[Merged by Bors] - refactor(LinearAlgebra/QuadraticForm/Basic): Use bilinear maps for the companion#10097
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[Merged by Bors] - refactor(LinearAlgebra/QuadraticForm/Basic): Use bilinear maps for the companion#10097
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Here are the benchmark results for commit 4a55b3a. Benchmark Metric Change
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+ ~Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit instructions -19.2%
- ~Mathlib.LinearAlgebra.QuadraticForm.Basic instructions 16.9% |
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Thank you so much, I would be very happy if we could remove BilinForm entirely from mathlib and this is a big step.
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Co-authored-by: Moritz Doll <[email protected]>
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Here are the benchmark results for commit bdecf41. Benchmark Metric Change
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- ~Mathlib.LinearAlgebra.QuadraticForm.Basic instructions 16.8% |
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…e companion (#10097) This PR replaces the companion `(B : BilinForm R M)` of a quadratic form with a bilinear map `(B : M →ₗ[R] M →ₗ[R] R)`. This is intended as a baby step towards generalising quadratic forms to quadratic maps. In the future we could allow for companion bilinear or even sesquilinear maps into an `R`-module. Co-authored-by: Christopher Hoskin <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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…e companion (#10097) This PR replaces the companion `(B : BilinForm R M)` of a quadratic form with a bilinear map `(B : M →ₗ[R] M →ₗ[R] R)`. This is intended as a baby step towards generalising quadratic forms to quadratic maps. In the future we could allow for companion bilinear or even sesquilinear maps into an `R`-module. Co-authored-by: Christopher Hoskin <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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| variable [Monoid S] [Monoid T] [DistribMulAction S R] [DistribMulAction T R] | ||
| variable [SMulCommClass S R R] [SMulCommClass T R R] | ||
| variable [SMulCommClass R S R] [SMulCommClass S R R] [SMulCommClass T R R] [SMulCommClass R T R] |
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This looks like a regression to me; one implies the other so there should be no need for both
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…lar valued bi `LinearMap` (#10238) Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps. The main change is to `LinearAlgebra/QuadraticForm/Basic`, but this necessitates changes throughout `LinearAlgebra/QuadraticForm/`. Minor changes are also required elsewhere: - `LinearAlgebra/CliffordAlgebra/` - `LinearAlgebra/Matrix/PosDef` - `LinearAlgebra/SesquilinearForm` - A number of additional results about tensor products and linear maps are also required. Co-authored-by: Eric Wieser <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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…lar valued bi `LinearMap` (#10238) Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps. The main change is to `LinearAlgebra/QuadraticForm/Basic`, but this necessitates changes throughout `LinearAlgebra/QuadraticForm/`. Minor changes are also required elsewhere: - `LinearAlgebra/CliffordAlgebra/` - `LinearAlgebra/Matrix/PosDef` - `LinearAlgebra/SesquilinearForm` - A number of additional results about tensor products and linear maps are also required. Co-authored-by: Eric Wieser <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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…lar valued bi `LinearMap` (#10238) Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps. The main change is to `LinearAlgebra/QuadraticForm/Basic`, but this necessitates changes throughout `LinearAlgebra/QuadraticForm/`. Minor changes are also required elsewhere: - `LinearAlgebra/CliffordAlgebra/` - `LinearAlgebra/Matrix/PosDef` - `LinearAlgebra/SesquilinearForm` - A number of additional results about tensor products and linear maps are also required. Co-authored-by: Eric Wieser <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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…lar valued bi `LinearMap` (#10238) Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps. The main change is to `LinearAlgebra/QuadraticForm/Basic`, but this necessitates changes throughout `LinearAlgebra/QuadraticForm/`. Minor changes are also required elsewhere: - `LinearAlgebra/CliffordAlgebra/` - `LinearAlgebra/Matrix/PosDef` - `LinearAlgebra/SesquilinearForm` - A number of additional results about tensor products and linear maps are also required. Co-authored-by: Eric Wieser <[email protected]> Co-authored-by: Christopher Hoskin <[email protected]>
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This PR replaces the companion
(B : BilinForm R M)of a quadratic form with a bilinear map(B : M →ₗ[R] M →ₗ[R] R).This is intended as a baby step towards generalising quadratic forms to quadratic maps. In the future we could allow for companion bilinear or even sesquilinear maps into an
R-module.I've previously tried to go straight to quadratic maps (#7569) but it's making for a PR that is too big and unwieldy. This PR is hopefully more achievable.