int Cauchy_Second_Bound_Interval(int Degree,VECTOR &Coeff,double *Bound);with:

`Degree`: degree of the polynomial`Coeff`: the`Degree+1`coefficients of the polynomial in increasing degree`bound`: the upper bound of the positive roots

int Cauchy_Second_Bound_Inverse_Interval(int Degree,VECTOR &Coeff,double *Bound);This procedure fail and returns 0 if

int Cauchy_Second_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL Bound);This procedure will return a failure code of 0 if

int Cauchy_Second_Bound_Inverse_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL Bound);In that case if

A global procedure enable to get at the same time the upper and lower bound of the positive roots:

int Cauchy_Second_Bound_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound); int Cauchy_Second_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff, INTERVAL &Lower,INTERVAL &Upper);In the latter case the interval lower bound is in

int Cauchy_Second_Bound_Negative_Interval(int Degree,VECTOR &Coeff,double *Bound); int Cauchy_Second_Bound_Negative_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &Bound);while the upper bound of the negative roots can be determined using:

int Cauchy_Second_Bound_Negative_Inverse_Interval(int Degree,VECTOR &Coeff,double *Bound); int Cauchy_Second_Bound_Negative_Inverse_Interval(int Degree,INTERVAL_VECTOR &Coeff, INTERVAL &Bound);Both the upper and lower bound of the negative roots can be found using:

int Cauchy_Second_Bound_Negative_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound); int Cauchy_Second_Bound_Negative_Interval(int Degree,INTERVAL_VECTOR &Coeff, INTERVAL &Lower,INTERVAL &Upper);