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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 each component of the variety
cascade(..., StartDimension => ...)
-- Option to specify the dimension to begin searching for positive dimensional components
constructEmbedding
-- constructs an embedding of a polynomial system
factorWitnessSet
-- applies monodromy to factor a witness set into irreducible components
gamma
-- the constant in the gamma trick, optional input for trackPaths
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
mixedVolume
-- computes mixed volume of a polynomial 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
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
refineSolutions
-- refines solutions of a system by increasing working precision
solveRationalSystem
-- approximates solutions to a rational system of equations
solveSystem
-- a numerical blackbox solver
StableMixedVolume
-- optional input for computation of the stable mixed volume
StartDimension
-- optional input for cascade and numericalIrreducibleDecomposition
StartSystem
-- optional input for computation of mixed volume by solving 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
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(..., tDegree => ...)
-- Option to specify the degree of the continuation parameter
Verbose
-- request verbose feedback
zeroFilter
-- returns solutions with k-th coordinate less than the given tolerance