On Fri, May 16, 2008 at 12:06 PM, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > > On May 16, 2008, at 12:01 PM, William Stein wrote: > >> >> On Fri, May 16, 2008 at 11:58 AM, Robert Bradshaw >> <[EMAIL PROTECTED]> wrote: >>> >>> On May 16, 2008, at 8:57 AM, Nick Alexander wrote: >>> >>>> >>>>> (specifically, sqrt(2) would >>>>> be an element of QQ[sqrt(2)] with a specified embedding into RR, so >>>>> stuff like RR(1) + sqrt(2) would work). >>>> >>>> Similar to why matrices are over ZZ rather than QQ: why is sqrt >>>> (2) in >>>> QQ[sqrt(2)] and not in ZZ[sqrt(2)]? >>> >>> Good point. >> >> Actually why isn't sqrt(2) in the multiplicative semigroup >> generated by sqrt(2)? > > Probably because it seems natural to embed parent(a) into parent(sqrt(a)).
Sorry, I was being silly. That's a good answer though. My silly response would be that 2 is the multiplicative generator of the semigroup <2> instead of an element of ZZ. I'm joking. Seriously +1 to sqrt(2) being in ZZ[sqrt(2)], since the coercion model is actually good enough that we can do this! -- William --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
