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NumericalAlgebraicGeometry : Table of Contents
NumericalAlgebraicGeometry
-- Numerical Algebraic Geometry
AffinePatches
-- reserved for developers
BERTINI
-- use Bertini for homotopy continuation
Certified
-- a value for the option Predictor that triggers certified tracking
decompose(WitnessSet)
-- decompose a witness set into irreducibles
deflate
-- first-order deflation
DoublePrecision
-- a constant equal to 53 (the number of bits of precision)
endGameCauchy
-- Cauchy end game for getting a better approximation of a singular solution
evaluateH(GateHomotopy,Matrix,Number)
-- evaluate gate homotopy and its derivatives
evaluateH(GateParameterHomotopy,Matrix,Matrix,Number)
-- evaluate (gate) parameter homotopy and its derivatives
gateHomotopy(...,Parameters=>...)
-- specifies parameter names
gateHomotopy(...,Software=>...)
-- specifies where evaluation should be done (M2=top level, M2engine=core)
gateHomotopy(...,Strategy=>...)
-- strategy is either to "compress" or not (any other value)
gateHomotopy(GateMatrix,GateMatrix,InputGate)
-- homotopy implemented via straight line programs
gateMatrix(GateSystem)
-- evaluation circuit used for the system
GateParameterHomotopy
-- a homotopy that involves parameters and is implemented via straight line programs
GateSystem
-- a system of functions evaluated via a straightline program
gateSystem
-- a constructor for GateSystem
goodInitialPair(List)
-- make an initial pair conjectured to be good by Shub and Smale
HOM4PS2
-- use HOM4PS for homotopy continuation
isOn
-- determines if a point belongs to a variety
isSolution(AbstractPoint,PolySystem)
-- check if a point satisfies a polynomial system approximately
isSubset(NumericalVariety,NumericalVariety)
-- check containment
jacobian(GateSystem)
-- jacobian of a (gate) system
NAGtrace(ZZ)
-- set the trace level in NumericalAlgebraicGeometry package
newton
-- Newton-Raphson method
numerical homotopy tracking options
-- options for core functions of Numerical Algebraic Geometry
numericalIntersection
-- intersection of numerical varieties
numericalIrreducibleDecomposition(Ideal)
-- constructs a numerical variety defined by the given ideal
parameterHomotopy(List,List,List)
-- solve a parametric system of equations
parameters(GateSystem)
-- the parameter gates in the evaluation circuit used for the system
parametricSegmentHomotopy
-- creates an ansatz for a segment homotopy
PHCPACK
-- use PHCpack for homotopy continuation
randomInitialPair
-- a random initial pair
randomSd(List)
-- a random homogeneous system of polynomial equations
refine(List,List)
-- refine numerical solutions to a system of polynomial equations
regeneration(List)
-- solve a system of polynomial equations with regeneration method
removeRedundantComponents(NumericalVariety)
-- remove redundant components
sample(WitnessSet)
-- sample a point on a component
segmentHomotopy
-- a segment homotopy
setDefault
-- set/get the default parameters for continuation algorithms
setDefault(...,Tolerance=>...)
-- specifies the tolerance of a numerical computation
Software
-- specify internal or external software
solveGenericSystemInTorus(List)
-- solve a generic system of sparse polynomial equations in the torus
solveSystem(...,PostProcess=>...)
-- specifies whether to postprocess the solutions
solveSystem(List)
-- solve a system of polynomial equations
specialize(GateParameterHomotopy,MutableMatrix)
-- specialize parameters in a (gate) parameter homotopy
squareUp
-- square up a polynomial system
totalDegreeStartSystem(List)
-- construct a start system for the total degree homotopy
track(List,List,List)
-- track a linear segment homotopy given start and target system
trackHomotopy(Homotopy,List)
-- follow points along a homotopy
union(NumericalVariety,NumericalVariety)
-- union of numerical varieties
vars(GateSystem)
-- the variable gates in the evaluation circuit used for the system