2008/6/6 Nick Alexander <[EMAIL PROTECTED]>: > >> This thread got slightly off topic to the original question though: >> where should sqrt(2) belong? Z[sqrt(2)], SR, or somewhere else? > > I always want my data to start as close to the initial object as > possible. In this case, Z[sqrt(2)] \into SR and not vice versa -- so > sqrt(2) should be in Z[sqrt(2)]. > > Nick
I agree: for exactly the same reason that I expect 2 to be in ZZ and not in SR! What about sqrt(8)? Would you put that in the maximal order Z[sqrt(2)] or in its own order Z[sqrt(8)]? I would recommenfd the former, otherwise every time you type sqrt(n) for some integer n then you would be forcing the factorization of n (on the grounds that there is no known algorithm for finding the square-free part of an integer which is faster than factorization). Similarly for other algebraic integers alpha (at least those which have a "symbolic" definition like sqrt(n)). What about sqrt(1/2)? (or anyother non-integral algebraic number)? This does not belong to any finitely-generated ring (I mean f.g. as Z-module of course) so I would put it straight into the field Q(sqrt(2)). John --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
