Example 2.8 (Rooted Binary Trees)

Some computational experiments with the generating function for rooted binary trees.
Requirements: ore_algebra package
Note: See the Maple worksheet corresponding to this example for a better treatment of algebraic functions

There is no good built-in method to compute series solutions to bivariate algebraic equations (Puiseux Series were officially added to Sage in 2020, closing a ticket open for 11 years!). The Maple gfun package of Salvy and Zimmerman has better support for solving algebraic equations. In Sage the best workaround is to use the fact that any algebraic function is D-finite, and use the ore_algebra package which can compute with D-finite functions.