unary operation

{{short description|Mathematical operation with only one operand}}

In mathematics, a unary operation is an operation with only one operand, i.e. a single input.{{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}} This is in contrast to binary operations, which use two operands.{{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}} An example is any function {{tmath|f : A \rightarrow A}}, where {{mvar|A}} is a 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|sin x}} or {{math|sin(x)}}), and superscripts (e.g. transpose {{math|A{{sup|T}}}}). 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.

Examples

= Absolute value =

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

=Negation=

Negation is used to find the negative value of a single number. Here are some examples:

: $-(3) = -3$

: $-( -3) = 3$

=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 numbers, the gamma function is a unary operation extension of factorial.

=Trigonometry=

In trigonometry, the trigonometric functions, such as $\sin$ , $\cos$ , and $\tan$ , 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:{{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}}

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

==JavaScript==

In JavaScript, these operators are unary:{{cite web |title=Unary Operators |url=https://www.javascripttutorial.net/javascript-unary-operators/}}

Increment: ++x, x++
Decrement: --x, x--
Positive: +x
Negative: -x
Ones' complement: ~x
Logical negation: !x

==C family of languages==

In the C family of languages, the following operators are unary:{{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}}{{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 }}

Increment: ++x, x++
Decrement: --x, x--
Address: &x
Indirection: *x
Positive: +x
Negative: -x
Ones' complement: ~x
Logical negation: !x
Sizeof: sizeof x, sizeof(type-name)
Cast: (type-name) cast-expression

==Unix shell (Bash)==

In the Unix shell (Bash/Bourne Shell), e.g., the following operators are unary:{{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}}{{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}}

Pre and Post-Increment: ++$x, $x++
Pre and Post-Decrement: --$x, $x--
Positive: +$x
Negative: -$x
Logical negation: !$x
Simple expansion: $x
Complex expansion: ${#x}

==PowerShell==

In the PowerShell, the following operators are unary:{{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}}

Increment: ++$x, $x++
Decrement: --$x, $x--
Positive: +$x
Negative: -$x
Logical negation: !$x
Invoke in current scope: .$x
Invoke in new scope: &$x
Cast: [type-name] cast-expression
Cast: +$x
Array: ,$array

References

External links

{{Commons category-inline|Unary operations}}

Category:Elementary algebra

Category:Operators (programming)