On Fri, Mar 23, 2018 at 6:56 AM, Yathartha Joshi <[email protected]> wrote:
> I am not sure of IndexSet usage but the reason I thought of it was that
> whenever we need to represent arbitrary set we have a notion of indexing so
> that is why I thought of having IndexSet.
> https://math.stackexchange.com/questions/485244/indexed-families-and-arbitrary-sets-notation
> http://www.math.umaine.edu/~farlow/sec22.pdf
You do need indexing to represent U A_i in general, but my point is
that ImageSet as you've defined it shouldn't be necessary.
To represent something like U [2*n, 2*n + 1] would require something
like BigUnion(Interval(2*n, 2*n + 1), n, Integers). The indexing is
done by the symbol that's used to define the set. We could also make
some way to create an arbitrary set parameterized by a variable, like
A_k so that U_{k \in I} A_k can be represented (do we currently have
any kind of arbitrary set object?).
>
>> And you still haven't answered where infinite unions are needed for
>> solveset.
>
> I thought of using BigUnion where there is a union of more than one
> imagesets, (like in case of trigonometric equations)
>
>>>> solveset(sin(x), x, S.Reals)
> Union(ImageSet(Lambda(_n, 2*_n*pi), S.Integers), ImageSet(Lambda(_n, 2*_n*pi
> + pi), S.Integers))
> # (sin(2*x) + sin(4*x) + sin(6*x)) will have lots of union of imagesets
> BigUnion could give `ImageSet(Lambda(_n, _n*pi), S.Integers)`, (although
> _union of imageset is under development, BigUnion can act as helper)
I'm still not following why it is needed, since this is still a union
of a finite number of sets (even though the sets themselves are
infinite). But maybe I'm missing something.
However, I suppose it could be useful for inequalities, and possibly
solutions in the complex domain or in higher dimensions. For instance,
sin(x) >= 0 has a solution set U_{n integer} [2*n*pi, (2*n + 1)*pi].
>
> I guess this is an idea that is in an initial stage (and that is why I can't
> imagine it in larger scale), and if you suggest that it won't be feasible I
> would rather remove it from the proposal.
I think it is feasible. BigUnion is probably quite straightforward to
implement, once we agree on an API.
Aaron Meurer
>
> Thanks
> Yathartha
> On Friday, March 23, 2018 at 11:56:03 AM UTC+5:30, Aaron Meurer wrote:
>>
>> I'm not seeing an instance where IndexSet is useful. For finite
>> collections of sets, it is redundant, as Union and Intersection can
>> already take a finite number of arguments. For infinite collections,
>> whatever symbol you index over would already exist in the collection
>> itself (for instance, n in Interval(2*n, 2*n + 1))
>>
>> And you still haven't answered where infinite unions are needed for
>> solveset.
>>
>> Aaron Meurer
>>
>> On Fri, Mar 23, 2018 at 12:14 AM, Yathartha Joshi <[email protected]>
>> wrote:
>> > What I understood about BigUnion and BigIntersection from here. BigUnion
>> > for
>> > set of finitesets will work similar to union but for set of imagesets
>> > (infinite sets) we will be returning a unified solution.
>> >
>> > say for eg: [2*n , 2*n - 1 for n in Integers] passing it to Bigunion
>> > will
>> > yield something like [n for n in Integers] and BigIntersection would
>> > yield
>> > EmptySet.
>> >
>> > See https://github.com/sympy/sympy/issues/9815#issuecomment-373978030
>> >
>> > In solveset when union of imagesets are returned we can apply big union
>> > to
>> > get the unified result (probably could help the _union of imagesets once
>> > its
>> > implemented).
>> >
>> > IndexSet will be implemented to get access to set of sets through
>> > indexing,
>> > a number of sets will be passed as parameters and an instance of
>> > IndexSet
>> > will be returned with indices mapped to each of the sets in the sets.
>> > This
>> > way we can get access to a set of sets.
