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why Z5 in Qp different with Zp(5)

asked 11 years ago

cjsh gravatar image

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

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answered 11 years ago

John Cremona gravatar image

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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thank you very much!

cjsh gravatar imagecjsh ( 11 years ago )

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Asked: 11 years ago

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Last updated: Dec 17 '13