Re: real/imag for t_QUAD

[Vincent Delecroix <vincent.delecroix@u-bordeaux.fr>]

Thanks Karim and Bill for your replies! I did not look further than
the simple '?real' and '?imag'.

Now, the real question: how can I convert a t_QUAD to a t_COMPLEX (in
the usual sense) with the pari library? greal/real_i and gimag/imag_i
have the same behavior as in GP.

Cheers
Vincent

Le 29/07/2019 à 23:52, Bill Allombert a écrit :
> On Mon, Jul 29, 2019 at 11:29:50PM +0200, Vincent Delecroix wrote:
> > Bonjour,
> >
> > I am confused by the behavior of the GP functions real and imag called
> > on quadratic numbers
> >
> > ? w1 = quadgen(-23);
> > ? real(w1)
> > %10 = 0
> > ? imag(w1)
> > %11 = 1
> >
> > According to the (ambiguous?) documentation of these functions, the
> > return values are supposed to be the real and imaginary parts. I would
> > have expected an answer closer to 0.5 and and 2.3979. But perhaps my
> > notion of real and imaginary part is not up to date.
>
> See ??t_QUAD:
> Quadratic numbers (t_QUAD):
> ....
>     Since  the  order is Z + wZ,  any other element can be input as z =
> x+y*w for some integers x and y. In fact, you may work in its fraction
> field Q(sqrt{d}) and use t_FRAC values for x and y.
>
>     The member function z.disc retrieves the discriminant d; x and y are
> obtained via real(z) and imag(z) respectively.
>
> Cheers,
> Bill.