NumericalAlgebraicGeometry : Index
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addition -- Union of polynomial spaces
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addition(..., Tolerance => ...) -- Union of polynomial spaces
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addition(PolySpace,PolySpace) -- Union of polynomial spaces
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AffinePatches -- reserved for developers
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AllVisible -- determine if the point is an embedded component of the scheme
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Attempts -- set/get the default parameters for continuation algorithms
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BERTINI -- use Bertini for homotopy continuation
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Bits -- options for core functions of Numerical Algebraic Geometry
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Certified -- a value for the option Predictor that triggers certified tracking
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colon -- colon of a (truncated) dual space
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colon(..., Tolerance => ...) -- colon of a (truncated) dual space
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colon(DualSpace,Ideal) -- colon of a (truncated) dual space
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colon(DualSpace,RingElement) -- colon of a (truncated) dual space
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CompiledHornerForm -- reserved for developers
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CorrectorTolerance -- options for core functions of Numerical Algebraic Geometry
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decompose(WitnessSet) -- decompose a witness set into irreducibles
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deflate -- first-order deflation
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deflate(..., Variable => ...) -- first-order deflation
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deflate(Ideal) -- first-order deflation
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deflate(PolySystem,List) -- first-order deflation
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deflate(PolySystem,Matrix) -- first-order deflation
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deflate(PolySystem,Point) -- first-order deflation
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deflate(PolySystem,Sequence) -- first-order deflation
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deflate(PolySystem,ZZ) -- first-order deflation
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deflateInPlace -- first-order deflation
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deflateInPlace(..., SquareUp => ...) -- first-order deflation
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deflateInPlace(Point,PolySystem) -- first-order deflation
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Deflation -- first-order deflation
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DeflationRandomMatrix -- first-order deflation
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DeflationSequence -- first-order deflation
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DeflationSequenceMatrices -- first-order deflation
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DoublePrecision -- a constant equal to 53 (the number of bits of precision)
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DynamicPatch -- reserved for developers
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endGameCauchy -- Cauchy end game for getting a better approximation of a singular solution
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endGameCauchy(..., CorrectorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., EndZoneFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., InfinityThreshold => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., maxCorrSteps => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., numberSuccessesBeforeIncrease => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., stepIncreaseFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., tStep => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(..., tStepMin => ...) -- options for core functions of Numerical Algebraic Geometry
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endGameCauchy(GateHomotopy,Number,MutableMatrix) -- Cauchy end game for getting a better approximation of a singular solution
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endGameCauchy(GateHomotopy,Number,Point) -- Cauchy end game for getting a better approximation of a singular solution
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EndZoneFactor -- options for core functions of Numerical Algebraic Geometry
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ErrorTolerance -- options for core functions of Numerical Algebraic Geometry
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Euler -- options for core functions of Numerical Algebraic Geometry
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evaluate(GateSystem,Matrix,Matrix) -- a system of functions evaluated via a straightline program
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Field -- follow points along a homotopy
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gamma -- options for core functions of Numerical Algebraic Geometry
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GateHomotopy -- homotopy implemented via straight line programs
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gateHomotopy -- homotopy implemented via straight line programs
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gateHomotopy(..., Parameters => ...) -- specifies parameter names
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gateHomotopy(..., Software => ...) -- specifies where evaluation should be done (M2=top level, M2engine=core)
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gateHomotopy(..., Strategy => ...) -- strategy is either to "compress" or not (any other value)
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gateHomotopy(GateMatrix,GateMatrix,InputGate) -- homotopy implemented via straight line programs
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gateMatrix(GateSystem) -- evaluation circuit used for the system
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GateParameterHomotopy -- a homotopy that involves parameters and is implemented via straight line programs
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GateSystem -- a system of functions evaluated via a straightline program
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gateSystem -- a constructor for GateSystem
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gateSystem(GateMatrix,GateMatrix) -- a constructor for GateSystem
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gateSystem(GateMatrix,GateMatrix,GateMatrix) -- a constructor for GateSystem
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gateSystem(Matrix) -- a constructor for GateSystem
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gateSystem(PolySystem) -- a constructor for GateSystem
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gateSystem(PolySystem,List) -- a constructor for GateSystem
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GeneralPosition -- make an intial pair conjectured to be good by Shub and Smale
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getDefault -- set/get the default parameters for continuation algorithms
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getDefault(Symbol) -- set/get the default parameters for continuation algorithms
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goodInitialPair -- make an intial pair conjectured to be good by Shub and Smale
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goodInitialPair(..., GeneralPosition => ...) -- make an intial pair conjectured to be good by Shub and Smale
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goodInitialPair(List) -- make an intial pair conjectured to be good by Shub and Smale
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HOM4PS2 -- use HOM4PS for homotopy continuation
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HornerForm -- reserved for developers
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hypersurfaceSection -- intersection of numerical varieties
