Over a million developers have joined DZone.
{{announcement.body}}
{{announcement.title}}

Continued Fractions with Sage

DZone's Guide to

Continued Fractions with Sage

· Big Data Zone ·
Free Resource

Hortonworks Sandbox for HDP and HDF is your chance to get started on learning, developing, testing and trying out new features. Each download comes preconfigured with interactive tutorials, sample data and developments from the Apache community.

My previous post looked at continued fractions and rational approximations for e and gave a little Python code.  I found out later there’s a more direct way to do this in Python using Sage.

At its simplest, the function continued_fraction takes a real number and returns a truncated continued fraction representation. For example, continued_fraction(e)returns

[2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1]

Optionally, you can also specify the number of bits of precision in the real argument and the number of terms desired.

By calling the convergents method on the return value of continued_fraction(e)you can find a sequence of rational approximations based on the continued fraction. For example,

print continued_fraction(e).convergents()

produces

[2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465,
1457/536, 2721/1001, 23225/8544, 25946/9545, 49171/18089,
517656/190435, 566827/208524, 1084483/398959,
13580623/4996032, 14665106/5394991, 28245729/10391023].

To get higher precision output, you need higher precision input. For example, you could pass in

RealField(200)(e)

rather than simply e to tell Sage that you’d like to use the 200-bit representation of erather than the default precision.

Hortonworks Community Connection (HCC) is an online collaboration destination for developers, DevOps, customers and partners to get answers to questions, collaborate on technical articles and share code examples from GitHub.  Join the discussion.

Topics:

Published at DZone with permission of

Opinions expressed by DZone contributors are their own.

{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}