[Merged by Bors] - feat(Algebra/Module): presentation of the cokernel of a linear map#18332
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[Merged by Bors] - feat(Algebra/Module): presentation of the cokernel of a linear map#18332
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…nto unbundled-module-presentation-more-api
PR summary 940bc7bb84Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…nto unbundled-module-presentation-more-api
…re-api' into unbundled-module-presentation-cokernel
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erdOne
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Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
erdOne
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| erw [← Finsupp.apply_linearCombination] | ||
| obtain (r | i) := x | ||
| · erw [pres₂.linearCombination_var_relation] | ||
| dsimp | ||
| · erw [data.π_lift] | ||
| simp |
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These erws are unfortunate but I can't find a way to avoid it.
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Thanks! |
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🚀 Pull request has been placed on the maintainer queue by erdOne. |
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bors merge |
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…18332) If `f : M₁ →ₗ[A] M₂` is a linear map between modules, `pres₂` is a presentation of `M₂` and `g₁ : ι → M₁` is a family of generators of `M₁` (which is expressed as `hg₁ : Submodule.span A (Set.range g₁) = ⊤`), then we provide a way to obtain a presentation of the cokernel of `f`. It requires an additional data `data : pres₂.CokernelData f g₁`, which consists of liftings of the images by `f` of the generators of `M₁` as linear combinations of the generators of `M₂`. Then, we obtain a presentation `pres₂.cokernel data hg₁ : Presentation A (M₂ ⧸ LinearMap.range f)`. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…18332) If `f : M₁ →ₗ[A] M₂` is a linear map between modules, `pres₂` is a presentation of `M₂` and `g₁ : ι → M₁` is a family of generators of `M₁` (which is expressed as `hg₁ : Submodule.span A (Set.range g₁) = ⊤`), then we provide a way to obtain a presentation of the cokernel of `f`. It requires an additional data `data : pres₂.CokernelData f g₁`, which consists of liftings of the images by `f` of the generators of `M₁` as linear combinations of the generators of `M₂`. Then, we obtain a presentation `pres₂.cokernel data hg₁ : Presentation A (M₂ ⧸ LinearMap.range f)`. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
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…18332) If `f : M₁ →ₗ[A] M₂` is a linear map between modules, `pres₂` is a presentation of `M₂` and `g₁ : ι → M₁` is a family of generators of `M₁` (which is expressed as `hg₁ : Submodule.span A (Set.range g₁) = ⊤`), then we provide a way to obtain a presentation of the cokernel of `f`. It requires an additional data `data : pres₂.CokernelData f g₁`, which consists of liftings of the images by `f` of the generators of `M₁` as linear combinations of the generators of `M₂`. Then, we obtain a presentation `pres₂.cokernel data hg₁ : Presentation A (M₂ ⧸ LinearMap.range f)`. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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If
f : M₁ →ₗ[A] M₂is a linear map between modules,pres₂is a presentation ofM₂andg₁ : ι → M₁is a family of generators ofM₁(which is expressed ashg₁ : Submodule.span A (Set.range g₁) = ⊤), then we provide a way to obtain a presentation of the cokernel off. It requires an additional datadata : pres₂.CokernelData f g₁, which consists of liftings of the images byfof the generators ofM₁as linear combinations of the generators ofM₂. Then, we obtain a presentationpres₂.cokernel data hg₁ : Presentation A (M₂ ⧸ LinearMap.range f).