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mattrobball
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Great to see this! I will wait for @eric-wieser to take a look.
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| @[reducible] | ||
| def exteriorPower := LinearMap.range (ι R : N →ₗ[R] ExteriorAlgebra R N) ^ n |
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Just to be explicit here
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| @[reducible] | |
| def exteriorPower := LinearMap.range (ι R : N →ₗ[R] ExteriorAlgebra R N) ^ n | |
| abbrev exteriorPower : Submodule R (ExteriorAlgebra R M) := | |
| LinearMap.range (ι R : N →ₗ[R] ExteriorAlgebra R N) ^ n |
(and @[reducible] def is basically the same as abbrev)
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Feb 29, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
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riccardobrasca
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Mar 1, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
kbuzzard
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Mar 12, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
dagurtomas
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Mar 22, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
utensil
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Mar 26, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
xgenereux
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Apr 15, 2024
…tion and notation for the exterior powers of a module (#10744) This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition `exteriorPower R n M` for the `n`th exterior power of the `R`-module `M`; this is of type `Submodule R (ExteriorAlgebra R M)` and defined as `LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n`. It also introduces the notation `Λ[R]^n M` for `exteriorPower R n M`. Note: for a reason that I don't understand, Lean becomes unable to synthesize the `SetLike.GradedMonoid` instance on `fun (i : ℕ) ↦ (Λ[R]^i) M`, so I added it manually in `ExteriorAlgebra/Graded.lean`. I am far from sure that this is the correct solution. Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>
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This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition
exteriorPower R n Mfor thenth exterior power of theR-moduleM; this is of typeSubmodule R (ExteriorAlgebra R M)and defined asLinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n.It also introduces the notation
Λ[R]^n MforexteriorPower R n M.Note: for a reason that I don't understand, Lean becomes unable to synthesize the
SetLike.GradedMonoidinstance onfun (i : ℕ) ↦ (Λ[R]^i) M, so I added it manually inExteriorAlgebra/Graded.lean. I am far from sure that this is the correct solution.