+1 for having the ambient group having a coercion from a subgroup. One
other bug is that
sage: H.gen(0).parent() is G
True
sage: H([2])
f^2
sage: _.parent()
Multiplicative Abelian subgroup isomorphic to C3 generated by {f^2}
Best,
Travis
On Thursday, June 24, 2021 at 5:24:40 AM UTC+10 David Roe wrote:
> 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....@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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>> .
>>
>
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