Exponential: Difference between revisions
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:''This page describes the monadic arithmetic function. For the dyadic function, see [[Power (function)]].''  :''This page describes the monadic arithmetic function. For the dyadic function, see [[Power (function)]].''  
{{BuiltinExponential*}} is a [[monadic]] [[scalar function]] which computes the [[wikipedia:exponential functionexponential function]] (i.e. the power of [[wikipedia:e (mathematical constant)Euler's constant e]]) of the [[argument]]. Exponential shares the [[glyph]] <  {{BuiltinExponential*}} is a [[monadic]] [[scalar function]] which computes the [[wikipedia:exponential functionexponential function]] (i.e. the power of [[wikipedia:e (mathematical constant)Euler's constant e]]) of the [[argument]]. Exponential shares the [[glyph]] <syntaxhighlight lang=apl inline>*</syntaxhighlight> with the dyadic arithmetic function [[Power]].  
== Examples ==  == Examples ==  
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Euler's constant itself can be obtained by supplying 1 as the argument.  Euler's constant itself can be obtained by supplying 1 as the argument.  
<  <syntaxhighlight lang=apl>  
*1  *1  
2.718281828  2.718281828  
</  </syntaxhighlight>  
On APL implementations that support [[complex]] numbers, one can demonstrate [[wikipedia:Euler's identityEuler's identity]] (with the help of [[Pi Times]] <  On APL implementations that support [[complex]] numbers, one can demonstrate [[wikipedia:Euler's identityEuler's identity]] (with the help of [[Pi Times]] <syntaxhighlight lang=apl inline>○</syntaxhighlight>):  
<  <syntaxhighlight lang=apl>  
1+*○0J1  1+*○0J1  
0  0  
</  </syntaxhighlight>{{Works in[[Dyalog APL]]}}  
== Properties ==  == Properties ==  
Exponential is a special case of [[Power]] with the default left argument of e (<  Exponential is a special case of [[Power]] with the default left argument of e (<syntaxhighlight lang=apl inline>*1</syntaxhighlight>).  
<  <syntaxhighlight lang=apl>  
((*1)∘* ≡ *) 0 1 ¯1 0J1  ((*1)∘* ≡ *) 0 1 ¯1 0J1  
1  1  
</  </syntaxhighlight>{{Works in[[Dyalog APL]]}}  
Exponential and [[Natural Logarithmnatural log]] <  Exponential and [[Natural Logarithmnatural log]] <syntaxhighlight lang=apl inline>⍟</syntaxhighlight> are inverses of each other, except where the natural log is undefined.  
<  <syntaxhighlight lang=apl>  
(⊢ ≡ ⍟∘*) 0 1 ¯1 0J1  (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1  
1  1  
(⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined  (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined  
1  1  
</  </syntaxhighlight>{{Works in[[Dyalog APL]]}}  
== See also ==  == See also ==  
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=== Documentation ===  === Documentation ===  
* [  * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Exponential.htm Dyalog]  
* [http://microapl.com/apl_help/ch_020_020_190.htm APLX]  * [http://microapl.com/apl_help/ch_020_020_190.htm APLX]  
* J [https://www.jsoftware.com/help/dictionary/d200.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hat NuVoc]  * J [https://www.jsoftware.com/help/dictionary/d200.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/hat NuVoc]  
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basicarithmetic BQN]  
{{APL builtins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]  {{APL builtins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]] 
Latest revision as of 22:25, 10 September 2022
 This page describes the monadic arithmetic function. For the dyadic function, see Power (function).
*

Exponential (*
) is a monadic scalar function which computes the exponential function (i.e. the power of Euler's constant e) of the argument. Exponential shares the glyph *
with the dyadic arithmetic function Power.
Examples
Euler's constant itself can be obtained by supplying 1 as the argument.
*1
2.718281828
On APL implementations that support complex numbers, one can demonstrate Euler's identity (with the help of Pi Times ○
):
1+*○0J1
0
Works in: Dyalog APL
Properties
Exponential is a special case of Power with the default left argument of e (*1
).
((*1)∘* ≡ *) 0 1 ¯1 0J1
1
Works in: Dyalog APL
Exponential and natural log ⍟
are inverses of each other, except where the natural log is undefined.
(⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
1
(⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
1
Works in: Dyalog APL
See also
External links
Documentation
 Dyalog
 APLX
 J Dictionary, NuVoc
 BQN