>> >
>> >>>> X = IndexSet(FiniteSet(1, 2, ,3), FiniteSet(4, 5)); X
>> >>>> X[0]
>> > FiniteSet(1, 2 ,3)
>> >>>>X[1]
>> > FiniteSet(4, 5)
>> >
>> >
>> > On Friday, March 23, 2018 at 5:44:13 AM UTC+5:30, Aaron Meurer wrote:
>> >>
>> >> Regarding BigUnion, what is the point of having it and IndexSet that
>> >> can only represent a finite number of sets? Union can already do this
>> >> without the indirection. I'm also unclear where this will be needed
>> >> for solveset.
>> >>
>> >> Aaron Meurer
>> >>
>> >> On Thu, Mar 22, 2018 at 4:38 PM, Yathartha Joshi <[email protected]>
>> >> wrote:
>> >> > Sorry I just gave the access to amit kumar, I have changed it, please
>> >> > have a
>> >> > look.
>> >> >
>> >> > Thanks!
>> >> >
>> >> >
>> >> > On Friday, March 23, 2018 at 1:54:31 AM UTC+5:30, Aaron Meurer wrote:
>> >> >>
>> >> >> When I click on that link it says I don't have access.
>> >> >>
>> >> >> I recommend starting your proposal on
>> >> >> https://summerofcode.withgoogle.com and linking the draft proposal
>> >> >> there. That will make it easier to find in the future.
>> >> >>
>> >> >> Aaron Meurer
>> >> >>
>> >> >> On Thu, Mar 22, 2018 at 4:01 PM, Yathartha Joshi
>> >> >> <[email protected]>
>> >> >> wrote:
>> >> >> > I have created a proposal here. It would be great if you could
>> >> >> > review
>> >> >> > it
>> >> >> > and
>> >> >> > suggest any changes.
>> >> >> >
>> >> >> > Thanks in advance.
>> >> >> > Yathartha
>> >> >> >
>> >> >> > On Thursday, March 22, 2018 at 11:08:27 PM UTC+5:30, Yathartha
>> >> >> > Joshi
>> >> >> > wrote:
>> >> >> >>
>> >> >> >>
>> >> >> >> On Thursday, March 22, 2018 at 2:26:18 PM UTC+5:30, Amit Kumar
>> >> >> >> wrote:
>> >> >> >>>
>> >> >> >>> Hey Yathartha,
>> >> >> >>>
>> >> >> >>> That sounds good.
>> >> >> >>>
>> >> >> >>> Cheers!
>> >> >> >>> Amit
>> >> >> >>
>> >> >> >>
>> >> >> >> Okay! Thanks.
>> >> >> >>
>> >> >> >> Also, I was thinking was making absolute value expressions to
>> >> >> >> work
>> >> >> >> in
>> >> >> >> complex domain. I found a few equations that have complex
>> >> >> >> solutions:
>> >> >> >>
>> >> >> >>
>> >> >> >>
>> >> >> >> http://www.wolframalpha.com/input/?i=solve(abs(x-2)+%2Babs(x)+-+7,+x)
>> >> >> >> http://www.wolframalpha.com/input/?i=solve(abs(x-2)+-2+,+x)
>> >> >> >>
>> >> >> >>
>> >> >> >>
>> >> >> >>
>> >> >> >> http://www.wolframalpha.com/input/?i=solve(abs(x-2)+%2Babs(x+%2B4)+-+16,+x)
>> >> >> >>
>> >> >> >> I was trying to figure out a possible way to solve this, but I am
>> >> >> >> facing
>> >> >> >> difficulty in getting to the solution. I tried asking the
>> >> >> >> question
>> >> >> >> here, and
>> >> >> >> got the only possible way. Can you provide me with some
>> >> >> >> suggestions
>> >> >> >> regarding this? Is there a specific reason as to why solveset
>> >> >> >> (and
>> >> >> >> even
>> >> >> >> solve) is not made to solve in complex domain.
>> >> >> >>
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