Re: real/imag for t_QUAD

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Vincent Delecroix [2019-07-29 23:32]:
> 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.

Hi Vincent,

(23:45) gp > ??real
real(x): [...] In the case where x is a quadratic number,  this is the
coefficient of 1 in the "canonical" integral basis (1,omega).

(23:45) gp > ??imag
imag(x): [...] When x is a quadratic number, this is the coefficient
of omega in the "canonical" integral basis (1,omega).

This is an old design bug, can't change it now. :-(

What you expected can be obtained by  wC = w1 * 1. then real(wC) / imag(wC).

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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