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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, …]```

## Properties

Versions 0.0.1, 0.0.2, 0.0.3, 0.0.4, 0.0.5, 0.0.5, 0.0.6 ChangeLog.md arithmoi (==0.4.*), base (>=4.6 && <4.8), containers (==0.5.*), mtl (==2.1.*), transformers (==0.3.*) [details] MIT Copyright © 2014 Johan Kiviniemi Johan Kiviniemi Johan Kiviniemi Math, Algorithms, Data https://github.com/ion1/quadratic-irrational https://github.com/ion1/quadratic-irrational/issues head: git clone https://github.com/ion1/quadratic-irrational.git Fri Mar 28 21:58:10 UTC 2014 by ion

## Modules

[Index]

#### Maintainers' corner

For package maintainers and hackage trustees

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# `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, …]
``````