[Merged by Bors] - feat(LinearAlgebra/PiTensorProduct): PiTensorProducts over Finsupp, DFinsupp, and DirectSum#32456
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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>
PiTensorProduct and MultilinearMapPiTensorProduct with Finsupp, DFinsupp, and DirectSum
PiTensorProduct with Finsupp, DFinsupp, and DirectSumPiTensorProducts over Finsupp, DFinsupp, and DirectSum
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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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…`, `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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PiTensorProducts over Finsupp, DFinsupp, and DirectSumPiTensorProducts over Finsupp, DFinsupp, and DirectSum
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…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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Adds linear equivalences for
PiTensorProducts taken overFinsupp,DFinsupp, andDirectSum. The main definitions are:PiTensorProduct.ofDFinsuppEquivis the linear equivalence of tensor products overDFinsuppto aDFinsuppof tensor productsPiTensorProduct.ofFinsuppEquivis the linear equivalence of tensor products overFinsuppto aFinsuppof tensor productsPiTensorProduct.ofDirectSumEquivis the linear equivalence of tensor products over a direct sum to the direct sum over tensor products