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Numerically Solving Polynomial Systems with Bertini

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Numerically Solving Polynomial Systems with Bertini

Numerically Solving Polynomial Systems with Bertini

Daniel J. Bates, Colorado State University
Jonathan D. Hauenstein, North Carolina State University
Andrew J. Sommese, University of Notre Dame, Indiana
Charles W. Wampler, General Motors
December 2013
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Paperback
9781611972696
£69.99
GBP
Paperback
    Description

    The Bertini software package provides a powerful toolset for the numerical solution of systems of polynomial equations. This book provides both a course, with numerous examples, on the use of Bertini to compute solutions, and a complete reference guide with documentation on syntax and usage options. It describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. This book serves scientists and engineers who need quick methods for finding isolated solutions to small systems. Those who wish to further refine their techniques can advance to using algorithms for finding positive-dimensional solution sets and learn how to use parallel computers on large problems, while readers of a more mathematical bent will find details of the theory underpinning the software.

    • Approaches numerical algebraic geometry from a user's point of view with many worked examples
    • Teaches the reader how to use Bertini and includes a complete reference guide
    • Treats the fundamental task of solving a given polynomial system and describes the latest advances in the field

    Product details

    December 2013
    Paperback
    9781611972696
    370 pages
    254 × 177 × 17 mm
    0.65kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    Table of Contents

    • List of figures
    • Conventions
    • Preface
    • Part I. Isolated Systems:
    • 1. Polynomial systems
    • 2. Basic polynomial continuation
    • 3. Adaptive precision and endgames
    • 4. Projective space
    • 5. Types of homotopies
    • 6. Parameter homotopies
    • 7. Advanced topics about isolated solutions
    • Part II. Positive-Dimensional Solution Sets:
    • 8. Positive-dimensional components
    • 9. Computing witness supersets
    • 10. The numerical irreducible decomposition
    • 11. Advanced topics about positive-dimensional solution sets
    • Part III. Further Algorithms and Applications:
    • 12. Intersection
    • 13. Singular sets
    • 14. Real solutions
    • 15. Applications to algebraic geometry
    • 16. Projections of algebraic sets
    • 17. Big polynomial systems arising from differential equations
    • Part IV. Bertini User's Manual: Appendix A. Bertini quick start guide
    • Appendix B. Input format
    • Appendix C. Calling options
    • Appendix D. Output files
    • Appendix E. Configuration settings
    • Appendix F. Tips and tricks
    • Appendix G. Parallel computing
    • Appendix H. Related software
    • Bibliography
    • Software index
    • Subject index.
      • Show more
    Courses
    Resources
    Resources for
    Type
    Bertini homepage
    Additional Information
    About the authors
      Authors
    • Daniel J. Bates , Colorado State University

      Daniel Bates was a Postdoctoral Fellow at the Institute for Mathematics and its Applications (IMA) before starting as an Assistant Professor of Mathematics at Colorado State University in 2008. Professor Bates is a member of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) and is an active member of the SIAM Activity Group on Algebraic Geometry.

    • Jonathan D. Hauenstein , North Carolina State University

      Jonathan Hauenstein was a Visiting Assistant Professor at Texas A&M University and Postdoctoral Fellow at the Fields Institute and Institut Mittag-Leffler before starting as an Assistant Professor of Mathematics at North Carolina State University in 2012. Professor Hauenstein is a member of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM). He is an active member of the SIAM Activity Group on Algebraic Geometry.

    • Andrew J. Sommese , University of Notre Dame, Indiana

      Andrew Sommese was Full Professor of Mathematics at the University of Notre Dame from 1983 to 2010, and has been Vincent J. and Annamarie Micus Duncan Professor of Mathematics at Notre Dame since 1994. He received an Alfred P. Sloan Fellowship in 1979, the Alexander von Humboldt Research Award for Senior U.S. Scientists in 1993, and became a Fellow of the American Mathematical Society in 2012. He is currently on the editorial boards of Advances in Geometry, the Milan Journal of Mathematics, and the Journal of Algebra and its Applications.

    • Charles W. Wampler , General Motors

      Charles Wampler has been employed at the General Motors Research and Development Center in Warren, Michigan since 1985, rising to the rank of Technical Fellow in 2003. He has also been an Adjunct Professor at the University of Notre Dame, first in the Department of Mathematics (2004–2010) and subsequently in the Department of Applied and Computational Mathematics and Statistics. He was named a Fellow of the American Society of Mechanical Engineers (ASME) in 2004 and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2010. He has been on the editorial boards of the ASME Journal of Mechanical Design and Mechanism and Machine Theory and currently serves on the board of the International Journal of Robotics Research. He is a member of the ASME, IEEE and SIAM.

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