On 08.12.2015 23:18, Nils Bruin wrote:
[..]
yea, you are right. i was not precise enough. So this should be the
better formulated properties:
* (xi_n in QQbar) == true
* xi.parent() == QQbar
* (exp(2 * pi * I / n) == xi_n)
sage: cyclotomic_polynomial(5).roots(QQbar)
[(-0.8090169943749474? - 0.5877852522924731?*I, 1),
(-0.8090169943749474? + 0.5877852522924731?*I, 1),
(0.3090169943749474? - 0.9510565162951536?*I, 1),
(0.3090169943749474? + 0.9510565162951536?*I, 1)]
that's exactly what i want to avoid.
It might make sense to write a routine that selects that element in
QQbar, and that could even be a method on QQbar. Whether it's worth it
printing such an element in a distinct fashion remains to be seen (and
if you don't care about the printing there is no need for a special
class representing such an element).
I need it to print it, even as further, it would be great if i can group
all appearances as additional factor, separated from the others.
Some more Information about the general setting:
I play around with actions of finite groups on a polynomial ring acting
by multiplication with a power of the n-th root of unity.
bg,
Johannes
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