Times: Difference between revisions

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:''This page describes the dyadic arithmetic function. For sign of a single argument, see [[Signum]].''
:''This page describes the dyadic arithmetic function. For sign of a single argument, see [[Signum]].''


{{Built-in|Times|×}}, '''Multiply''', or '''Product''' is a [[dyadic]] [[scalar function]] which gives the arithmetic product of its [[argument]]s. Times shares the [[glyph]] <source lang=apl inline>×</source> with the monadic arithmetic function [[Signum]].
{{Built-in|Times|×}}, '''Multiply''', or '''Product''' is a [[dyadic]] [[scalar function]] which gives the arithmetic product of its [[argument]]s. Times shares the [[glyph]] <syntaxhighlight lang=apl inline>×</syntaxhighlight> with the monadic arithmetic function [[Signum]].


== Examples ==
== Examples ==
A long, slow way to write <source lang=apl inline>!10</source>, assuming <source lang=apl inline>⎕IO←1</source>:
A long, slow way to write <syntaxhighlight lang=apl inline>!10</syntaxhighlight>, assuming <syntaxhighlight lang=apl inline>⎕IO←1</syntaxhighlight>:
<source lang=apl>
<syntaxhighlight lang=apl>
×/⍳10
×/⍳10
</source>
</syntaxhighlight>


== Properties ==
== Properties ==
Line 13: Line 13:
Multiplication is [[wikipedia:Commutative property|commutative]] and [[wikipedia:Associative property|associative]], but, due to floating point error, may result in small differences between mathematically equivalent expressions.
Multiplication is [[wikipedia:Commutative property|commutative]] and [[wikipedia:Associative property|associative]], but, due to floating point error, may result in small differences between mathematically equivalent expressions.


The [[identity element]] for Times is <source lang=apl inline>1</source>.
The [[identity element]] for Times is <syntaxhighlight lang=apl inline>1</syntaxhighlight>.


=== Reduction ===
=== Reduction ===
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* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Multiply.htm Dyalog]
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Multiply.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_060.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_060.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/d110.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/star#dyadic NuVoc] (as <source lang=j inline>*</source>)
* J [https://www.jsoftware.com/help/dictionary/d110.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/star#dyadic NuVoc] (as <syntaxhighlight lang=j inline>*</syntaxhighlight>)
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basic-arithmetic BQN]
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basic-arithmetic BQN]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]

Latest revision as of 10:48, 11 September 2022

This page describes the dyadic arithmetic function. For sign of a single argument, see Signum.
×

Times (×), Multiply, or Product is a dyadic scalar function which gives the arithmetic product of its arguments. Times shares the glyph × with the monadic arithmetic function Signum.

Examples

A long, slow way to write !10, assuming ⎕IO1:

×/10

Properties

Multiplication is commutative and associative, but, due to floating point error, may result in small differences between mathematically equivalent expressions.

The identity element for Times is 1.

Reduction

Reduction with Multiply gives the product of the whole list.

See also

External links

Documentation

APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace