A few questions about solve and exact polynomial roots
- Subject: A few questions about solve and exact polynomial roots
- From: Mike Valenzuela
- Date: Mon, 2 Dec 2013 14:10:26 -0700
Well for cubic functions, you can check the discriminate. If the
discriminate indicates 3 real unique solutions, then use the trig-like
functions.
On Mon, Dec 2, 2013 at 2:08 PM, Barton Willis <willisb at unk.edu> wrote:
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> http://en.wikipedia.org/wiki/Casus_irreducibilis#Non-algebraic_solution_in_terms_of_real_quantities<http://en.wikipedia.org/wiki/Casus_irreducibilis#Non-algebraic_solution_in_terms_of_real_quantities>;
> > (and here)
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> http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method<http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method>;
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> > Anyways, I am wondering if maxima natively supports
> > (1) Returning non-algebraic solutions from its solving system,
> especially if they are simplier.
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> Maxima doesn't have a user option that switches between solutions of cubic
> in terms of radicals or solutions in terms of
> trig-like functions. If you have a heuristic in mind for doing this, it
> might be worthwhile to try.
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> > (2) Some combination of trig simplification rules to recover the
> simple form given in the above link.
> > I suppose users could manually use the above identities when applicable,
> but they would have to be aware of it.
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> Likely Maxima has the tools to do things like this, but the various
> functions might need to be composed.
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> --Barton
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