GSoC 2023: Implementing functions from toric topology #35640
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### Implementing Golod (simplicial) complexes <!-- Describe your changes here in detail. --> <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes #12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> This is a part of #35640 (GSoC 20223), relies on #35430 (bigraded Betti numbers). Added two methods: `is_golod()` and `is_minimally_non_golod()`, defined for simplicial complexes. These are significant invariants used in toric topology. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x ]`. --> - [x] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [x] I have updated the documentation accordingly. URL: #35802 Reported by: Ognjen Petrov Reviewer(s): Travis Scrimshaw
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### Description This is a part of sagemath#35640 (GSoC 2023). Implementing moment-angle complexes, one of the key constructions in toric topology. Many methods are yet to be implemented, which will be closely related to the simplicial complex over which the moment-angle complex is constructed. ### Checklist <!-- Put an `x` in all the boxes that apply. It should be `[x]` not `[x ]`. --> - [x] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [x] I have updated the documentation accordingly. ### Dependencies - sagemath#35802 URL: sagemath#35875 Reported by: Ognjen Petrov Reviewer(s): Ognjen Petrov, Travis Scrimshaw
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This pull request expands the functionality of ``bigraded_betti_number()`` methods of a ``SimplicialComplex`` by adding an additional parameter ``verbose``. The ``verbose`` option increases verbosity while computing the invariant by printing the subcomplexes along with their non-trivial homology groups. This PR is a part of sagemath#35640 (GSoC 2023). ### 📝 Checklist - [x] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation accordingly. URL: sagemath#36166 Reported by: Ognjen Petrov Reviewer(s): Ognjen Petrov, Travis Scrimshaw
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Description
This is a meta-issue for the 2023 Google Summer of Code project
The aim of this project is to further expand Sage's library for topology, by implementing various functions from toric topology. Though this field might sound specific, a lot of properties can be viewed combinatorially, and that's why they are particularly interesting. These functions are also of interest to researchers in other fields, not just toric topologists. The main idea is to implement as many functions as possible to broaden the library and further make research in this and related areas much easier.
Mentor: @tscrim
Progress, relevant issues and pull requests
cubical_complex()method ofMomentAngleComplex#36215The text was updated successfully, but these errors were encountered: