Inaccurate results in padic function: _polynomial_list

[gh-n-vi]

Using version 9.1 of sage, the function _polynomial_list() which is implemented in: sage/src/sage/rings/padics/padic_ZZ_pX_CR_element.pyx,
sometimes returns inaccurate results.
For example, of the first 10 powers of 5 in the following example, only 5⁰, 5⁵ get accurate results:

sage: T.<a> = Qp(5).extension(x^2-5)
sage: l = [T(5^i)._polynomial_list() for i in range(10)]
sage: l
[[1 + O(5^20)],
 [5 + 4*5^20 + O(5^21)],
 [5^2 + 3*5^21 + O(5^22)],
 [5^3 + 2*5^22 + O(5^23)],
 [5^4 + 5^23 + O(5^24)],
 [5^5 + O(5^25)],
 [5^6 + 4*5^25 + O(5^26)],
 [5^7 + 3*5^26 + O(5^27)],
 [5^8 + 2*5^27 + O(5^28)],
 [5^9 + 5^28 + O(5^29)]]

• This bug was mentioned in ticket #29925 and is repeated here in detail.

[pbruin]

See #30041 for another bug in _polynomial_list().

[mkoeppe]

Moving to 9.4, as 9.3 has been released.