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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 -- evaluates the homotopy
- evaluateH(GateParameterHomotopy,Matrix,Matrix,Number) -- evaluate (gate) parameter homotopy and its derivatives
- evaluateHt -- evaluates the derivative of the homotopy with respect to the continuation parameter
- evaluateHx -- evaluates the jacobian of the homotopy
- 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
- GateSystem ^ List -- a subsystem with specified equations
- goodInitialPair(List) -- make an initial pair conjectured to be good by Shub and Smale
- HOM4PS2 -- use HOM4PS for homotopy continuation
- Homotopy -- a homotopy abstract type
- 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
- numParameters(ParameterHomotopy) -- the number of parameters in the parameter homotopy
- numVariables(ParameterHomotopy) -- the number of variables in the parameter homotopy
- numVariables(SpecializedParameterHomotopy) -- the number of variables in the parameter homotopy
- ParameterHomotopy -- a homotopy that involves parameters
- parameterHomotopy(List,List,List) -- solve a parametric system of equations
- Parameters -- a collection of parameters
- parameters(GateSystem) -- the parameter gates in the evaluation circuit used for the system
- parameters(ParameterHomotopy) -- the parameters in the parameter homotopy
- parametricSegmentHomotopy -- creates an ansatz for a segment homotopy
- PHCPACK -- use PHCpack for homotopy continuation
- polySystem(GateSystem,PolynomialRing) -- classical polynomial system associated to a gate system
- 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(GateSystem,AbstractPoint) -- specialize parameters in a gate system
- specialize(ParameterHomotopy,Matrix) -- specialize a parameter homotopy
- SpecializedParameterHomotopy -- a homotopy obtained from a parameter homotopy by specializing parameters
- 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