Re: [sage-devel] Re: libgap_wrapper.is_subgroup change behaviour
That is my motivation as well. -- a baseclass for automorphism groups. Want to help me with that? :) On Friday, February 9, 2018 at 8:48:44 PM UTC+1, mathzeta2 wrote: > > On 09/02/18 15:07, Simon Brandhorst wrote: > > > > The application I have in mind is to create an abstract base class for > > group homomorphisms of libgap groups. And if we want to compute the > > inverse image of a subgroup, then this should be decided by the method > > "is_subgroup". > > > > A bit off-topic, but after having group homomorphisms, it will be very > nice to have a method to compute the automorphism group of a group G > which better than: > > G._gap_().AutomorphismGroup() or > libgap(G).AutomorphismGroup() > > The same goes as to create methods for the inner automorphism group, the > outer automorphism group and the holomorph. One motivation is just > examples in a group theory course, but obviously there many other. > > Regards, > TB > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: libgap_wrapper.is_subgroup change behaviour
On 09/02/18 15:07, Simon Brandhorst wrote: The application I have in mind is to create an abstract base class for group homomorphisms of libgap groups. And if we want to compute the inverse image of a subgroup, then this should be decided by the method "is_subgroup". A bit off-topic, but after having group homomorphisms, it will be very nice to have a method to compute the automorphism group of a group G which better than: G._gap_().AutomorphismGroup() or libgap(G).AutomorphismGroup() The same goes as to create methods for the inner automorphism group, the outer automorphism group and the holomorph. One motivation is just examples in a group theory course, but obviously there many other. Regards, TB -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Re: libgap_wrapper.is_subgroup change behaviour
I think 1) is the reasonable way.
G.is_subgroup(H) should return if G is (in a natural way) a subset of H
such that it is closed under the group operations i.e. a subset.
For example for permutation groups (of {1,...,n} ) the "natural way" Is to
regard all of them as permutation groups of the natural numbers NN.
In the concrete situation of libgap groups I would say that the function
should return if gap considers them as subgroups. (Which should be
compatible with the above.)
If one wants to have more restricted behaviour in a derived class, then one
should override is_subgroup !?
The application I have in mind is to create an abstract base class for
group homomorphisms of libgap groups. And if we want to compute the inverse
image of a subgroup, then this should be decided by the method
"is_subgroup".
On Friday, February 9, 2018 at 9:58:44 AM UTC+1, vdelecroix wrote:
>
> On 09/02/2018 09:47, Simon Brandhorst wrote:
> > Return whether the group was defined as a subgroup of a bigger
> > group.
>
> This description is very unclear anyway. See also #24535 for ambiguities
> concerning group comparisons.
>
> For me there are two relevant concepts
>
> 1) whether H is a subgroup of G, for example
>
> sage: G = PermutationGroup([ [4,3,2,1], [2,1,4,3] ])
> sage: H = PermutationGroup([ [4,3,2,1] ])
> sage: H.is_subgroup(G)
> True
>
> Here I did *not* defined H as a subgroup of G (so the above description
> does not apply). Note that in order for this comparison to make sense,
> G and H must be subgroups of a same ambient group (here
> SymmetricGroup(4)). But there is no such thing as an .ambient_group
> method.
>
> 2) whether G contains a subgroup isomorphic to H. In this situation no
>need to have a common ambient group
>
> I think that more generally discussing and fixing the semantic of group
> comparisons (and more generally algebraic structures) would be a good
> idea... and the behavior would ideally be coherent among all of Sage!
>
> Vincent
>
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Re: [sage-devel] Re: libgap_wrapper.is_subgroup change behaviour
On 09/02/2018 09:47, Simon Brandhorst wrote: Return whether the group was defined as a subgroup of a bigger group. This description is very unclear anyway. See also #24535 for ambiguities concerning group comparisons. For me there are two relevant concepts 1) whether H is a subgroup of G, for example sage: G = PermutationGroup([ [4,3,2,1], [2,1,4,3] ]) sage: H = PermutationGroup([ [4,3,2,1] ]) sage: H.is_subgroup(G) True Here I did *not* defined H as a subgroup of G (so the above description does not apply). Note that in order for this comparison to make sense, G and H must be subgroups of a same ambient group (here SymmetricGroup(4)). But there is no such thing as an .ambient_group method. 2) whether G contains a subgroup isomorphic to H. In this situation no need to have a common ambient group I think that more generally discussing and fixing the semantic of group comparisons (and more generally algebraic structures) would be a good idea... and the behavior would ideally be coherent among all of Sage! Vincent -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
[sage-devel] Re: libgap_wrapper.is_subgroup change behaviour
I forgot to say this is in sage.groups.libgap_wrapper On Friday, February 9, 2018 at 9:45:50 AM UTC+1, Simon Brandhorst wrote: > > Currently: > >def is_subgroup(self): > """ > Return whether the group was defined as a subgroup of a bigger > group. > > You can access the containing group with :meth:`ambient`. > > OUTPUT: > > Boolean. > > EXAMPLES:: > > sage: G = FreeGroup(3) > sage: G.is_subgroup() > False > """ > return self._ambient is not None > > > But in any sensible derived class i would expect > > def is_subgroup(self, other): > """ >Returns "True" if "self" is a subgroup of "other". >""" > > The suggestion is to change the name of he first method to > "is_defined_as_subgroup" > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
