NAGtypes : Index

• AbstractPoint -- a type used to store a point in complex space
• AbstractPoint == AbstractPoint -- determine if solutions are equal
• addition -- Union of polynomial spaces
• addition(...,Tolerance=>...) -- Union of polynomial spaces
• addition(PolySpace,PolySpace) -- Union of polynomial spaces
• AffineChart -- a projective witness set
• Ambient -- (under construction!) new types and methods needed to generalize WitnessSet
• ambient(SlicingVariety) -- (under construction!) new types and methods needed to generalize WitnessSet
• ambient(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• areEqual -- determine if solutions are equal
• areEqual(...,Projective=>...) -- determine if solutions are equal
• areEqual(...,Tolerance=>...) -- the tolerance of a numerical computation
• areEqual(AbstractPoint,AbstractPoint) -- determine if solutions are equal
• areEqual(BasicList,BasicList) -- determine if solutions are equal
• areEqual(CC,CC) -- determine if solutions are equal
• areEqual(DualSpace,DualSpace) -- approximate equality of dual spaces
• areEqual(List,List) -- determine if solutions are equal
• areEqual(Matrix,Matrix) -- determine if solutions are equal
• areEqual(MutableMatrix,MutableMatrix) -- determine if solutions are equal
• areEqual(Number,Number) -- determine if solutions are equal
• areEqual(PolySpace,PolySpace) -- approximate equality of subspaces spanned by polynomials
• check(NumericalVariety) -- a numerical variety
• codim(SlicingVariety) -- (under construction!) new types and methods needed to generalize WitnessSet
• codim(WitnessSet) -- a witness set
• codim(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• components(NumericalVariety) -- list components of a numerical variety
• components(NumericalVariety,ZZ) -- list components of a numerical variety
• components(NumericalVariety,ZZ,InfiniteNumber) -- list components of a numerical variety
• components(NumericalVariety,ZZ,ZZ) -- list components of a numerical variety
• ConditionNumber -- a type used to store a point in complex space
• ContinuationParameter -- a polynomial system
• Coordinates -- a type used to store a point in complex space
• coordinates -- a type used to store a point in complex space
• coordinates(AbstractPoint) -- a type used to store a point in complex space
• coordinates(Point) -- a type used to store a point in complex space
• DecreasePrecision -- a type used to store a point in complex space
• DeflationNumber -- a type used to store a point in complex space
• degree(NumericalVariety) -- a numerical variety
• degree(WitnessSet) -- a witness set
• degree(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• differencePointSet(...,Tolerance=>...) -- the tolerance of a numerical computation
• dim(Ambient) -- (under construction!) new types and methods needed to generalize WitnessSet
• dim(DualSpace) -- a dual functional vector subspace
• dim(NumericalVariety) -- a numerical variety
• dim(PolySpace) -- a polynomial vector subspace
• dim(SlicingVariety) -- (under construction!) new types and methods needed to generalize WitnessSet
• dim(WitnessSet) -- a witness set
• dim(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• DualSpace -- a dual functional vector subspace
• dualSpace -- construct a DualSpace
• dualSpace(DualSpace) -- construct a DualSpace
• dualSpace(Matrix,AbstractPoint) -- construct a DualSpace
• dualSpace(PolySpace,AbstractPoint) -- construct a DualSpace
• Equations -- a witness set
• equations -- a witness set
• equations(PolySystem) -- a polynomial system
• equations(WitnessSet) -- a witness set
• ErrorBoundEstimate -- a type used to store a point in complex space
• evaluate -- evaluate a polynomial system or matrix at a point
• evaluate(Matrix,AbstractPoint) -- evaluate a polynomial system or matrix at a point
• evaluate(Matrix,Matrix) -- evaluate a polynomial system or matrix at a point
• evaluate(PolySystem,Matrix) -- evaluate a polynomial system or matrix at a point
• evaluate(System,AbstractPoint) -- a system of functions
• evaluate(System,AbstractPoint,AbstractPoint) -- a system of functions
• evaluate(System,Matrix) -- a system of functions
• evaluate(System,Matrix,Matrix) -- a system of functions
• evaluateJacobian -- a system of functions
• evaluateJacobian(PolySystem,AbstractPoint) -- evaluate a polynomial system or matrix at a point
• evaluateJacobian(System,AbstractPoint) -- a system of functions
• evaluateJacobian(System,AbstractPoint,AbstractPoint) -- a system of functions
• evaluateJacobian(System,Matrix) -- a system of functions
• evaluateJacobian(System,Matrix,Matrix) -- a system of functions
