Package quadratic-irrational version 0.1.1-2

quadratic-irrational

Version 0.1.1 revision 2 uploaded 2023-09-27T20:31:32.000Z by Bodigrim.

Synopsis

An implementation of quadratic irrationals

Description

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, …]

Author

Johan Kiviniemi <devel@johan.kiviniemi.name>

Bug reports

https://github.com/ion1/quadratic-irrational/issues

Category

Math, Algorithms, Data

Copyright

Homepage

https://github.com/ion1/quadratic-irrational

Maintainer

Andrew Lelechenko andrew dot lelechenko at gmail dot com

Package URL

n/a

Stability

provisional