Strict transform of an ideal in Cox ring #4154
Conversation
TODO: tests, docstrings, documentation
Codecov ReportAttention: Patch coverage is
Additional details and impacted files@@ Coverage Diff @@
## master #4154 +/- ##
==========================================
- Coverage 84.40% 84.35% -0.05%
==========================================
Files 656 663 +7
Lines 87247 87879 +632
==========================================
+ Hits 73641 74133 +492
- Misses 13606 13746 +140
|
|
@paemurru : Just a question, because this has been sitting here for 2 weeks now. What is the status here? Are you making progress on this? Are you waiting for comments from someone else? If so, please ping this person. |
|
@afkafkafk13 I am working on this, this will probably stay as a draft pull request for quite some time. The current code only handles simple examples, the general case is a bit more complicated. The proof that it works uses a lot of notation, so is not suitable for a docstring or comment and must be typed in LaTeX. So it probably should be included in a research paper, unless an existing reference is found. Essentially, we have an abelian group homomorphism, in general not a C-algebra homomorphism and in general not unique, between the Cox rings that takes homogeneous ideals to homogeneous ideals. And the image of a homogeneous ideal is its total transform. |
Still need a corresponding function for ideals.
To match the order of the documentation.
There was a problem hiding this comment.
Thank you for your work here @paemurru. As I understand, these things have not yet been written up or implemented properly and it looks like you took care of working out the details. That said, I have to admit that I am probably not in the position to check all the mathematical details of this implementation, but I feel that this is also why we have people like you on board: You probably know best what's correct here and I would like to trust you with this.
From what I can see, the contributions to the code base seem to fit with the existing code. I left some comments to indicate potential for streamlining a bit more. Let me know what you think.
Co-authored-by: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com>
Co-authored-by: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com>
Co-authored-by: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com>
Co-authored-by: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com>
Co-authored-by: Lars Göttgens <lars.goettgens@gmail.com>
Co-authored-by: Lars Kastner <lkastner@users.noreply.github.com>
Also: add more tests, move `@req` from `cox_ring_module_homomorphism` to `strict_transform`, `total_transform` and `strict_transform_with_index`. Changed `minimal_supercone` to `minimal_supercone_indices`, which is what is needed for `minimal_supercone_coordinates`, which is what I actually need for strict transforms. Everything should be fixed now and should work properly.
Also fix `minimal_supercone_coordinates` and add alias `minimal_generator`.
Add test for nonsimplicial, add comment to `minimal_supercone_coordinates` for the nonsimplicial case.
Co-authored-by: Lars Kastner <lkastner@users.noreply.github.com>
Done.