On Sat, Feb 3, 2024 at 1:13 PM 'Ruchit Jagodara' via sage-devel < sage-devel@googlegroups.com> wrote:
> So, why is the quotient function implemented in Sage is > giving RegularActionHomomorphism of G/N ? Is there any particular reason > for it? Should I change it (because I found a FIXME note also, saying that > gap has a better way to find quotient)? I am implementing some functions > related to group theory, and I can work on this as well. > The function quotient in the PermutationGroups class is returning another instance of that class. What you want is in a different Python class. Instead of "fixing" the quotient function, you can simply implement another quotient function, call it quotient_to_cosets or something like that. > On Saturday, February 3, 2024 at 10:24:54 PM UTC+5:30 David Roe wrote: > >> You can lift elements via the quotient map to get representatives of each >> coset. I'm not sure that this is wrapped in Sage, but using gap directly >> you have: >> >> sage: Pgap = p._libgap_() >> sage: Ngap = N._libgap_() >> sage: phi = Pgap.NaturalHomomorphismByNormalSubgroup(Ngap); phi >> [ (2,3,4,5,6,7) ] -> [ f1^2 ] >> sage: PN = phi.ImagesSource() # the quotient as an isomorphic group >> sage: preimages_gens = [phi.PreImagesRepresentative(g) for g in >> PN.GeneratorsOfGroup()] >> sage: preimages_gens >> [(2,4,6)(3,5,7)] >> sage: all_preimages = [phi.PreImagesRepresentative(g) for g in PN.List()] >> sage: all_preimages >> [(), (2,4,6)(3,5,7), (2,6,4)(3,7,5)] >> >> David >> >> On Sat, Feb 3, 2024 at 10:58 AM 'Ruchit Jagodara' via sage-devel < >> sage-...@googlegroups.com> wrote: >> >>> I think this is giving a group isomorphic to the actual quotient group >>> but I need the actual quotient group. Therefor, I don't know how to find >>> that exact group. Below is one example, >>> >>> sage: p = PermutationGroup([(2,3,4,5,6,7)]) >>> sage: N = p.minimal_normal_subgroups()[0] >>> sage: N >>> Subgroup generated by [(2,5)(3,6)(4,7)] of (Permutation Group with >>> generators [(2,3,4,5,6,7)]) >>> sage: N.list() >>> [(), (2,5)(3,6)(4,7)] >>> sage: p.quotient(N) >>> Permutation Group with generators [(1,2,3)] >>> sage: _.list() >>> [(), (1,2,3), (1,3,2)] >>> >>> If this is the collection of representative elements(for cosets) then >>> ``1`` should not be in any of the permutations. >>> >>> I need a quotient group structure whose elements(the cosets) have the >>> representative element (from the original group) and the normal subgroup >>> (which was used to create the quotient group) as their properties or >>> available in some other form. >>> On Friday, January 19, 2024 at 10:33:21 PM UTC+5:30 Dima Pasechnik wrote: >>> >>>> >>>> >>>> On 19 January 2024 15:18:45 GMT, 'Ruchit Jagodara' via sage-devel < >>>> sage-...@googlegroups.com> wrote: >>>> >In case my questions have caused any confusion, I am rephrasing them >>>> as >>>> >below. >>>> > >>>> >I have a group G and its minimal normal subgroup N. >>>> > >>>> >I want to find G/N. Do you know how I can do that? (I also want G/N to >>>> be >>>> >an object of the same class as G.) >>>> >>>> It's G.quotient(N), no? >>>> >>>> > >>>> >My another question is: How can I find the group operation of a group >>>> G? >>>> >On Thursday, January 18, 2024 at 7:13:50 PM UTC+5:30 Dima Pasechnik >>>> wrote: >>>> > >>>> >> On Thu, Jan 18, 2024 at 11:39 AM 'Ruchit Jagodara' via sage-devel >>>> >> <sage-...