It is possible to determine an approximation of the region of the parameters space (a dimensional space where each of the dimension corresponds to one of the parameters) that contain all the possible values of the parameters such that the corresponding polynomial has all its roots in a given range. This approximation will be constituted of a set of dimensional boxes written in a file. The procedure to be used is:

MinMax_Polynom_Area(Func,Vars,Init,Strong,Solve,Rand,Points,Out,Lim,Type)where

`Out`: a string which is the name of the file in which the result will be written`Lim`: during the calculation all the boxes that have a width lower than this value will be neglected`Type`: a string that may be "Real" (if only the real root or the polynomial are considered), "RealPart" (for the real part of the root), "AllReal" (for polynomial having only real root), "OneReal" (for polynomial having at least one real root)

`Strong` is a list of two elements: the first element may be 1 or
2. If it is 2 the derivative of the coefficients of the polynomial
will be used. This algorithm uses a secondary bisection process and
the second element of `Strong` gives the maximum number of boxes
that can be used for the secondary algorithm.

The range for the real roots of the polynomial is defined as:

[`ALIAS/opt_sol_min`,`ALIAS/opt_sol_max`]It is possible to improve incrementally the quality of the approximation. During the first run the flag

The largest square enclosed in the parameters space such that the polynomials defined by parameter values within the square have all their real roots within a given range can be computed using:

MinMax_Square_Polynom_Gradient(Func,Grad,Vars,Range,Init,Rand,Points,Center,Edge)where