Possible bug in NumberField's valuation()

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Benjamin Matschke

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Jan 8, 2020, 4:12:11 AM1/8/20
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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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