• generalEquations -- random linear combinations of equations/generators
• generalEquations(WitnessSet) -- random linear combinations of equations/generators
• generalEquations(ZZ,Ideal) -- random linear combinations of equations/generators
• generalEquations(ZZ,List) -- random linear combinations of equations/generators
• generators(DualSpace) -- a dual functional vector subspace
• generators(PolySpace) -- a polynomial vector subspace
• homogenize(PolySystem,Ring,RingElement) -- homogenize a polynomial system
• Homotopy -- a homotopy abstract type
• ideal(PolySystem) -- a polynomial system
• ideal(WitnessSet) -- a witness set
• IncreasePrecision -- a type used to store a point in complex space
• Infinity -- a type used to store a point in complex space
• intersection(PolySpace,PolySpace) -- Intersection of polynomial spaces
• intersection(PolySpace,PolySpace,Tolerance=>...) -- 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
• isGEQ -- compare two points
• isGEQ(...,Tolerance=>...) -- the tolerance of a numerical computation
• isGEQ(AbstractPoint,AbstractPoint) -- compare two points
• isGEQ(List,List) -- compare two points
• isHomogeneous(PolySystem) -- a polynomial system
• IsIrreducible -- a witness set
• isRealPoint -- determine whether a point is real
• isRealPoint(...,Tolerance=>...) -- the tolerance of a numerical computation
• isRealPoint(AbstractPoint) -- determine whether a point is real
• jacobian(PolySystem) -- a polynomial system
• LastT -- a type used to store a point in complex space
• map(SlicingVariety) -- (under construction!) new types and methods needed to generalize WitnessSet
• matrix(AbstractPoint) -- a type used to store a point in complex space
• MaxPrecision -- a type used to store a point in complex space
• MinStepFailure -- a type used to store a point in complex space
• Multiplicity -- a type used to store a point in complex space
• NAGtypes -- Common types used in Numerical Algebraic Geometry
• net(AbstractPoint) -- a type used to store a point in complex space
• net(Ambient) -- (under construction!) new types and methods needed to generalize WitnessSet
• net(DualSpace) -- a dual functional vector subspace
• net(NumericalVariety) -- a numerical variety
• net(PolySpace) -- a polynomial vector subspace
• net(PolySystem) -- a polynomial system
• net(SlicingVariety) -- (under construction!) new types and methods needed to generalize WitnessSet
• net(WitnessSet) -- a witness set
• net(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• Norm -- p in the p-norm
• norm(Thing,AbstractPoint) -- p-norm of the point
• NumberOfPolys -- a polynomial system
• NumberOfSteps -- a type used to store a point in complex space
• NumberOfVariables -- a polynomial system
• numericalAffineSpace -- affine space as a numerical variety
• numericalAffineSpace(PolynomialRing) -- affine space as a numerical variety
• NumericalRankFailure -- a type used to store a point in complex space
• NumericalVariety -- a numerical variety
• numericalVariety -- construct a numerical variety
• numericalVariety(List) -- construct a numerical variety
• numFunctions -- a system of functions
• numFunctions(PolySystem) -- a polynomial system
• numFunctions(System) -- a system of functions
• numParameters -- a system of functions
• numParameters(PolySystem) -- a polynomial system
• numParameters(System) -- a system of functions
• numVariables -- a system of functions
• numVariables(PolySystem) -- a polynomial system
• numVariables(System) -- a system of functions
• Origin -- a type used to store a point in complex space
• ParameterHomotopy -- a homotopy that involves parameters
• Parameters -- a collection of parameters
• parameters -- a polynomial system
• parameters(PolySystem) -- a polynomial system
• Point -- a type used to store a point in complex space
• point -- construct a Point
• point(AbstractPoint) -- construct a Point
• point(DualSpace) -- a dual functional vector subspace
• point(List) -- construct a Point
• point(List,CacheTable) -- construct a Point
• point(Matrix) -- construct a Point
• Points -- a witness set
• points -- a witness set
• points(WitnessSet) -- a witness set
• points(WSet) -- (under construction!) new types and methods needed to generalize WitnessSet
• PolyMap -- a polynomial system
• PolySpace -- a polynomial vector subspace
• polySpace -- construct a PolySpace
• polySpace(...,Reduced=>...) -- construct a PolySpace
• polySpace(Matrix) -- construct a PolySpace
• polySpace(PolySpace) -- construct a PolySpace
• PolySystem -- a polynomial system
• polySystem -- construct a polynomial system
