Up: First Cauchy theorem
Previous: Mathematical background
This procedure is implemented as:
int Cauchy_First_Bound_Interval(int Degree,VECTOR &Coeff,INTERVAL &Bound);
This procedure returns 0 if Degree=0, Coeff(1)=0 or Coeff(Degree+1)=0 and Degree=1.
On success the return code is 1.
There is also an implementation for interval polynomial:
- Degree: degree of the polynomial
- Coeff: the Degree+1 coefficients of the
polynomial in increasing degree
- Bound: the interval on the absolute value of the roots
int Cauchy_First_Bound_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL &Bound);
This procedure returns an interval
such that for any
polynomial in the set and for any root of this polynomial
A failure code of 0 is returned if Coeff(1) or Coeff(Degree+1) contains 0 or if Degree=0. On success the
returned code is 1.