Report: Workshop on Efficient Linear Algebra for Gröbner Basis Computations

As you may know, today is the last day of the wokshop on Efficient Linear Algebra for Gröbner Basis Computations that Christian Eder, Burcin Eröcal, Alexander Dreyer and I organised.

I have to say that I am quite pleased with how the workshop played out. We planned the whole thing to be hands on: people were strongly encouraged to work on projects, i.e., to write code preferably together, in addition to attending talks. Those who attended a Sage Days workshop in the past, will know what workshop format I am referring to.

In the beginning adoption was a bit slow. The idea of simply ordering pizza to write code till late seemed rather alien. However, in the end, it worked out I think and, looking back, the workshop reminded me of Sage Days 2 which was  my first Sage workshop and which left a considerable impression on me. Sage Days 2 in October 2006 – which was my first Sage Days – was this “magical” workshop where people found each other who were equally obsessed with fast open-source mathematics software. Attendees had a lot to say to each other and many projects (and friendships) got started at these early Sage workshops. For example, I got hold of Gregory Bard’s M4RI code at Sage Days 3. My involvement in Sage has fundamentally shaped me as a researcher and Sage Days 2 set the bar very high for what I consider a good workshop. One could say that Sage Days 2 shaped me as a workshop organiser. Thank you William!

Anyway, I haven’t felt the same buzz about Sage workshops in a while, I guess thing become routine. Or it’s just that the “bureaucracy” – most of which is necessary – doesn’t work so well with that pioneering spirit thing. However, something similar to early Sage Days – in my mind – happened at this workshop.

Many people attended who had their own open-source implementation of F4 or linear algebra routines suitable for the algorithm. So people had a lot to say to each other: “How do you deal with this …” type of things. For example, we had Severin (parallelGBC), Daniel (F4v6), Bradford (LELA), Alexander and Michael (PolyBoRi), Fayssal (LELA stuff), Christian (C++ F5), Brice (LinBox), … Also, Jean-Charles attended which provided a good opportunity inquire about his implementation. Overall, this provided an atmosphere which – for me – was a lot more engaging than the usual conference/workshop where you listen to a bunch of talks and then talk about anything but research over dinner.

On a meta point, it also seems there is a general movement towards much more open development models. Most of the developers at the workshop maintained bitbucket or github pages with their code which actively encourage collaboration. It’s quite a step forward from the old days when the best you could hope for was for a rather closed research groups to dump a source tarball every once in a while.

Okay, buzz or no buzz, what got done?

  • First of all, Alexander uploaded all videos for all talks and linked them on our wiki page. Also, slides for all talks should be available or become available soon, if they are missing in 2-3 days please bug me about it.
  • Burcin and Oleksandr worked on turning Severin’s code into a generic framework to test linear algebra implementations. Burcin promised to finish it over the weekend.
  • Oleksandre started the same with Daniel’s code. So hopefully, we’ll have some “frameworks” soon to test our linear algebra ideas.
  • Brice implemented multiplication of finite extension field matrices using prime-slicing in LinBox and fixed a bunch of bugs in LinBox 1.3.x. As a result, we are very close to upgrading LinBox in Sage to a more recent version.
  • Alexander and Michael worked on PolyBoRi’s interface to M4RI so that conversion is cheaper. Also, PolyBori will use M4RI’s PNG writer to export matrices in the future which uses less memory and is faster.
  • Emmanuel worked on CADO-NFS’ Wiedemann such that it (again) supports primes > 2. He’s close I believe to get it working.
  • Bradford worked on improving splicing in LELA (converting a matrix to the internal format) over GF(2).
  • Jakob got sucked into decrypting g++ template error messages and
  • I played a bit with LELA (see projects page) and worked on upgrading LinBox in Sage (see #12883).

Thanks everyone involved.


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