>To be clear, I don't think that a Module class should necessarily subclass an AbelianGroup class. Using subclasses to represent shared relationships between mathematical objects is tricky.
That was what I was thinking, but couldn't say it properly.The idea of decomposing the Module into abelian groups seems to be a good idea. But its not something that had seen on other CAS systems before, but i really like it. Regarding the group theory another important addition I would like to make to the current AGCA module is StructureDescription() which would act like a man page every time. like for example: `StructureDescription(Group)` would print: 1 : trivial group C(size) : cyclic group S(degree) : Symmetric group .... and so on all the group structures and a small description. This can be extended to other structures like modules and any other. And a similar addition to my group theory module, like some more descriptive. Currently I am following `An introduction to theory of groups`. What do you think ? kaushik On Mon, Feb 2, 2015 at 4:21 AM, Aaron Meurer <[email protected]> wrote: > To be clear, I don't think that a Module class should necessarily subclass > an AbelianGroup class. Using subclasses to represent shared relationships > between mathematical objects is tricky. I personally don't think of every > module as being an Abelian group. I think of every module as containing an > Abelian group as part of its structure. Mathematically we might say a > module is a triple (R, M, *) where R is a unital ring, M is an Abelian > group, and *: R x M -> M is an operation satisfying some identities. > > From a programming perspective, I would expect an AbelianGroup object to > have a lot of methods on it that are very group theoretic, and it would be > distracting at best to have these methods all be inherited directly into a > Module object. I would rather expect to be able to do something like > M.as_abelian_group().some_group_theory_method. > > Aaron Meurer > > > On Sun, Feb 1, 2015 at 3:32 PM, vamsi kaushik <[email protected] > > wrote: > >> Hi Aaron >> >> >I don't remember if I mentioned this earlier, but for Abelian groups, >> we should try to reuse as much of the stuff from the AGCA module as >> possible. It already implements a lot of what you are suggesting for >> modules, and since Abelian groups are just Z-modules >> >> I completely agree. >> >> > Perhaps we should structure the classes along the definition of a >> module that a module is a ring and an Abelian group, IMHO, Abelian >> groups are better thought of in terms of module theory than group theory, >> but it would be nice to have a group theory interface on top of Z-modules. >> >> I am not quite sure about this. I might be completely wrong, but just my >> two cents: Module theory is more about ring action like group actions >> rather than the group itself, like vector spaces for fields. So by >> definition even though ring action over an abelian group is a module ( If >> that is what you meant by "Ring and abelian group"), I think we should >> better not use this as a subclass structure because they are fundamentally >> different. And moreover I feel Module theory should be left aside to study >> ring actions extensively, while being able to have their representations in >> group theory as well. Like you said Z-modules can inherit a lot from >> AbelianGroups while still being a part of module theory. Again I have >> little knowledge of ring theory so clarify me if I am wrong. what do you >> think ? >> >> > so that the Z-module representation is just an extension of the >> Abelian group representation (rather than the other way around). >> Yes. >> >> > Take a look at the AGCA stuff and see what you think. >> It looks a lot like what I had in mind. Though I din't read every line of >> it, I am sure it would be a lot helpful for me and will focus more when I >> start implementing. >> >> I have few doubts, >> >> What do you think so far ? >> Are there any areas in group theory where sympy would like to focus ? >> >> Thanks, >> kaushik >> >> On Sun, Feb 1, 2015 at 6:01 AM, Aaron Meurer <[email protected]> wrote: >> >>> I don't remember if I mentioned this earlier, but for Abelian groups, we >>> should try to reuse as much of the stuff from the AGCA module as possible. >>> It already implements a lot of what you are suggesting for modules, and >>> since Abelian groups are just Z-modules. IMHO, Abelian groups are better >>> thought of in terms of module theory than group theory, but it would be >>> nice to have a group theory interface on top of Z-modules. >>> >>> Perhaps we should structure the classes along the definition of a module >>> that a module is a ring and an Abelian group, so that the Z-module >>> representation is just an extension of the Abelian group representation >>> (rather than the other way around). Take a look at the AGCA stuff and see >>> what you think. >>> >>> Aaron Meurer >>> >>> On Sat, Jan 31, 2015 at 4:19 PM, Joachim Durchholz <[email protected]> >>> wrote: >>> >>>> Am 31.01.2015 um 00:01 schrieb vamsi kaushik: >>>> >>>>> Hi Aaron, >>>>> >>>>> Thanks for the interest. I had actually created a rough draft of my >>>>> proposal. But I am very doubtful it has the minute implementation >>>>> details. >>>>> However I had outlined my idea very briefly in the wiki here >>>>> <https://github.com/kaushik94/Proposal/wiki>. >>>>> >>>> >>>> That looks like a lot of thought and code reading went into it, which >>>> is great. >>>> >>>> What's the reasoning behind not subclassing from magma/semi-group? >>>> >>>> Regards, >>>> Jo >>>> >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "sympy" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to [email protected]. >>>> To post to this group, send email to [email protected]. >>>> Visit this group at http://groups.google.com/group/sympy. >>>> To view this discussion on the web visit https://groups.google.com/d/ >>>> msgid/sympy/54CD54F9.5060201%40durchholz.org. >>>> >>>> For more options, visit https://groups.google.com/d/optout. >>>> >>> >>> -- >>> You received this message because you are subscribed to a topic in the >>> Google Groups "sympy" group. >>> To unsubscribe from this topic, visit >>> https://groups.google.com/d/topic/sympy/xH18C-g-ySQ/unsubscribe. >>> To unsubscribe from this group and all its topics, send an email to >>> [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/sympy. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msgid/sympy/CAKgW%3D6KfH6Bw%3D2yfS6R1iBjHeXC10On_Uk4gr6sNBqyiWDM6Bw%40mail.gmail.com >>> <https://groups.google.com/d/msgid/sympy/CAKgW%3D6KfH6Bw%3D2yfS6R1iBjHeXC10On_Uk4gr6sNBqyiWDM6Bw%40mail.gmail.com?utm_medium=email&utm_source=footer> >>> . >>> >>> For more options, visit https://groups.google.com/d/optout. >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/CAK61vZooxm6N%2BmNaUCeRKoDkziCYw%3D3At_FGH6MCwd2spjze%3DA%40mail.gmail.com >> <https://groups.google.com/d/msgid/sympy/CAK61vZooxm6N%2BmNaUCeRKoDkziCYw%3D3At_FGH6MCwd2spjze%3DA%40mail.gmail.com?utm_medium=email&utm_source=footer> >> . >> >> For more options, visit https://groups.google.com/d/optout. >> > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/xH18C-g-ySQ/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6KZowdcKBPa-SouHArANu9c2tnQTQkmze04dbLm0uWinw%40mail.gmail.com > <https://groups.google.com/d/msgid/sympy/CAKgW%3D6KZowdcKBPa-SouHArANu9c2tnQTQkmze04dbLm0uWinw%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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