Example

We use as example the Wilkinson polynomial of degree $n$ where $P$:

$$P= \prod_{i =1}^{i =n} (x-i)$$

and we are looking for roots in the interval [0.5,0.7] the procedure Sturm_Interval returns always 0 for order 4 to 20. But starting at order 9 the safe procedure returns [0,3] while the safe Budan-Fourier procedure still returns 0.

The test program Test_Nb_Root_Up enable to test Budan-Fourier and Sturm method on any polynomial whose coefficients are defined in a file, by increasing degree of the power of the unknown.