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feat(LinearAlgebra/Multilinear/DirectSum, LinearAlgebra/DirectSum/{PiTensorProduct,Finsupp}): interaction between `MultilinearMap` and `DirectSum`, and between `PiTensorProduct` and `DirectSum`
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This does three things:
MultilinearMap.fromDirectSumEquiv(inLinearAlgebra/MultilinearMap/DirectSum.lean) calculatesMultilinearMaps on a family ofDirectSums. More precisely, if 'ιis aFintype, ifκ iis a family of types indexed byιand we have aR-moduleM i jfor everyi : ιandj : κ i, this is the linear equivalence betweenΠ p : (i : ι) → κ i, MultilinearMap R (fun i ↦ M i (p i)) M'andMultilinearMap R (fun i ↦ ⨁ j : κ i, M i j) M'`.PiTensorProduct.directSum(inLinearAlgebra/DirectSum/PiTensorProduct.lean): the distributivity property of aPiTensorProductwith respect toDirectSums in all its arguments.finsuppPiTensorProduct(inLinearAlgebra/DirectSum/Finsupp.lean): Ifιis aFintype,κ iis a family of types indexed byιandM iis a family ofR-modules indexed byι, then the tensor product of the familyκ i →₀ M iis linearly equivalent to∏ i, κ i →₀ ⨂[R] i, M i.
- [x] depends on: #11152
- [x] depends on: #11196