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{{Built-in|Equal to|<nowiki>=</nowiki>}} is a [[comparison function]] which tests whether argument elements are [[Tolerant comparison|tolerantly]] equal to each other: it returns 1 if the [[element]]s being compared [[match]] and 0 if they do not. It is the [[Not|negation]] of [[Not | {{Built-in|Equal to|<nowiki>=</nowiki>}} is a [[comparison function]] which tests whether argument elements are [[Tolerant comparison|tolerantly]] equal to each other: it returns 1 if the [[element]]s being compared [[match]] and 0 if they do not. It is the [[Not|negation]] of [[Not Equal to]] (<source lang=apl inline>≠</source>). | ||
APL's <source lang=apl inline>=</source> differs from the usage of <math>=</math> in [[Comparison with traditional mathematics|traditional mathematical notation]] by having an implied [[Ken_Iverson#Iverson_bracket|Iverson bracket]]. Thus, <source lang=apl inline>i=j</source> is APL is equivalent to <math>[i=j]</math> or <math>\delta_{ij}</math> ([[wikipedia:Kronecker delta|Kronecker delta]]) in mathematics. | |||
== Examples == | == Examples == | ||
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In a [[Nested array model|nested]] APL, Equal to is pervasive, and compares all [[simple scalar]]s found in a [[nested array]]. | In a [[Nested array model|nested]] APL, Equal to is pervasive, and compares all [[simple scalar]]s found in a [[nested array]]. | ||
<source lang=apl> | <source lang=apl> | ||
⎕←n ← ((2 1)0)(1 0 3)(2 2⍴4 0) | |||
┌───────┬─────┬───┐ | ┌───────┬─────┬───┐ | ||
│┌───┬─┐│1 0 3│4 0│ | │┌───┬─┐│1 0 3│4 0│ | ||
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== Boolean function == | == Boolean function == | ||
{{Main|Boolean function}} | |||
When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments. | When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments): | ||
{|class=wikitable | |||
!<source lang=apl inline>=</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>0</source> | |||
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source> | |||
|- | |||
!<source lang=apl inline>1</source> | |||
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source> | |||
|} | |||
In the context of logic, it can be read as ''if and only if''. This function is also known as xnor or the Kronecker delta. | |||
[[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | [[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | ||
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* [http://microapl.com/apl_help/ch_020_020_310.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_310.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d000.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/eq#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d000.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/eq#dyadic NuVoc] | ||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Comparison functions]] | |||