quadratic-irrational

An implementation of quadratic irrationals https://github.com/ion1/quadratic-irrational

Latest on Hackage:0.0.5

This package is not currently in any snapshots. If you're interested in using it, we recommend adding it to Stackage Nightly. Doing so will make builds more reliable, and allow stackage.org to host generated Haddocks.

MIT licensed and maintained by Johan Kiviniemi

quadratic-irrational

Build Status

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

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, …]

Changes

0.0.5 (2014-03-28)

  • Add an Ord instance.

0.0.4 (2014-03-27)

  • Make the description more precise.
  • Add continuedFractionApproximate for rational partial evaluations of continued fractions.

0.0.3 (2014-03-26)

  • Add a more verbose description of the library.

0.0.2 (2014-03-25)

  • Add doctests.
  • Fix qiModify potentially constructing qi 1 0 5 1 instead of the equivalent but simpler qi 1 0 0 1.
  • Add lenses.

0.0.1 (2014-03-24)

  • Initial release.
Used by 1 package:
comments powered byDisqus