[Merged by Bors] - feat(linear_algebra/bilinear_map): semilinearize bilinear maps #10373
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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By the way, typechecks, so this should be good enough to generalize |
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This PR generalizes most of `linear_algebra/bilinear_map` to semilinear maps. Along the way, we introduce an instance for `module S (E →ₛₗ[σ] F)`, with `σ : R →+* S`. This allows us to define "semibilinear" maps of type `E →ₛₗ[σ] F →ₛₗ[ρ] G`, where `E`, `F` and `G` are modules over `R₁`, `R₂` and `R₃` respectively, and `σ : R₁ →+* R₃` and `ρ : R₂ →+* R₃`. See `mk₂'ₛₗ` to see how to construct such a map. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR generalizes most of `linear_algebra/bilinear_map` to semilinear maps. Along the way, we introduce an instance for `module S (E →ₛₗ[σ] F)`, with `σ : R →+* S`. This allows us to define "semibilinear" maps of type `E →ₛₗ[σ] F →ₛₗ[ρ] G`, where `E`, `F` and `G` are modules over `R₁`, `R₂` and `R₃` respectively, and `σ : R₁ →+* R₃` and `ρ : R₂ →+* R₃`. See `mk₂'ₛₗ` to see how to construct such a map. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR generalizes most of `linear_algebra/bilinear_map` to semilinear maps. Along the way, we introduce an instance for `module S (E →ₛₗ[σ] F)`, with `σ : R →+* S`. This allows us to define "semibilinear" maps of type `E →ₛₗ[σ] F →ₛₗ[ρ] G`, where `E`, `F` and `G` are modules over `R₁`, `R₂` and `R₃` respectively, and `σ : R₁ →+* R₃` and `ρ : R₂ →+* R₃`. See `mk₂'ₛₗ` to see how to construct such a map. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR generalizes most of `linear_algebra/bilinear_map` to semilinear maps. Along the way, we introduce an instance for `module S (E →ₛₗ[σ] F)`, with `σ : R →+* S`. This allows us to define "semibilinear" maps of type `E →ₛₗ[σ] F →ₛₗ[ρ] G`, where `E`, `F` and `G` are modules over `R₁`, `R₂` and `R₃` respectively, and `σ : R₁ →+* R₃` and `ρ : R₂ →+* R₃`. See `mk₂'ₛₗ` to see how to construct such a map. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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This PR generalizes most of
linear_algebra/bilinear_mapto semilinear maps. Along the way, we introduce an instance formodule S (E →ₛₗ[σ] F), withσ : R →+* S. This allows us to define "semibilinear" maps of typeE →ₛₗ[σ] F →ₛₗ[ρ] G, whereE,FandGare modules overR₁,R₂andR₃respectively, andσ : R₁ →+* R₃andρ : R₂ →+* R₃. Seemk₂'ₛₗto see how to construct such a map.