I never use these canonical embeddings, and cannot think of a reason for defining one field twice in this way...
Now this would be more useful: sage: K.<a> = NumberField(x^2+3) sage: L.<w> = NumberField(x^2+x+1) sage: K.has_coerce_map_from(L) False sage: L.has_coerce_map_from(K) False sage: K.is_isomorphic(L) True sage: K.embeddings(L) [ Ring morphism: From: Number Field in a with defining polynomial x^2 + 3 To: Number Field in w with defining polynomial x^2 + x + 1 Defn: a |--> 2*w + 1, Ring morphism: From: Number Field in a with defining polynomial x^2 + 3 To: Number Field in w with defining polynomial x^2 + x + 1 Defn: a |--> -2*w - 1 ] to turn into a coercion! John On Wed, Nov 24, 2010 at 9:34 PM, Simon King <simon.k...@uni-jena.de> wrote: > Hi! > > When defining a number field, it is optional to provide a canonical > embedding into the real lazy field. > > If two number fields are defined by the same polynomial and the same > generator name, they are still considered different, if only one of > them defines a canonical embedding. > > Example: > sage: K.<a> = NumberField(x^3-5,embedding=0) > sage: L.<a> = NumberField(x^3-5) > sage: K==L > False > > But even more, there is no coercion: > sage: K.has_coerce_map_from(L) > False > sage: L.has_coerce_map_from(K) > False > > Shouldn't there be one coercion? But in what direction? L to K or K to > L? > > Cheers, > Simon > > -- > 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 > -- 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
