PolyExp

Package for the decomposition of polynomial-exponential series.

Introduction

Sequences $(\sigma_{\alpha})_{\alpha} \in \mathbb{K}^{\mathbb{N}^{n}}$ or series

\[\sigma(y) = \sum_{\alpha \in \mathbb{K}^{\mathbb{N}^{n}}} \sigma_{\alpha} \frac{y^{\alpha}}{\alpha!}\]

which can be decomposed as polynomial-exponential series

\[\sum_{i=1}^r \omega_i(y) e^{\xi_{i,1} y_1+ \cdots + \xi_{i,n} y_n}\]

with polynomials $\omega_{i}(y)$ and points $\xi_{i}= (\xi_{i,1}, \ldots, \xi_{i,n})\in \mathbb{K}^{n}$ appear in many problems (see Examples). The package PolyExp provides functions to manipulate (truncated) series and to compute such a decomposition from the first terms of the sequence.

Examples

Functions and types

Installation

The package is available at https://gitlab.inria.fr/mourrain/PolyExp.

To install it from Julia:

Pkg.clone("https://gitlab.inria.fr/mourrain/PolyExp.git")

It can then be used as follows:

using PolyExp

See the Examples for more details.