[Maxima] realroots, documentation.

sen1 at math.msu.edu sen1
Fri Aug 25 12:36:14 CDT 2006

Actually, I think just adding your comments

> realroots does not look for (or find) approximations to complex roots. It
> only finds rational bounding intervals around each of the real roots, of
> width rootsepsilon, and then returns the center-points of those
> intervals.

to the documentation of realroots would be sufficient.

Who would be responsible for that?


On Fri, 25 Aug 2006, Richard Fateman wrote:

> Definitely, reading the documentation is advisable. Maybe the name of the
> program should be improved, though the classical name for the computation is
> "real root isolation".
> rootsepsilon influences the bound on permissible error.

> It uses Sturm sequences, or at least originally did so, to find isolating
> intervals. The refinement can be done in any number of ways, but I suspect
> something not very clever, like bisection, is used.
> Realroots will always compute rational numbers. In the commercial macsyma,
> if rootsepsilon is a floating-point number, the rational number is converted
> to float. similarly for bfloats.
> Perhaps the documentation should be made more explicit, leaving no doubt as
> to what is being computing, how and why.
> Raising another point:  when the documentation is changed, do the versions
> in Portuguese, Spanish, German... also get fixed?

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