On Tuesday, December 8, 2015 at 12:54:04 PM UTC-8, Johhannes wrote: > > Hey Guys, > > I want to add a symbolic expression to CC representing an primitive n-th > root of unity analogous to 'I'. > > Lets call this Element xi_n, besides the usual rules xi_n should satisfy > the following properties: > > * (xi_n in CC) == true > * xi.parent() == CC
The first one already works for z=exp(2*pi*I/n) The second one fundamentally doesn't work: an (exact) symbolic expression doesn't lie in CC. The rational number 1/3 doesn't even have an exact representative in CC. We do have QQbar to represent algebraic numbers (and hence roots of unity), so you can do: 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)] Each of those elements can readily be turned into elements of CC (losing their exact nature in the process), so you could select the one of minimal positive argument for your purposes. 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). -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