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hypersurfaceSection(..., Software => ...) -- specify internal or external software
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hypersurfaceSection(NumericalVariety,RingElement) -- intersection of numerical varieties
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InfinityThreshold -- options for core functions of Numerical Algebraic Geometry
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intersection -- Intersection of polynomial spaces
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intersection(..., Tolerance => ...) -- Intersection of polynomial spaces
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intersection(PolySpace,PolySpace) -- Intersection of polynomial spaces
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isContained -- Is one space contained in the other
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isContained(..., Tolerance => ...) -- Is one space contained in the other
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isContained(DualSpace,DualSpace) -- Is one space contained in the other
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isContained(PolySpace,PolySpace) -- Is one space contained in the other
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isFullNumericalRank -- numerical rank of a matrix
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isFullNumericalRank(Matrix) -- numerical rank of a matrix
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isOn -- determines if a point belongs to a variety
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isOn(..., Software => ...) -- specify internal or external software
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isOn(..., Tolerance => ...) -- determines if a point belongs to a variety
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isOn(Point,Ideal) -- determines if a point belongs to a variety
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isOn(Point,NumericalVariety) -- determines if a point belongs to a variety
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isOn(Point,RingElement) -- determines if a point belongs to a variety
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isOn(Point,WitnessSet) -- determines if a point belongs to a variety
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isOn(Point,WitnessSet,ZZ) -- determines if a point belongs to a variety
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isPointEmbedded -- determine if the point is an embedded component of the scheme
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isPointEmbedded(..., AllVisible => ...) -- determine if the point is an embedded component of the scheme
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isPointEmbedded(Point,Ideal,List) -- determine if the point is an embedded component of the scheme
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isPointEmbeddedInCurve -- determine if the point is an embedded component of a 1-dimensional scheme
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isPointEmbeddedInCurve(Point,Ideal) -- determine if the point is an embedded component of a 1-dimensional scheme
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isSolution -- check if a point satisfies a polynomial system approximately
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isSolution(..., Tolerance => ...) -- check if a point satisfies a polynomial system approximately
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isSolution(Point,PolySystem) -- check if a point satisfies a polynomial system approximately
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isSubset(NumericalVariety,NumericalVariety) -- check containment
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isSubset(WitnessSet,WitnessSet) -- check containment
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Iterations -- options for core functions of Numerical Algebraic Geometry
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LiftedPoint -- first-order deflation
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LiftedSystem -- first-order deflation
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liftPointToDeflation -- first-order deflation
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liftPointToDeflation(Point,PolySystem,ZZ) -- first-order deflation
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M2 -- specify internal or external software
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M2engine -- specify internal or external software
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M2enginePrecookedSLPs -- specify internal or external software
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maxCorrSteps -- options for core functions of Numerical Algebraic Geometry
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Multistep -- options for core functions of Numerical Algebraic Geometry
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MultistepDegree -- options for core functions of Numerical Algebraic Geometry
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NAGtrace -- set the trace level in NumericalAlgebraicGeometry package
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NAGtrace(ZZ) -- set the trace level in NumericalAlgebraicGeometry package
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net(GateSystem) -- a system of functions evaluated via a straightline program
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newton -- Newton-Raphson method
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newton(PolySystem,Matrix) -- Newton-Raphson method
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newton(PolySystem,Point) -- Newton-Raphson method
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NoOutput -- options for core functions of Numerical Algebraic Geometry
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Normalize -- options for core functions of Numerical Algebraic Geometry
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numberSuccessesBeforeIncrease -- options for core functions of Numerical Algebraic Geometry
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numerical homotopy tracking options -- options for core functions of Numerical Algebraic Geometry
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NumericalAlgebraicGeometry -- Numerical Algebraic Geometry
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numericalIntersection -- intersection of numerical varieties
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numericalIntersection(NumericalVariety,Ideal) -- intersection of numerical varieties
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numericalIntersection(NumericalVariety,NumericalVariety) -- intersection of numerical varieties
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numericalIntersection(WitnessSet,WitnessSet) -- intersection of numerical varieties
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numericalIrreducibleDecomposition -- constructs a numerical variety defined by the given ideal
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numericalIrreducibleDecomposition(..., Software => ...) -- specify internal or external software
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numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal
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numericalRank -- numerical rank of a matrix
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numericalRank(..., Threshold => ...) -- numerical rank of a matrix
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numericalRank(Matrix) -- numerical rank of a matrix
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numFunctions(GateSystem) -- a system of functions evaluated via a straightline program
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numParameters(GateSystem) -- a system of functions evaluated via a straightline program
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numVariables(GateHomotopy) -- homotopy implemented via straight line programs
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numVariables(GateSystem) -- a system of functions evaluated via a straightline program
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Output -- solve a system of polynomial equations with regeneration method
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parameterHomotopy -- solve a parametric system of equations
