phcpy Documentation Contents

• Getting Started
  • what is phcpy?
  • installing phcpy
  • extending Sage with phcpy
  • project history
  • references
  • acknowledgments
  • about this document
• Tutorial
  • the circle problem of Apollonius
    • a general configuration
    • a special configuration
    • a perturbed configuration
  • the design of a 4-bar mechanism
    • a general configuration
    • visualization of a straight line design
  • lines meeting four given lines
    • a general configuration
    • a real configuration
  • tangent lines to a circle
    • lines through the origin intersecting a circle
    • defining the equations for the singular locus
    • intersecting two algebraic sets
  • all lines tangent to four spheres
    • four mutually touching spheres
    • tangents lines of multiplicities two
    • twelve real single tangent lines
• User Manual
  • a blackbox solver for isolated solutions
    • solving random trinomials and a particular trinomial system
    • representations of solutions of polynomial systems
    • reproducible runs with fixed seeds
    • root counting methods
    • Newton’s method and deflation
    • the multiplicity of an isolated solution
    • equation and variable scaling
    • reduction of polynomial systems
  • path trackers and sweep homotopies
    • a simple example
    • fixing the gamma constant
    • give the next solution on a path
    • solving with polyhedral homotopies
    • Newton’s method at higher precision
    • multitasked path tracking
    • GPU accelerated path tracking
    • sweep homotopies
    • real versus complex sweeps
    • tuning parameters, settings, and tolerances
    • a polyhedral end game
  • positive dimensional solution sets
    • witness sets
    • homotopy membership test
    • cascade of homotopies
    • factoring into irreducibles
    • numerical irreducible decomposition
    • diagonal homotopies
  • some interesting examples and families
    • interactive regression testing
    • the cyclic n-roots problem
  • numerical Schubert calculus
    • Pieri homotopies
    • Littlewood-Richardson homotopies
  • Newton polytopes, monomial maps, and power series
    • convex hulls of lattice polytopes
    • mixed volumes
    • solving binomial systems
    • power series solutions
    • approximating algebraic curves
  • a graphical user interface
    • solving with a click of a button
    • scrolling a list of solutions
    • making a coordinate plot of solutions
  • the module server
    • functions in the module server
  • the module phcpy.phcpy2c3
    • design of the Python to C interface
    • the interface to PHCpack
    • wrappers to the C interface to PHCpack
  • code snippets
    • blackbox solver
    • path trackers
    • solution sets
    • families of systems
    • Schubert calculus
    • Newton polytopes
    • the extension module
• Reference Manual
  • a blackbox solver for isolated solutions
    • functions in the module solver
    • functions in the module solutions
    • the module polynomials
  • path trackers and sweep homotopies
    • functions in the module trackers
    • functions in the module sweepers
    • functions in the module tuning
    • functions in the module tropisms
  • positive dimensional solution sets
    • functions in the module sets
    • functions in the module cascades
    • functions in the module factor
    • functions in the module diagonal
  • some interesting families and examples
    • functions in the module examples
    • functions in the module families
  • numerical Schubert calculus
    • functions in the module schubert
  • Newton polytopes, monomial maps, and power series
    • functions in the module polytopes
    • functions in the module maps
    • functions in the module series
    • functions in the module curves
  • a graphical user interface
    • functions in the module dashboard
  • the module phcpy.phcpy2c3
    • functions in the module interface
    • functions in the module phcpy2c3
• Indices and tables