Implementation

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

• Degree: degree of the polynomial
• Coeff: the Degree+1 coefficients of the polynomial in increasing degree
• min: the lower bound on the distance between two real roots

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.