So, I was following a branching path of internet tangenting, and came across
this little blurb.
The first complete real-root isolation algorithm results from Sturm's theorem
(1829). However, when real-root-isolation algorithms began to be implemented on
computers it appeared that algorithms derived from Sturm's theorem are less
efficient than those derived from Descartes' rule of signs (1637).
Perhaps that's not the whole story - or there's some licensing issue with the
Descarte-based algorithm, or ....?
I found the discussion here to very interesting as well.
Definitely seems to be a challenging topic with a whole host of rules and
theorems and methods .
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