# quadratic-irrational: An implementation of quadratic irrationals

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, …]

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## Downloads

- quadratic-irrational-0.1.1.tar.gz [browse] (Cabal source package)
- Package description (revised from the package)

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#### Maintainer's Corner

For package maintainers and hackage trustees

Candidates

Versions [RSS] | 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.5, 0.0.6, 0.1.0, 0.1.1 |
---|---|

Change log | ChangeLog.md |

Dependencies | arithmoi (>=0.9), base (>=4.9 && <5), containers (>=0.5 && <0.8), integer-roots (>=1.0), semigroups (>=0.8), transformers (>=0.3 && <0.7) [details] |

License | MIT |

Copyright | Copyright © 2014 Johan Kiviniemi |

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

Maintainer | Andrew Lelechenko andrew dot lelechenko at gmail dot com |

Revised | Revision 2 made by Bodigrim at 2023-09-27T20:31:32Z |

Category | Math, Algorithms, Data |

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

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

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

Uploaded | by Bodigrim at 2020-04-15T19:35:42Z |

Distributions | LTSHaskell:0.1.1, NixOS:0.1.1, Stackage:0.1.1 |

Reverse Dependencies | 1 direct, 0 indirect [details] |

Downloads | 5679 total (25 in the last 30 days) |

Rating | (no votes yet) [estimated by Bayesian average] |

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Status | Docs available [build log] Last success reported on 2020-04-15 [all 1 reports] |