NumericalCertification : Index

• (certifyCount, PolySystem, List) -- executes alpha-certification on a given system and list of points
• (certifyRealSoln, PolySystem, Point) -- determine whether a given point is an real approximate solution to the system
• (certifySolution, PolySystem, List) -- certify whether a given point is an approximate solution to the system
• (certifySolution, PolySystem, Point, Point) -- determine whether given points are distinct approximate solutions to the system
• (computeConstants, PolySystem, Point) -- compute the auxiliary quantities related to alpha theory
• (newtonOper, PolySystem, Point) -- apply Newton's method on a given point.
• (pointNorm, Point) -- compute the "projectivized" norm of the given point
• (polyNorm, RingElement) -- compute the "Bombieri-Weyl" norm of the given polynomial
• (polySysNorm, PolySystem) -- compute the norm of the given polynomial system
• certifyCount -- executes alpha-certification on a given system and list of points
• certifyCount(PolySystem,List) -- executes alpha-certification on a given system and list of points
• certifyDistinctSoln -- determine whether given points are distinct approximate solutions to the system
• certifyDistinctSoln(PolySystem,Point,Point) -- determine whether given points are distinct approximate solutions to the system
• certifyRealSoln -- determine whether a given point is an real approximate solution to the system
• certifyRealSoln(PolySystem,Point) -- determine whether a given point is an real approximate solution to the system
• certifySolution -- certify whether a given point is an approximate solution to the system
• certifySolution(PolySystem,List) -- certify whether a given point is an approximate solution to the system
• computeConstants -- compute the auxiliary quantities related to alpha theory
• computeConstants(PolySystem,Point) -- compute the auxiliary quantities related to alpha theory
• identityIntMat -- compute the identity diagonal interval matrix.
• identityIntMat(ZZ) -- compute the identity diagonal interval matrix.
• Interval -- a class of all intervals
• interval -- construct an interval
• interval(Interval) -- construct an interval
• interval(Number) -- construct an interval
• interval(Number,Number) -- construct an interval
• interval(Number,RingElement) -- construct an interval
• interval(RingElement,Interval) -- construct an interval
• interval(RingElement,Number) -- construct an interval
• interval(RingElement,RingElement) -- construct an interval
• IntervalMatrix -- a class of all interval matrices
• intervalMatrix -- construct an interval matrix from the given list
• intervalMatrix(List) -- construct an interval matrix from the given list
• intervalMatrixNorm -- compute the infinity norm for interval matrix.
• intervalMatrixNorm(IntervalMatrix) -- compute the infinity norm for interval matrix.
• intervalNorm(Interval) -- compute a norm of an interval
• IntervalOptionList -- a class of lists for options related to intervals
• intervalOptionList -- convert a list type object to list of options for intervals
• intervalOptionList(List) -- convert a list type object to list of options for intervals
• InvertibleMatrix -- invertible matrix for computing Krawczyk operator (option for "krawczykOper" and "krawczykMethod")
• krawczykMethod -- certify the interval box for square polynomial system
• krawczykMethod(...,InvertibleMatrix=>...) -- invertible matrix for computing Krawczyk operator (option for "krawczykOper" and "krawczykMethod")
• krawczykMethod(PolySystem,IntervalOptionList) -- certify the interval box for square polynomial system
• krawczykMethodOptions -- invertible matrix for computing Krawczyk operator (option for "krawczykOper" and "krawczykMethod")
• krawczykOper -- compute the Krawczyk operator
• krawczykOper(...,InvertibleMatrix=>...) -- invertible matrix for computing Krawczyk operator (option for "krawczykOper" and "krawczykMethod")
• krawczykOper(PolySystem,IntervalOptionList) -- compute the Krawczyk operator
• mInterval(Interval) -- compute a midpoint of an interval
• newtonOper -- apply Newton's method on a given point.
• newtonOper(PolySystem,Point) -- apply Newton's method on a given point.
• NumericalCertification -- certify the solution for the square system using alpha theory or interval arithmetic
• pointNorm -- compute the "projectivized" norm of the given point
• pointNorm(Point) -- compute the "projectivized" norm of the given point
• polyNorm -- compute the "Bombieri-Weyl" norm of the given polynomial
• polyNorm(RingElement) -- compute the "Bombieri-Weyl" norm of the given polynomial
• polySysNorm -- compute the norm of the given polynomial system
• polySysNorm(PolySystem) -- compute the norm of the given polynomial system
• wInterval(Interval) -- compute a width of an interval.