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Challenges with subgroup elements

asked 2022-02-05 01:11:27 +0200

AlonAmit gravatar image

updated 2022-02-05 01:49:28 +0200

I'm running into apparent inconsistencies when studying subgroups of the unit group of a cyclotomic field.

k = CyclotomicField(7,'z')
U = k.unit_group()
z = k.gen()
a = 1+z
b = a^(-1)
T = U.subgroup([U(a)])
print(U(a) in U)
print(U(b) in U)
print(U(a) in T)
print(U(b) in T)

What I'm getting is:

True
True
True
False

which doesn't make sense. $T$ is a subgroup, so if it contains $a$ it must also contain $a^{-1}$. The group $U$ gets it right, but the subgroup $T$ does not. I'm guessing this is some coercion issue, but I'm not sure why it's happening, if it's a bug, and how to work around it.

(Checked this on the Sage Cell Server and CoCalc with Sage 9.4)

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Comments

Please try SageMath 9.5, as there was a fix in this area recently.

rburing gravatar imagerburing ( 2022-02-05 11:42:27 +0200 )edit

Implentation of subgroups of unit groups is known to be buggy. E.g., see https://ask.sagemath.org/question/59558 along the same lines.

Max Alekseyev gravatar imageMax Alekseyev ( 2022-02-05 13:43:01 +0200 )edit

Wow. Thank you both. Yeah, ver 9.5 resolves this issue. Whew!

AlonAmit gravatar imageAlonAmit ( 2022-02-07 03:06:40 +0200 )edit

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answered 2022-02-07 10:25:24 +0200

rburing gravatar image

The issue is fixed in SageMath 9.5.

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Asked: 2022-02-05 01:11:27 +0200

Seen: 204 times

Last updated: Feb 07