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We use as example the Wilkinson polynomial of degree where :

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.

Jean-Pierre Merlet
2012-12-20