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The procedure is able to determine a lower bound on the distance between two real roots of a polynomial:
int Min_Sep_Root_Interval(int Degree,VECTOR &Coeff,double &min);
with Similarly an upper bound may be determined with:
int Max_Sep_Root_Interval(int Degree,VECTOR &Coeff,double &max);
while upper and lower bounds may be determined with:
int Bound_Sep_Root_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound);
There is also a procedure to determine a lower bound for interval polynomial:
int Min_Sep_Root_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &Lower);
If Lower=[a,b] then some polynomials in the set will have a minimal distance between the roots greater than b while all the polynomials in the set have a minimal distance greater than a.

Jean-Pierre Merlet 2012-12-20