Formal Solutions of a Class of Pfaffian Systems in Two Variables

TL;DR

This paper introduces a Moser-based algorithm for computing formal solutions of integrable Pfaffian systems with normal crossings in two variables, enhancing previous methods with efficient invariants derivation via Maple.

Contribution

It presents a novel Moser-based approach for solving Pfaffian systems, improving upon prior rank reduction techniques and integrating with the ISOLDE package for invariant computation.

Findings

Developed an algorithm for formal solutions of Pfaffian systems

Enhanced the computation of formal invariants using Maple's ISOLDE

Provided a systematic approach for integrable systems with normal crossings

Abstract

In this paper, we present an algorithm which computes a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in two variables, based on (Barkatou, 1997). A first step was set in (Barkatou-LeRoux, 2006) where the problem of rank reduction was tackled via the approach of (Levelt, 1991). We give instead a Moser-based approach. And, as a complementary step, we associate to our problem a system of ordinary linear singular differential equations from which the formal invariants can be efficiently derived via the package ISOLDE, implemented in the computer algebra system Maple.