I would argue that P.root_field() should return a p-adic field here, not a polynomial quotient ring. This would be consistent with the behaviour of root_field for polynomials over QQ and number fields; generally, when we have a choice of several different Sage representations of the same mathematical object, it probably makes sense to return the one with the most functionality, doesn't it? I've opened a ticket for this change to root_field (#14893).
David On Wednesday, July 10, 2013 10:49:54 PM UTC+1, Paul Mercat wrote: > > If I define 'a' like this: > > R.<x>=PolynomialRing(Qp(2)); > P=2*x^2+1; > K.<a>=P.root_field(); > > > why 'a' has no attribute abs ? > It's not a big problem, because it's easy to compute the absolute value > from the norm, but it don't work : > > a.norm() > > gives > > TypeError: cannot construct an element of Full MatrixSpace of 2 by 2 dense > matrices over 2-adic > > Field with capped relative precision 20 from [0, 1 + O(2^20), 2^-1 + 1 + 2 + > 2^2 + 2^3 + 2^4 + 2^5 + > > 2^6 + 2^7 + 2^8 + 2^9 + 2^10 + 2^11 + 2^12 + 2^13 + 2^14 + 2^15 + 2^16 + 2^17 > + 2^18 + O(2^19), 0, > > O(2^20)]! > > > Somebody knows why this don't work ? > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
