On 05/22/2013 12:24 AM, Michael Orlitzky wrote:
Singular (included in sage) has a library that can quickly count the
number of real roots in an interval:
http://mate.dm.uba.ar/~alidick/etobis/rrc.pdf
I don't see an easy way to interface with it, but you could probably
come up with something based on other code that uses singular.
This seems to do what you want:
sturmha(p, 0, maxabs(p))
Same for PARI, where the function is called polsturm().
gp> ?polsturm()
polsturm(pol,{a},{b}): number of real roots of the squarefree polynomial
pol in the interval ]a,b] (which are respectively taken to be -oo or +oo
when omitted).
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