Numerically solving polynomial systems with Bertini / Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler.

Format:

Book

Author/Creator:

Bates, Daniel J. (Daniel James), 1979- author.

Hauenstein, Jonathan D., author.

Sommese, Andrew J., author.

Wampler, Charles W., author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Software, environments, and tools.

Software, environments, and tools

Language:

English

Subjects (All):

Polynomials--Data processing.

Polynomials.

Geometry, Algebraic--Data processing.

Geometry, Algebraic.

Physical Description:

1 PDF (xx, 352 pages).

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2013.

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This book is a guide to concepts and practice in numerical algebraic geometry -- the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and 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. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Contents:

Part I. Isolated Systems

Polynomial Systems

Basic Polynomial Continuation

Adaptive Precision and Endgames

Projective Space

Types of Homotopies

Parameter Homotopies

Advanced Topics about Isolated Solutions

Part II. Positive-Dimensional Solution Sets

Positive-Dimensional Components

Computing Witness Supersets

The Numerical Irreducible Decomposition

Advanced Topics about Positive-Dimensional Solution Sets

Part III. Further Algorithms and Applications

Intersection

Singular Sets

Real Solutions

Applications to Algebraic Geometry

Projections of Algebraic Sets

Big Polynomial Systems Arising from

Differential Equations

Part IV. Bertini Users 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.

Notes:

Includes bibliographical references and index.

Title from title screen, viewed 08/30/2013.

ISBN:

9781611972702

1611972698

OCLC:

873160025

Publisher Number:

SE25 SIAM