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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