POINCARÉ CODE: A package of open-source implements for normalization and computer algebra reduction near equilibria of coupled ordinary differential equations Original Research Article

The Poincaré code is a Maple project package that aims to gather significant computer algebra normal form (and subsequent reduction) methods for handling nonlinear ordinary differential equations. As a first version, a set of fourteen easy-to-use Maple commands is introduced for symbolic creation of (improved variants of Poincaré’s) normal forms as well as their associated normalizing transformations. The software is the implementation by the authors of carefully studied and followed up selected normal form procedures from the literature, including some authors’ contributions to the subject. As can be seen, joint-normal-form programs involving Lie-point symmetries are of special interest and are published in CPC Program Library for the first time, Hamiltonian variants being also very useful as they lead to encouraging results when applied, for example, to models from computational physics like Hénon–Heiles.