# quadratic-irrational: An implementation of quadratic irrationals

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**Warnings:**

- 'ghc-options: -O2' is rarely needed. Check that it is giving a real benefit and not just imposing longer compile times on your users.

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

`7/2`

,`√2`

,`(1 + √5)/2`

(the golden ratio),solutions to some quadratic equations – the quadratic formula has a familiar shape.

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

Versions | 0.0.1, 0.0.2, 0.0.3, 0.0.3, 0.0.4, 0.0.5 |
---|---|

Change log | ChangeLog.md |

Dependencies | arithmoi (==0.4.*), base (>=4.6 && <4.8), containers (==0.5.*), mtl (==2.1.*), transformers (==0.3.*) [details] |

License | MIT |

Copyright | Copyright © 2014 Johan Kiviniemi |

Author | Johan Kiviniemi <devel@johan.kiviniemi.name> |

Maintainer | Johan Kiviniemi <devel@johan.kiviniemi.name> |

Category | Math, Algorithms, Data |

Home page | https://github.com/ion1/quadratic-irrational |

Bug tracker | https://github.com/ion1/quadratic-irrational/issues |

Source repository | head: git clone https://github.com/ion1/quadratic-irrational.git |

Uploaded | Tue Mar 25 23:59:15 UTC 2014 by ion |

## Modules

[Index]

## Downloads

- quadratic-irrational-0.0.3.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)

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