Formal Solutions of Completely Integrable Pfaffian Systems With Normal Crossings

TL;DR

This paper introduces an algorithm for computing formal solutions of complex Pfaffian systems with normal crossings, extending previous bivariate methods and implemented in Maple for multi-variable cases.

Contribution

It generalizes a bivariate solution method to multiple variables, providing an algorithm for formal solutions of integrable Pfaffian systems with normal crossings.

Findings

Algorithm successfully computes formal solutions in multiple variables.

Implementation in Maple facilitates practical computation.

Extends previous bivariate methods to higher dimensions.

Abstract

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for the bivariate case based on a combination of several reduction techniques and is implemented in the computer algebra system Maple.