An implementation of quadratic irrationals

 Version on this page: 0.1.0 LTS Haskell 22.29: 0.1.1@rev:2 Stackage Nightly 2024-07-19: 0.1.1@rev:2 Latest on Hackage: 0.1.1@rev:2

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Module documentation for 0.1.0

Depends on 4 packages(full list with versions):

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, …]

0.1.0 (2019-04-26)

• Allow imaginary square roots, e. g., qi 1 1 (-5) 1.
• Remove Ord QI instance: complex values cannot be ordered.
• Roots of 0 are reduced: qi a b 0 d becomes qi a 0 2 d.
• Remove qiZero and qiOne.

0.0.6 (2018-08-29)

• Support GHC up to 8.6.1.

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.