allroots patch



Andrej Vodopivec wrote:
> The polynomial which can't be solved is
> x^6-24576*x^5+402653184*x^4-4947802415966*x^3+40532397764222976*x^2+9157742690304*x+2069067169.
>
> I tried bfallroots with fpprec=32 and is still didn't find any roots.
> With fpprec 64 it only finds 2 roots. With fpprec 128 it finds all
> roots.
>   
Interesting.  I wonder what makes the polynomial so difficult to solve. 
The roots are pretty well separated, except for a pair near the origin.

And for me with fpprec = 64, I get an error.  Maxima prints out the
message that only two roots are found and then an error about 0 not
being a symbol.  Need to look into that.

I have to say, I was a bit surprised that solve returns floating point
results.  I was expecting exact results but solve is documented to
return float results in some situations.  For the original problem, you
can obtain exact results since we know the 3 roots for y.

Ray