Okay , thank you for your help ! : ) On Saturday, February 3, 2024 at 11:59:31 PM UTC+5:30 David Joyner wrote:
> On Sat, Feb 3, 2024 at 1:13 PM 'Ruchit Jagodara' via sage-devel < > sage-...@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+...@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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