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In [[mathematics]], a '''unary operation''' is an [[Operation (mathematics)|operation]] with only one [[operand]], i.e. a single input. Specifically, it is a function
:<math>f:\ A\to A</math>
where ''A'' is a [[Set (mathematics)|set]]. In this case ''f'' is called a unary operation on ''A''.


Common notations are [[prefix notation]] (e.g. +, −, not), [[postfix notation]] (e.g. [[factorial]] n!),  functional notation (e.g. sin x or sin (x)), and [[superscript]]s (e.g. [[transpose]] ''A<sup>T</sup>''). Other notations exist as well. For example, in the case of the [[square root]], a horizontal bar extending the square root sign over the argument can indicate the extent of the argument.


==Unary negative and positive==
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As unary operations have only one operand they are evaluated before other operations containing them {{Citation needed|date=July 2013}}. Here is an example using negation:
 
:3 − −2
 
Here the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is equal to:
 
:3 − (−2) = 5
 
Technically there is also a unary positive but it is not needed since we assume a value to be positive:
 
:(+2) = 2
 
Unary positive does not change the sign of a negative operation:
 
:(+(−2)) = (−2)
 
In this case a unary negative is needed to change the sign:
 
:(−(−2)) = (+2)
 
Unary operators (called "monadic" in APL) are also used in programming languages.
 
===C family of languages===
In the [[C (programming language)|C]] family of languages, the following operators are unary:
 
*Increment: <code>++<span style="color:gray;">x</span>, <span style="color:gray;">x</span>++</code>
*Decrement: <code>−−<span style="color:gray;">x</span>, <span style="color:gray;">x</span>−−</code>
*[[Reference (computer science)|Address]]: <code>&<span style="color:gray;">x</span></code>
*[[Indirection]]: <code>*<span style="color:gray;">x</span></code>
*Positive: <code>+<span style="color:gray;">x</span></code>
*Negative: <code>−<span style="color:gray;">x</span></code>
*[[Signed number representations|One's complement]]: <code>~<span style="color:gray;">x</span></code>
*[[Negation|Logical negation]]: <code>!<span style="color:gray;">x</span></code>
*[[Sizeof]]: <code>sizeof <span style="color:gray;">x</span>, sizeof(<span style="color:gray;">type-name</span>)</code>
*[[Type conversion|Cast]]: <code>(''type-name'') ''<span style="color:gray;">cast-expression</span></code>
 
===Unix Shell (Bash)===
 
In the Unix/Linux shell (bash/sh), ''''$'''' is a unary operator, used for parameter expansion, replacing the name of a variable by its (sometimes modified) value. For example:
 
* Simple expansion:  <code>$<span style="color:gray;">x</span></code>
* Complex expansion:  <code>${#<span style="color:gray;">x</span>}</code>
* Command substitution:  <code>$(<span style="color:gray;">cmd</span>)</code>
* Arithmetic expansion:  <code>$((<span style="color:gray;">expr</span>))</code>
 
===Other languages===
 
====Windows PowerShell====
*Increment: <code>++<span style="color:gray;">$x</span>, <span style="color:gray;">$x</span>++</code>
*Decrement: <code>−−<span style="color:gray;">$x</span>, <span style="color:gray;">$x</span>−−</code>
*Positive: <code>+<span style="color:gray;">$x</span></code>
*Negative: <code>−<span style="color:gray;">$x</span></code>
*Logical negation: <code>-not <span style="color:gray;">$x</span></code>
*[[Execution (computing)|Invoke]] in current [[Scope (programming)|scope]]: <code>.<span style="color:gray;">$x</span></code>
*Invoke in new scope: <code>&<span style="color:gray;">$x</span></code>
*Cast: <code>[''type-name''] ''<span style="color:gray;">cast-expression</span></code>
 
==See also==
* [[Binary operation]]
* [[Ternary operation]]
* [[Arity]]
* [[Operation (mathematics)]]
* [[Operator (programming)]]
 
==References==
*{{MathWorld|title=Unary Operation|urlname=UnaryOperation|author=Matt Insall}}
 
{{DEFAULTSORT:Unary Operation}}
[[Category:Elementary algebra]]
[[Category:Operators (programming)]]

Revision as of 13:23, 23 February 2014


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