Some programming languages provide a built-in (primitive) rational data type
Data type
In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
s like 1/3 and -11/17 without rounding, and to do arithmetic on them. Examples are the ratio type of Common Lisp
Common Lisp
Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
, and analogous types provided by most languages for algebraic computation, such as Mathematica
Mathematica
Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...
Acer is a genus of trees or shrubs commonly known as maple.Maples are variously classified in a family of their own, the Aceraceae, or together with the Hippocastanaceae included in the family Sapindaceae. Modern classifications, including the Angiosperm Phylogeny Group system, favour inclusion in...
. Many languages that do not have a built-in rational type still provide it as a library
Library (computer science)
In computer science, a library is a collection of resources used to develop software. These may include pre-written code and subroutines, classes, values or type specifications....
-defined type.
Representation
A variable or value of that type is usually represented as a fraction
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values....
numbers, either with a fixed or arbitrary precision. Depending on the language, the denominator n may be constrained to be non-zero, and the two numbers may be kept in reduced form (without any common divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s except 1).
Languages that support a rational data type usually provide special syntax for building such values, and also extend the basic arithmetic operations ('+', '−', '×', '/', integer powers) and comparisons ('=', '<', '>', '≤') to act on them — either natively or through operator overloading
Operator overloading
In object oriented computer programming, operator overloading—less commonly known as operator ad-hoc polymorphism—is a specific case of polymorphism, where different operators have different implementations depending on their arguments...
facilities provided by the language. These operations may be translated by the compiler
Compiler
A compiler is a computer program that transforms source code written in a programming language into another computer language...
into a sequence of integer machine instructions, or into library
Library (computer science)
In computer science, a library is a collection of resources used to develop software. These may include pre-written code and subroutines, classes, values or type specifications....
calls. Support may also extend to other operations, such as formatting, rounding to an integer or floating point
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, those languages often interpret an integer value as equivalent to a rational value with a unit denominator.
Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, "a function is a first-class citizen" of the programming language. As a functional programming language, the...
provides a Rational type, which is really an alias for Ratio Integer (Ratio being a polymorphic type implementing rational numbers for any Integral type of numerators and denominators). The fraction is constructed using the % operator.
OCaml's Num library implements arbitrary-precision rational numbers.
Perl is a high-level, general-purpose, interpreted, dynamic programming language. Perl was originally developed by Larry Wall in 1987 as a general-purpose Unix scripting language to make report processing easier. Since then, it has undergone many changes and revisions and become widely popular...
's Math::BigRat core module implements arbitrary-precision rational numbers. The bigrat pragma can be used to turn on transparent BigRat support.
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
's standard library includes a Fraction class in the module fractions.
Ruby is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...
's standard library includes a Rational class in the module rational.
Java is a programming language originally developed by James Gosling at Sun Microsystems and released in 1995 as a core component of Sun Microsystems' Java platform. The language derives much of its syntax from C and C++ but has a simpler object model and fewer low-level facilities...
Clojure |closure]]") is a recent dialect of the Lisp programming language created by Rich Hickey. It is a general-purpose language supporting interactive development that encourages a functional programming style, and simplifies multithreaded programming....
can perform arithmetic on rational numbers and offers a literal form to represent them.
Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...
provides a numeric data type for arbitrarily sized rational numbers: RATIO.
1/3
⇒ 1/3
The type of a rational number is RATIO:
(type-of 1/3)
⇒ RATIO
Dividing two integers may return a rational number and the multiplication of a rational number may return an integer number:
(/ 6 8)
⇒ 3/4
(* 3/4 16)
⇒ 12
The numerator and denominator may be obtained by their eponymous functions, that reduce a rational to canonical form and compute the numerator or denominator of that form respectively:
(numerator 12/16)
⇒ 3
(denominator 12/16)
⇒ 4
Computing with large integers returning a large rational number:
(/ (1- (expt 2 200)) (1- (expt 2 43)))
⇒ 1606938044258990275541962092341162602522202993782792835301375/8796093022207
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