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# PHCpack : Table of Contents

- PHCpack -- a package for Polynomial Homotopy Continuation
- cascade -- runs a cascade of homotopies to get witness sets for the variety
- cascade(...,StartDimension=>...) -- Option to specify the dimension to begin searching for positive dimensional components
- cascade(...,Verbose=>...) -- option to specify whether additional output is wanted
- computingPrecision -- flag to switch to double double or quad double precision
- constructEmbedding -- constructs an embedding of a polynomial system
- constructEmbedding(...,Verbose=>...) -- option to specify whether additional output is wanted
- factorWitnessSet -- applies monodromy to factor a witness set into irreducible components
- factorWitnessSet(...,Verbose=>...) -- option to specify whether additional output is wanted
- gamma -- the constant in the gamma trick, optional input for trackPaths
- interactive -- flag to run phc -p or phc -m in interactive mode
- intermediateSolutions -- option of trackPaths to get all intermediate solutions on a path
- intersectSlice -- intersects a witness set by a slice
- isCoordinateZero -- checks if coordinate has absolute value less than a given tolerance
- isWitnessSetMember -- tests whether a point belongs to a solution set
- isWitnessSetMember(...,Verbose=>...) -- option to specify whether additional output is wanted
- loadSettingsPath -- option of trackPaths to load the settings for a reproducible rerun
- mixedVolume -- computes mixed volume of a polynomial system
- mixedVolume(...,interactive=>...) -- option to switch to the interactive mode of phc -m
- mixedVolume(...,numThreads=>...) -- option to set the number of threads when solving a start system
- mixedVolume(...,StableMixedVolume=>...) -- optional input for computation of the stable mixed volume
- mixedVolume(...,StartSystem=>...) -- optional input for computation of mixed volume by solving a random coefficient system
- mixedVolume(...,Verbose=>...) -- option to specify whether additional output is wanted
- nonZeroFilter -- returns solutions with coordinate larger than given tolerance
- numericalIrreducibleDecomposition -- finds the irreducible components of the zero set of a system of polynomials
- numericalIrreducibleDecomposition(...,StartDimension=>...) -- Option to specify the dimension to begin searching for positive dimensional components
- numericalIrreducibleDecomposition(...,Verbose=>...) -- option to specify whether additional output is wanted
- numThreads -- the number of threads in the path tracker
- randomSeed -- seed for the random number generators
- realSlice1D -- computes a real slice for a one dimensional witness set
- realSlice1D(...,searchDelta=>...) -- option of realSlice1D
- realSlice1D(...,searchNpoints=>...) -- option of realSlice1D
- realSlice1D(...,searchTolerance=>...) -- option of realSlice1D
- realSlice2D -- computes a real slice for a two dimensional witness set
- realSlice2D(...,searchDelta=>...) -- option of realSlice2D
- realSlice2D(...,searchNpoints=>...) -- option of realSlice2D
- realSlice2D(...,searchTolerance=>...) -- option of realSlice2D
- refineSolutions -- refines solutions of a system by increasing working precision
- refineSolutions(...,Verbose=>...) -- option to specify whether additional output is wanted
- saveSettingsPath -- option of trackPaths to save the settings for a reproducible rerun
- searchDelta -- option of realSlice1D
- searchNpoints -- option of realSlice1D
- searchTolerance -- option of realSlice1D
- seeProgress -- flag to monitor the progress of the multithreaded path tracker
- solveRationalSystem -- approximates solutions to a rational system of equations
- solveRationalSystem(...,Verbose=>...) -- option to specify whether additional output is wanted
- solveSystem -- a numerical blackbox solver
- solveSystem(...,computingPrecision=>...) -- option to specify the working precision
- solveSystem(...,numThreads=>...) -- option to set the number of threads
- solveSystem(...,randomSeed=>...) -- option to set the seed of the random number generators
- solveSystem(...,Verbose=>...) -- option to specify whether additional output is wanted
- StableMixedVolume -- optional input for computation of the stable mixed volume
- StartDimension -- optional input for cascade and numericalIrreducibleDecomposition
- StartSystem -- optional input to construct and solve a random coefficient system
- tDegree -- the degree of the continuation parameter
- toLaurentPolynomial -- converts a list of rational polynomials into Laurent polynomials
- topWitnessSet -- returns a witness set and nonsolutions for the top dimensional solution set
- topWitnessSet(...,Verbose=>...) -- option to specify whether additional output is wanted
- trackPaths -- tracks paths defined by a typical homotopy between start and end systems
- trackPaths(...,gamma=>...) -- Option to specify the value of the constant in the gamma trick
- trackPaths(...,interactive=>...) -- Option to run phc -p in interactive mode.
- trackPaths(...,intermediateSolutions=>...) -- option to get all intermediate solutions on a path
- trackPaths(...,loadSettingsPath=>...) -- option to load the settings of the path trackers for a reproducible rerun
- trackPaths(...,numThreads=>...) -- Option to define the number of threads in the path tracker.
- trackPaths(...,saveSettingsPath=>...) -- option to save the settings of the path trackers for a reproducible rerun
- trackPaths(...,seeProgress=>...) -- Option to follow the progress of the multithreaded path tracker.
- trackPaths(...,tDegree=>...) -- Option to specify the degree of the continuation parameter
- trackPaths(...,Verbose=>...) -- option to specify whether additional output is wanted
- versionNumber -- returns the version number and release date of phc
- versionNumber(...,Verbose=>...) -- option to print the output of phc --version to screen
- zeroFilter -- returns solutions with k-th coordinate less than the given tolerance