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[Merged by Bors] - feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum#32456

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[Merged by Bors] - feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum#32456
morrison-daniel wants to merge 99 commits intoleanprover-community:masterfrom
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@morrison-daniel morrison-daniel commented Dec 5, 2025

Adds linear equivalences for PiTensorProducts taken over Finsupp, DFinsupp, and DirectSum. The main definitions are:

  • PiTensorProduct.ofDFinsuppEquiv is the linear equivalence of tensor products over DFinsupp to a DFinsupp of tensor products
  • PiTensorProduct.ofFinsuppEquiv is the linear equivalence of tensor products over Finsupp to a Finsupp of tensor products
  • PiTensorProduct.ofDirectSumEquiv is the linear equivalence of tensor products over a direct sum to the direct sum over tensor products

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morel and others added 30 commits March 4, 2024 17:45
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
…community/mathlib4 into SM.PiTensorProduct.DirectSum
…community/mathlib4 into SM.PiTensorProduct.DirectSum
Co-authored-by: Eric Wieser <efw@google.com>
Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>
@github-actions github-actions bot removed the large-import Automatically added label for PRs with a significant increase in transitive imports label Dec 5, 2025
@morrison-daniel morrison-daniel changed the title feat(LinearAlgebra/Multilinear): interactions of PiTensorProduct and MultilinearMap feat(LinearAlgebra/Multilinear): interactions of PiTensorProduct with Finsupp, DFinsupp, and DirectSum Dec 5, 2025
@morrison-daniel morrison-daniel changed the title feat(LinearAlgebra/Multilinear): interactions of PiTensorProduct with Finsupp, DFinsupp, and DirectSum feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum Dec 6, 2025
@morrison-daniel morrison-daniel removed the WIP Work in progress label Dec 6, 2025
@morrison-daniel morrison-daniel marked this pull request as ready for review December 6, 2025 02:52
@ocfnash ocfnash self-assigned this Dec 8, 2025
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Thanks!

bors d+

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mathlib-bors bot commented Dec 8, 2025

✌️ morrison-daniel can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@ghost ghost added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Dec 8, 2025
morrison-daniel and others added 4 commits December 8, 2025 16:42
Co-authored-by: Oliver Nash <7734364+ocfnash@users.noreply.github.com>
Co-authored-by: Oliver Nash <7734364+ocfnash@users.noreply.github.com>
remove duplicate fix
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bors r+

mathlib-bors bot pushed a commit that referenced this pull request Dec 9, 2025
…`, `DFinsupp`, and `DirectSum` (#32456)

Adds linear equivalences for `PiTensorProduct`s taken over `Finsupp`, `DFinsupp`, and `DirectSum`. The main definitions are:
* `PiTensorProduct.ofDFinsuppEquiv` is the linear equivalence of tensor products over `DFinsupp` to a `DFinsupp` of tensor products
* `PiTensorProduct.ofFinsuppEquiv` is the linear equivalence of tensor products over `Finsupp` to a `Finsupp` of tensor products
* `PiTensorProduct.ofDirectSumEquiv` is the linear equivalence of tensor products over a direct sum to the direct sum over tensor products
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mathlib-bors bot commented Dec 9, 2025

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum [Merged by Bors] - feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum Dec 9, 2025
@mathlib-bors mathlib-bors bot closed this Dec 9, 2025
@morrison-daniel morrison-daniel deleted the multilinear-pitensor branch December 9, 2025 01:16
mathlib-bors bot pushed a commit that referenced this pull request Dec 10, 2025
…and map for the tensor product of dual space (#32613)

Constructs a basis for `PiTensorProduct` given bases for the component spaces and defines maps between the tensor product of dual spaces and the dual of a tensor product.

Main definitions:
* `Basis.piTensorProduct`: Given bases `b : Π i, Basis (κ i) R (M i)` for each component space `M i`, constructs a basis for `⨂[R] i, M i` indexed by `Π i, κ i` defined by sending `p : Π i, κ i` to `⨂ₜ[R] i, (b i) (p i)`.

* `PiTensorProduct.dualDistrib`: The canonical linear map from `⨂[R] i, Dual R (M i)` to
  `Dual R (⨂[R] i, M i)`, sending `⨂ₜ[R] i, f i` to the composition of
  `PiTensorProduct.map f` with the linear equivalence `⨂[R] i, R →ₗ R` given by multiplication.

* `PiTensorProduct.dualDistribEquiv`: A linear equivalence between `⨂[R] i, Dual R (M i)`
  and `Dual R (⨂[R] i, M i)` when all `M i` are finite free modules. If
  `f : (i : ι) → Dual R (M i)`, then this equivalence sends `⨂ₜ[R] i, f i` to the composition of
  `PiTensorProduct.map f` with the natural isomorphism `⨂[R] i, R ≃ R` given by multiplication.

- [x] depends on: #32456
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