On Oct 29, 2008, at 8:28 AM, Georg wrote: > Hi Robert, > thanks for your fast answer, just one more question, > >> RDF and RealField(35) are canonically isomorphic, > > what does that mean exactly,
There is a bijection between them which preserves addition and multiplication. > as far is I know, sage uses the 'gsl' for > computations with 'RDF', and computations with 'RR' are done through > 'mpfr', so if I write for example 'sqrt(5. + RDF(5))' and 'sqrt(RDF(5) > + 5.)', does sage rely on the correctnes of both implementations of > sqrt (one from gsl, one from mpfr) to be comutative? Technically, the real numbers to a fixed precision do not form a field. They are not associative nor do they (always) satisfy the distributive property. No matter what the implementation, there are positive numbers such that sqrt(x^2) != x. So really, here, we just to do the best we can. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
