I just think of another idea in number theory that may be pursuing: *General number field sieve*.
As it's written here [0] that Sage (at that time) only supported *quadratic sieve* and *elliptic curve factorization *for factoring integers, so I think having the general number field sieve could be another helpful and nice addition for Sage. [0]: https://github.com/sagemath/sage/blob/a89f81d7783df2d4e4a187bf209e94d128301f83/src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/integer_factorization.rst 在2022年4月12日星期二 UTC+8 18:36:21<Jing Guo> 写道： > Dear all and mentors, > > I have background knowledge in math (graph theory, number theory, > commutative algebra, and algebraic geometry) and computer science, so I am > interested in the following two projects: > > 1. Improve Height Functionality > 2. Edge connectivity and edge disjoint spanning trees in digraphs > > However, I do have some questions that are not answered by the > documentation and/or project descriptions. I was wondering that could you > please help me clarify? > > 1. For the first project, it's mentioned that interested participants > should know "basic algebraic geometry and number theory". So I was > wondering that could you clarify more specifically what one needs to know: > Does one need to know schemes and elliptic curves? Being able to read and > understand Krumm's and Kutz15 [1] papers? First chapter of Hartshorne > and/or "Ideals, Varieties, and Algorithms"? > > 2. While the second project is interesting on its own, I have a potential > project idea to suggest: *Odd-cycle transversal* [0], which removes some > vertices in a graph to make it bipartite. > > After doing a simple search in the source code, I could not find anything > related to this, so I think it may be a nice addition to Sage. I have > experience implementing relevant approximation, heuristics, and (recent) > FPT (fixed-parameter tractable) algorithms in Python (with networkx) and > C++ as part of my undergraduate research project. > > Thank you for your time. > > Jing > > [1]: https://en.wikipedia.org/wiki/Odd_cycle_transversal > [2]: https://arxiv.org/abs/1210.6246 > > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-gsoc/9568602d-feb4-4d96-a4f4-477492e7f9d2n%40googlegroups.com.
