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NumericalCertification : Index
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(alphaTheoryCertification, PolySystem, List)
-- executes alpha-certification on a given system and list of points
(certifyDistinctSolutions, PolySystem, AbstractPoint, AbstractPoint)
-- determine whether given points are distinct approximate solutions to the system
(certifyDistinctSolutions, PolySystem, Matrix, Matrix)
-- determine whether given points are distinct approximate solutions to the system
(certifyRealSolution, PolySystem, AbstractPoint)
-- determine whether a given point is an real approximate solution to the system
(certifyRealSolution, PolySystem, Matrix)
-- determine whether a given point is an real approximate solution to the system
(certifyRegularSolution, PolySystem, AbstractPoint)
-- certify whether a given point is an approximate solution to the system
(certifyRegularSolution, PolySystem, Matrix)
-- certify whether a given point is an approximate solution to the system
(certifySolutions, PolySystem, List)
-- executes certification on a given system and list of points
(computeConstants, PolySystem, AbstractPoint)
-- compute the square of the auxiliary quantities related to alpha theory
(computeConstants, PolySystem, Matrix)
-- compute the square of the auxiliary quantities related to alpha theory
alphaCertified
-- certify a list of numerical solutions via alphaCertified
alphaCertified(PolySystem,List)
-- certify a list of numerical solutions via alphaCertified
alphaTheory
-- options for certification method
alphaTheoryCertification
-- executes alpha-certification on a given system and list of points
alphaTheoryCertification(PolySystem,List)
-- executes alpha-certification on a given system and list of points
CCi
-- a class of all complex intervals
CCiMatrix
-- a class of matrices of complex intervals
CertificationOptions
-- options for certification method
certifyDistinctSolutions
-- determine whether given points are distinct approximate solutions to the system
certifyDistinctSolutions(PolySystem,AbstractPoint,AbstractPoint)
-- determine whether given points are distinct approximate solutions to the system
certifyDistinctSolutions(PolySystem,Matrix,Matrix)
-- determine whether given points are distinct approximate solutions to the system
certifyRealSolution
-- determine whether a given point is an real approximate solution to the system
certifyRealSolution(PolySystem,AbstractPoint)
-- determine whether a given point is an real approximate solution to the system
certifyRealSolution(PolySystem,Matrix)
-- determine whether a given point is an real approximate solution to the system
certifyRegularSolution
-- certify whether a given point is an approximate solution to the system
certifyRegularSolution(PolySystem,AbstractPoint)
-- certify whether a given point is an approximate solution to the system
certifyRegularSolution(PolySystem,Matrix)
-- certify whether a given point is an approximate solution to the system
certifySingularSolution
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(...,Strategy=>...)
-- options for certification method
certifySingularSolution(PolySystem,AbstractPoint)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(PolySystem,AbstractPoint,Number)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(PolySystem,CCiMatrix)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(PolySystem,CCiMatrix,Number)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(PolySystem,Matrix)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySingularSolution(PolySystem,Matrix,Number)
-- certify if a given point is a singular solution for a given system using the deflation method.
certifySolutions
-- executes certification on a given system and list of points
certifySolutions(...,Strategy=>...)
-- options for certification method
certifySolutions(PolySystem,List)
-- executes certification on a given system and list of points
certifySolutions(PolySystem,List,Number)
-- executes certification on a given system and list of points
computeConstants
-- compute the square of the auxiliary quantities related to alpha theory
computeConstants(PolySystem,AbstractPoint)
-- compute the square of the auxiliary quantities related to alpha theory
computeConstants(PolySystem,Matrix)
-- compute the square of the auxiliary quantities related to alpha theory
entries(CCiMatrix)
-- a class of matrices of complex intervals
imaginaryPart(CCi)
-- a class of all complex intervals
intersect(CCi,CCi)
-- a class of all complex intervals
intersect(CCi,RRi)
-- a class of all complex intervals
intersect(RRi,CCi)
-- a class of all complex intervals
intervalArithmetic
-- options for certification method
intervalCCi
-- a class of all complex intervals
intervalCCi(CCi)
-- a class of all complex intervals
isSubset(CCi,CCi)
-- a class of all complex intervals
krawczykOperator
-- compute the Krawczyk operator
krawczykOperator(Matrix,AbstractPoint)
-- compute the Krawczyk operator
krawczykOperator(Matrix,CCiMatrix)
-- compute the Krawczyk operator
krawczykOperator(Matrix,Matrix)
-- compute the Krawczyk operator
krawczykOperator(PolySystem,AbstractPoint)
-- compute the Krawczyk operator
krawczykOperator(PolySystem,CCiMatrix)
-- compute the Krawczyk operator
krawczykOperator(PolySystem,Matrix)
-- compute the Krawczyk operator
krawczykRealnessTest
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(Matrix,AbstractPoint)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(Matrix,CCiMatrix)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(Matrix,List)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(PolySystem,AbstractPoint)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(PolySystem,CCiMatrix)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykRealnessTest(PolySystem,List)
-- certify the realness of the associated solution for the square polynomial system from the given interval box
krawczykTest
-- certify the interval box for square polynomial system
krawczykTest(Matrix,AbstractPoint)
-- certify the interval box for square polynomial system
krawczykTest(Matrix,CCiMatrix)
-- certify the interval box for square polynomial system
krawczykTest(Matrix,List)
-- certify the interval box for square polynomial system
krawczykTest(Matrix,Matrix)
-- certify the interval box for square polynomial system
krawczykTest(PolySystem,AbstractPoint)
-- certify the interval box for square polynomial system
krawczykTest(PolySystem,CCiMatrix)
-- certify the interval box for square polynomial system
krawczykTest(PolySystem,List)
-- certify the interval box for square polynomial system
krawczykTest(PolySystem,Matrix)
-- certify the interval box for square polynomial system
matrixCCi
-- a class of matrices of complex intervals
midpointCCi
-- a class of all complex intervals
midpointCCi(CCi)
-- a class of all complex intervals
norm(CCi)
-- a class of all complex intervals
norm(CCiMatrix)
-- a class of matrices of complex intervals
numColumns(CCiMatrix)
-- a class of matrices of complex intervals
NumericalCertification
-- certify a numerical solution for a square system
numRows(CCiMatrix)
-- a class of matrices of complex intervals
pointToInterval
-- finds an interval box from a given point
pointToInterval(AbstractPoint,Number)
-- finds an interval box from a given point
pointToInterval(PolySystem,AbstractPoint)
-- finds an interval box from a given point
realPart(CCi)
-- a class of all complex intervals
Strategy
-- options for certification method
transpose(CCiMatrix)
-- a class of matrices of complex intervals