo.htm The Story of <source lang=apl inline>○</source>]. Recreational APL. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref> | |||
* [[Ken Iverson]] stating that [[Semantic density|a concise programming language]] must group together related monadic functions as a dyadic function that takes a "controlling parameter" as left argument to select specific function. | |||
* The sine, tangent, hyperbolic sine, and hyperbolic tangent are [[wikipedia:odd function|odd functions]]. | |||
* No better symbol could be found for circular functions than the circle itself. | |||
== Examples == | == Examples == | ||
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1j2 3j_4 _5j_6 | 1j2 3j_4 _5j_6 | ||
</source>{{Works in|[[J]]}} | </source>{{Works in|[[J]]}} | ||
== References == | |||
<references/> | |||
== External links == | == External links == | ||