# ContinuedFractions

## Description

Generates quotients and convergents for a given number.

## Synopsis

``````require 'continued_fractions'

pi = Math::PI
=> 3.14159265358979

cf = ContinuedFraction.new(pi,10)
=> #<ContinuedFractions::ContinuedFraction:0x00000101101368 @number=3.14159265358979, @limit=10,
@quotients=[3, 7, 15, 1, 292, 1, 1, 1, 2, 1],
@convergents=[[0, 1], [1, 0], [3, 1], [22, 7], [333, 106],
[355, 113], [103993, 33102], [104348, 33215], [208341, 66317], [312689, 99532], [833719, 265381], [1146408, 364913]]>

cf.convergents
=> [[3,1], [22,7], [333,106], [355,113], [103993,33102], [104348,33215], [208341,66317], [312689,99532], [833719,265381], [1146408,364913]]

# Convergents can be output as an array of Rationals too
cf.convergents_as_rationals
[(3/1), (22/7), (333/106), (355/113), (103993/33102), (104348/33215), (208341/66317), (312689/99532), (833719/265381), (1146408/364913)]

cf.convergent(1)
=> [22,7]

cf.quotients
=> [3, 7, 15, 1, 292, 1, 1, 1, 2, 1]

# Add, subtract, multiply and divide continued fractions.  The limit of the result is the max limit of the operands.
cf2 = ContinuedFraction.new(rand,20)
=> #<ContinuedFractions::ContinuedFraction:0x000001009dde50 @number=0.03834175394982653, @limit=20, @quotients=[0, 26, 12, 3, 4, 1, 2, 24, 5, 1, 1, 1, 2, 1, 2, 2, 1, 7, 1, 5], @convergents=[[0, 1], [1, 26], [12, 313], [37, 965], [160, 4173], [197, 5138], [554, 14449], [13493, 351914], [68019, 1774019], [81512, 2125933], [149531, 3899952], [231043, 6025885], [611617, 15951722], [842660, 21977607], [2296937, 59906936], [5436534, 141791479], [7733471, 201698415], [59570831, 1553680384], [67304302, 1755378799], [396092341, 10330574379]]>
cf + cf2
=> #<ContinuedFractions::ContinuedFraction:0x000001009d2708 @number=3.1799344075396196, @limit=20, @quotients=[3, 5, 1, 1, 3, 1, 5, 3, 7, 25, 1, 2, 15, 6, 1, 1, 2, 3, 1, 2], @convergents=[[3, 1], [16, 5], [19, 6], [35, 11], [124, 39], [159, 50], [919, 289], [2916, 917], [21331, 6708], [536191, 168617], [557522, 175325], [1651235, 519267], [25326047, 7964330], [153607517, 48305247], [178933564, 56269577], [332541081, 104574824], [844015726, 265419225], [2864588259, 900832499], [3708603985, 1166251724], [10281796229, 3233335947]]>
``````

## Install

sudo gem install continued_fractions

## Requirements/Dependencies

• Ruby 2.2+
• Depends on Ruby's Rational class

## Developers

• RSpec required to run tests