Series

Hi, this is a ruby gem to help with math homework for an ODE's class! I've been using a hacky version of this for years and thought I'd clean it up and release it as it might be useful to others.

Next I really want it to be able to figure out convergence. It's an awfully hard task with many ways to do them so I'd be open to suggestions/help. You can see some of my thoughts down below!

Add this line to your application's Gemfile:

gem 'series'

And then execute:

$ bundle

Or install it yourself as:

$ gem install series

require "series"

series = Series.new { |n| Rational(1, 2 * n) }
series[1] #=> (1/2)
series[2] #=> (1/4)
series.partial_sum(5) #=> (137/120)

# You can even provide an upper bound
series = Series.new(upper_bound: 3) { |n| Rational(1, 2 * n) }
series[1] #=> (1/2)
series[2] #=> (1/4)
# Although you can still evaluate the expression at any `n` solving will halt at the bound
series[4] #=> (1/16)
series.first(8) #=> [ (1/2), (1/4), (1/9)]
series.partial_sum(5) #=> (137/120)

# Lower bounds work too!
series = Series.new(lower_bound: 3) { |n| Rational(1, 2 * n) }
series.first #=> (1/9)

Just finding the result at n or the partial sum of n isn't all that interesting; finding if a series is convergent or not is.

There are so many possible ways to go about this, but since this is more geared towards students I think the best approach would be to have it run a bunch of convergence tests and be able to say why one worked or failed. To do this though it has to do operations on the expression which requires it to know about the expression so I've started another gem called Nelson to help write fluent expressions that this library can then manipulate to test for convergence.

After checking out the repo, run bin/setup to install dependencies. Then, run rake rspec to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and tags, and push the .gem file to rubygems.org.

Bug reports and pull requests are welcome on GitHub at https://github.com/pducks32/series.

The gem is available as open source under the terms of the MIT License.