PHCpack Documentation Contents

• Getting Started
  • What is PHCpack?
  • Downloading and Extracting the Executable
  • Compiling from Source
  • Project History
  • phcpy: An Application Programming Interface to PHCpack
  • PHCpack.jl: an interface to Julia
  • References
  • Users
  • Acknowledgments
• Tutorial
  • Input Formats
  • Interfaces
  • The Blackbox Solvers
  • Running the Program in Full Mode
  • Running Toolbox Mode
    • For Isolated Solutions Only
    • Computing Components of Solutions
• User Manual
  • Text Options of the Executable phc
    • phc –version : displays the current version string
    • phc –license : writes the license to screen
    • phc –cite : how to cite PHCpack
    • phc –help : writes helpful information to screen
  • Options of the Executable phc
    • phc -0 : random numbers with fixed seed for repeatable runs
    • phc -a : solving polynomial systems equation-by-equation
    • phc -b : batch or blackbox processing
    • phc -B : numerical irreducible decomposition in blackbox mode
    • phc -c : irreducible decomposition for solution components
    • phc -d : linear and nonlinear reduction w.r.t. the total degree
    • phc -e : SAGBI/Pieri/Littlewood-Richardson homotopies
    • phc -f : factor a pure dimensional solution set into irreducibles
    • phc -g : check the format of an input polynomial system
    • phc -h : writes helpful information to screen
    • phc -j : path tracking with algorithmic differentiation
    • phc -k : realization of dynamic output feedback placing poles
    • phc -l : witness set for hypersurface cutting with random line
    • phc -m : mixed volumes, MixedVol, DEMiCs, polyhedral homotopies
    • phc -o : writes the symbol table of an input system
    • phc -p : polynomial continuation in one parameter
    • phc -q : tracking solution paths with incremental read/write
    • phc -r : root counting and construction of start systems
    • phc -s : equation and variable scaling on system and solutions
    • phc -t : tasking for tracking paths using multiple threads
    • phc -u : Newton’s method and continuation with power series
    • phc -v : verification, refinement and purification of solutions
    • phc -V : run in verbose mode
    • phc -w : witness set intersection using diagonal homotopies
    • phc -x : convert solutions from PHCpack into Python dictionary
    • phc -y : sample points from an algebraic set, given witness set
    • phc -z : strip phc output solution lists into Maple format
    • phc -z -p : extract start system and its solutions
• Reference Manual
  • The Test Procedures
  • Organization of the Ada code
    • System: OS Dependencies such as Timing
    • The Mathematical Library
    • Deforming Polynomial Systems
    • Homotopy Construction via Root Counting Methods
    • Numerical Schubert Calculus
    • Numerical Irreducible Decomposition
    • Calling Ada Code From C
    • Calling C Code From Ada
    • Multitasking
    • The Main Program
  • Numbers, Linear Algebra, Polynomials and Polytopes
    • Numbers
    • Multiple Double Arithmetic
    • Vectors and Matrices
    • Linear Systems with Integer Coefficients
    • Linear Systems with Floating-Point Coefficients
    • Polynomials in Several Variables
    • Nested Horner Forms for Evaluation
    • Support Sets and Linear Programming
    • Circuits for Algorithmic Differentiation
    • AD: Algorithmic Differentiation of the Path Library
    • Truncated Power Series
  • Homotopies, Newton’s Method, and Path Trackers
    • Solutions of Systems and Homotopies
    • Polynomial Homotopies
    • Newton’s Method and Deflation for Isolated Singularities
    • Curves, Univariate Solvers, and Newton for Power Series
    • Polyhedral End Games
    • Path Trackers for Artificial-Parameter Homotopies
    • Sweeping for Singularities
    • Polynomial Continuation
  • Root Counts and Start Systems
    • Linear-Product Start Systems
    • Binomials are Polynomials with Two Terms
    • Implicit Lifting
    • Static Lifting
    • Dynamic Lifting
    • Exploitation of Permutation Symmetry
    • MixedVol to Compute Mixed Volumes Fast
    • DEMiCs applies dynamic enumeration to compute mixed cells
    • The Newton-Puiseux Method
  • Determinantal Systems and Schubert Problems
    • SAGBI Homotopies to Solve Pieri Problems
    • Pieri Homotopies
    • Littlewood-Richardson Homotopies
  • Positive Dimensional Solution Sets
    • Witness Sets, Extrinsic and Intrinsic Trackers
    • Equations for Solution Components
    • Absolute Factorization into Irreducible Components
    • Cascades of Homotopies and Diagonal Homotopies
    • An Equation-by-Equation Solver
    • Tropicalization of Witness Sets
  • Organization of the C and C++ code
    • The Main Gateway Function
    • Persistent Objects
    • The Library libPHCpack
  • Message Passing
  • GPU Acceleration
  • The Web Interface
  • The Python Package phcpy