Sorry for the late reply. You should take a look at the work that is
being done at https://github.com/sympy/sympy/pull/2508.

Also remember that for GSoC there is a patch requirement (pardon me if
you already submitted one; I'm still sifting through emails).

Aaron Meurer

On Tue, Mar 11, 2014 at 2:01 AM, Rigel Bezerra de Melo
<[email protected]> wrote:
> Hi,
>
> First I quick introduction. My name is Rigel Bezerra de Melo, I am a senior
> Computer Science student at Federal University of Campina Grande, in Brazil.
> I am really into Algorithms and Data Structures. As a hobby, I like contests
> like TopCoder, Codeforces, etc. As previous professional experience, I have
> interned last year at Microsoft. Also, I have studied abroad at UC Berkeley.
>
> I really really want to do a GSoC with you guys. I always thought the
> symbolic capabilities of Mathematica were awesome, but always looked for
> alternatives, as I am FOSS enthusiast. I came across sympy a few months ago,
> while doing stuff in graph theory (yeah, I know, sympy doesn't have graph
> theory capabilities). Soon I discovered the number theory features and was
> amazed.
>
> By far, the project idea the really strike me as working in the Assumptions
> system. I know this system will be highly tied to the Set Theory system, as
> lots of people have already pointed out. But I think you guys are all
> thinking the inverse way of organizing it. It looked to me like you guys
> wants to do the Set Theory system dependent of the Assumptions system, but
> it should be the other way around! My idea of what would be a perfect
> organization of Assumptions, Set Theory an Formal Logic is:
>
> 1. Formal Logic system is the base for everything. It is totally
> independent. In its core, it will have Propositions, and will decide on
> them.
>
> 2. Set theory system depends on the Formal Logic one. I think the most
> useful feature of Sets in symbolic calculations is testing pertinence. I
> mean, I think that by far, that would be the most common ultimate goal of
> using it. Having it depending on the Formal Logic allow as to construct Sets
> from Propositions (the Set of all elements the satisfies the Proposition).
> The would make the code of deciding pertinence only a matter of calling the
> Formal Logic system to check satisfaction.
>
> 3. The assumptions system should depends on the Set Theory system. I think
> that, in the core, all assumptions should be of the type "x in S", where S
> is a Set. That would have 2 advantages. First, the code for assumptions is
> already done, because all we have to do now is convert Expressions to Set
> pertinence assumptions (things like "x > y" = "x-y in Z+", "x in A" and "x
> in B" = "x in A^B"). Asking would them be only a matter of evaluating
> pertinence, what would call the formal logic system to decide satisfaction
> over propositions, that is the guy that should know about this kind o thing.
> The second advantage is that, now that there is not much logic left in the
> assumptions system, we can spread the assumptions everywhere. I mean, all
> packages should add their our set of assumptions. There is a prime_number
> basic assumption, but prime numbers make only sense in the number theory
> context. Is number theory special? Is there other number theory assumptions
> that should be added? Is there other packages with "same importance"
> assumptions? To me, the answer is No, No and No. I think the right way to do
> it is, the number theory module have Prime Number Set, them a prime_number
> assumption based on this set. Now, with you care about prime numbers and
> stuff, you import the number theory package, and get it all.
>
> I know those ideas may be a little bit of diverging from what you guys are
> building. That's why I would like to work on the assumptions system now (it
> seems like you guys need help removing the old system). That way I would get
> a deeper understanding of the assumptions system and re-work these ideas in
> my head.
>
> Sorry for the long message.
>
> Thanks.
>
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