$realroots already uses psqfr. But of course that requires exact
coefficients (not floats); I suppose it could use factor and do even
better. It could also be a little smarter about top-level multiplications
and exact coefficients: no good reason that realroots((x-2/3)*(x-1/5))
should be [x = 6710887/33554432,x = 22369621/33554432].
A counterargument says: realroots isn't in the business of doing psqfr,
polynomial factorization, and symbolic analysis: it should be purely
numerical. In that case, though, I'd think we should rename it to make it
clear that that's what it does, e.g. numerical_realroots_by_sturm.
-s
On Wed, Jan 9, 2013 at 6:15 PM, Richard Fateman
<fateman at eecs.berkeley.edu>wrote:
> well, not the general issue, but finding roots of polynomials.
>
> These programs tend to have difficulty when there are multiple roots.
> e.g. (x-3)^2.
>
> But we can remove multiple roots and count them by using sqfr.
> It is a feature of computer algebra that we seem to have neglected.
>
>
> Anyone willing to muck around with this? Maybe for bfallroots?
>
> RJF
>
>
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