To summarize: What is norm for number theorists, is pathology to the ordinary folks! :-)
On Apr 27, 8:25 pm, Johan Grönqvist <johan.gronqv...@gmail.com> wrote: > 2010-04-27 13:29, Gonzalo Tornaria skrev: > > > 2010/4/27 Johan Grönqvist<johan.gronqv...@gmail.com>: > >> Those did not even mention that > >> there is an alternative definition of norm used in number theory. > > > Here it is:http://en.wikipedia.org/wiki/Field_norm > > Thanks. Now I learned something new. > > >> The norm on complex numbers is not consistent with viewing the complex > >> numbers as a two-dimensional real vector space, according to the > >> definitions > >> mentioned above. > > > One caveat: "the" norm of a two-dimensional real vector space is not > > canonical. In contrast, the norm of a two-dimensional field extension > > is uniquely defined. > > True, but the argument was not about the particular choice of norm, but > the property > > norm(a*v) == abs(a) * norm(v) [for any scalar a and any vector v] > > required for any vector-space norm. That property does not seem to hold > for the field norm. > > Regards > > Johan > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group athttp://groups.google.com/group/sage-devel > URL:http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
