Hi!
Trying to review #9457, I found the following:
sage: R.<T> = QQ.completion(5,5)[[]]
sage: R
Power Series Ring in T over 5-adic Field with capped relative precision 5
sage: O(T^2) == 0
False
Shouldn't the answer be True, because O(T^2) is indistinguishable from zero? At
#9457, niles provides a patch that fixes it. Unfortunately,
sage.schemes.elliptic_curves.sha_tate.Sha.an_padic relies on the wrong answer.
More precisely,
sage: EllipticCurve('53a1').sha().an_padic(5)
results in an error if O(T^2)==0 returns True.
Could please someone competent in elliptic curves explain how this can be fixed?
Cheers,
Simon
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