** Next:** Sturm method
** Up:** Budan-Fourier method
** Previous:** Implementation
** Contents**

Let
, `In` be the interval [0,2] and the
procedure:
Coeff(1)= -3;Coeff(2)=2;Coeff(3)=-1;Coeff(4)=1;
P=INTERVAL(0.0,2.0);
Num= Budan_Fourier_Interval(3,Coeff,P);

`Num` is 3 meaning that has either 3 or 1 roots in the
interval.
Now assume that we have an interval polynomial:
Coeff_App(1)= INTERVAL(-3.1,-2.9);
Coeff_App(2)=INTERVAL(1.9,2.1);
Coeff_App(3)=INTERVAL(-1.1,-0.9);
Coeff_App(4)=INTERVAL(0.9,1.1);
Num= Budan_Fourier_Interval(Degree,Coeff_App,P,&Confidence);

`Num` is also 3 with `Confidence`=1 meaning that the number of
roots for any polynomial is either 3 or 1.

Jean-Pierre Merlet
2012-12-20