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]] <source 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 <source lang=apl inline>!10</syntaxhighlight>, assuming <source lang=apl inline>⎕IO←1</syntaxhighlight>:
<source lang=apl>
<source 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 <source 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 <source 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]]

Revision as of 10:29, 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 <source lang=apl inline>×</syntaxhighlight> with the monadic arithmetic function Signum.

Examples

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

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 <source lang=apl inline>1</syntaxhighlight>.

Reduction

Reduction with Multiply gives the product of the whole list.

See also

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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