Dear Jamie, Thank you for your interest. There are no specific suggested references, but it is very easy to find the necessary background information on Groebner bases for polynomial rings through a Google search. It is also easy to find information regarding those for the exterior algebra (also somethings known as a skew-commutative polynomial ring or Grassmann algebra). For example, you would quickly find starting points such as
http://www.reduce-algebra.com/reduce38-docs/xideal.pdf For the project itself, you are free to propose whatever you want to do. My dream would be to have a faster native version of graded commutative algebras within Sage that also implements fast GBs (relative to what plural does for us currently). However, if you want to focus specifically on getting the exterior case super quick, that is also fine. Best, Travis On Monday, March 20, 2023 at 1:22:58 PM UTC+9 jamie...@gmail.com wrote: > Hello SageMath team, > > My name is Jamie Kai, I'm at the University of British Columbia in > Vancouver, Canada. I'm in year 1 of a 2-year Second Bachelor of Computer > Science program, and I have a previous BA in Math from McGill University. > > I have experience with Python and Cython programming for large-scale > statistical calculations, and several years of MATLAB and professional > full-stack experience. > > I've also taken several upper-year/grad math courses: advanced linear > algebra (tensor, exterior and symmetric algebras, topological vector > spaces), group theory, analysis (real, complex, harmonic). I have a growing > interest in abstract algebra, so SageMath's list of project ideas this year > is very exciting! > > I am quite interested in submitting a proposal for one of the project > ideas in computational algebra under Travis Scrimshaw, in particular: > *Improve > exterior algebra and Gröbner bases code and expand to graded commutative > algebras* > <https://wiki.sagemath.org/GSoC/2023#Improve_exterior_algebra_and_Gr.2BAPY-bner_bases_code_and_expand_to_graded_commutative_algebras> > > I have a couple of questions: > > Are there any suggested references (books, papers, websites) for > computational ring theory or commutative algebra that I can read to get > some theoretical background? > > Would the 175 hour version of the exterior algebra & Gröbner bases project > include just the first goal of improving performance with Gröbner bases, or > also some work on the case of general graded commutative algebras? > > Cheers, > Jamie > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-gsoc+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-gsoc/a45e665f-3fa9-49ed-9eff-70b918c95db0n%40googlegroups.com.
