why Z5 in Qp different with Zp(5)
K = Qp(5, print_mode='digits') Z5 = K.integer_ring();Z5;Z5;Z5 ==Zp(5)
5-adic Ring with capped relative precision 20 5-adic Ring with capped relative precision 20 False
K = Qp(5, print_mode='digits') Z5 = K.integer_ring();Z5;Z5;Z5 ==Zp(5)
5-adic Ring with capped relative precision 20 5-adic Ring with capped relative precision 20 False
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
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Asked: 2013-12-15 03:12:15 +0100
Seen: 352 times
Last updated: Dec 17 '13