Infix notation: Difference between revisions

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{{Short description|Mathematics notation with operators between operands}}

{{Infobox notation

|{{Operator notation sidebar |logo=[[ImageFile:Infix-dia.pngsvg|125px]]}}

}}'''Infix notation''' is the common arithmetic and logical formula notation, in which [[operator]]s are written [[infix]]-style between the [[operand]]s they act on (e.g. 2 '''+''' 2). It is not as simple to [[Parsing|parse]] by computers as [[prefix notation]] ( e.g. '''+''' 2 2 ) or [[postfix notation]] ( e.g. 2 2 '''+''' ), but many [[programming language]]s use it due to its familiarity.

'''Infix notation''' is the notation commonly used in [[arithmetic]]al and [[logic]]al formulae and statements. It is characterized by the placement of [[Operator (mathematics)|operator]]s between [[operand]]s—"infixed operators"—such as the [[plus sign]] in {{nowrap|2 '''+''' 2}}.

In infix notation, unlike in prefix or postfix notations, [[Bracket#Parentheses_.28_.29|parentheses]] surrounding groups of operands and operators are necessary to indicate the intended order in which operations are to be performed. In the absence of parentheses, certain precedence rules determine the [[order of operations]].

==See alsoUsage==

[[Binary relation]]s are often denoted by an infix symbol such as [[set membership]] ''a'' ∈ ''A'' when the set ''A'' has ''a'' for an element. In [[geometry]], [[perpendicular line]]s ''a'' and ''b'' are denoted <math>a \perp b \ ,</math> and in [[projective geometry]] two points ''b'' and ''c'' are in [[perspective (geometry)|perspective]] when <math>b \ \doublebarwedge \ c</math> while they are connected by a projectivity when <math>b \ \barwedge \ c .</math>

*postfix notation, also called [[Reverse Polish notation]]

*prefix notation, also called [[Polish notation]]

*[[Shunting yard algorithm]], used to convert infix notation to postfix notation or to a tree

Infix notation is more difficult to [[parsing|parse]] by computers than [[prefix notation]] (e.g. '''+''' 2 2) or [[postfix notation]] (e.g. 2 2 '''+'''). However many [[programming language]]s use it due to its familiarity. It is more used in arithmetic, e.g. 5 '''×''' 6.<ref name="Infix, Postfix and Prefix">{{cite web | url=http://www.cs.man.ac.uk/~pjj/cs212/fix.html | title=The Implementation and Power of Programming Languages | access-date=30 August 2014 | archive-url=https://web.archive.org/web/20220827171346/https://www.cs.man.ac.uk/~pjj/cs212/fix.html | archive-date=27 August 2022}}</ref>

==External links==

*[http://www.xnumber.com/xnumber/rpn_or_adl.htm ''RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic'']

==Further notations==

{{math-stub}}

Infix notation may also be distinguished from [[Function (mathematics)|function]] notation, where the name of a function suggests a particular operation, and its [[Argument of a function|arguments]] are the operands. An example of such a [[Function application|function notation]] would be {{math|S(1, 3)}} in which the function {{math|S}} denotes addition ("sum"): {{math|1=S (1, 3) = 1 + 3 = 4}}.

[[Category:Mathematical notation]]

==Order of operations==

[[cs:Infixová notace]]

In infix notation, unlike in prefix or postfix notations, [[Bracket#Parentheses_.28_.29Parentheses|parentheses]] surrounding groups of operands and operators are necessary to indicate the intended order in which operations are to be performed. In the absence of parentheses, certain precedence rules determine the [[order of operations]].

[[de:Infixnotation]]

[[hr:Infiksna notacija]]

== See also ==

[[ja:中置記法]]

* [[Tree traversal]]: Infix (In-order) is also a tree traversal order. It is described in a more detailed manner on this page.

[[simple:Infix notation]]

* [[Calculator input methods]]: comparison of notations as used by pocket calculators

[[sr:Инфиксна нотација]]

*postfix Postfix notation, also called [[Reverse Polish notation]]

*prefix Prefix notation, also called [[Polish notation]]

* [[Shunting yard algorithm]], used to convert infix notation to postfix notation or to a tree

* [[Operator (computer programming)]]

* [[Subject–verb–object word order]]

==References==

{{Reflist}}

== External links ==

* [http://www.xnumber.com/xnumber/rpn_or_adl.htm ''RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic'']

*[https://web.archive.org/web/20130925214440/http://www.meta-calculator.com/learning-lab/how-to-build-scientific-calculator/infix-to-postifix-convertor.php Infix to postfix convertor]''[sic]''

[[Category:Mathematical notation]]

[[Category:Operators (programming)]]