### Calculating the Sturm sequence of a squarefree polynomial

Here f(x) = a[n]x^{n} + ··· + a[0] has integer coefficients, a[n] ≠ 0.

The polynomial coefficients a[0],...,a[n] (n > 1) are entered, separated by spaces.
The Sturm sequence is printed and evaluated at x = b.

The number V(b) of sign-changes in the evaluated sequence is also printed.

(Sturm's theorem states that if a < b and f(a)f(b) ≠ 0, then V(a) – V(b) is the number of reals roots of f(x) in the open interval (a,b).

See A.G. Akritas, *Elements of computer algebra with applications*, p. 341 and N. Jacobson, *Basic Algebra I*, p. 298.)

*Last modified 20th July 2006*

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