Re: rational roots

[Max Alekseyev <maxale@gmail.com>]

Another approach would be to convert obtained floating point roots in
rational numbers as follows:

? polroots(x^2-0.25)
%1 = [-0.50000000000000000000000000000000000000 + 0.E-38*I,
0.50000000000000000000000000000000000000 + 0.E-38*I]~
? apply(t->algdep(t,1),%)
%2 = [2*x + 1, 2*x - 1]~

Regards,
Max

On Tue, Sep 24, 2013 at 1:41 PM, Andreas Enge <andreas.enge@inria.fr> wrote:
> On Tue, Sep 24, 2013 at 10:20:17AM -0700, somayeh didari wrote:
>> I need to find rational roots of a polynomial in Pari/gp. But when I use polroots command, Pari gives all complex roots. On the other hand rational points are returned in complex type, too. How can i find rational roots in rational type? for example
>>
>> ? polroots(x^2-0.25)
>> %14 = [-0.5000000000000000000000000000 + 0.E-28*I, 0.500000000000000000000000000
>> 0 + 0.E-28*I]~
>>
>> But I need [-0.5, 0.5]!!!!!!!!!
>
> Try factor, and prefer to specify the coefficient as a rational if you look
> for rational roots:
>
> ? factor (x^2-1/4)
> %1 =
> [2*x - 1 1]
>
> [2*x + 1 1]
>
>
> ? factor (x^2-0.25)
> %2 =
> [x + 0.50000000000000000000000000000000000000 1]
>
> [x - 0.50000000000000000000000000000000000000 1]
>
> seems to work and look for real roots. Otherwise, you still have the option
> to round rounding errors away:
>
> ? real (polroots (x^2-0.25))
> %3 = [-0.50000000000000000000000000000000000000, 0.50000000000000000000000000000000000000]
>
> Andreas
>
>