4,494
edits
Identity element: Difference between revisions
Jump to navigation
Jump to search
m
Text replacement - "http://help.dyalog.com" to "https://help.dyalog.com"
(→Left and right identities: Prove left and right identities can't be distinct) |
m (Text replacement - "http://help.dyalog.com" to "https://help.dyalog.com") |
||
| (6 intermediate revisions by 2 users not shown) | |||
| Line 41: | Line 41: | ||
| [[Power]] || <source lang=apl inline>*</source> || <source lang=apl inline>1</source> || {{No}} || {{Yes}} || | | [[Power]] || <source lang=apl inline>*</source> || <source lang=apl inline>1</source> || {{No}} || {{Yes}} || | ||
|- | |- | ||
| [[ | | [[Circle function]] || <source lang=apl inline>○</source> || <source lang=apl inline>¯9</source> || {{Yes}} || {{No}} || | ||
|- | |- | ||
| [[Binomial]] || <source lang=apl inline>!</source> || <source lang=apl inline>1</source> || {{Yes}} || {{No}} || | | [[Binomial]] || <source lang=apl inline>!</source> || <source lang=apl inline>1</source> || {{Yes}} || {{No}} || | ||
| Line 47: | Line 47: | ||
| [[Root]] || <source lang=apl inline>√</source> || <source lang=apl inline>1</source> || {{Yes}} || {{No}} || | | [[Root]] || <source lang=apl inline>√</source> || <source lang=apl inline>1</source> || {{Yes}} || {{No}} || | ||
|- | |- | ||
| [[And]]/[[LCM]] || <source lang=apl inline>∧</source> || <source lang=apl inline> | | [[And]]/[[LCM]] || <source lang=apl inline>∧</source> || <source lang=apl inline>1</source> || {{Yes}} || {{Yes}} || | ||
|- | |- | ||
| [[Or]]/[[GCD]] || <source lang=apl inline>∨</source> || <source lang=apl inline> | | [[Or]]/[[GCD]] || <source lang=apl inline>∨</source> || <source lang=apl inline>0</source> || {{Yes}} || {{Yes}} || Non-negative reals only | ||
|- | |- | ||
| [[Less]] || <source lang=apl inline><</source> || <source lang=apl inline>0</source> || {{Yes}} || {{No}} || [[Boolean]]s only | | [[Less]] || <source lang=apl inline><</source> || <source lang=apl inline>0</source> || {{Yes}} || {{No}} || [[Boolean]]s only | ||
| Line 79: | Line 79: | ||
| [[Take]] || <source lang=apl inline>↑</source> || <source lang=apl inline>⍬</source> or <source lang=apl inline>⍴P</source>|| {{Yes}} || {{No}} || | | [[Take]] || <source lang=apl inline>↑</source> || <source lang=apl inline>⍬</source> or <source lang=apl inline>⍴P</source>|| {{Yes}} || {{No}} || | ||
|- | |- | ||
| [[Squad | | [[Squad Index]] || <source lang=apl inline>⌷</source> || <source lang=apl inline>⍬</source> or <source lang=apl inline>⍳¨⍴P</source>|| {{Yes}} || {{No}} || | ||
|- | |- | ||
| [[Without]] || <source lang=apl inline>~</source> || <source lang=apl inline>0⌿P</source> || {{No}} || {{Yes}} || <source lang=apl inline>1≤≢⍴Y</source> | | [[Without]] || <source lang=apl inline>~</source> || <source lang=apl inline>0⌿P</source> || {{No}} || {{Yes}} || <source lang=apl inline>1≤≢⍴Y</source> | ||
| Line 100: | Line 100: | ||
== External links == | == External links == | ||
* [[wikipedia:Identity element| | * [[wikipedia:Identity element|Identity element]] | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/#Language/Primitive%20Operators/Reduce.htm Dyalog APL] | ||
* [https://www.ibm.com/downloads/cas/ZOKMYKOY#page=227 APL2] | * [https://www.ibm.com/downloads/cas/ZOKMYKOY#page=227 APL2] | ||
{{APL features}} | {{APL features}}[[Category:Function characteristics]] | ||