Hi Alejandro,

Yes, we would still like to have CAD. I believe the work on it has
stalled probably because mmaaz-git is busy with other things. I think
a first step would be to try to finish the PR that did not get merged
by taking the commits from there, rebasing them to current master, and
then opening a new PR.

Oscar

On Fri, 21 Mar 2025 at 18:12, Alex Garcia <[email protected]> wrote:
>
> Hello to the entire SymPy community!
>
> My name is Alejandro García Prada, and I am a third-year student pursuing a 
> Double Degree in Mathematics and Software Engineering at Universidad Rey Juan 
> Carlos in Madrid, Spain.
>
> I am interested in the Cylindrical Algebraic Decomposition (CAD) project. I 
> have been studying the topic for several weeks through the references listed 
> on the ideas page, and I have also read with interest the existing PRs 
> related to it. From what I’ve seen, CAD is an algorithm with doubly 
> exponential worst-case complexity. However, there are several approaches to 
> reduce this algorithmic complexity. One of them is using the Hong projection 
> operator, for which there is already an open PR: 
> https://github.com/sympy/sympy/pull/26785.
>
> I would like to know the current status of this algorithm. As far as I 
> understand, the two main PRs currently related to this topic are the one 
> mentioned above and this one, which deals with computing subresultants that 
> could be used for the CAD algorithm: 
> https://github.com/sympy/sympy/pull/27088.
>
> Do you think a good approach to developing this idea would be to continue 
> working from the code by mmaaz-git (author of the mentioned PRs), or would it 
> be better to start from scratch? Are there any additional PRs or SymPy 
> modules that you consider essential to be familiar with in order to take on 
> this project?
>
> Finally, I would like to mention that I have also read about some 
> improvements to the algorithm, such as TTICAD, which are detailed in the 
> following document: 
> https://davidjohnwilson.github.io/publications/djwthesis.pdf. While it may 
> not be applicable in all cases, it helps avoid some unnecessary 
> decompositions in certain situations.
>
> Thank you very much in advance. I truly appreciate any feedback, additional 
> guidance, or corrections.
>
> Best regards,
> Alejandro
>
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