Scalar function: Difference between revisions

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72 bytes added ,  09:07, 29 October 2019
m
Text replacement - "</code>" to "</source>"
Miraheze>Adám Brudzewsky
m (Text replacement - "<code>" to "<source lang=apl inline>")
Miraheze>Adám Brudzewsky
m (Text replacement - "</code>" to "</source>")
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A scalar function is one of a class of primitive functions that apply to arguments one [[element]] at a time. Dyadic scalar functions pair elements of their arguments based on [[conformability]] rules, and thus are subject to [[scalar extension]]. In [[Nested array model|nested]] array languages scalar functions recursively descend into nested arrays until they can be applied to [[simple scalars]]; in [[Flat array model|flat]] array languages they usually do not apply inside [[boxes]].
A scalar function is one of a class of primitive functions that apply to arguments one [[element]] at a time. Dyadic scalar functions pair elements of their arguments based on [[conformability]] rules, and thus are subject to [[scalar extension]]. In [[Nested array model|nested]] array languages scalar functions recursively descend into nested arrays until they can be applied to [[simple scalars]]; in [[Flat array model|flat]] array languages they usually do not apply inside [[boxes]].


Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <source lang=apl inline>~</code> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <source lang=apl inline>?</code>.
Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <source lang=apl inline>~</source> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <source lang=apl inline>?</source>.


== Standard scalar functions ==
== Standard scalar functions ==
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{|
{|
| <source lang=apl inline>+</code> || [[Conjugate]]
| <source lang=apl inline>+</source> || [[Conjugate]]
|-
|-
| <source lang=apl inline>-</code> || [[Negate]]
| <source lang=apl inline>-</source> || [[Negate]]
|-
|-
| <source lang=apl inline>×</code> || [[Signum]] or Direction
| <source lang=apl inline>×</source> || [[Signum]] or Direction
|-
|-
| <source lang=apl inline>÷</code> || [[Reciprocal]]
| <source lang=apl inline>÷</source> || [[Reciprocal]]
|-
|-
| <source lang=apl inline>⌊</code> || [[Floor]]
| <source lang=apl inline>⌊</source> || [[Floor]]
|-
|-
| <source lang=apl inline>⌈</code> || [[Ceiling]]
| <source lang=apl inline>⌈</source> || [[Ceiling]]
|-
|-
| <source lang=apl inline>*</code> || [[Exponential]]
| <source lang=apl inline>*</source> || [[Exponential]]
|-
|-
| <source lang=apl inline>⍟</code> || [[Natural Logarithm]]
| <source lang=apl inline>⍟</source> || [[Natural Logarithm]]
|-
|-
| <source lang=apl inline><nowiki>|</nowiki></code> || [[Magnitude]]
| <source lang=apl inline><nowiki>|</nowiki></source> || [[Magnitude]]
|-
|-
| <source lang=apl inline>!</code> || [[Factorial]]
| <source lang=apl inline>!</source> || [[Factorial]]
|-
|-
| <source lang=apl inline>○</code> || [[Pi Times]]
| <source lang=apl inline>○</source> || [[Pi Times]]
|-
|-
| <source lang=apl inline>~</code> || [[Not]]
| <source lang=apl inline>~</source> || [[Not]]
|-
|-
| <source lang=apl inline>∊</code> || [[Type]]
| <source lang=apl inline>∊</source> || [[Type]]
|}
|}


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{|
{|
| <source lang=apl inline>+</code> || [[Plus]]
| <source lang=apl inline>+</source> || [[Plus]]
|-
|-
| <source lang=apl inline>-</code> || [[Minus]]
| <source lang=apl inline>-</source> || [[Minus]]
|-
|-
| <source lang=apl inline>×</code> || [[Times]]
| <source lang=apl inline>×</source> || [[Times]]
|-
|-
| <source lang=apl inline>÷</code> || [[Divide]]
| <source lang=apl inline>÷</source> || [[Divide]]
|-
|-
| <source lang=apl inline>⌊</code> || [[Minimum]]
| <source lang=apl inline>⌊</source> || [[Minimum]]
|-
|-
| <source lang=apl inline>⌈</code> || [[Maximum]]
| <source lang=apl inline>⌈</source> || [[Maximum]]
|-
|-
| <source lang=apl inline>*</code> || [[Power function]]
| <source lang=apl inline>*</source> || [[Power function]]
|-
|-
| <source lang=apl inline>⍟</code> || [[Logarithm]]
| <source lang=apl inline>⍟</source> || [[Logarithm]]
|-
|-
| <source lang=apl inline><nowiki>|</nowiki></code> || [[Residue]]
| <source lang=apl inline><nowiki>|</nowiki></source> || [[Residue]]
|-
|-
| <source lang=apl inline>!</code> || [[Binomial]] coefficient or combination function
| <source lang=apl inline>!</source> || [[Binomial]] coefficient or combination function
|-
|-
| <source lang=apl inline>○</code> || [[Circle function]]
| <source lang=apl inline>○</source> || [[Circle function]]
|-
|-
| <source lang=apl inline>∧</code> || [[Logical And]]
| <source lang=apl inline>∧</source> || [[Logical And]]
|-
|-
| <source lang=apl inline>∨</code> || [[Logical Or]]
| <source lang=apl inline>∨</source> || [[Logical Or]]
|-
|-
| <source lang=apl inline>⍲</code> || [[Nand]]
| <source lang=apl inline>⍲</source> || [[Nand]]
|-
|-
| <source lang=apl inline>⍱</code> || [[Nor]]
| <source lang=apl inline>⍱</source> || [[Nor]]
|-
|-
| <source lang=apl inline><</code> || [[Less than]]
| <source lang=apl inline><</source> || [[Less than]]
|-
|-
| <source lang=apl inline>≤</code> || [[Less than or equal to]]
| <source lang=apl inline>≤</source> || [[Less than or equal to]]
|-
|-
| <source lang=apl inline>=</code> || [[Equal to]]
| <source lang=apl inline>=</source> || [[Equal to]]
|-
|-
| <source lang=apl inline>≥</code> || [[Greater than or equal to]]
| <source lang=apl inline>≥</source> || [[Greater than or equal to]]
|-
|-
| <source lang=apl inline>></code> || [[Greather than]]
| <source lang=apl inline>></source> || [[Greather than]]
|-
|-
| <source lang=apl inline>≠</code> || [[Not equal to]]
| <source lang=apl inline>≠</source> || [[Not equal to]]
|}
|}

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