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Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components

  • A. J. Sommese
  • J. Verschelde
  • C. W. Wampler
Chapter
Part of the NATO Science Series book series (NAII, volume 36)

Abstract

To decompose solution sets of polynomial systems into irreducible components, homotopy continuation methods generate the action of a natural monodromy group which partially classifies generic points onto their respective irreducible components. As illustrated by the performance on several test examples, this new method achieves a great increase in speed and accuracy, as well as improved numerical conditioning of the multivariate interpolation problem.

Key words

components of solutions embedding generic points homotopy continuation irreducible components monodromy group numerical algebraic geometry polynomial system primary decomposition 

Mathematics Subject Classification (2000)

Primary 65H10 Secondary 13P05 14Q99 68W30 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • A. J. Sommese
    • 1
    • 4
  • J. Verschelde
    • 2
    • 5
  • C. W. Wampler
    • 3
  1. 1.University of Notre DameUSA
  2. 2.University of Illinois at ChicagoUSA
  3. 3.General Motors Research LaboratoriesWarrenUSA
  4. 4.Department of MathematicsNotre DameUSA
  5. 5.Department of MathematicsChicagoUSA

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