Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

TL;DR

This paper discusses a cloud-based implementation of polynomial homotopy continuation methods for solving polynomial systems, utilizing graph isomorphism for classification and reuse of solutions.

Contribution

It introduces a web interface for polynomial homotopy continuation and applies graph isomorphism to classify and identify previously solved systems.

Findings

Successful implementation of cloud-based polynomial system solving

Effective classification of systems using graph canonical forms

Potential for solution reuse and efficiency improvement

Abstract

Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and reflect on the application of polynomial homotopy continuation methods to solve polynomial systems in the cloud. Via the graph isomorphism problem we organize and classify the polynomial systems we solved. The classification with the canonical form of a graph identifies newly submitted systems with systems that have already been solved.