Numerically Solving Polynomial Systems with Bertini

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.