Numerically Solving Polynomial Systems with Bertini

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 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 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 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.

List of Figures Conventions Preface Part I: Isolated Systems Chapter 1: Polynomial Systems Chapter 2: Basic Polynomial Continuation Chapter 3: Adaptive Precision and Endgames Chapter 4: Projective Space Chapter 5: Types of Homotopies Chapter 6: Parameter Homotopies Chapter 7: Advanced Topics about Isolated Solutions Part II: Positive-Dimensional Solution Sets Chapter 8: Positive-Dimensional Components Chapter 9: Computing Witness Supersets Chapter 10: The Numerical Irreducible Decomposition Chapter 11: Advanced Topics about Positive-Dimensional Solution Sets Part III: Further Algorithms and Applications Chapter 12: Intersection Chapter 13: Singular Sets Chapter 14: Real Solutions Chapter 15: Applications to Algebraic Geometry Chapter 16: Projections of Algebraic Sets Chapter 17: 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.