Regular Article: Symmetrical Newton Polytopes for Solving Sparse Polynomial Systems

Authors:
J. Verschelde;K. Gatermann
Affiliations:
Katholieke Univ Leuven, Dept Comp Sci, B 3001 Heverlee, Belgium and Konrad Zuse Zentrum Inform Tech Berlin, D 10711 Berlin Wilmersdor, Germany;Katholieke Univ Leuven, Dept Comp Sci, B 3001 Heverlee, Belgium and Konrad Zuse Zentrum Inform Tech Berlin, D 10711 Berlin Wilmersdor, Germany
Venue:
Advances in Applied Mathematics
Year:
1995

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Preface

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Abstract

The aim of this paper is to compute all isolated solutions to symmetric polynomial systems. Recently, it has been proved that modelling the sparse structure of the system by its Newton polytopes leads to a computational breakthrough in solving the system. In this paper, it will be shown how the Lifting Algorithm, proposed by Huber and Sturmfels, can be applied to symmetric Newton polytopes. This symmetric version of the Lifting Algorithm enables the efficient construction of the symmetric subdivision, giving rise to a symmetric homotopy, so that only the generating solutions have to be computed. Efficiency is obtained by combination with the product homotopy. Applications illustrate the practical significance of the presented approach.