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why Z5 in Qp different with Zp(5)

asked 2013-12-14 20:12:15 -0500

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 2013-12-14 23:56:31 -0500

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 ( 2013-12-16 22:27:03 -0500 )edit

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Asked: 2013-12-14 20:12:15 -0500

Seen: 61 times

Last updated: Dec 16 '13