error in precision of p-adic L-functions

[wuthrich]

The following was reported by Mark Watkins.

sage: E=EllipticCurve('389a')
sage: Lp = E.padic_lseries(3)
sage: Lp.series(4)
O(3^6) + O(3^3)*T + (2 + 2*3 + 2*3^2 + O(3^3))*T^2 + (2 + O(3^2))*T^3 +
 (1 + 2*3 + O(3^3))*T^4 + O(T^5)
sage: Lp.series(5)
O(3^7) + O(3^4)*T + (2 + 2*3 + 2*3^2 + 3^3 + O(3^4))*T^2 + (2 + O(3^3))*T^3 +
 (1 + 2*3 + 2*3^2 + 2*3^3 + O(3^4))*T^4 + O(T^5)

Note that the term 2*3² in T⁴ has appeared in the second computation.

[wuthrich]

As Mark suggests further, this is likely a problem with _prec_bounds

"Should the _prec_bounds take some sort of maximum over valuation of coefficients (say all i up to j) rather than just the valuation of the jth one?"

[wuthrich]

patch, exported against 4.6.1

[wuthrich]

I rewrote e_bounds in padic_lseries.py. The new code is exactly as in the  paper

[wuthrich]

Note that the changes in the docstring at line 1019 are a new bug, reported as #10698.

[wuthrich]

both patches should be applied

[was]

Looks good, and matches with the paper. Thanks again to Mark Watkins for finding this.

[was]

The following comment is about the purposely slightly incorrect output in the second/third patch:

Note that this is mainly a problem about the printing. The
coefficients print as zero when they should be in fact zero up to some
(negative) precision.

The docstring is still a good documentation for someone who wants to
use the function.
I can not fix #10698, nor #4656, and I fear they are not going to be fixed soon.
I could have removed the docstring or cut the precision in T to 3, but
I would like to have it like that once the #10698 is fixed. The person
fixing that would maybe not want to do it.

Chris Wuthrich.

[was]

Release manager: apply all three patches.