1 | initial version |
As with your other question, please ask the question in the body of the posting and explain yourself.
The answer is that you created K=Q5 with a non-default option print_mode. So you have ended up with two different version of Z5, with different print modes. To illustrate this:http://ask.sagemath.org/question/3140/artin-decomposition-for-p-adic-numbers
sage: Z5(11).sqrt()
...433234102330200211
sage: Zp(5)(11).sqrt()
1 + 5 + 2*5^2 + 2*5^5 + 3*5^7 + 3*5^8 + 2*5^9 + 5^11 + 4*5^12 + 3*5^13 + 2*5^14 + 3*5^15 + 3*5^16 + 4*5^17 + O(5^20)
By contrast note that
sage: Qp(5).integer_ring() == Zp(5)
True