@googlegroups.com> wrote: >>>> >> > >>>> >> > Actually, that won't work according to the implementation. >>>> >> >>>> >> sorry, I don't understand what won't work. >>>> >> Did you mean to ask a different question? >>>> >> >>>> >> > Can you please take a look at the code I wrote (although I have >>>> not >>>> >> written it according to codestyle of sage, yet. But I will do that >>>> when the >>>> >> code starts working.), where minimum_generating_set is the main >>>> function? >>>> >> > >>>> >> > Link- >>>> >> >>>> https://github.com/RuchitJagodara/sage/blob/8b642329b6d579c536511d5f1d1511fb842c9c54/src/sage/groups/libgap_wrapper.pyx#L405C1-L513C1 >>>> >> > >>>> >> > I have implemented this code according to the research paper. >>>> >> >>>> >> Sorry, what paper are you talking about? >>>> >> >>>> >> >>>> >> > The algorithm can find the minimum generating set in polynomial >>>> time, >>>> >> which is very cool! So, I thought it would be good to implement this >>>> in >>>> >> Sage, especially since the paper has been recently published. >>>> >> > >>>> >> > I've almost completed the code, but I'm unsure about how to find >>>> the >>>> >> Quotient group and its representative elements. I need help with >>>> this. >>>> >> > >>>> >> > I've outlined my doubts in the code, which you can see in the >>>> following >>>> >> link:- >>>> >> > >>>> >> > >>>> >> >>>> https://github.com/RuchitJagodara/sage/blob/8b642329b6d579c536511d5f1d1511fb842c9c54/src/sage/groups/libgap_wrapper.pyx#L478-L486 >>>> >> > >>>> >> > GAP has a function named RightCosets that can be used to form a >>>> quotient >>>> >> group, but there is a problem: how can I find representative >>>> elements of >>>> >> that group? Additionally, how can I create a Quotient group using >>>> >> RightCosets in Sage, given that the algorithm uses a recursive call, >>>> and >>>> >> the quotient group must have the ParentLibGAP.minimum_generating_set >>>> >> function? >>>> >> > On Wednesday, January 17, 2024 at 2:35:55 PM UTC+5:30 Dima >>>> Pasechnik >>>> >> wrote: >>>> >> >> >>>> >> >> Functions such as Group(), PermutationGroup() take such lists as >>>> inputs. >>>> >> >> >>>> >> >> >>>> >> >> On 17 January 2024 06:35:07 GMT, 'Ruchit Jagodara' via sage-devel >>>> < >>>> >> sage-...@googlegroups.com> wrote: >>>> >> >>> >>>> >> >>> And to implement the function, I want a function that takes a >>>> list of >>>> >> generators and returns a group. Does anyone know of any function >>>> that can >>>> >> do this? >>>> >> >>> On Friday, January 12, 2024 at 8:38:18 PM UTC+5:30 Ruchit >>>> Jagodara >>>> >> wrote: >>>> >> >>>> >>>> >> >>>> I am implementing the minimum_generating_set function in Sage, >>>> but I >>>> >> am facing some issues, such as where I should implement that >>>> function as my >>>> >> implementation uses some gap methods. And I found one class >>>> ParentLibGAP >>>> >> which can be used for this but I am not sure because I found that >>>> >> PermutationGroup class is not derived from this class so if I >>>> implement >>>> >> this function here then function will not be available for this >>>> group (And >>>> >> I don't know if there are many more), plus I have to use some >>>> functions of >>>> >> GroupMixinLibGAP class, so can you please suggest me a location or >>>> any fix >>>> >> for this. >>>> >> > >>>> >> > -- >>>> >> > 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+...@googlegroups.com. >>>> >> > To view this discussion on the web visit >>>> >> >>>> https://groups.google.com/d/msgid/sage-devel/db166267-6491-42e3-bc58-01ea447a5c9bn%40googlegroups.com >>>> >> . >>>> >> >>>> > >>>> >>> -- >>> 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+...@googlegroups.com. >>> >> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sage-devel/2119b5d7-b98d-4edb-acb7-3e7704cbaffen%40googlegroups.com >>> <https://groups.google.com/d/msgid/sage-devel/2119b5d7-b98d-4edb-acb7-3e7704cbaffen%40googlegroups.com?utm_medium=email&utm_source=footer> >>> . >>> >> -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/41e28657-e22b-4cdc-846b-87cf6c4870d8n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/41e28657-e22b-4cdc-846b-87cf6c4870d8n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. 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