NumericalAlgebraicGeometry : Index

• AffinePatches -- reserved for developers
• Attempts -- set/get the default parameters for continuation algorithms
• BERTINI -- use Bertini for homotopy continuation
• Bits -- options for core functions of Numerical Algebraic Geometry
• Certified -- a value for the option Predictor that triggers certified tracking
• CompiledHornerForm -- reserved for developers
• CorrectorTolerance -- options for core functions of Numerical Algebraic Geometry
• decompose(WitnessSet) -- decompose a witness set into irreducibles
• deflate -- first-order deflation
• deflate(...,Variable=>...) -- first-order deflation
• deflate(Ideal) -- first-order deflation
• deflate(PolySystem,AbstractPoint) -- first-order deflation
• deflate(PolySystem,List) -- first-order deflation
• deflate(PolySystem,Matrix) -- first-order deflation
• deflate(PolySystem,Sequence) -- first-order deflation
• deflate(PolySystem,ZZ) -- first-order deflation
• deflateAndStoreDeflationSequence -- first-order deflation
• deflateAndStoreDeflationSequence(...,SquareUp=>...) -- first-order deflation
• deflateAndStoreDeflationSequence(AbstractPoint,PolySystem) -- first-order deflation
• Deflation -- first-order deflation
• DeflationRandomMatrix -- first-order deflation
• DeflationSequence -- first-order deflation
• DeflationSequenceMatrices -- first-order deflation
• DoublePrecision -- a constant equal to 53 (the number of bits of precision)
• DynamicPatch -- reserved for developers
• endGameCauchy -- Cauchy end game for getting a better approximation of a singular solution
• endGameCauchy(...,CorrectorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,EndZoneFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,InfinityThreshold=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,maxCorrSteps=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,numberSuccessesBeforeIncrease=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,stepIncreaseFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,tStep=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(...,tStepMin=>...) -- options for core functions of Numerical Algebraic Geometry
• endGameCauchy(GateHomotopy,Number,AbstractPoint) -- Cauchy end game for getting a better approximation of a singular solution
• endGameCauchy(GateHomotopy,Number,MutableMatrix) -- Cauchy end game for getting a better approximation of a singular solution
• EndZoneFactor -- options for core functions of Numerical Algebraic Geometry
• ErrorTolerance -- options for core functions of Numerical Algebraic Geometry
• Euler -- options for core functions of Numerical Algebraic Geometry
• evaluate(GateSystem,Matrix,Matrix) -- a system of functions evaluated via a straightline program
• evaluateH -- evaluates the homotopy
• evaluateH(GateHomotopy,Matrix,Number) -- evaluates the homotopy
• evaluateH(GateParameterHomotopy,Matrix,Matrix,Number) -- evaluate (gate) parameter homotopy and its derivatives
• evaluateH(Homotopy,Matrix,Number) -- evaluates the homotopy
• evaluateH(ParameterHomotopy,Matrix,Matrix,Number) -- evaluates the homotopy
• evaluateH(SpecializedParameterHomotopy,Matrix,Number) -- evaluates the homotopy
• evaluateHt -- evaluates the derivative of the homotopy with respect to the continuation parameter
• evaluateHt(GateHomotopy,Matrix,Number) -- evaluates the derivative of the homotopy with respect to the continuation parameter
• evaluateHt(GateParameterHomotopy,Matrix,Matrix,Number) -- evaluate (gate) parameter homotopy and its derivatives
• evaluateHt(Homotopy,Matrix,Number) -- evaluates the derivative of the homotopy with respect to the continuation parameter
• evaluateHt(ParameterHomotopy,Matrix,Matrix,Number) -- evaluates the derivative of the homotopy with respect to the continuation parameter
• evaluateHt(SpecializedParameterHomotopy,Matrix,Number) -- evaluates the derivative of the homotopy with respect to the continuation parameter
• evaluateHx -- evaluates the jacobian of the homotopy
• evaluateHx(GateHomotopy,Matrix,Number) -- evaluates the jacobian of the homotopy
• evaluateHx(GateParameterHomotopy,Matrix,Matrix,Number) -- evaluate (gate) parameter homotopy and its derivatives
• evaluateHx(Homotopy,Matrix,Number) -- evaluates the jacobian of the homotopy
• evaluateHx(ParameterHomotopy,Matrix,Matrix,Number) -- evaluates the jacobian of the homotopy
• evaluateHx(SpecializedParameterHomotopy,Matrix,Number) -- evaluates the jacobian of the homotopy
• Field -- follow points along a homotopy
• gamma -- options for core functions of Numerical Algebraic Geometry
• GateHomotopy -- homotopy implemented via straight line programs
• gateHomotopy -- homotopy implemented via straight line programs
• 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
• gateSystem(BasicList,BasicList,GateMatrix) -- a constructor for GateSystem
• gateSystem(GateMatrix,GateMatrix) -- a constructor for GateSystem
• gateSystem(GateMatrix,GateMatrix,GateMatrix) -- a constructor for GateSystem
• gateSystem(Matrix) -- a constructor for GateSystem
• gateSystem(PolySystem) -- a constructor for GateSystem
• gateSystem(PolySystem,List) -- a constructor for GateSystem
• GeneralPosition -- make an initial pair conjectured to be good by Shub and Smale
• getDefault -- set/get the default parameters for continuation algorithms
• getDefault(Symbol) -- set/get the default parameters for continuation algorithms
