You can see some of the ideas that are already in sympy idea page in wiki.

On Sunday, March 3, 2024 at 10:10:08 AM UTC+5:30 mariyala...@gmail.com 
wrote:

>
> I am writing to express my interest in contributing to the SymPy project 
> for the GSoC 2024.
>
> I have been exploring SymPy and find its mission and projects align well 
> with my skills and interests. I am particularly interested in contributing 
> to the areas that could enhance the functionality and performance of SymPy.
>
> Before I proceed with drafting my proposal, I would greatly appreciate it 
> if you could provide some guidance on the areas where you are currently 
> seeking contributions. Are there any specific features, enhancements, or 
> areas of the codebase that you would like to see improved or expanded in 
> the near future?
>
> I am eager to contribute in a way that would be most beneficial to the 
> SymPy community and your insights would be invaluable in helping me to 
> align my contributions to the SymPy.
>
> Mariyala Rohith   
> On Sunday 3 March 2024 at 00:16:10 UTC+5:30 Oscar wrote:
>
>> On Sat, 2 Mar 2024 at 17:16, Mariyala Rohith <mariyala...@gmail.com> 
>> wrote: 
>> > 
>> > Dear Sympy Mentors, 
>> > 
>> > I hope this message finds you well! 
>> > I am writing to propose a couple of enhancements to the Pow class in 
>> SymPy that I believe could extend its functionality and usefulness. 
>> > 
>> > 1. Roots of Unity: I propose to add a method to the Pow class that 
>> checks if an expression represents a root of unity. This would involve 
>> checking if a complex number, when raised to some positive integer power, 
>> equals 1. This feature could be useful in various areas of mathematics, 
>> including numbers theory and algebra. 
>>
>> There is already a way to do this in SymPy although it is perhaps not 
>> obvious: 
>>
>> In [52]: is_root_of_unity = lambda e: minpoly(e, 
>> polys=True).is_cyclotomic 
>>
>> In [53]: is_root_of_unity(-sqrt(5)/4 - S(1)/4 - I*sqrt(S(5)/8 - 
>> sqrt(5)/8)) 
>> Out[53]: True 
>>
>> In [54]: is_root_of_unity(sqrt(5)) 
>> Out[54]: False 
>>
>>
>> Oscar 
>>
>

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