NumericalAlgebraicGeometry : Index
- addition -- Union of polynomial spaces
- addition(..., Tolerance => ...) -- Union of polynomial spaces
- addition(PolySpace,PolySpace) -- Union of polynomial spaces
- AffinePatches -- reserved for developers
- AllVisible -- determine if the point is an embedded component of the scheme
- 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
- colon -- colon of a (truncated) dual space
- colon(..., Tolerance => ...) -- colon of a (truncated) dual space
- colon(DualSpace,Ideal) -- colon of a (truncated) dual space
- colon(DualSpace,RingElement) -- colon of a (truncated) dual space
- 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,List) -- first-order deflation
- deflate(PolySystem,Matrix) -- first-order deflation
- deflate(PolySystem,Point) -- first-order deflation
- deflate(PolySystem,Sequence) -- first-order deflation
- deflate(PolySystem,ZZ) -- first-order deflation
- deflateInPlace -- first-order deflation
- deflateInPlace(..., SquareUp => ...) -- first-order deflation
- deflateInPlace(Point,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,MutableMatrix) -- Cauchy end game for getting a better approximation of a singular solution
- endGameCauchy(GateHomotopy,Number,Point) -- 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
- 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(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 intial 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 intial pair conjectured to be good by Shub and Smale
- goodInitialPair(..., GeneralPosition => ...) -- make an intial pair conjectured to be good by Shub and Smale
- goodInitialPair(List) -- make an intial pair conjectured to be good by Shub and Smale
- HOM4PS2 -- use HOM4PS for homotopy continuation
- 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
- intersection -- Intersection of polynomial spaces
- intersection(..., Tolerance => ...) -- Intersection of polynomial spaces
- intersection(PolySpace,PolySpace) -- Intersection of polynomial spaces
- isContained -- Is one space contained in the other
- isContained(..., Tolerance => ...) -- Is one space contained in the other
- isContained(DualSpace,DualSpace) -- Is one space contained in the other
- isContained(PolySpace,PolySpace) -- Is one space contained in the other
- isFullNumericalRank -- numerical rank of a matrix
- isFullNumericalRank(Matrix) -- numerical rank of a matrix
- 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(Point,Ideal) -- determines if a point belongs to a variety
- isOn(Point,NumericalVariety) -- determines if a point belongs to a variety
- isOn(Point,RingElement) -- determines if a point belongs to a variety
- isOn(Point,WitnessSet) -- determines if a point belongs to a variety
- isOn(Point,WitnessSet,ZZ) -- determines if a point belongs to a variety
- isPointEmbedded -- determine if the point is an embedded component of the scheme
- isPointEmbedded(..., AllVisible => ...) -- determine if the point is an embedded component of the scheme
- isPointEmbedded(Point,Ideal,List) -- determine if the point is an embedded component of the scheme
- isPointEmbeddedInCurve -- determine if the point is an embedded component of a 1-dimensional scheme
- isPointEmbeddedInCurve(Point,Ideal) -- determine if the point is an embedded component of a 1-dimensional scheme
- isSolution -- check if a point satisfies a polynomial system approximately
- isSolution(..., Tolerance => ...) -- check if a point satisfies a polynomial system approximately
- isSolution(Point,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
- LiftedPoint -- first-order deflation
- LiftedSystem -- first-order deflation
- liftPointToDeflation -- first-order deflation
- liftPointToDeflation(Point,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(PolySystem,Matrix) -- Newton-Raphson method
- newton(PolySystem,Point) -- Newton-Raphson method
- NoOutput -- options for core functions of Numerical Algebraic Geometry
- Normalize -- 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
- numericalRank -- numerical rank of a matrix
- numericalRank(..., Threshold => ...) -- numerical rank of a matrix
- numericalRank(Matrix) -- numerical rank of a matrix
- numFunctions(GateSystem) -- a system of functions evaluated via a straightline program
- numParameters(GateSystem) -- a system of functions evaluated via a straightline program
- numVariables(GateHomotopy) -- homotopy implemented via straight line programs
- numVariables(GateSystem) -- a system of functions evaluated via a straightline program
- Output -- solve a system of polynomial equations with regeneration method
- 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(GateSystem) -- the parameter gates in the evaluation circuit used for the system
- 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
- 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(List,List) -- refine numerical solutions to a system of polynomial equations
- refine(Point) -- refine numerical solutions to a system of polynomial equations
- refine(PolySystem,List) -- refine numerical solutions to a system of polynomial equations
- refine(PolySystem,Point) -- 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
- SquaredUpSystem -- square up a polynomial system
- SquareUp -- first-order deflation
- squareUp -- square up a polynomial system
- squareUp(PolySystem) -- square up a polynomial system
- squareUp(PolySystem,Matrix) -- square up a polynomial system
- squareUp(PolySystem,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