Editing Unary operation

{{short description|Mathematical operation with only one operand}}
{{More citations needed|date=March 2010}}

In [[mathematics]], a '''unary operation''' is an [[Operation (mathematics)|operation]] with only one [[operand]], i.e. a single input.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Unary Operation|url=https://mathworld.wolfram.com/UnaryOperation.html|access-date=2020-07-29|website=mathworld.wolfram.com|language=en}}</ref> This is in contrast to ''[[binary operation]]s'', which use two operands.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Binary Operation|url=https://mathworld.wolfram.com/BinaryOperation.html|access-date=2020-07-29|website=mathworld.wolfram.com|language=en}}</ref> An example is any [[function (mathematics)|function]] {{tmath|f : A \rightarrow A}}, where {{mvar|A}} is a [[Set (mathematics)|set]]; the function {{tmath|f}} is a unary operation on {{mvar|A}}.

Common notations are [[prefix notation]] (e.g. [[¬]], [[−]]), [[postfix notation]] (e.g. [[factorial]] {{math|''n''!}}), functional notation (e.g. {{math|[[sine|sin]]&thinsp;''x''}} or {{math|sin(''x'')}}), and [[superscript]]s (e.g. [[transpose]] {{math|''A''{{sup|T}}}}). Other notations exist as well, for example, in the case of the [[square root]], a [[Vinculum (symbol)|horizontal bar]] extending the square root sign over the argument can indicate the extent of the argument.

==Examples==

=== Absolute value ===
Obtaining the [[absolute value]] of a number is a unary operation. This function is defined as <math>|n| = \begin{cases} n, & \mbox{if } n\geq0 \\ -n, & \mbox{if } n<0 \end{cases}</math> where <math>|n|</math> is the absolute value of <math>n</math>.

===Negation===
[[Negation (arithmetic)|Negation]] is used to find the negative value of a single number. Here are some examples:

:<math>-(3) = -3</math>

:<math>-( -3) = 3</math>

===Factorial===
For any positive integer ''n'', the product of the integers less than or equal to ''n'' is a unary operation called [[factorial]]. In the context of [[complex number]]s, the [[gamma function]] is a unary operation extension of factorial.

===Trigonometry===
In [[trigonometry]], the [[trigonometric functions]], such as <math>\sin</math>, <math>\cos</math>, and <math>\tan</math>, can be seen as unary operations. This is because it is possible to provide only one term as input for these functions and retrieve a result. By contrast, binary operations, such as [[addition]], require two different terms to compute a result.

===Examples from programming languages===
Below is a table summarizing common unary operators along with their symbols, description, and examples:<ref name="summarytable">{{cite web |title=Unary Operators in Programming |url=https://www.geeksforgeeks.org/unary-operators-in-programming/ |website=GeeksforGeeks |access-date=24 April 2024 |date=20 March 2024}}</ref>

{| class="wikitable"
|-
! Operator !! Symbol !! Description !! Example
|-
| Increment || <code>++</code> || Increases the value of a variable by 1 || <code>x = 2; ++x; // x is now 3</code>
|-
| Decrement || <code>−-</code> || Decreases the value of a variable by 1 || <code>y = 10; --y; // y is now 9</code>
|-
| Unary Plus || <code>+</code> || Indicates a positive value || <code>a = -5; b = +a; // b is -5</code>
|-
| Unary Minus || <code>-</code> || Indicates a negative value || <code>c = 4; d = -c; // d is -4</code>
|-
| [[Logical NOT]] || <code>!</code> || Negates the truth value of a Boolean expression || <code>flag = true; result = !flag; // result is false</code>
|-
| [[Bitwise|Bitwise NOT]] || <code>~</code> || Bitwise negation, flips the bits of an integer || <code>num = 5; result = ~num; // result is -6</code>
|}

====JavaScript====
In [[JavaScript]], these operators are unary:<ref>{{cite web |title=Unary Operators |url=https://www.javascripttutorial.net/javascript-unary-operators/}}</ref>
*[[Increment and decrement operators|Increment]]: <code>++<span style="color:gray;">x</span></code>, <code><span style="color:gray;">x</span>++</code>
*[[Increment and decrement operators|Decrement]]: <code>--<span style="color:gray;">x</span></code>, <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>
*[[Ones' complement]]: <code>~<span style="color:gray;">x</span></code>
*[[Negation|Logical negation]]: <code>!<span style="color:gray;">x</span></code>

