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This page is about the primitive function. For system limits, see LIMIT ERROR and Maximum rank.

Maximum (), Max, Greater of, or Larger of is a dyadic scalar function which returns the larger of its two arguments. The name "Maximum" is sometimes also used for the Maximum Reduce /, which returns the largest element of a vector (this usage is related to the maximum of a function). Maximum is paired with Minimum, and shares the glyph with the Ceiling function. It is not subject to comparison tolerance, since the result will be exactly equal to one argument, and there is no reason to choose a smaller argument even if the two arguments are tolerantly equal. As a Boolean function, Maximum is identical to Or.


See also Minimum#examples.

Maximum finds the larger of two numbers:

      2.4  1.9

Maximum Reduce finds the largest element in a vector:

      / 4 3 2 7 5 1 3

The index of this element can be found with Index Of, but is also the First element of the Grade Down of the vector.

      {⍳⌈/} 4 3 2 7 5 1 3
      ⊃⍒ 4 3 2 7 5 1 3

Reducing over an empty axis yields the smallest representable number, as that is the identity element for Maximum. This value is usually ¯∞ (for dialects that support infinities) or ¯1.797693135E308 (with 64-bit floats) or ¯1E6145 (with 128-bit decimal floats).

External links


APL built-ins [edit]
Primitive functions
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollType
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (AndOrNandNor) ∙ CircleComplex
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpand ∙ Set functions (IntersectionUnionWithout) ∙ Bracket indexSquad Indexing
Selector Index generatorGrade UpGrade DownIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveBaseRepresentMatrix InverseMatrix DivideFormatExecuteMaterialise
Primitive operators Monadic EachCommuteConstantReplicateReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic Inner ProductPower operatorRank operatorBindBesideReverse ComposeAtopOverAtVariantStencil
Quad names
Arrays Index originMigration level