I agree that this is a bug. There are several issues, and I don't know if
there's an easy fix.
1. The elements of the enumeration are produced by passing in exponent
vectors in terms of the generators of H:
sage: H([1])
f
sage: H([1])^3
1
It's unfortunate that we choose the same letter to represent the generator
of H as we do for the generator of G; this is just the default variable
name for multiplicative groups.
2. The generators of H are elements of G, not of H, but they print in a
reasonable way:
sage: H.0
f^2
sage: (H.0).parent()
Multiplicative Abelian group isomorphic to C6
sage: H.0.parent() is G
True
I think that they should be elements of H, but that will mean they print
incorrectly unless we update the element class.
3. There is no coercion from H to G:
sage: G.has_coerce_map_from(H)
False
There should be.
I'm not going to be able to work on this soon, but am happy to help advise
anyone who wants to.
David
On Wed, Jun 23, 2021 at 2:36 PM Altario <hamdad.mick...@gmail.com> wrote:
> SageMath version 9.0, Release Date: 2020-01-01
> Using Python 3.8.5.
> Ubuntu 20.04 LTS
> 64bit
>
> Hi,
>
> I want to create the multiplicative group (Z/7Z)*={1,2,3,4,5,6}
>
> I did these steps:
>
> sage:
> n=7
>
>
> sage:
> Zn=Zmod(n)
>
>
> sage: G=Zn.unit_group()
>
> sage: list(G)
>
> [1, f, f^2, f^3, f^4, f^5]
>
>
> sage:
> G.inject_variables()
>
> Defining f
>
> Then I want to create the subgroups H generated by f^2=2 mod 7 which is {1
> ,2,4}.
>
> I did the following steps:
> sage: H =
> G.subgroup([f^2])
>
>
> sage:
> list(H)
>
>
> [1, f, f^2]
>
> sage:
> Zn(f)
>
>
> 3
>
> "There seems to be a bug in the subgroup method: H should consist of [1,
> f^2, f^4]."
> cf:
>
> https://ask.sagemath.org/question/57703/how-can-i-manipulate-a-multiplicative-group-of-zmodn/
>
> Is there a solution for this ? Or I miss something?
>
>
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