Contents

• Introduction
• Polynomial Homotopy Continuation Methods
• Related software
• The main features of our software
• The four stages of the solver
• Tools and modes
• The major tools of the four stages
  • Scal: Scaling of systems and solutions
  • Redu: Linear and nonlinear reduction
  • RoCo: root counting and homotopy construction
    • Modeling the structure
    • Linear-product start systems
    • Symmetric set structure analysis
  • MVC: four lifting strategies
    • Implicit lifting
    • Static lifting
    • Dynamic lifting
    • Symmetric lifting
    • Combinations
  • PoCo: Polynomial Continuation
  • Vali: Validation of the computations
• Database of benchmark systems
• Programming in Ada
• The design: PHC as workbench
• PHCPACK: calling from other programs
• Computers and compilers
• Obtaining and installing the program
• Conclusions and future directions
• References
• About this document ...