• polySystem(Ideal) -- construct a polynomial system
• polySystem(List) -- construct a polynomial system
• polySystem(Matrix) -- construct a polynomial system
• polySystem(PolySystem) -- construct a polynomial system
• project -- project a point
• project(AbstractPoint,ZZ) -- project a point
• project(Point,ZZ) -- project a point
• ProjectionDimension -- a witness set
• ProjectiveNumericalVariety -- a projective numerical variety
• projectiveNumericalVariety -- construct a numerical variety
• projectiveNumericalVariety(List) -- construct a numerical variety
• projectiveSliceEquations -- slicing linear functions
• projectiveSliceEquations(Matrix,Ring) -- slicing linear functions
• ProjectiveWitnessSet -- a projective witness set
• projectiveWitnessSet -- construct a ProjectiveWitnessSet
• projectiveWitnessSet(Ideal,Matrix,Matrix,List) -- construct a ProjectiveWitnessSet
• random(DualSpace) -- random element of a subspace
• random(PolySpace) -- random element of a subspace
• random(ZZ,DualSpace) -- random element of a subspace
• random(ZZ,PolySpace) -- random element of a subspace
• realPoints -- select real points
• realPoints(...,Tolerance=>...) -- the tolerance of a numerical computation
• realPoints(List) -- select real points
• Reduced -- construct a PolySpace
• reduceSpace -- reduce the generators of a space
• reduceSpace(...,Monomials=>...) -- reduce the generators of a space
• reduceSpace(...,Tolerance=>...) -- the tolerance of a numerical computation
• reduceSpace(DualSpace) -- reduce the generators of a space
• reduceSpace(PolySpace) -- reduce the generators of a space
• RefinementFailure -- a type used to store a point in complex space
• Regular -- a type used to store a point in complex space
• residual -- residual of a polynomial function at a point
• residual(...,Norm=>...) -- p in the p-norm
• residual(List,Point) -- residual of a polynomial function at a point
• residual(Matrix,Matrix) -- residual of a polynomial function at a point
• residual(System,AbstractPoint) -- residual of a polynomial function at a point
• residual(System,Point) -- residual of a polynomial function at a point
• ring(DualSpace) -- a dual functional vector subspace
• ring(PolySpace) -- a polynomial vector subspace
• ring(PolySystem) -- a polynomial system
• ring(WitnessSet) -- a witness set
• Singular -- a type used to store a point in complex space
• Slice -- a witness set
• slice -- a witness set
• slice(WitnessSet) -- a witness set
• sliceEquations -- slicing linear functions
• sliceEquations(Matrix,Ring) -- slicing linear functions
• SlicingVariety -- (under construction!) new types and methods needed to generalize WitnessSet
• SolutionStatus -- a type used to store a point in complex space
• solutionsWithMultiplicity -- replaces clusters of approximately equal points by single points with multiplicity
• solutionsWithMultiplicity(...,Tolerance=>...) -- the tolerance of a numerical computation
• solutionsWithMultiplicity(List) -- replaces clusters of approximately equal points by single points with multiplicity
• sortSolutions -- sort the list of solutions
• sortSolutions(...,Tolerance=>...) -- the tolerance of a numerical computation
• sortSolutions(...,Weights=>...) -- sort the list of solutions
• sortSolutions(List) -- sort the list of solutions
• SpecializationRing -- a polynomial system
• SpecializedParameterHomotopy -- a homotopy obtained from a parameter homotopy by specializing parameters
• status(AbstractPoint) -- a type used to store a point in complex space
• substitute(PolySystem,Ring) -- substitute a ring in a polynomial system
• System -- a system of functions
• texMath(AbstractPoint) -- convert to TeX math format
• texMath(DualSpace) -- convert to TeX math format
• texMath(PolySpace) -- convert to TeX math format
• texMath(PolySystem) -- convert to TeX math format
• texMath(WitnessSet) -- convert to TeX math format
• toAffineChart -- coordinates of a point in the projective space in an affine chart
• toAffineChart(ZZ,List) -- coordinates of a point in the projective space in an affine chart
• unionPointSet(...,Tolerance=>...) -- the tolerance of a numerical computation
• WindingNumber -- a type used to store a point in complex space
• WitnessSet -- a witness set
• witnessSet -- construct a WitnessSet
• witnessSet(Ideal,Ideal,List) -- construct a WitnessSet
• witnessSet(Ideal,Matrix,List) -- construct a WitnessSet
• witnessSet(PolySystem,Matrix,List) -- construct a WitnessSet
• witnessSet(PolySystem,PolySystem,List) -- construct a WitnessSet
• WSet -- (under construction!) new types and methods needed to generalize WitnessSet