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...on rank]]. For the operator that applies a function at a given rank, see [[Rank (operator)]].'' ...ucture, or the length of its [[shape]]. The traditional expression for the rank of an array <syntaxhighlight lang=apl inline>A</syntaxhighlight> is <syntax

...yalog APL]], the maximum rank is 15, so taking an [[Outer Product]] of two rank-8 arrays fails: LIMIT ERROR: Rank of resultant array would exceed maximum permitted

...e primitive function. For system limits, see [[LIMIT ERROR]] and [[Maximum rank]].'' ...s are [[tolerant comparison|tolerantly]] equal. As a [[Boolean function]], Maximum is identical to [[Or]].

...ines [[Close composition|"close" composition operators]] which inherit the rank of their right operand—the [[derived function]] produced by such a compos ....</ref> In [[J]] every function, primitive or user-defined, has a function rank.

...he term sub-array may also be used to refer part of an array with lesser [[rank]] (i.e. a [[cell]]) or [[depth]].'' ...ght call such subarrays ''equal-rank'' subarrays. Otherwise a subarray has rank less than or equal to its containing array.

...ed as if the shape is prepended with ones. If the left argument has higher rank, Find does not error, but it is never found in the right argument (resultin ...'DAY'⍷WEEK ⍝ Find the pattern 'DAY' in WEEK; right arg may have higher rank

...l to the [[maximum rank]]. The length of an array's shape is the array's [[rank]], and the product of the shape is its [[bound]]. If the shape is [[Empty a

...n over an axis other than the first is performed via the [[Rank (operator)|Rank operator]], which [[mix|mixes]] the results into a flat array. Reduction by [[Minimum]] or [[Maximum]] gives the minimum or maximum over several numbers. Same goes for [[And]], [[Or]], [[GCD]], [[LCM]], and

...right in the same way. Like Take, the left argument is subject to [[scalar rank extension]], and in some APLs the right is as well. s ,← ((0=≢s)×≢⍺)⍴1 ⍝ Scalar rank extension

All scalar functions have rank zero. ...ghlight lang=apl inline>⌈</syntaxhighlight> || [[Ceiling]] || [[Maximum]]

...ighlight> in [[Dyalog APL]] (where 99 exceeds the system's maximum array [[rank]]). ...ntaxhighlight lang=j inline>{</syntaxhighlight> has a left [[Function rank|rank]] of 0, so that results are [[mix]]ed together and those with different sha

...btract]], [[Multiply]], [[Divide]], [[Floor]], [[Ceiling]], [[Minimum]], [[Maximum]], [[Absolute value]], [[Modulus]], [[Exponential]], [[Power]], [[Not]], [[ ...ending [[Compress]] ([[Bob Bernecky|Bernecky]] 1980) <br/> dyadic and high-rank [[Grade]] (proposed Howard Smith 1979)

...ystem implemented [[Phil Abrams]]' [[subscript calculus]] by storing the [[rank]] and [[shape]] of an array, along with delta and offset vectors, separatel ...this process. Combined functions such as <syntaxhighlight inline lang=apl>RANK</syntaxhighlight>, produced from two adjacent [[Shape]] functions, and <syn

...ighlight lang=apl inline>⌈</syntaxhighlight> || [[Ceiling]] || [[Maximum]] | <syntaxhighlight lang=apl inline>⍴</syntaxhighlight> || Rank vector ([[Shape]]) || Replication ([[Reshape]])

...b''. <syntaxhighlight lang=apl inline>⌈⌿</syntaxhighlight> is the columnar maximum-[[reduce|reduction]]: The [[Rank operator]] (<syntaxhighlight lang=apl inline>⍤</syntaxhighlight>) allows

| <code>⌈</code> || [[Ceiling]] || [[Maximum]] | <code>=</code> || [[Rank]] || [[Equals]]

...|| Compress extended to [[Replicate]]; [[LCM]] and [[GCD]]; [[Grade]] on rank >1<ref>IPSA. [https://www.softwarepreservation.org/projects/apl/Manuals/Sha | 15 || 1983-05 || [[Rank operator]] and [[Function rank]]; [[Left|Lev]] (<syntaxhighlight lang=apl inline>⊣</syntaxhighlight>), [

| <code>↥</code> || [[Maximum]]/[[Logical Or]] || Take the maximum of two arrays (Can use for logical OR.) || max | <code>☇</code> || Rerank || Change the rank of an array's rows

...o did significant work on Dyalog's interpreter, in particular optimising [[Maximum]], [[Minimum]], and [[Plus]] [[Reduce|reductions]] using [[vector instructi ...olved in designing several extensions to Dyalog primitives, including high-rank [[Unique]] in [[Dyalog APL 17.0]] and the decision to allow duplicate left

...so in the very specific context of the right operand of [[Rank (operator)|Rank]], 15=∞.

...log has also popularised [[SHARP APL]] and [[J]] innovations such as the [[Rank operator]] and [[train]]s among nested APLs. ...mitives on flat arrays, and brought concepts such as the [[Rank (operator)|Rank operator]], [[trains]], and [[Function composition|composition operators]],

...yntaxhighlight lang=apl inline>></syntaxhighlight>, and given a [[function rank]] of 0, which causes it to behave as [[Mix]]. [[First]] is not a primitive. ...[[singleton extension]]. Most support it fully, so that a singleton of any rank is extended. [[APL2]] supports it only for scalars and one-element vectors

| <syntaxhighlight lang=apl inline>⌈</syntaxhighlight> [[Maximum]] || Maximieren<ref name="Lattermann"/> | [[Rank]] || Rang

...l inline>↓</syntaxhighlight> ([[Mix]] and [[Split]]) increase and decrease rank (if possible) when used monadically. ...an also be seen as indicators on a vertical number line, pointing at the [[maximum]] and [[minimum]], respectively.

...e]]s: 1-byte, 2-byte, or 4-byte code points could be used depending on the maximum code point in the string. In each case a single element is a single code po ...). [[Function train]]s, another J feature, were also introduced. Of these, Rank differs from J's definition because it does not allow complete [[leading ax

A number following the type indicates the rank, e.g. |<syntaxhighlight lang=apl inline>A0</syntaxhighlight>||Any scalar (rank 0)

* '''19: Heterogeneous Development with Maximum Reuse of APL Assets''', Lars Stampe Villadsen & Martin Petri (SimCorp) * '''26: The Rank Operator''', [[Roger Hui]] ([https://www.dyalog.com/uploads/conference/dyal

* '''An extension of the domain of the APL domino function to rank deficient linear least squares systems'''. Augustin A. Dubrulle. [https://d * '''Determining probability distributions by maximum entropy and minimum cross-entropy'''. Rodney W. Johnson. [https://doi.org/1