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parameterHomotopy(..., Software => ...) -- specify internal or external software
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parameterHomotopy(List,List,List) -- solve a parametric system of equations
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parameters(GateSystem) -- the parameter gates in the evaluation circuit used for the system
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parametricSegmentHomotopy -- creates an ansatz for a segment homotopy
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parametricSegmentHomotopy(GateSystem) -- creates an ansatz for a segment homotopy
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parametricSegmentHomotopy(PolySystem) -- creates an ansatz for a segment homotopy
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PHCPACK -- use PHCpack for homotopy continuation
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PostProcess -- specifies whether to postprocess the solutions
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Predictor -- options for core functions of Numerical Algebraic Geometry
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Projectivize -- options for core functions of Numerical Algebraic Geometry
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randomInitialPair -- a random initial pair
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randomInitialPair(List) -- a random initial pair
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randomSd -- a random homogeneous system of polynomial equations
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randomSd(List) -- a random homogeneous system of polynomial equations
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refine -- refine numerical solutions to a system of polynomial equations
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refine(..., Bits => ...) -- options for core functions of Numerical Algebraic Geometry
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refine(..., ErrorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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refine(..., Iterations => ...) -- options for core functions of Numerical Algebraic Geometry
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refine(..., ResidualTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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refine(..., SingularConditionNumber => ...) -- set/get the default parameters for continuation algorithms
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refine(..., Software => ...) -- specify internal or external software
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refine(List,List) -- refine numerical solutions to a system of polynomial equations
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refine(Point) -- refine numerical solutions to a system of polynomial equations
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refine(PolySystem,List) -- refine numerical solutions to a system of polynomial equations
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refine(PolySystem,Point) -- refine numerical solutions to a system of polynomial equations
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regeneration -- solve a system of polynomial equations with regeneration method
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regeneration(..., Output => ...) -- solve a system of polynomial equations with regeneration method
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regeneration(..., Software => ...) -- specify internal or external software
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regeneration(List) -- solve a system of polynomial equations with regeneration method
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removeRedundantComponents -- remove redundant components
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removeRedundantComponents(..., Tolerance => ...) -- remove redundant components
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removeRedundantComponents(NumericalVariety) -- remove redundant components
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ResidualTolerance -- options for core functions of Numerical Algebraic Geometry
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RungeKutta4 -- options for core functions of Numerical Algebraic Geometry
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sample -- sample a point on a component
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sample(..., Tolerance => ...) -- sample a point on a component
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sample(WitnessSet) -- sample a point on a component
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Secant -- options for core functions of Numerical Algebraic Geometry
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segmentHomotopy -- a segment homotopy
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segmentHomotopy(..., gamma => ...) -- options for core functions of Numerical Algebraic Geometry
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segmentHomotopy(GateSystem,GateSystem) -- a segment homotopy
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segmentHomotopy(List,List) -- a segment homotopy
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segmentHomotopy(PolySystem,PolySystem) -- a segment homotopy
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setDefault -- set/get the default parameters for continuation algorithms
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setDefault() -- set/get the default parameters for continuation algorithms
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setDefault(..., AffinePatches => ...) -- reserved for developers
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setDefault(..., Attempts => ...) -- set/get the default parameters for continuation algorithms
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setDefault(..., Bits => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., CorrectorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., EndZoneFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., ErrorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., gamma => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., InfinityThreshold => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., Iterations => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., maxCorrSteps => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., MultistepDegree => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., NoOutput => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., Normalize => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., numberSuccessesBeforeIncrease => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., Precision => ...) -- set/get the default parameters for continuation algorithms
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setDefault(..., Predictor => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., Projectivize => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., ResidualTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., SingularConditionNumber => ...) -- set/get the default parameters for continuation algorithms
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setDefault(..., SLP => ...) -- reserved for developers
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setDefault(..., SLPcorrector => ...) -- reserved for developers
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setDefault(..., SLPpredictor => ...) -- reserved for developers
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setDefault(..., Software => ...) -- specify internal or external software
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setDefault(..., stepIncreaseFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., tDegree => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., Tolerance => ...) -- specifies the tolerance of a numerical computation
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setDefault(..., tStep => ...) -- options for core functions of Numerical Algebraic Geometry
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setDefault(..., tStepMin => ...) -- options for core functions of Numerical Algebraic Geometry
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SingularConditionNumber -- set/get the default parameters for continuation algorithms
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SLP -- reserved for developers
