Andrej Vodopivec wrote:
> On Tue, Jan 12, 2010 at 4:24 PM, Raymond Toy <toy.raymond at gmail.com> wrote:
>
>>
>> I vaguely remember reading somewhere that sometimes it's better to use
>> the complex Jenkins-Traub algorithm, even if the polynomial has real
>> coefficients. And indeed, this is the case for this polynomial. If we
>> multiply the polynomial by %i, then allroots, and bfallroots (with
>> fpprec = 16) instantly finds all 6 roots. The complex conjugates are
>> exactly conjugates, but pretty close.
>>
>
> The issue is how to force the complex algorithm from algsys (for the
> initial system allroots gets called with the above polynomial).
> Multiplying with %i does not work in this case. Maybe maxima should
> try with the complex algorithm if the special algorithm for real
> polynomials fails.
>
>
Yeah, we could do that, and I was thinking about it. But in this
particular example, the real algorithm spends a lot of time before it
fails, so that doesn't seem so appealing, especially when the complex
algorithm finds the solutions very quickly.
Ray