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Solving Polynomial Systems Using Numeric Gröbner Bases

  • Daniel LichtblauEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

Systems of polynomial or algebraic equations with finitely many solutions arise in many areas of applied mathematics. I will discuss the design and implementation of a hybrid symbolic-numeric method based on the endomorphism matrix approach pioneered by Stetter and others. It makes use of numeric Gröbner bases and arbitrary-precision eigensystem computations. I will describe how to assess accuracy, find and remove parasite solutions in the case of fractional degrees in the system, handle multiplicity, as well as some of the other finer points not usually covered in the literature. This work is one of the methods used in the Wolfram Language NSolve function.

Keywords

Polynomial systems Numeric Gröbner bases Endomorphism matrix Eigensystem 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Wolfram ResearchChampaignUSA

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