On Friday, March 4, 2016 at 12:09:18 AM UTC+5:30, Kshitij Saraogi wrote:
>
> This post is with regards to the *Set Infrastructure* part of the project 
> idea.
>
> After reading a few resources and the ``sets`` module, I would like to 
> know about a few of these points:
>
>    - Handling multidimensional sets
>   The Ideas Page states that we need to implement few functions to handle 
>    multidimensional set objects.
>    We have a ProductSet class which represents Cartesian Product of Sets.
>    Shouldn't a n-ary ProductSet object represent a n-dimensional set 
>    object ?
>    If not, I would like to know more about this topic.
>    
>
Yes, that can work as well. See the implementation of ComplexRegion for 
Two-Dimensional representation of the argand plane.
 

>
>    - 
>    
>     While reading Harsh's GSoC Application Proposal, I came across a few 
> points that I think need to be addressed.
>
>    - Sets need to get more powerful to deal with countable infinite sets. 
>    I think this needs to be implemented as it enhances over power to deal 
> with 
>    ImageSet objects. I will read the relevant resources and try to implement 
>    them. Harsh's PR #2904 might come in handy as well. 
>    - Better imageset evaluator I would like to know what exactly is the 
>    inspiration behind this ?
>
>
See this: https://github.com/sympy/sympy/pull/10713#issuecomment-191472434 
The following could be much simplified with a better Imageset evaluator.

In [11]: solveset(sin(3*x), x)
Out[11]: 
                                        ⎧        2⋅π        ⎫   ⎧        2⋅π 
 
{2⋅n⋅π | n ∊ ℤ} ∪ {2⋅n⋅π + π | n ∊ ℤ} ∪ ⎨2⋅n⋅π - ─── | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─── 
|
                                       ⎩         3         ⎭   ⎩         3 
  

      ⎫   ⎧        π        ⎫   ⎧        π        ⎫
n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π - ─ | n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─ | n ∊ ℤ⎬
     ⎭   ⎩        3        ⎭   ⎩        3        ⎭


>    - 
>    
>    More general set to native type converters, they include Bool to Set 
>    and Set to Bool conversion for multidimensional sets and bools.
>    
>    I read that we already have Boolean to Set converters in SymPy but I 
>    am not able to find them.
>    
> as_relational and as_set functions are implemented.

In [18]: bool = Interval(3, 5).as_relational(x)

In [19]: bool
Out[19]: 3 ≤ x ∧ x ≤ 5

In [20]: bool.as_set()
Out[20]: [3, 5]


 

>
>    - 
>    
>    Do we still have them in our codebase or has it been removed ?
>    Moreover, I would like to know a good usecase for this.
>    
> Feel free to add the points I might have overlooked here.
>
> -------------------
> Kshitij Saraogi
>


Amit Kumar

 

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