Hi Pedro,
The exterior algebra is a subclass of the Clifford algebra (as it is a
special case), and the problem is the basis is indexed by subsets of {1,
..., n}, which is a bit wasteful in terms of memory and manipulations.
These are much more compactly written as integers with n bits. So the first
step would be to change the implementation to use these. One of the
fundamental principles of that project would be to make the exterior
algebras very fast over a variety of rings in order to compute quotients
and modules. As mentioned in the description, another related project would
be combine the polynomial ring implementation with the exterior algebra to
compute natively graded-commutative algebras.
Best,
Travis
On Tuesday, April 5, 2022 at 6:05:12 PM UTC+9 [email protected] wrote:
> Hello everyone,
>
> I'm Pedro Orlando and I am currently doing a double degree between the
> State University of Campinas (Unicamp), Brazil and Télécom Paris, France.
> At Unicamp I was in the last year of my BSc in Applied Mathematics, and now
> I'm specialising in Applied Algebra and Theoretical Computer Science at
> Télécom Paris during the double degree.
>
> The Applied Maths syllabus at Unicamp is quite open-ended and, as such, I
> dedicated about half of my graduation to pure mathematics, and the other
> half to algorithmics.
> At Télécom, I've had, most notably, courses dedicated to the
> implementation of graph algorithms and even an entire semester dedicated to
> using Sage for algebraic applications, and with it I gained some experience
> with its uses.
>
> Albeit never having worked with open-source per se, I'm very passionate
> about it. In terms of experience, however, I have worked for two years as a
> full-stack developer using Python, C++ and other languages (SQL,
> javascript, shellscript, ...), even acting as code maintainer for a while,
> and thus I am quite accustomed to the git workflow of big projects; I have
> even already started getting acquainted with your development flow by
> making a small contribution to a documentation ticket #33271
> <https://trac.sagemath.org/ticket/33271> in Sage.
>
> From the ideas list, the two topics which have interested me the most were:
> - Rewrite exterior algebra and implement Gröbner bases
> - Edge connectivity and edge disjoint spanning trees in digraphs
>
> The first idea is very closely related to the subjects I've studied in
> Applied Algebra, with special mention to Gröbner bases which were often
> used during courses (I might need a refresher though). In this topic, I'd
> love further clarification on ticket #32369
> <https://trac.sagemath.org/ticket/32369> for rewriting exterior algebra
> (namely, the starting point: is the problem in the ExteriorAlgebra class in
> algebras/clifford_algebra.py ?). This project might require me to
> understand Cython more deeply, as well as find out how one would go about
> implementing the bonus "ambitious" goal, but I'm up for the task of
> learning these!
>
> As for the second one, I've always been very interested in graph theory
> and their algorithms, this being one of my favourite topics, and it seems
> to be very well documented, discussed and explained in Sage's trac, even
> containing a paper with the related algorithm, so I'm ready to dive
> head-first into all of the discussions relating to this project. Should
> this be of interest to anyone, I have a small project on GitHub
> <https://github.com/scramblerdoodle/MITRO209_densest_subgraph>
> implementing an algorithm for an approximation to the densest subgraph
> problem in linear time.
>
> Cheers and all the best,
> Pedro
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