# The quadratic-irrational package

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

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, …]

## Properties

Versions | 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.4, 0.0.5 |
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Dependencies | arithmoi (==0.4.*), base (>=4.6 && <4.8), containers (==0.5.*), mtl (==2.1.*), transformers (==0.3.*) |

License | MIT |

Copyright | Copyright © 2014 Johan Kiviniemi |

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

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

Stability | provisional |

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 |

Upload date | Thu Mar 27 21:52:08 UTC 2014 |

Uploaded by | ion |

## Modules

*Numeric*- Numeric.QuadraticIrrational
- Numeric.QuadraticIrrational.CyclicList
*Internal*- Numeric.QuadraticIrrational.Internal.Lens

- Numeric.QuadraticIrrational

## Downloads

- quadratic-irrational-0.0.4.tar.gz [browse] (Cabal source package)
- Package description (included in the package)

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