On Mon, 21 Oct 2019, 17:34 Nils Bruin, <nbr...@sfu.ca> wrote: > 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) >
ok, fine, but let us fix a complex embedding, and compute the signature. why does one need a real embedding for it? > -- > 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 sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/b9027310-c620-44a0-ace0-80fa091319ae%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/b9027310-c620-44a0-ace0-80fa091319ae%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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 sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq3KbKOf4hWLAQXgNQXt2WC%3DE%3DerPNnHkmihE3npCzdJbw%40mail.gmail.com.
