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Natural Logarithm: Difference between revisions
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:''This page describes the monadic arithmetic function. For the dyadic logarithm function, see [[Logarithm]].'' | :''This page describes the monadic arithmetic function. For the dyadic logarithm function, see [[Logarithm]].'' | ||
{{Built-in|Natural Logarithm|⍟}}, or '''Natural Log''', is a [[monadic]] [[scalar function]] which computes the [[wikipedia:natural logarithm|natural logarithm]] of the [[argument]]. Logarithm shares the [[glyph]] < | {{Built-in|Natural Logarithm|⍟}}, or '''Natural Log''', is a [[monadic]] [[scalar function]] which computes the [[wikipedia:natural logarithm|natural logarithm]] of the [[argument]]. Logarithm shares the [[glyph]] <syntaxhighlight lang=apl inline>⍟</syntaxhighlight> with the dyadic arithmetic function [[Logarithm]]. The [[glyph]], a composition of the glyphs for [[Circular]] (<syntaxhighlight lang=apl inline>○</syntaxhighlight>) and [[Exponential]] (<syntaxhighlight lang=apl inline>*</syntaxhighlight>) to indicate its close mathematical ties with these two functions, is a stylised tree log.<ref>[[E. E. McDonnell|McDonnell, E. E.]]. [https://www.jsoftware.com/papers/eem/storyofo.htm Recreational APL: The Story of <syntaxhighlight lang=apl inline>○</syntaxhighlight>]. [[APL Quote-Quad]], Volume 8, Number 2, 1977-12.</ref> | ||
== Examples == | == Examples == | ||
< | <syntaxhighlight lang=apl> | ||
⍟1 2 (*1) (*10) | ⍟1 2 (*1) (*10) | ||
0 0.6931471806 1 10 | 0 0.6931471806 1 10 | ||
| Line 13: | Line 13: | ||
== Properties == | == Properties == | ||
Natural logarithm is a special case of [[Logarithm]] with the default left argument of e (< | Natural logarithm is a special case of [[Logarithm]] with the default left argument of e (<syntaxhighlight lang=apl inline>*1</syntaxhighlight>). | ||
< | <syntaxhighlight lang=apl> | ||
((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1 | ((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1 | ||
1 | 1 | ||
</syntaxhighlight>{{Works in|[[Dyalog APL]]}} | </syntaxhighlight>{{Works in|[[Dyalog APL]]}} | ||
Natural logarithm and [[exponential]] < | Natural logarithm and [[exponential]] <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 | ||