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Dixon-EDF: The Premier Method for Solution of Parametric Polynomial Systems

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Applications of Computer Algebra (ACA 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 198))

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Abstract

Using examples of interest from real problems, we will discuss the Dixon-EDF resultant as a method of solving parametric polynomial systems. We will briefly describe the method itself, then discuss problems arising in geometric computing, flexibility of structures, pose estimation, robotics, image analysis, physics, differential equations, and others. We will compare Dixon-EDF to several respected implementations of Gröbner bases algorithms on several systems. We find that Dixon-EDF is greatly superior, usually by orders of magnitude, in both CPU usage and RAM usage.

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Author information

Authors and Affiliations

  1. Fordham University, New York, NY, 10458, USA

    Robert H. Lewis

Authors
  1. Robert H. Lewis
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Correspondence to Robert H. Lewis .

Editor information

Editors and Affiliations

  1. Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Institute of Mathematics, University of Valladolid, Valladolid, Spain

    Edgar Martínez-Moro

Appendix

Appendix

The Maple-FGb commands for the pose example:

figure e

Magma 1 commands for the pose example:

figure f

Magma 2 commands for the pose example:

figure g

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Lewis, R.H. (2017). Dixon-EDF: The Premier Method for Solution of Parametric Polynomial Systems. In: Kotsireas, I., Martínez-Moro, E. (eds) Applications of Computer Algebra. ACA 2015. Springer Proceedings in Mathematics & Statistics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-56932-1_16

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