Re: [sage-support] Creat fp group using addition relation.
On Wednesday, May 25, 2022 at 6:22:48 PM UTC+8 wdjo...@gmail.com wrote:
> On Wed, May 25, 2022 at 6:08 AM Hongyi Zhao wrote:
> >
> > As commented here [1], the following two methods can be used to define
> an Cyclic Group:
> >
> > ```
> > Generators
> > If the group operation is multiplication then:
> >
> > If the group operation is addition then:
> >
> > ```
> >
> > For the first case, the corresponding code snippet in GAP is as follows:
> >
> > ```
> > gap> f:=FreeGroup("P");;
> > gap> g:=f/ParseRelators(f, "P^8" );
> >
> > gap> StructureDescription(g);
> > "C8"
> > ```
> >
> > But I'm not sure if GAP also supports the second method mentioned above
> to define a group.
> >
>
> While SageMath does use GAP for a lot of group theory, it uses different
> command
> syntax for cyclic groups. In SageMath, you can use both
> CyclicPermutationGroup(8)
> for the multiplicative cyclic group of order 8, or
> IntegerModRing(8)
> for the additive version.
Thank you for your tips and tricks. In fact, I'm working in SageMath with
GAP, so I'm interested in the additive version implemented in GAP, and am
not sure if it also such a counterpart.
Best,
HZ
> Please see the additional examples given in
> the tutorials
> https://doc.sagemath.org/html/en/thematic_tutorials/group_theory.html
> and
> https://doc.sagemath.org/html/en/constructions/groups.html
>
>
> > [1]
> http://www.euclideanspace.com/maths/discrete/groups/categorise/types/abelian/cyclic/index.htm
>
> >
> > Regards,
> > HZ
> >
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>
>
>
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Re: [sage-support] Creat fp group using addition relation.
On Wed, May 25, 2022 at 6:08 AM Hongyi Zhao wrote:
>
> As commented here [1], the following two methods can be used to define an
> Cyclic Group:
>
> ```
> Generators
> If the group operation is multiplication then:
>
> If the group operation is addition then:
>
> ```
>
> For the first case, the corresponding code snippet in GAP is as follows:
>
> ```
> gap> f:=FreeGroup("P");;
> gap> g:=f/ParseRelators(f, "P^8" );
>
> gap> StructureDescription(g);
> "C8"
> ```
>
> But I'm not sure if GAP also supports the second method mentioned above to
> define a group.
>
While SageMath does use GAP for a lot of group theory, it uses different command
syntax for cyclic groups. In SageMath, you can use both
CyclicPermutationGroup(8)
for the multiplicative cyclic group of order 8, or
IntegerModRing(8)
for the additive version. Please see the additional examples given in
the tutorials
https://doc.sagemath.org/html/en/thematic_tutorials/group_theory.html
and
https://doc.sagemath.org/html/en/constructions/groups.html
> [1]
> http://www.euclideanspace.com/maths/discrete/groups/categorise/types/abelian/cyclic/index.htm
>
> Regards,
> HZ
>
> --
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[sage-support] Creat fp group using addition relation.
As commented here [1], the following two methods can be used to define an
Cyclic Group:
```
Generators
If the group operation is multiplication then:
If the group operation is addition then:
```
For the first case, the corresponding code snippet in GAP is as follows:
```
gap> f:=FreeGroup("P");;
gap> g:=f/ParseRelators(f, "P^8" );
gap> StructureDescription(g);
"C8"
```
But I'm not sure if GAP also supports the second method mentioned above to
define a group.
[1]
http://www.euclideanspace.com/maths/discrete/groups/categorise/types/abelian/cyclic/index.htm
Regards,
HZ
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