On Monday, October 21, 2019 at 6:35:28 AM UTC-7, Dima Pasechnik wrote: > > However, having a real embedding seems to be an unnecessary restriction, > as > a symmetric matrix of real cyclotomics will have real eigenvalues, and > it has a signature. > (I don't know whether the signature will stay invariant if the > embedding changes - it should be either > easy to prove or easy to give a counterexample...) > > The signature need not be galois-invariant for a form over a totally real field, since totally real algebraic numbers need not be totally positive/negative. For instance:
X^2+ sqrt(2) * Y^2 (and sqrt(2) is indeed a cyclotomic number) -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/b9027310-c620-44a0-ace0-80fa091319ae%40googlegroups.com.
