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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
Paperback
9781611972696
AUD$210.00
inc GST
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

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