Add support for pseudomorphisms #38650
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kwankyu
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@kryzar Please tell me if you have some comment on this PR. |
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Here are some suggestions to enhance the doc:
Co-authored-by: Antoine Leudière <[email protected]>
Co-authored-by: Antoine Leudière <[email protected]>
Co-authored-by: Antoine Leudière <[email protected]>
Co-authored-by: Antoine Leudière <[email protected]>
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Thanks Xavier! |
kryzar
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Feb 14, 2025
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Also, thank you @ymusleh for the original contribution! |
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Great, thanks! |
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sagemathgh-38650: Add support for pseudomorphisms This PR implements pseudomorphisms. Let $M, M'$ be modules over a ring $R$, $\theta: R \to R$ be a ring homomorphism, and $\delta: R \to R$ be a $\theta$-derivation, which is a map such that $\delta(xy) = \theta(x)\delta(y) + \delta(x)y$. A *pseudomorphism* $f : M \to M$ is an additive map such that $f(\lambda x) = \theta(\lambda)f(x) + \delta(\lambda) x$ for all $\lambda$ and $x$. This PR is based on a former PR by @ymusleh (that I could not find, I don't know why). ### 📝 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. - [x] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies URL: sagemath#38650 Reported by: Xavier Caruso Reviewer(s): Antoine Leudière, Kwankyu Lee, Xavier Caruso
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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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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 pseudomorphisms.
Let$M, M'$ be modules over a ring $R$ , $\theta: R \to R$ be a ring homomorphism, and $\delta: R \to R$ be a $\theta$ -derivation, which is a map such that $\delta(xy) = \theta(x)\delta(y) + \delta(x)y$ .$f : M \to M$ is an additive map such that $f(\lambda x) = \theta(\lambda)f(x) + \delta(\lambda) x$ for all $\lambda$ and $x$ .
A pseudomorphism
This PR is based on a former PR by @ymusleh (that I could not find, I don't know why).
📝 Checklist
⌛ Dependencies