The p-adic valuation code is fairly new, and this needs to be looked at by
someone who knows it.

If you set P1,P2,P3 = K.primes_above(2) then K.valuation(P1) and
K.valuation(P2) are OK while K.valuation(P3) gives this error.  All the
primes have norm 2 and are ramified with ramification index 2.

John

On Wed, 8 Jan 2020 at 09:38, Dima Pasechnik <[email protected]> wrote:

> ---------- Forwarded message ---------
> From: 'Benjamin Matschke' via sage-devel <[email protected]>
> Date: Wed, Jan 8, 2020 at 9:12 AM
> Subject: [sage-devel] Possible bug in NumberField's valuation()
> To: sage-devel <[email protected]>
>
>
> Dear all,
>
> The following code raises an unexpected AssertionError:
>
> R.<x> = QQ[]
> K.<theta_K> = NumberField(x^6 - 18*x^4 - 24*x^3 + 27*x^2 + 36*x - 6)
> fp = K.fractional_ideal((2, -7/44*theta_K^5 + 19/44*theta_K^4 +
> 87/44*theta_K^3 - 87/44*theta_K^2 - 5/2*theta_K + 39/22))
> print(fp.norm())               # yields 2
> print(fp in K.primes_above(2)) # yields True
> v = K.valuation(fp)            # raises AssertionError
>
> ... coming from the following assert():
>
> --> 303         assert(len(candidates_for_I) > 0) # This should not be
> possible, unless I contains a unit
>
> Am I missing something? This was run on Sage 9.0, Linux Mint 19.2, 64 bit.
>
> Thanks,
> Benjamin
>
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