Thanks, Nick and Carl, that is very helpful! Now I am not sure whether to use QQbar just to determine which embeddings are (and are not) real, and then revert to RealField(precision) and ComplexField(Precision); or whether to try to do everything using QQbar. That sounds worth a try, despite Carl's warning about comparing real parts.
John 2008/8/29 Carl Witty <[EMAIL PROTECTED]>: > > On Aug 29, 11:47 am, "John Cremona" <[EMAIL PROTECTED]> wrote: >> If f is a real polynomial then f.roots(RR) gives the real roots, and >> f.roots(CC) gives the complex (including real) roots. Is there a >> fool-proof way of getting at the non-real roots? (You may assume that >> the coefficients of f are exact, perhaps they are rationals, so the >> questions is certainly well-defined.) > > You can do f.roots(QQbar), and then go through the roots and check > r.imag()!=0 (this is an exact computation). > >> But now I need it again in the context of K.embeddings(L) for K a >> number field. With L=RR it gives the real embeddings, and with K=CC >> it gives the real-and-complex embeddings, all of which have codomain >> CC even if they are actually real. But in my code I need to treat >> real embeddings differently from complex ones! I cannot be the first >> person to need this. > > Again, you can do K.embeddings(QQbar) and then check the imaginary > part of the image of the generator. > > Unfortunately, this may be much slower than the corresponding call to > f.roots(QQbar), because of technical details in the implementation > of .embeddings() (it sorts the roots of the polynomial; over QQbar, > this sorting involves a lot of exact computation to prove that the > real parts of conjugate pairs are actually equal). > > Carl > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
