Contents
I Background
1. Polynomial Systems
2. Homotopy Continuation
3. Projective Spaces
4. Genericity and Probability One
5. Polynomial of One Variable
6. Other Methods
II Isolated Solutions
7. Coefficient-Parameter Homotopy
8. Polynomial Structures
9. Case Studies
10. Endpoint Estimation
11. Checking Results and Other Implementation Tips
III Positive Dimensional Solutions
12. Basic Algebraic Geometry
13. Basic Numerical Algebraic Geometry
14. A Cascade Algorithm for Witness Supersets
15. The Numerical Irreducible Decomposition
16. The Intersection of Algebraic Sets
Appendices
A Algebraic Geometry
B Software for Polynomial Continuation
C HomLab User's Guide