GSOC 2016: mutivariate factorization and univariate factorization over global fields

[Daniel Nichols]

Hello! My name is Dan Nichols, and I am a graduate student in the mathematics PhD program at the University of Massachusetts Amherst. I'm working on applying for GSOC 2016 and I'm very interested in some of the SymPy projects, including the two ideas concerning polynomial factorization. I've done a lot of reading on this topic as a part of my thesis work, and this seems like a great opportunity to put that knowledge to a practical use.

Before I submit my application, can I ask for some clarification about the goal of the idea "Multivariate polynomials and factorization"? I understand general-purpose factorization algorithms (e.g. Van Hoeij) which involve factoring over a finite field, hensel lifting, and then recombining factors with something like LLL. And I have read the 2004 paper by Bostan, Lecerf, etc. on applying this method to multivariate factorization. Is the main goal of the project just to improve the current implementation of the method in Wang's 1978 paper by using more efficient multivariate arithmetic and GCD? Or is the goal more generally to explore ways to improve SymPy's multivariate factorization?

I notice from looking at factortools.py that multivariate factorization over finite fields is not implemented yet. As an additional goal of this project, it could be interesting to implement this, perhaps following the 1997 paper by Bernardin and Monagan. I'm also very interested in another project idea concerning univariate factorization over global fields, so I will certainly apply for that one too. I have read Van Hoeij's paper on factoring over global fields and I think this would be a very useful project.

Thanks very much for your help, and I hope to have a chance to contribute to SymPy this summer!

     -Dan

[Jason Moore]

Daniel,

You may or may not get much feedback at this late in the game. The proposals are due tomorrow. You will also need to submit a patch to be considered.

Here is our application info: https://github.com/sympy/sympy/wiki/GSoC-2016-Student-Instructions

Best to type up whatever you can come up with on your own and get a patch in ASAP!

Jason
moorepants.info
+01 530-601-9791

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