I had a look at your PR 13045 <https://github.com/sympy/sympy/pull/13045> & made some comments.
On Saturday, March 24, 2018 at 7:11:39 PM UTC, Yathartha Joshi wrote: > > Sorry for my late response (I was busy traveling). I see what you are > trying to suggest of implementing for imageset, but I am still not sure > about it whether it will be a good idea or not. > I will open an issue-cum-discussion for discussing the API. > > Thanks! > Yathartha > On Saturday, March 24, 2018 at 7:14:54 AM UTC+5:30, Aaron Meurer wrote: >> >> On Fri, Mar 23, 2018 at 6:56 AM, Yathartha Joshi <yatha...@gmail.com> >> 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 <yatha...@gmail.com> >> >> >> 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 < >> yatha...@gmail.com> >> >> >> 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 >> >> >> >> <yatha...@gmail.com> >> >> >> >> 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. >> >> >> >> >> >> >> >> >> > -- >> >> >> >> > 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 sympy+un...@googlegroups.com. >> >> >> >> > To post to this group, send email to sy...@googlegroups.com. >> >> >> >> > Visit this group at https://groups.google.com/group/sympy. >> >> >> >> > To view this discussion on the web visit >> >> >> >> > >> >> >> >> > >> >> >> >> > >> >> >> >> > >> https://groups.google.com/d/msgid/sympy/aecef52c-4e2e-40b0-9b1c-3cf7c022374c%40googlegroups.com. >> >> >> >> >> >> > >> >> >> >> > 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 sympy+un...@googlegroups.com. >> >> >> > To post to this group, send email to sy...@googlegroups.com. >> >> >> > Visit this group at https://groups.google.com/group/sympy. >> >> >> > To view this discussion on the web visit >> >> >> > >> >> >> > >> >> >> > >> https://groups.google.com/d/msgid/sympy/862ac528-e77b-46e6-b751-e5ef532a2e46%40googlegroups.com. >> >> >> >> >> > >> >> >> > 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 sympy+un...@googlegroups.com. >> >> > To post to this group, send email to sy...@googlegroups.com. >> >> > Visit this group at https://groups.google.com/group/sympy. >> >> > To view this discussion on the web visit >> >> > >> >> > >> https://groups.google.com/d/msgid/sympy/34765644-ae2a-4332-9a17-52e54c056f9c%40googlegroups.com. >> >> >> >> > >> >> > 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 sympy+un...@googlegroups.com. >> > To post to this group, send email to sy...@googlegroups.com. >> > Visit this group at https://groups.google.com/group/sympy. >> > To view this discussion on the web visit >> > >> https://groups.google.com/d/msgid/sympy/5f6aa7cc-6d9e-4ef6-8190-5f9581d858bc%40googlegroups.com. >> >> >> > >> > 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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