For some applications it may be interesting to determine if a polynomial in a set defined by a parametric polynomial has the real part of one of its roots equal to a pre-defined value. This may be done by using the procedure

int ALIAS_Is_Root_RealPart(int Degree, int NbParameter, int HasInterval, INTERVAL_VECTOR (* TheCoeff)(INTERVAL_VECTOR &), INTERVAL_VECTOR (* TheCoeffCentered)(INTERVAL_VECTOR&,double a), int Iteration, INTERVAL_VECTOR &Par, double *Root, INTERVAL_VECTOR (* EvaluateComplex)(int,int,INTERVAL_VECTOR &), int (* Simp)(INTERVAL_VECTOR &))where

`Degree`: the degree of the polynomial`NbParameter`: the number of parameters that appear in the coefficient of the polynomial`HasInterval`: 1 if the coefficient include intervals not defined by parameters, 0 otherwise`TheCoeff`: a procedure to calculate the coefficients of the polynomial being given range for the parameters`TheCoeffCentered`: a procedure to calculate the coefficients of the polynomial`Iteration`: the maximum number of box that may be used by the algorithm`Par`: the ranges for the parameters`Root`: we look for polynomial whose real part of the root is either Root[0] or Root[1]`EvaluateComplex`: a procedure that returns 4 intervals. The input interval vector has dimension`NbParameter+1`elements, the first one being the parameters, the last one being . The procedure should evaluate and should return the real part of , the complex part of , the real part of and the complex part of`Simp`: an optional simplification procedure that returns -1 if the polynomials in a set cannot roots with real part equal to Root[0] or Root[1]