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SLPcorrector -- reserved for developers
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SLPpredictor -- reserved for developers
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Software -- specify internal or external software
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SolutionSystem -- first-order deflation
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solveGenericSystemInTorus -- solve a generic system of sparse polynomial equations in the torus
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solveGenericSystemInTorus(List) -- solve a generic system of sparse polynomial equations in the torus
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solveGenericSystemInTorus(PolySystem) -- solve a generic system of sparse polynomial equations in the torus
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solveSystem -- solve a system of polynomial equations
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solveSystem(..., CorrectorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., EndZoneFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., gamma => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., InfinityThreshold => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., maxCorrSteps => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., Normalize => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., numberSuccessesBeforeIncrease => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., PostProcess => ...) -- specifies whether to postprocess the solutions
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solveSystem(..., Precision => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., Predictor => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., Projectivize => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., ResidualTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., SingularConditionNumber => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., Software => ...) -- specify internal or external software
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solveSystem(..., stepIncreaseFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., tDegree => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., tStep => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(..., tStepMin => ...) -- options for core functions of Numerical Algebraic Geometry
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solveSystem(List) -- solve a system of polynomial equations
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solveSystem(PolySystem) -- solve a system of polynomial equations
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SquaredUpSystem -- square up a polynomial system
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SquareUp -- first-order deflation
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squareUp -- square up a polynomial system
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squareUp(PolySystem) -- square up a polynomial system
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squareUp(PolySystem,Matrix) -- square up a polynomial system
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squareUp(PolySystem,ZZ) -- square up a polynomial system
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SquareUpMatrix -- square up a polynomial system
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stepIncreaseFactor -- options for core functions of Numerical Algebraic Geometry
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Tangent -- options for core functions of Numerical Algebraic Geometry
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tDegree -- options for core functions of Numerical Algebraic Geometry
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totalDegreeStartSystem -- construct a start system for the total degree homotopy
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totalDegreeStartSystem(List) -- construct a start system for the total degree homotopy
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track -- track a linear segment homotopy given start and target system
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track(..., AffinePatches => ...) -- reserved for developers
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track(..., CorrectorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., EndZoneFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., gamma => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., InfinityThreshold => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., maxCorrSteps => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., MultistepDegree => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., NoOutput => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., Normalize => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., numberSuccessesBeforeIncrease => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., Predictor => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., Projectivize => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., SingularConditionNumber => ...) -- set/get the default parameters for continuation algorithms
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track(..., SLP => ...) -- reserved for developers
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track(..., SLPcorrector => ...) -- reserved for developers
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track(..., SLPpredictor => ...) -- reserved for developers
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track(..., Software => ...) -- specify internal or external software
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track(..., stepIncreaseFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., tDegree => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., tStep => ...) -- options for core functions of Numerical Algebraic Geometry
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track(..., tStepMin => ...) -- options for core functions of Numerical Algebraic Geometry
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track(List,List,List) -- track a linear segment homotopy given start and target system
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track(PolySystem,PolySystem,List) -- track a linear segment homotopy given start and target system
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trackHomotopy -- follow points along a homotopy
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trackHomotopy(..., CorrectorTolerance => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., EndZoneFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., Field => ...) -- follow points along a homotopy
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trackHomotopy(..., InfinityThreshold => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., maxCorrSteps => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., NoOutput => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., numberSuccessesBeforeIncrease => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., Precision => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., Predictor => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., Software => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., stepIncreaseFactor => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., tStep => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(..., tStepMin => ...) -- options for core functions of Numerical Algebraic Geometry
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trackHomotopy(Homotopy,List) -- follow points along a homotopy
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trackHomotopy(Matrix,List) -- follow points along a homotopy
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trackHomotopy(Sequence,List) -- follow points along a homotopy
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tStep -- options for core functions of Numerical Algebraic Geometry
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tStepMin -- options for core functions of Numerical Algebraic Geometry
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union -- union of numerical varieties
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union(NumericalVariety,NumericalVariety) -- union of numerical varieties
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vars(GateSystem) -- the variable gates in the evaluation circuit used for the system