• goodInitialPair -- make an initial pair conjectured to be good by Shub and Smale
• goodInitialPair(...,GeneralPosition=>...) -- make an initial pair conjectured to be good by Shub and Smale
• 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
• HornerForm -- reserved for developers
• hypersurfaceSection -- intersection of numerical varieties
• hypersurfaceSection(...,Software=>...) -- specify internal or external software
• hypersurfaceSection(NumericalVariety,RingElement) -- intersection of numerical varieties
• InfinityThreshold -- options for core functions of Numerical Algebraic Geometry
• isOn -- determines if a point belongs to a variety
• isOn(...,Software=>...) -- specify internal or external software
• isOn(...,Tolerance=>...) -- determines if a point belongs to a variety
• isOn(AbstractPoint,Ideal) -- determines if a point belongs to a variety
• isOn(AbstractPoint,NumericalVariety) -- determines if a point belongs to a variety
• isOn(AbstractPoint,RingElement) -- determines if a point belongs to a variety
• isOn(AbstractPoint,WitnessSet) -- determines if a point belongs to a variety
• isOn(AbstractPoint,WitnessSet,ZZ) -- determines if a point belongs to a variety
• isSolution -- check if a point satisfies a polynomial system approximately
• isSolution(...,Tolerance=>...) -- check if a point satisfies a polynomial system approximately
• isSolution(AbstractPoint,PolySystem) -- check if a point satisfies a polynomial system approximately
• isSubset(NumericalVariety,NumericalVariety) -- check containment
• isSubset(WitnessSet,WitnessSet) -- check containment
• Iterations -- options for core functions of Numerical Algebraic Geometry
• jacobian(GateSystem) -- jacobian of a (gate) system
• jacobian(List,GateSystem) -- jacobian of a (gate) system
• LiftedPoint -- first-order deflation
• LiftedSystem -- first-order deflation
• liftPointToDeflation -- first-order deflation
• liftPointToDeflation(AbstractPoint,PolySystem,ZZ) -- first-order deflation
• M2 -- specify internal or external software
• M2engine -- specify internal or external software
• M2enginePrecookedSLPs -- specify internal or external software
• maxCorrSteps -- options for core functions of Numerical Algebraic Geometry
• Multistep -- options for core functions of Numerical Algebraic Geometry
• MultistepDegree -- options for core functions of Numerical Algebraic Geometry
• NAGtrace -- set the trace level in NumericalAlgebraicGeometry package
• NAGtrace(ZZ) -- set the trace level in NumericalAlgebraicGeometry package
• net(GateSystem) -- a system of functions evaluated via a straightline program
• newton -- Newton-Raphson method
• newton(System,AbstractPoint) -- Newton-Raphson method
• NoOutput -- options for core functions of Numerical Algebraic Geometry
• numberSuccessesBeforeIncrease -- options for core functions of Numerical Algebraic Geometry
• numerical homotopy tracking options -- options for core functions of Numerical Algebraic Geometry
• NumericalAlgebraicGeometry -- Numerical Algebraic Geometry
• numericalIntersection -- intersection of numerical varieties
• numericalIntersection(NumericalVariety,Ideal) -- intersection of numerical varieties
• numericalIntersection(NumericalVariety,NumericalVariety) -- intersection of numerical varieties
• numericalIntersection(WitnessSet,WitnessSet) -- intersection of numerical varieties
• numericalIrreducibleDecomposition -- constructs a numerical variety defined by the given ideal
• numericalIrreducibleDecomposition(...,Software=>...) -- specify internal or external software
• numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal
• numFunctions(GateSystem) -- a system of functions evaluated via a straightline program
• numParameters(GateSystem) -- a system of functions evaluated via a straightline program
• numParameters(ParameterHomotopy) -- the number of parameters in the parameter homotopy
• numVariables(GateHomotopy) -- homotopy implemented via straight line programs
• numVariables(GateSystem) -- a system of functions evaluated via a straightline program
• numVariables(ParameterHomotopy) -- the number of variables in the parameter homotopy
• numVariables(SpecializedParameterHomotopy) -- the number of variables in the parameter homotopy
• Output -- solve a system of polynomial equations with regeneration method
• ParameterHomotopy -- a homotopy that involves parameters
• parameterHomotopy -- solve a parametric system of equations
• parameterHomotopy(...,Software=>...) -- specify internal or external software
• 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
• parametricSegmentHomotopy(GateSystem) -- creates an ansatz for a segment homotopy
• parametricSegmentHomotopy(PolySystem) -- creates an ansatz for a segment homotopy
• PHCPACK -- use PHCpack for homotopy continuation
• polySystem(GateSystem,PolynomialRing) -- classical polynomial system associated to a gate system
• PostProcess -- specifies whether to postprocess the solutions
• Predictor -- options for core functions of Numerical Algebraic Geometry
• Projectivize -- options for core functions of Numerical Algebraic Geometry
• randomInitialPair -- a random initial pair
• randomInitialPair(List) -- a random initial pair
• randomSd -- a random homogeneous system of polynomial equations
• randomSd(List) -- a random homogeneous system of polynomial equations
