NumericalCertification : Table of Contents

• NumericalCertification -- certify the solution for the square system using alpha theory or interval arithmetic
• certifyCount -- executes alpha-certification on a given system and list of points
• certifyDistinctSoln -- 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
• certifySolution -- certify whether a given point is an approximate solution to the system
• computeConstants -- compute the auxiliary quantities related to alpha theory
• identityIntMat -- compute the identity diagonal interval matrix.
• Interval -- a class of all intervals
• interval -- construct an interval
• IntervalMatrix -- a class of all interval matrices
• intervalMatrix -- construct an interval matrix from the given list
• intervalMatrixNorm -- 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
• krawczykMethod -- 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
• mInterval(Interval) -- compute a midpoint of an interval
• newtonOper -- apply Newton's method on a given point.
• pointNorm -- compute the "projectivized" norm of the given point
• polyNorm -- compute the "Bombieri-Weyl" norm of the given polynomial
• polySysNorm -- compute the norm of the given polynomial system
• wInterval(Interval) -- compute a width of an interval.