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