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A library for exact computation with quadratic irrationals with support for exact conversion from and to (potentially periodic) simple continued fractions.

A quadratic irrational is a number that can be expressed in the form

(a + b √c) / d

where a, b and d are integers and c is a square-free natural number.

Some examples of such numbers are

• 7/2,

• √2,

• (1 + √5)/2 (the golden ratio),

• solutions to quadratic equations with rational constants – the quadratic formula has a familiar shape.

A simple continued fraction is a number expressed in the form

a + 1/(b + 1/(c + 1/(d + 1/(e + …))))

or alternatively written as

[a; b, c, d, e, …]

where a is an integer and b, c, d, e, … are positive integers.

Every finite SCF represents a rational number and every infinite, periodic SCF represents a quadratic irrational.

3.5      = [3; 2]
(1+√5)/2 = [1; 1, 1, 1, …]
√2       = [1; 2, 2, 2, …]

Versions 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.5 ChangeLog.md arithmoi (==0.4.*), base (>=4.6 && <4.8), containers (==0.5.*), mtl (==2.1.*), transformers (==0.3.*) [details] MIT Copyright © 2014 Johan Kiviniemi Johan Kiviniemi Johan Kiviniemi Math, Algorithms, Data https://github.com/ion1/quadratic-irrational https://github.com/ion1/quadratic-irrational/issues head: git clone https://github.com/ion1/quadratic-irrational.git by ion at Fri Mar 28 21:58:19 UTC 2014 NixOS:0.0.5 1813 total (75 in the last 30 days) (no votes yet) [estimated by rule of succession] λ λ λ Docs uploaded by userBuild status unknown Hackage Matrix CI

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# quadratic-irrational

A library for exact computation with quadratic irrationals with support for exact conversion from and to (potentially periodic) simple continued fractions.

A quadratic irrational is a number that can be expressed in the form

(a + b √c) / d


where a, b and d are integers and c is a square-free natural number.

Some examples of such numbers are

• 7/2,

• √2,

• (1 + √5)/2 (the golden ratio),

• solutions to quadratic equations with rational constants – the quadratic formula has a familiar shape.

A simple continued fraction is a number in the form

a + 1/(b + 1/(c + 1/(d + 1/(e + …))))


or alternatively written as

[a; b, c, d, e, …]


where a is an integer and b, c, d, e, … are positive integers.

Every finite SCF represents a rational number and every infinite, periodic SCF represents a quadratic irrational.

3.5      = [3; 2]
(1+√5)/2 = [1; 1, 1, 1, …]
√2       = [1; 2, 2, 2, …]