Numerical Local Irreducible Decomposition

  • Daniel A. BrakeEmail author
  • Jonathan D. Hauenstein
  • Andrew J. Sommese
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible decomposition. We define local witness sets and describe a numerical algebraic geometric approach for computing a numerical local irreducible decomposition for polynomial systems. Several examples are presented.


Numerical algebraic geometry Numerical irreducible decomposition Local irreducible decomposition Numerical local irreducible decomposition 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Daniel A. Brake
    • 1
    Email author
  • Jonathan D. Hauenstein
    • 1
  • Andrew J. Sommese
    • 1
  1. 1.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA

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