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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