> > - Currently trying to create an element in a "lazy" ring leads to a > > Exception (click to the left for traceback): > > File "integer.pyx", line 669, in integer.Integer.__pow__ > > TypeError: exponent (=lazy) must be an integer > > Coerce your numbers to real or complex numbers first. > > (that's the pyrex "**" thing I guess) > > What code did you run to try to create the lazy element?
My mistake, but the errors let me think it was sage's fault. I typed pAdicRing(3,prec="lazy") which gets accepted. Doing anything with the ring afterwards leads to the above error. You should probably validate all construction parameters at construction time. > > In general, the ramified extensions cannot completely be implemented > > via polynomial quotient rings. > > Why not? Can't we just use an Eisenstein polynomial f(x) and have x > be the uniformizer? If the user wants to use a different polynomial, > we convert between x and the user defined variables... On second thought, yes, possibly you can. Your Valuation(polyquoelt) would be min([n*valuation(polyquoelt[i])+i for i in 0..n-1]) and similar for precision. The problems will arise when you start working with precisions that are not a nice multiple of the extension degree n, i.e., what if you want to find the unit part of pi+3+O(pi^3) where pi=sqrt(3) in Z_3? > We haven't yet decided how to do this. Generally, we're trying to > have fields be uniquely determined by the parameters that define > them. We could have no automatic coercion from the number field to > the localization and have the user have to use __call__ instead. > Maybe syntax like def __call__(self, x, absprec = None, place = None) > where place determines the embedding of K into Q5? Feel free to share > any thoughts you have on this. The place can't be a parameter on the receiving end. (imagine places of higher degrees?) I wouldn't mind a field homomorphism K -> K_p that you have to call explicitly. --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
