Scalar function: Difference between revisions
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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>~</ | 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>+</ | | <source lang=apl inline>+</source> || [[Conjugate]] | ||
|- | |- | ||
| <source lang=apl inline>-</ | | <source lang=apl inline>-</source> || [[Negate]] | ||
|- | |- | ||
| <source lang=apl inline>×</ | | <source lang=apl inline>×</source> || [[Signum]] or Direction | ||
|- | |- | ||
| <source lang=apl inline>÷</ | | <source lang=apl inline>÷</source> || [[Reciprocal]] | ||
|- | |- | ||
| <source lang=apl inline>⌊</ | | <source lang=apl inline>⌊</source> || [[Floor]] | ||
|- | |- | ||
| <source lang=apl inline>⌈</ | | <source lang=apl inline>⌈</source> || [[Ceiling]] | ||
|- | |- | ||
| <source lang=apl inline>*</ | | <source lang=apl inline>*</source> || [[Exponential]] | ||
|- | |- | ||
| <source lang=apl inline>⍟</ | | <source lang=apl inline>⍟</source> || [[Natural Logarithm]] | ||
|- | |- | ||
| <source lang=apl inline><nowiki>|</nowiki></ | | <source lang=apl inline><nowiki>|</nowiki></source> || [[Magnitude]] | ||
|- | |- | ||
| <source lang=apl inline>!</ | | <source lang=apl inline>!</source> || [[Factorial]] | ||
|- | |- | ||
| <source lang=apl inline>○</ | | <source lang=apl inline>○</source> || [[Pi Times]] | ||
|- | |- | ||
| <source lang=apl inline>~</ | | <source lang=apl inline>~</source> || [[Not]] | ||
|- | |- | ||
| <source lang=apl inline>∊</ | | <source lang=apl inline>∊</source> || [[Type]] | ||
|} | |} | ||
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{| | {| | ||
| <source lang=apl inline>+</ | | <source lang=apl inline>+</source> || [[Plus]] | ||
|- | |- | ||
| <source lang=apl inline>-</ | | <source lang=apl inline>-</source> || [[Minus]] | ||
|- | |- | ||
| <source lang=apl inline>×</ | | <source lang=apl inline>×</source> || [[Times]] | ||
|- | |- | ||
| <source lang=apl inline>÷</ | | <source lang=apl inline>÷</source> || [[Divide]] | ||
|- | |- | ||
| <source lang=apl inline>⌊</ | | <source lang=apl inline>⌊</source> || [[Minimum]] | ||
|- | |- | ||
| <source lang=apl inline>⌈</ | | <source lang=apl inline>⌈</source> || [[Maximum]] | ||
|- | |- | ||
| <source lang=apl inline>*</ | | <source lang=apl inline>*</source> || [[Power function]] | ||
|- | |- | ||
| <source lang=apl inline>⍟</ | | <source lang=apl inline>⍟</source> || [[Logarithm]] | ||
|- | |- | ||
| <source lang=apl inline><nowiki>|</nowiki></ | | <source lang=apl inline><nowiki>|</nowiki></source> || [[Residue]] | ||
|- | |- | ||
| <source lang=apl inline>!</ | | <source lang=apl inline>!</source> || [[Binomial]] coefficient or combination function | ||
|- | |- | ||
| <source lang=apl inline>○</ | | <source lang=apl inline>○</source> || [[Circle function]] | ||
|- | |- | ||
| <source lang=apl inline>∧</ | | <source lang=apl inline>∧</source> || [[Logical And]] | ||
|- | |- | ||
| <source lang=apl inline>∨</ | | <source lang=apl inline>∨</source> || [[Logical Or]] | ||
|- | |- | ||
| <source lang=apl inline>⍲</ | | <source lang=apl inline>⍲</source> || [[Nand]] | ||
|- | |- | ||
| <source lang=apl inline>⍱</ | | <source lang=apl inline>⍱</source> || [[Nor]] | ||
|- | |- | ||
| <source lang=apl inline><</ | | <source lang=apl inline><</source> || [[Less than]] | ||
|- | |- | ||
| <source lang=apl inline>≤</ | | <source lang=apl inline>≤</source> || [[Less than or equal to]] | ||
|- | |- | ||
| <source lang=apl inline>=</ | | <source lang=apl inline>=</source> || [[Equal to]] | ||
|- | |- | ||
| <source lang=apl inline>≥</ | | <source lang=apl inline>≥</source> || [[Greater than or equal to]] | ||
|- | |- | ||
| <source lang=apl inline>></ | | <source lang=apl inline>></source> || [[Greather than]] | ||
|- | |- | ||
| <source lang=apl inline>≠</ | | <source lang=apl inline>≠</source> || [[Not equal to]] | ||
|} | |} |