The quadratic-irrational package

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An implementation of quadratic irrationals with support for conversion from and to periodic 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

A continued fraction is a number that can be expressed in the form

 a + 1/(b + 1/(c + 1/(d + 1/(e + …))))

alternatively expressed using the notation

 [a; b, c, d, e, …]

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

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

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

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Properties

Versions0.0.1, 0.0.2, 0.0.3, 0.0.3, 0.0.4, 0.0.5
Change logChangeLog.md
Dependenciesarithmoi (==0.4.*), base (>=4.6 && <4.8), containers (==0.5.*), mtl (==2.1.*), transformers (==0.3.*) [details]
LicenseMIT
CopyrightCopyright © 2014 Johan Kiviniemi
AuthorJohan Kiviniemi <devel@johan.kiviniemi.name>
MaintainerJohan Kiviniemi <devel@johan.kiviniemi.name>
CategoryMath, Algorithms, Data
Home pagehttps://github.com/ion1/quadratic-irrational
Bug trackerhttps://github.com/ion1/quadratic-irrational/issues
Source repositoryhead: git clone https://github.com/ion1/quadratic-irrational.git
UploadedTue Mar 25 23:59:15 UTC 2014 by ion

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Readme for quadratic-irrational-0.0.3

quadratic-irrational

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An implementation of quadratic irrationals with support for conversion from and to periodic 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

A continued fraction is a number that can be expressed in the form

a + 1/(b + 1/(c + 1/(d + 1/(e + …))))

alternatively expressed using the notation

[a; b, c, d, e, …]

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

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

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