> > Yep. And I'll remark again that > > sum(sqrt(p) for p in primes(1000)) > > *better* work instantly no matter what we do, or I'm not > happy with the plan. And you can't do the above as > far as I can tell by constructing explicitly a number field > of degree 2^168. > > William
Hmm this seems like a convincing argument for keeping sqrt(p) and hence also sqrt(-1) symbolic. Some thoughts (1) Sage has different types of functions. Symbolic ones (like sin) and numeric ones like zeta_symmetric. I am strongly convinced that in order not to confuse the user numeric functions should make every effort to convert their arguments to numeric form. I.e. I think zeta_symmetric(1/2+I) should just work (TM). (2) Blue sky. Do we need numeric functions at all? Why not keeping zeta_symmetric symbolic and only make it spit out a value after applying the N(...) operator. E.g. sage: zeta_symmetric(1/2+I) zeta_symmetric(1/2+I) sage: N(_) 0.485757429670983 - 1.38777878078145e-17*I This has the advantage that for example diff(zeta_symmetric(z),z)(1/2+I) could still have a meaning. After applying N it might attempt to do numeric differentiation in the point 1/2+I (yes I know this depends on zeta_symmetric being holomorphic, it is only an example). Michel --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
