Linear PDE with Constant Coefficients

TL;DR

This paper presents practical computational methods for solving homogeneous linear PDEs with constant coefficients, leveraging the Ehrenpreis-Palamodov fundamental principle and recent advances in computational algebra.

Contribution

It extends existing theoretical frameworks by developing practical algorithms based on computational commutative algebra for solving linear PDE systems.

Findings

Provides algorithms for solution space computation

Utilizes Ehrenpreis-Palamodov principle in a computational setting

Enhances solution methods with recent algebraic techniques

Abstract

We discuss practical methods for computing the space of solutions to an arbitrary homogeneous linear system of partial differential equations with constant coefficients. These rest on the Fundamental Principle of Ehrenpreis-Palamodov from the 1960s. We develop this further using recent advances in computational commutative algebra.