• refine -- refine numerical solutions to a system of polynomial equations
• refine(...,Bits=>...) -- options for core functions of Numerical Algebraic Geometry
• refine(...,ErrorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• refine(...,Iterations=>...) -- options for core functions of Numerical Algebraic Geometry
• refine(...,ResidualTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• refine(...,SingularConditionNumber=>...) -- set/get the default parameters for continuation algorithms
• refine(...,Software=>...) -- specify internal or external software
• refine(AbstractPoint) -- refine numerical solutions to a system of polynomial equations
• refine(List,List) -- refine numerical solutions to a system of polynomial equations
• refine(PolySystem,AbstractPoint) -- refine numerical solutions to a system of polynomial equations
• refine(PolySystem,List) -- refine numerical solutions to a system of polynomial equations
• regeneration -- solve a system of polynomial equations with regeneration method
• regeneration(...,Output=>...) -- solve a system of polynomial equations with regeneration method
• regeneration(...,Software=>...) -- specify internal or external software
• regeneration(List) -- solve a system of polynomial equations with regeneration method
• removeRedundantComponents -- remove redundant components
• removeRedundantComponents(...,Tolerance=>...) -- remove redundant components
• removeRedundantComponents(NumericalVariety) -- remove redundant components
• ResidualTolerance -- options for core functions of Numerical Algebraic Geometry
• RungeKutta4 -- options for core functions of Numerical Algebraic Geometry
• sample -- sample a point on a component
• sample(...,Tolerance=>...) -- sample a point on a component
• sample(WitnessSet) -- sample a point on a component
• Secant -- options for core functions of Numerical Algebraic Geometry
• segmentHomotopy -- a segment homotopy
• segmentHomotopy(...,gamma=>...) -- options for core functions of Numerical Algebraic Geometry
• segmentHomotopy(GateSystem,GateSystem) -- a segment homotopy
• segmentHomotopy(List,List) -- a segment homotopy
• segmentHomotopy(PolySystem,PolySystem) -- a segment homotopy
• setDefault -- set/get the default parameters for continuation algorithms
• setDefault() -- set/get the default parameters for continuation algorithms
• setDefault(...,AffinePatches=>...) -- reserved for developers
• setDefault(...,Attempts=>...) -- set/get the default parameters for continuation algorithms
• setDefault(...,Bits=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,CorrectorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,EndZoneFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,ErrorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,gamma=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,InfinityThreshold=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,Iterations=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,maxCorrSteps=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,MultistepDegree=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,NoOutput=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,Normalize=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,numberSuccessesBeforeIncrease=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,Precision=>...) -- set/get the default parameters for continuation algorithms
• setDefault(...,Predictor=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,Projectivize=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,ResidualTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,SingularConditionNumber=>...) -- set/get the default parameters for continuation algorithms
• setDefault(...,SLP=>...) -- reserved for developers
• setDefault(...,SLPcorrector=>...) -- reserved for developers
• setDefault(...,SLPpredictor=>...) -- reserved for developers
• setDefault(...,Software=>...) -- specify internal or external software
• setDefault(...,stepIncreaseFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,tDegree=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,Tolerance=>...) -- specifies the tolerance of a numerical computation
• setDefault(...,tStep=>...) -- options for core functions of Numerical Algebraic Geometry
• setDefault(...,tStepMin=>...) -- options for core functions of Numerical Algebraic Geometry
• SingularConditionNumber -- set/get the default parameters for continuation algorithms
• SLP -- reserved for developers
• SLPcorrector -- reserved for developers
• SLPpredictor -- reserved for developers
• Software -- specify internal or external software
• SolutionSystem -- first-order deflation
• solveGenericSystemInTorus -- solve a generic system of sparse polynomial equations in the torus
• solveGenericSystemInTorus(List) -- solve a generic system of sparse polynomial equations in the torus
• solveGenericSystemInTorus(PolySystem) -- solve a generic system of sparse polynomial equations in the torus
• solveSystem -- solve a system of polynomial equations
• solveSystem(...,CorrectorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,EndZoneFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,gamma=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,InfinityThreshold=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,maxCorrSteps=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,Normalize=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,numberSuccessesBeforeIncrease=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,PostProcess=>...) -- specifies whether to postprocess the solutions
