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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]].''  
{{BuiltinTimes×}}, '''Multiply''', or '''Product''' is a [[dyadic]] [[scalar function]] which gives the arithmetic product of its [[argument]]s. Times shares the [[glyph]] <  {{BuiltinTimes×}}, '''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 <  A long, slow way to write <syntaxhighlight lang=apl inline>!10</syntaxhighlight>, assuming <syntaxhighlight lang=apl inline>⎕IO←1</syntaxhighlight>:  
<  <syntaxhighlight lang=apl>  
×/⍳10  ×/⍳10  
</syntaxhighlight>  </syntaxhighlight>  
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Multiplication is [[wikipedia:Commutative propertycommutative]] and [[wikipedia:Associative propertyassociative]], but, due to floating point error, may result in small differences between mathematically equivalent expressions.  Multiplication is [[wikipedia:Commutative propertycommutative]] and [[wikipedia:Associative propertyassociative]], but, due to floating point error, may result in small differences between mathematically equivalent expressions.  
The [[identity element]] for Times is <  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 <  * 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#basicarithmetic BQN]  * [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basicarithmetic BQN]  
{{APL builtins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]  {{APL builtins}}[[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 ⎕IO←1
:
×/⍳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
 Dyalog
 APLX
 J Dictionary, NuVoc (as
*
)  BQN