Formal power series towards formal group laws - Nat Stapleton

Power series arise naturally in essentially every area of mathematics. However, working with power series using a computer is challenging. 

By definition each power series is equipped with an infinite amount of data: its coefficients. The purpose of this project is to get a computer to lazily calculate with power series and formal group laws. This means that we should be able to be able to specify and manipulate power series without calculating any coefficients. Calculation should only occur when the user finally asks to see the coefficients of a power series and then the program should only calculate precisely what is needed to see those coefficients. 

We have decided to write our program in Sage. This gives us access to a large library of mathematical functions and also a basic multivariable power series package. Our programs are built on top of this package, extending its functionality and usefulness. We intend to contribute our code to Sage this year! We will report on our multivariable power series program when it is done. Then we will shift our energy to writing a formal group law package built on top of our multivariable power series program.