====C family of languages====
In the [[C (programming language)|C]] family of languages, the following operators are unary:<ref>{{cite book |url=http://www-01.ibm.com/support/docview.wss?uid=swg27002103&aid=1 |page=109 |chapter=5. Expressions and Operators |title=C/C++ Language Reference |version=Version 6.0 |archive-url=https://web.archive.org/web/20121016081612/http://www-01.ibm.com/support/docview.wss?uid=swg27002103&aid=1 |archive-date=2012-10-16}}</ref><ref>{{cite web |url=http://www.sanfoundry.com/c-tutorials-different-unary-operators-operate-operands/ |title=Unary Operators - C Tutorials - Sanfoundry |website=www.sanfoundry.com|date=2 March 2014 }}</ref>

*[[Increment and decrement operators|Increment]]: <code>++<span style="color:gray;">x</span></code>, <code><span style="color:gray;">x</span>++</code>
*[[Increment and decrement operators|Decrement]]: <code>--<span style="color:gray;">x</span></code>, <code><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>
*[[Ones' 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 shell]] ([[Bash (Unix shell)|Bash]]/[[Bourne shell|Bourne Shell]]), e.g., the following operators are unary:<ref name="unixbash">{{cite web |title=Shell Arithmetic (Bash Reference Manual) |url=https://www.gnu.org/software/bash/manual/html_node/Shell-Arithmetic.html |website=www.gnu.org |publisher=GNU Operating System |access-date=24 April 2024}}</ref><ref name="unarybash">{{cite web |last1=Miran |first1=Mohammad Shah |title=Unary Operators in Bash |url=https://linuxsimply.com/bash-scripting-tutorial/operator/unary-operators/ |website=LinuxSimply |access-date=24 April 2024 |date=26 October 2023}}</ref>
*Pre and Post-Increment: <code>++<span style="color:gray;">$x</span></code>, <code><span style="color:gray;">$x</span>++</code>
*Pre and Post-Decrement: <code>--<span style="color:gray;">$x</span></code>, <code><span style="color:gray;">$x</span>--</code>
*Positive: <code>+<span style="color:gray;">$x</span></code>
*Negative: <code>-<span style="color:gray;">$x</span></code>
*Logical negation: <code>!<span style="color:gray;">$x</span></code>
* Simple expansion:  <code>$<span style="color:gray;">x</span></code>
* Complex expansion:  <code>${#<span style="color:gray;">x</span>}</code>

====PowerShell====
In the [[PowerShell]], the following operators are unary:<ref name="powershell">{{cite web |title=Expressions - PowerShell |url=https://learn.microsoft.com/en-us/powershell/scripting/lang-spec/chapter-07 |website=learn.microsoft.com |publisher=Microsoft |access-date=23 April 2024 |language=en-us |date=3 September 2021}}</ref>
*Increment: <code>++<span style="color:gray;">$x</span></code>, <code><span style="color:gray;">$x</span>++</code>
*Decrement: <code>--<span style="color:gray;">$x</span></code>, <code><span style="color:gray;">$x</span>--</code>
*Positive: <code>+<span style="color:gray;">$x</span></code>
*Negative: <code>-<span style="color:gray;">$x</span></code>
*Logical negation: <code>!<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;">$x</span></code>
*Cast: <code>[''type-name''] ''<span style="color:gray;">cast-expression</span>''</code>
*Cast: <code>+<span style="color:gray;">$x</span></code>
*Array: <code>,<span style="color:gray;">$array</span></code>

==See also==
* [[Unary function]]
* [[Binary operation]]
* [[Iterated binary operation]]
* [[Binary function]]
* [[Ternary operation]]
* [[Arity]]
* [[Operation (mathematics)]]
* [[Operator (programming)]]

==References==
{{Reflist}}

==External links==
*{{Commons category-inline|Unary operations}}

{{DEFAULTSORT:Unary Operation}}
[[Category:Elementary algebra]]
[[Category:Operators (programming)]]
[[Category:Unary operations| ]]