• solveSystem(...,Precision=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,Predictor=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,Projectivize=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,ResidualTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,SingularConditionNumber=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,Software=>...) -- specify internal or external software
• solveSystem(...,stepIncreaseFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,tDegree=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,tStep=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(...,tStepMin=>...) -- options for core functions of Numerical Algebraic Geometry
• solveSystem(List) -- solve a system of polynomial equations
• solveSystem(PolySystem) -- solve a system of polynomial equations
• specialize -- specialize a parameter homotopy
• 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
• SquaredUpSystem -- square up a polynomial system
• SquareUp -- first-order deflation
• squareUp -- square up a polynomial system
• squareUp(...,Field=>...) -- square up a polynomial system
• squareUp(...,Strategy=>...) -- square up a polynomial system
• squareUp(...,Verbose=>...) -- square up a polynomial system
• squareUp(AbstractPoint,AbstractPoint,GateSystem) -- square up a polynomial system
• squareUp(AbstractPoint,GateSystem) -- square up a polynomial system
• squareUp(System) -- square up a polynomial system
• squareUp(System,Matrix) -- square up a polynomial system
• squareUp(System,ZZ) -- square up a polynomial system
• SquareUpMatrix -- square up a polynomial system
• stepIncreaseFactor -- options for core functions of Numerical Algebraic Geometry
• Tangent -- options for core functions of Numerical Algebraic Geometry
• tDegree -- options for core functions of Numerical Algebraic Geometry
• totalDegreeStartSystem -- construct a start system for the total degree homotopy
• totalDegreeStartSystem(List) -- construct a start system for the total degree homotopy
• track -- track a linear segment homotopy given start and target system
• track(...,AffinePatches=>...) -- reserved for developers
• track(...,CorrectorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,EndZoneFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,gamma=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,InfinityThreshold=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,maxCorrSteps=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,MultistepDegree=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,NoOutput=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,Normalize=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,numberSuccessesBeforeIncrease=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,Predictor=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,Projectivize=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,SingularConditionNumber=>...) -- set/get the default parameters for continuation algorithms
• track(...,SLP=>...) -- reserved for developers
• track(...,SLPcorrector=>...) -- reserved for developers
• track(...,SLPpredictor=>...) -- reserved for developers
• track(...,Software=>...) -- specify internal or external software
• track(...,stepIncreaseFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,tDegree=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,tStep=>...) -- options for core functions of Numerical Algebraic Geometry
• track(...,tStepMin=>...) -- options for core functions of Numerical Algebraic Geometry
• track(List,List,List) -- track a linear segment homotopy given start and target system
• track(PolySystem,PolySystem,List) -- track a linear segment homotopy given start and target system
• trackHomotopy -- follow points along a homotopy
• trackHomotopy(...,CorrectorTolerance=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,EndZoneFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,Field=>...) -- follow points along a homotopy
• trackHomotopy(...,InfinityThreshold=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,maxCorrSteps=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,NoOutput=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,numberSuccessesBeforeIncrease=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,Precision=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,Predictor=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,Software=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,stepIncreaseFactor=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,tStep=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(...,tStepMin=>...) -- options for core functions of Numerical Algebraic Geometry
• trackHomotopy(Homotopy,List) -- follow points along a homotopy
• trackHomotopy(Matrix,List) -- follow points along a homotopy
• trackHomotopy(Sequence,List) -- follow points along a homotopy
• tStep -- options for core functions of Numerical Algebraic Geometry
• tStepMin -- options for core functions of Numerical Algebraic Geometry
• union -- union of numerical varieties
• union(NumericalVariety,NumericalVariety) -- union of numerical varieties
• vars(GateSystem) -- the variable gates in the evaluation circuit used for the system