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Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation

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Computer Algebra in Scientific Computing (CASC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

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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.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street (m/c 249), Chicago, IL, 60607-7045, USA

    Nathan Bliss, Jeff Sommars, Jan Verschelde & Xiangcheng Yu

Authors
  1. Nathan Bliss
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  2. Jeff Sommars
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  3. Jan Verschelde
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  4. Xiangcheng Yu
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Corresponding author

Correspondence to Nathan Bliss .

Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Hessen, Germany

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Bliss, N., Sommars, J., Verschelde, J., Yu, X. (2015). Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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