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• Complex number
  ...751:2001]]), and complex numbers are available in many APLs. Usually these numbers are written with a syntax such as <syntaxhighlight lang=apl inline>5j2</syn ...e usually written with a "J" joining the real and imaginary parts. Complex numbers are added component-wise.
  2 KB (354 words) - 22:08, 10 September 2022
• Complex (function)
  ...ng=j inline>j.</syntaxhighlight> together with initial support for complex numbers, and was adopted in [[Extended Dyalog APL]] using the [[glyph]] <syntaxhigh ...gers and <syntaxhighlight lang=apl inline>÷</syntaxhighlight> for rational numbers. </blockquote>
  4 KB (508 words) - 22:25, 10 September 2022
• Conjugate
  ...ot have a dedicated [[Identity]] function, but also do not support complex numbers, Conjugate is often used to return the argument unchanged. This usage is di ...te leaves real numbers unchanged but negates the imaginary part of complex numbers.
  5 KB (719 words) - 01:19, 18 March 2024
• Magnitude
  ...uals the original number [[times]] (or [[Divide|divided]] by, for non-zero numbers) its [[Signum|sign]]. For complex numbers, the magnitude is defined as the Euclidean distance from the number 0 on th
  2 KB (221 words) - 22:10, 10 September 2022
• Mixed array
  ...mple scalar). However, mixed arrays with depth one can be formed by mixing numbers and characters. While such an array is [[Simple array|simple]], it is neith
  1 KB (182 words) - 15:02, 30 April 2020
• Complex floor
  ...ion for the built-in function [[Floor]] to accept [[complex number|complex numbers]]. It was originally designed by [[Eugene McDonnell]]<ref>McDonnell, Eugene ...uses of [[Floor]]: calculating the quotient and [[remainder]] between two numbers, and calculating the [[GCD]] via the [[wikipedia:Euclidean algorithm|Euclid
  5 KB (632 words) - 22:14, 10 September 2022
• Number
  ...]. Traditionally, APL provides only one user-visible numeric type, so that numbers round identically regardless of how they are represented, but newer APLs ma ...erformance reasons but converts them automatically on overflow to give all numbers the semantics of 64-bit [[wikipedia:IBM_hexadecimal_floating_point|HFP]] fl
  5 KB (703 words) - 22:50, 26 February 2024
• Total array ordering
  ...gh it differs from the native implementation in ordering characters before numbers instead of the opposite.<ref>[[Dfns workspace]]. [http://dfns.dyalog.com/n_ ...be compatible with multiplication in the sense that the product of any two numbers greater than zero is greater than zero.<ref name=bfh/>
  3 KB (504 words) - 10:45, 11 September 2022
• Imaginary
  ...ex (function)|Complex]]. In other APL implementations that support complex numbers, [[Circular]] with the left argument of <syntaxhighlight lang=apl inline>¯
  2 KB (228 words) - 22:05, 10 September 2022
• Add
  ...m''', is a [[dyadic]] [[scalar function]] that [[wikipedia:Addition|adds]] numbers together. As a basic arithmetic operation, Add is subject to the language's ...also be considered an element-wise operation, since each of these types of numbers forms a vector space over the reals. Addition of scalars is always performe
  4 KB (525 words) - 22:11, 10 September 2022
• GCD
  ...teger arguments, the GCD is the largest positive number which divides both numbers. If one of the arguments is zero, the GCD function returns the other number ...edia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers).
  4 KB (497 words) - 21:37, 17 February 2024
• LCM
  ...common multiple is the smallest positive number which is divisible by both numbers. If one of the arguments is zero, the LCM function returns zero. ...edia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers).
  2 KB (230 words) - 21:28, 10 September 2022
• Strand notation
  ...tion''' and is a part of token formation rather than execution. Only plain numbers are stranded. ...tibility]] with APL and does not allow stranding by juxtaposition even for numbers. Instead, the "ligature" character <code>‿</code> is used for a more expl
  3 KB (397 words) - 10:34, 11 September 2022
• Negate
  Negating a vector of positive numbers. Note that the result array is displayed with a [[high minus]] on each elem ...sign bit because they distribute numbers exponentially. But only positive numbers can be represented as the result of an exponent, so an additional sign bit
  3 KB (502 words) - 22:05, 10 September 2022
• High minus
  ...her be parenthesized or cannot be stranded at all. It also allows negative numbers to be used as left [[argument]]s to functions, or as [[operand]]s. * [https://help.dyalog.com/latest/index.htm#Language/Introduction/Variables/Numbers.htm Dyalog]
  3 KB (423 words) - 22:09, 10 September 2022
• Ceiling
  Ceiling rounds up the given numbers to the nearest integers. The extension for [[complex number|complex numbers]] is derived from [[complex Floor]] via this property.
  2 KB (269 words) - 21:57, 28 November 2022
• Deal
  ...mutation by selecting <syntaxhighlight lang=apl inline>k</syntaxhighlight> numbers from the first <syntaxhighlight lang=apl inline>n</syntaxhighlight> [[Index numbers←'23456789TJQKA'
  4 KB (521 words) - 16:54, 8 February 2023
• Minimum
  Minimum finds the smaller of two numbers: Together with [[Maximum]], it can clamp an array of numbers to a range (closed interval), here from 0 to 1:
  3 KB (415 words) - 22:23, 10 September 2022
• Factorial
  ...n]] <math>\Gamma(n)</math>, so that it is defined for real and [[complex]] numbers. Because <math>\Gamma(n)</math> equals <math>(n-1)!</math>, <syntaxhighligh The Gamma function diverges at 0 or negative numbers, so <syntaxhighlight lang=apl inline>!Y</syntaxhighlight> is undefined at n
  2 KB (289 words) - 21:21, 10 September 2022
• Roll
  ...is a [[monadic]] [[scalar function]] which returns random or pseudo-random numbers. The name ''Roll'' comes from the analogy of rolling dice. Each [[scalar]] ...to predict algorithm) or taken from the operating system. They way random numbers are generated is controlled by the [[random link]] <syntaxhighlight lang=ap
  3 KB (373 words) - 22:14, 10 September 2022

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