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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
• Residue
  ...[[wikipedia:Remainder|remainder]] of [[divide|division]] between two real numbers. It takes the divisor as the left [[argument]], and the dividend as the rig For negative arguments, one may decide to return non-negative numbers in all cases or follow the sign of the dividend or the divisor. For complex
  2 KB (311 words) - 21:10, 10 September 2022
• Comparison tolerance
  The rule for tolerant comparison is that numbers <syntaxhighlight lang=apl inline>a</syntaxhighlight> and <syntaxhighlight l ...evaluated intolerantly. This means that the allowed difference between the numbers increases as they become larger in magnitude (a relative tolerance). Compar
  4 KB (601 words) - 13:30, 26 February 2024
• NARS2000
  ...as) Normed Division Algebra] datatypes: Complex, Quaternion, and Octonion numbers, along with several Multi-Precision datatypes, and signed Infinities: ...http://wiki.nars2000.org/index.php?title=Rational_and_VFP_Numbers Rational Numbers]
  10 KB (1,101 words) - 02:29, 9 March 2024
• Jobs
  ...Ler for hire, can be a difficult task. This is both because of the limited numbers involved, but also because there is no obvious place for potential employee
  887 bytes (129 words) - 06:34, 10 February 2022
• Gene McDonnell
  ...ell, Eugene. [https://www.jsoftware.com/papers/satn40.htm SATN-40: Complex Numbers].</ref>. His suggestion that zero divided by zero should be zero rather tha * SATN-40: [https://www.jsoftware.com/papers/satn40.htm Complex Numbers]. 1981-06-20.
  5 KB (678 words) - 11:23, 16 December 2022
• Rank
  :''This page is about array rank, a number associated with every array. For numbers associated with a function specifying its argument rank, see [[function ran
  1 KB (175 words) - 21:45, 10 September 2022
• Character arithmetic
  In [[K]], characters are converted to numbers to participate in arithmetic. This system differs from affine character ari
  1 KB (182 words) - 02:58, 7 February 2024
• Equal to
  It is subject to [[comparison tolerance]]: floating-point numbers which are very close together are considered equal, even though they are sl x ← 1 + (⎕CT×0.6)ׯ2 ¯1 0 1 2 ⍝ Numbers close to 1
  4 KB (500 words) - 21:57, 28 November 2022
• Group (K)
  ...s Group to arrays, where an array corresponds to a dictionary with natural numbers for its keys.<ref>[[Marshall Lochbaum]]. [https://mlochbaum.github.io/BQN/c
  1 KB (199 words) - 23:29, 17 March 2024
• Array model
  ...|nested array theory]] the elements can only be arrays, and characters and numbers are held to be contained in [[simple scalar]]s, arrays which by convention ...Ls such as APL2 allow any array to be used as an element, including scalar numbers or characters (written with quotes) as well as larger arrays. In order to i
  14 KB (2,301 words) - 20:27, 3 March 2024
• Simple array
  ...nclude all arrays of a single type, as well as arrays which mix types like numbers and characters. Arrays which would not be representable in flat array theor
  1 KB (175 words) - 10:46, 20 April 2021
• GNU APL
  GNU APL supports both 64-bit floats and 64-bit integers, as well as complex numbers whose components are floating-point. The integer type is used when a value
  4 KB (565 words) - 12:28, 22 February 2024
• Array ordering
  2 KB (277 words) - 01:03, 11 March 2024
• Boolean
  ...such as [[Less Than]] is always composed of Booleans. Because Booleans are numbers, arithmetic functions can be used on them directly, for example by [[sum]]m The use of numbers for Booleans also allows functions to be extended from a Boolean domain to
  9 KB (1,140 words) - 22:10, 10 September 2022
• Box
  ...can store any array, boxes may be used to define arrays which contain both numbers and characters, as well as arrays with a nested structure.
  1 KB (239 words) - 15:27, 30 April 2020
• Array
  2 KB (249 words) - 08:56, 13 May 2020
• Circular
  ...nships between them. On some implementations with [[complex number|complex numbers]], Circular also includes functions to decompose and assemble a complex num ...with <syntaxhighlight lang=apl inline>5○¯6○Y</syntaxhighlight> for complex numbers.
  7 KB (900 words) - 22:28, 10 September 2022
• Exponential
  On APL implementations that support [[complex]] numbers, one can demonstrate [[wikipedia:Euler's identity|Euler's identity]] (with
  2 KB (241 words) - 22:25, 10 September 2022
• Floor
  Floor rounds down the given numbers to the nearest integers. ...nnell]] designed the domain extension of Floor to [[complex number|complex numbers]].<ref>McDonnell, Eugene. [https://www.jsoftware.com/papers/eem/complexfloo
  5 KB (582 words) - 16:27, 24 December 2023
• Character
  2 KB (268 words) - 02:46, 25 February 2024
• Interval Index
  ...r numbers before the first interval boundary, index 0 is returned, and for numbers after the last, index 4 is returned.
  9 KB (1,337 words) - 23:27, 10 March 2024
• Ivy
  ...ion, using exact rationals when possible and high-precision floating-point numbers otherwise.
  2 KB (264 words) - 22:44, 24 January 2024
• April
  | numeric types = [[wikipedia:Common_Lisp#Scalar_types|CL numbers]] including [[complex]] and [[rational]]
  2 KB (260 words) - 19:02, 7 March 2023
• Signum
  2 KB (320 words) - 21:32, 10 September 2022
• Replicate
  === Negative numbers === ...side is a [[singleton]]). [[APL2]] defined a different extension: negative numbers do not correspond to any element of the right argument, but still indicate
  16 KB (2,092 words) - 19:15, 16 March 2024
• Roger Hui
  * [[Dyalog '09]] 15: Complex Numbers Implementation Stories ([https://www.dyalog.com/uploads/conference/dyalog09 * Dyalog '11 D05: [https://dyalog.tv/Dyalog11/?v=CkaQQYcxpfM Rational Numbers] ([https://www.dyalog.com/uploads/conference/dyalog11/presentations/D05_rat
  20 KB (2,702 words) - 10:41, 20 August 2023
• Reciprocal
  For any non-zero real or complex numbers, the [[signum]] of reciprocal is equal to the [[conjugate]] of signum, and
  2 KB (235 words) - 21:56, 10 September 2022
• Maximum
  Maximum finds the larger of two numbers:
  2 KB (317 words) - 21:28, 10 September 2022
• Square Root
  ...t]], 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
  2 KB (322 words) - 11:05, 11 September 2022
• Direct definition (operator)
  ...d true cases, it's placed first, and returns a scalar or vector of natural numbers. Each number indicates one of the following groups of statements (separated
  2 KB (341 words) - 02:32, 8 March 2024

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