2024-01-25 04:04:20 +0200 commented question Trouble installing database_cremona_ellcurve Thank you, @FredericC, I'm happy to try but I'm not entirely clear on how that would help. 2024-01-24 07:25:11 +0200 asked a question Trouble installing database_cremona_ellcurve Trouble installing database_cremona_ellcurve I'm using SageMath 10.2 on macOS Sonoma 14.1.2, installed via the binary bu 2022-10-13 14:40:13 +0200 received badge ● Notable Question (source) 2022-04-15 15:53:52 +0200 received badge ● Popular Question (source) 2022-02-11 18:23:43 +0200 marked best answer Challenges with subgroup elements 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) 2022-02-07 03:06:40 +0200 commented question Challenges with subgroup elements Wow. Thank you both. Yeah, ver 9.5 resolves this issue. Whew! 2022-02-05 01:49:28 +0200 received badge ● Editor (source) 2022-02-05 01:49:28 +0200 edited question Challenges with subgroup elements Challenges with subgroup elements I'm running into apparent inconsistencies when studying subgroups of the unit group of 2022-02-05 01:11:27 +0200 asked a question Challenges with subgroup elements Challenges with subgroup elements I'm running into apparent inconsistencies when studying subgroups of the unit group of 2022-02-03 20:35:01 +0200 commented answer Subgroup of unit group @rburing quick follow up if that's ok - how can I determine the index of the subgroup inside U, and find coset represent 2022-02-03 17:11:02 +0200 marked best answer Subgroup of unit group k = CyclotomicField(5) U = k.unit_group() v = U.gens() u = U.gens_values() T1 = U.subgroup([v[0]]) T2 = U.subgroup([u[0]])  This code attempts to generate a subgroup of the unit group of $\mathbb{Q}(\zeta_{5})$. The subgroup call for T1 works fine. The one for T2 breaks. This is close to bug #18863 that was already fixed, but this version of the problem persists. The elements of u are recognized as elements of the group U. Still, Sage is unable to compute the subgroup generated by those elements. For my use case, it's important to manipulate the elements of u as elements in the field (including addition), which I don't think I can do with the elements of v. 2022-02-03 17:11:02 +0200 received badge ● Scholar (source) 2022-02-03 17:10:57 +0200 commented answer Subgroup of unit group I see! That's perfect, thank you. 2022-02-03 17:10:34 +0200 received badge ● Supporter (source) 2022-02-02 23:34:00 +0200 received badge ● Student (source) 2022-02-02 23:33:23 +0200 asked a question Subgroup of unit group Subgroup of unit group k = CyclotomicField(5) U = k.unit_group() v = U.gens() u = U.gens_values() T1 = U.subgroup([v[0]]