Specificity for the analysis of parametric polynomials

The following variables play a role in the procedures involving a parametric polynomial:

``ALIAS/opt_min``,``ALIAS/opt_max``: initial value for the minimum and maximum real roots of a parametric polynomial``ALIAS/stop_opt_sol``: if set to 1 the algorithm will exit soon as a maximum greater than``ALIAS/opt_sol_max``**or**a minimum lower than``ALIAS/opt_sol_min``has been found. If set to 2 while looking for a minimum and a maximum the algorithm will exit if both the minimum is lower than``ALIAS/opt_sol_min``**and**the maximum is greater than``ALIAS/opt_sol_max``

- the variable
``ALIAS/user_CoeffINIT``allows to define auxiliary variable in the C++ procedure that implement the evaluation of the coefficients of the polynomial - a procedure
`ALIAS_Coeff(fid,i)`may be created that determine if the coefficient`i`may be evaluated and if not affect to him an arbitrary large value.

To create the procedure `ALIAS_Coeff` we may also use the
`Problem_Expression` package (see section 2.1.5).
The procedure `ALIAS_Coeff` will be obtained from a list
of coefficients `Coeff` in the variable `Vars` with the following
maple code:

`ALIAS/low_value_expr_violated`:= -1e20; `ALIAS/high_value_expr_violated`:= 1e20; Verify_Problem_Expression(Coeff,Vars,"ALIAS_Coeff","ALIAS_Coeff");

Finally the above procedures may use the simplification procedure `BoundUP`, see section 8.1.1.1, that uses general roots bound
algorithms for determining if a polynomial may have a root within a
given interval.