Adam Majewski wrote:
> Hi Ray,
>
> Thx for bfallroots and answer.
>
>
>>> I use bfallroots function :
>>> https://apps.sourceforge.net/mediawiki/maxima/index.php?title=Image:Centers_9_new.png
>>> Can it be done for higher periods ? ( for me (GCL) it fails for period
>>> 10 and fpprec:150 or 256)
>>>
>>>
>> Assuming I did this right, I see that the polynomial for period 10 is of
>> order 495.
>>
> Yes
>
>> The largest coefficient has about 285 bits in it. So maybe
>> you need to use fpprec of 300 or more?
>>
> Does it mean that I should look for size of largest coefficient to find
> appropriate fpprec ?
>
I do not know if that's the right approach, but certainly if you don't
have enough bits, some coefficients that are different may no longer be,
which changes the actual polynomial. It all depends on how sensitive
the roots are to the coefficients. I think this is a well-studied
problem, but I don't know the results.
> BTW, I can comput list of coeeficients :
> degree:GiveDegree(ff):=hipow(expand(ff),c);
> a:makelist(coeff(ff,c,degree-i),i,0,degree);
>
> but how to find which is max ?
>
apply(max, <coeff-list>)
But maybe you want the absolute value of the coefficients.
I tried running your code with fpprec=300, but I got tired of waiting.
I think it was making progress and had found about 20 roots.
Ray