quadratic-irrational: An implementation of quadratic irrationals
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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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Properties
| Versions | 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.5, 0.0.5, 0.0.6, 0.1.0, 0.1.1 |
|---|---|
| Change log | ChangeLog.md |
| Dependencies | arithmoi (>=0.4 && <0.5), base (>=4.6 && <4.8), containers (>=0.5 && <0.6), mtl (>=2.1 && <2.2), transformers (>=0.3 && <0.4) [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 repo | head: git clone https://github.com/ion1/quadratic-irrational.git |
| Uploaded | by ion at 2014-03-28T21:58:10Z |
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- quadratic-irrational-0.0.5.tar.gz [browse] (Cabal source package)
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Readme for quadratic-irrational-0.0.5
[back to package description]quadratic-irrational
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 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, …]