The Piranha algebraic manipulator

Abstract

In this paper we present a specialised algebraic manipulation package devoted to Celestial Mechanics. The system, called Piranha, is built on top of a generic and extensible framework, which allows to treat efficiently and in a unified way the algebraic structures most commonly encountered in Celestial Mechanics (such as multivariate polynomials and Poisson series). In this contribution we explain the architecture of the software, with special focus on the implementation of series arithmetics, show its current capabilities, and present benchmarks indicating that Piranha is competitive, performance-wise, with other specialised manipulators.

24 pages, 2 figures

Cited by in corpus (4)

• Methods of algebraic manipulation in perturbation theory
• The construction of averaged planetary motion theory by means of computer algebra system Piranha
• Multiplication of sparse Laurent polynomials and Poisson series on modern hardware architectures
• Domains of analyticity of Lindstedt expansions of KAM tori in dissipative perturbations of Hamiltonian systems