Multivariate Resultants

[Nikoleta-v3]

Hello all

My name is Nikoleta Glynatsi. I am a PhD student at the School of Mathematics, Cardiff University. My field of research is Game Theory and I am software developer.

I have received a fellowship from the Software Sustainability Institute, I am a contributor to the Axelrod Python library and the main developer of Arcas, a python tool designed to help with collecting academic articles from various APIs.

I have been working with the programming language Python for the past two years and I am an active member of the community. I have at attended  PyCon UK 2016, 2017 and Pycon Namibia 2017. I have given talks to all these events (https://nikoleta-v3.github.io/talks/) and I am one of the organisers of Django Girls UK.

I’ve been using SymPy regularly for my research for the past two years. One of my recent areas of focus has been resultant theory. There are a few resultants implemented within the SymPy such as, Sylvester's and Bezout’s

(https://github.com/sympy/sympy/blob/master/sympy/polys/subresultants_qq_zz.py).

However, there are not any multivariate resultants within the library.

I have implemented the following two multivariate resultants,

• Dixon's. Reference: https://dl.acm.org/citation.cfm?doid=190347.190372

• Macaulay's. Reference: https://dl.acm.org/citation.cfm?id=550525

The source code is available on GitHub: https://github.com/Nikoleta-v3/resultant-theory and I have also written suitable tests for each implementation.

I understand that the SymPy team would prefer contributions to already existing code or work on ideas that are listed on the Project Ideas Page.

However, I was wondering if you would find any of the above resultants useful and would be interested in adding them to the library.

Thank you very much for your time.

Kind regards

Nikoleta

[Aaron Meurer]

That project ideas page isn't very complete. A much better ideas page
is the GSoC ideas page
https://github.com/sympy/sympy/wiki/GSoC-2018-Ideas, or even the issue
tracker.

But really any mathematics that is generally useful, well established,
and symbolic in nature is in scope for SymPy. Do these multivariate
resultants fit these criteria? I think they do, but I'm not entirely
familiar with them so I can't say for sure.

Aaron Meurer

[Nikoleta-v3]

Thank you for your reply Aaron. 

I believe that the multivariate resultants are a good follow up from what is already within the library,

I will go ahead and open a pull request.

Kind regards

Nikoleta