Implementation of Ore modules#38703
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Quick question: why is it necessary that Also: love that you're creating these intermediate facilities that can be relevant in their own right, instead of just putting all of this in the implementation of Anderson motives. |
Well, it is not for the definition. But for the implementation, it is really useful as we want to represent the map |
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Fix another E302 "expected 2 blank lines, found " error of pycodestyle-minimal (sorry, blame the TGV's WiFi)
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Documentation preview for this PR (built with commit c7a800b; changes) is ready! 🎉 |
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We had many discussions with Xavier, and he did everything I wanted to be done. He told me that he also did corrections asked by @fchapoton, so except if there is another thing he wants to add, now this PR looks ready to be merged for me. |
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Hi! Understood. I removed my review request. |
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Sorry, what was your review request? I can address it, no problem! |
No, you're good! I meant the fact that I was (or maybe self-requested) as a reviewer! Everything is fine! :) |
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Ah ok, I then misunderstood your comment. |
sagemathgh-38703: Implementation of Ore modules This PR implements modules over Ore polynomial rings. More precisely, if $A[X;\theta,\partial]$ is a Ore polynomial ring, we propose an implementation of finite free modules $M$ over $A$ equipped with a map $f : M \to M$ such that $f(ax) = \theta(a) f(x) + \partial(a) x$ for all $a \in R$ and $x \in M$. Such a map is called *pseudolinear* and it endows `M` with a structure of module over $A[X;\theta,\partial]$ (the map $f$ corresponding to the multiplication by $X$). This PR includes: - an implementation of the category of Ore modules - an implementation of Ore modules, their submodules and their quotients (with an option to give chosen names to elements in a distinguished basis) - a constructor to create quotients of the form $A[X;\theta,\partial] / A[X;\theta,\partial]P$ - an implementation of morphisms between Ore modules, including methods for computing kernels, cokernels, images and coimages This is the second step (after PR sagemath#38650) towards the implemetation of Anderson motives. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [ ] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies sagemath#38650: pseudomorphisms URL: sagemath#38703 Reported by: Xavier Caruso Reviewer(s): Rubén Muñoz--Bertrand
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This PR implements modules over Ore polynomial rings.
More precisely, if$A[X;\theta,\partial]$ is a Ore polynomial ring, we propose an implementation of finite free modules $M$ over $A$ equipped with a map $f : M \to M$ such that $f(ax) = \theta(a) f(x) + \partial(a) x$ for all $a \in R$ and $x \in M$ .$A[X;\theta,\partial]$ (the map $f$ corresponding to the multiplication by $X$ ).
Such a map is called pseudolinear and it endows
Mwith a structure of module overThis PR includes:
This is the second step (after PR #38650) towards the implemetation of Anderson motives.
📝 Checklist
⌛ Dependencies
#38650: pseudomorphisms