There is some preliminary work 
at https://github.com/sympy/sympy/issues/23665 that aims to improve 
exponentiation of certain types of polynomials. It might be a good GSOC 
task.

/c
On Saturday, March 18, 2023 at 9:18:10 PM UTC-5 Chris Smith wrote:

> update: When reviewing this it is not clear to me how much of this already 
> made it in in some form or another. Look for PRs be author:pernici that 
> were committed. Search also for lpoly.
>
> /c
>
> On Saturday, March 18, 2023 at 11:57:58 AM UTC-5 Chris Smith wrote:
>
>> There was some promising work (as I recall) that stalled at 
>> https://github.com/sympy/sympy/pull/609. See discussion there for idea 
>> to get that work from level 0 representation of Poly to level 1.
>>
>> /c
>>
>> On Friday, March 17, 2023 at 8:16:48 PM UTC-5 Oscar wrote:
>>
>>> On Fri, 17 Mar 2023 at 20:39, Aaron Meurer <[email protected]> wrote: 
>>> > 
>>> > On Sun, Mar 12, 2023 at 3:04 PM Atahan Haznedar 
>>> > <[email protected]> wrote: 
>>> > > 
>>> > > Hello Oscar, 
>>> > > 
>>> > > Sorry for the late reply, after seeing the post you have made, I can 
>>> pretty much can say that I am really excited! There are lots of things on 
>>> the polynomial side to be done as far as I can see. I am not that familiar 
>>> with Sympy at the moment so probably I am just going to tinker and try to 
>>> get used to using Sympy in my leisure time by implementing some examples 
>>> and algorithms that I have studied so far. So probably I am not going to be 
>>> able to make a contribution soon. Is this a problem for my submission on 
>>> GSoC? 
>>> > 
>>> > Most polynomial algorithms are already implemented in SymPy, but if 
>>> > you find something that's missing that would definitely be a good 
>>> > submission. Otherwise, I would recommend finding some bugs to fix 
>>> > (e.g. from the sympy issue tracker). That's generally the best way to 
>>> > learn about the codebase in my experience. 
>>>
>>> While many of the most needed algorithms are implemented there is 
>>> plenty of scope to improve those implementations or to implement 
>>> better algorithms. More commonly though the problem is that the 
>>> algorithms are not being used very well by the rest of SymPy. Groebner 
>>> bases are a good example here because the algorithms are there and 
>>> they work but: 
>>>
>>> 1. By default Groebner uses the slower buchberger algorithm even 
>>> though f5b is implemented and similarly many places want a zero 
>>> dimensional basis but don't make use of the existing fglm algorithm. 
>>> 2. The code that consumes the output of Groebner can be massively 
>>> improved. The code to solve systems of polynomial equations in solve 
>>> and nonlinsolve uses Groebner but really does not do a good job of 
>>> processing the output of groebner: 
>>> https://github.com/sympy/sympy/issues/24868 
>>>
>>> The number one priority around Groebner bases is not implementing new 
>>> algorithms to compute them but rather improving the way that the 
>>> existing algorithms are used in the codebase. 
>>>
>>> -- 
>>> Oscar 
>>>
>>

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