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 auxilary 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 auxilary quantities related to alpha theory
- computeConstants(PolySystem,Point) -- compute the auxilary 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.