[Merged by Bors] - feat(Algebra/TensorAlgebra): support towers of algebras #6073
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This provide `Algebra R (FreeAlgebra A X)` when `Algebra R A`. This also fixes some diamonds that would arise as a result of this new instance.
… eric-wieser/tower-FreeAlgebra
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eric-wieser
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Jul 24, 2023
eric-wieser
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Thanks! bors merge |
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This is pre-work towards a base-change of clifford algebras.
The main result here is
```lean
@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
[Algebra R A] [Module R M] [Module A M]
[IsScalarTower R A M] :
Algebra R (TensorAlgebra A M)
```
Note that strictly the `IsScalarTower R A M` argument isn't needed, but I'd claim the instance doesn't make any sense without it.
In order to prevent diamonds in the `algebraMap` fields of the `Int` and `Nat` algebra instances, we have stop having `natCast` as an `irreducible_def`, and we have to add a missing `intCast` customization for `RingQuot`. In order to prevent diamonds in the `smul` fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the `smul` definition as an `irreducible_def`. We already had to make a similar refactor to prevent diamonds for `Algebra R (Polynomial A)`.
If we backport any of this to mathlib3, we'd additionally have to change the `smul` definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.
These diamonds are tested with inline `examples`.
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This is pre-work towards a base-change of clifford algebras.
The main result here is
```lean
@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
[Algebra R A] [Module R M] [Module A M]
[IsScalarTower R A M] :
Algebra R (TensorAlgebra A M)
```
Note that strictly the `IsScalarTower R A M` argument isn't needed, but I'd claim the instance doesn't make any sense without it.
In order to prevent diamonds in the `algebraMap` fields of the `Int` and `Nat` algebra instances, we have stop having `natCast` as an `irreducible_def`, and we have to add a missing `intCast` customization for `RingQuot`. In order to prevent diamonds in the `smul` fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the `smul` definition as an `irreducible_def`. We already had to make a similar refactor to prevent diamonds for `Algebra R (Polynomial A)`.
If we backport any of this to mathlib3, we'd additionally have to change the `smul` definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.
These diamonds are tested with inline `examples`.
kim-em
pushed a commit
that referenced
this pull request
Aug 2, 2023
This is pre-work towards a base-change of clifford algebras.
The main result here is
```lean
@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
[Algebra R A] [Module R M] [Module A M]
[IsScalarTower R A M] :
Algebra R (TensorAlgebra A M)
```
Note that strictly the `IsScalarTower R A M` argument isn't needed, but I'd claim the instance doesn't make any sense without it.
In order to prevent diamonds in the `algebraMap` fields of the `Int` and `Nat` algebra instances, we have stop having `natCast` as an `irreducible_def`, and we have to add a missing `intCast` customization for `RingQuot`. In order to prevent diamonds in the `smul` fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the `smul` definition as an `irreducible_def`. We already had to make a similar refactor to prevent diamonds for `Algebra R (Polynomial A)`.
If we backport any of this to mathlib3, we'd additionally have to change the `smul` definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.
These diamonds are tested with inline `examples`.
kim-em
pushed a commit
that referenced
this pull request
Aug 3, 2023
This is pre-work towards a base-change of clifford algebras.
The main result here is
```lean
@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
[Algebra R A] [Module R M] [Module A M]
[IsScalarTower R A M] :
Algebra R (TensorAlgebra A M)
```
Note that strictly the `IsScalarTower R A M` argument isn't needed, but I'd claim the instance doesn't make any sense without it.
In order to prevent diamonds in the `algebraMap` fields of the `Int` and `Nat` algebra instances, we have stop having `natCast` as an `irreducible_def`, and we have to add a missing `intCast` customization for `RingQuot`. In order to prevent diamonds in the `smul` fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the `smul` definition as an `irreducible_def`. We already had to make a similar refactor to prevent diamonds for `Algebra R (Polynomial A)`.
If we backport any of this to mathlib3, we'd additionally have to change the `smul` definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.
These diamonds are tested with inline `examples`.
kim-em
pushed a commit
that referenced
this pull request
Aug 14, 2023
This is pre-work towards a base-change of clifford algebras.
The main result here is
```lean
@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
[Algebra R A] [Module R M] [Module A M]
[IsScalarTower R A M] :
Algebra R (TensorAlgebra A M)
```
Note that strictly the `IsScalarTower R A M` argument isn't needed, but I'd claim the instance doesn't make any sense without it.
In order to prevent diamonds in the `algebraMap` fields of the `Int` and `Nat` algebra instances, we have stop having `natCast` as an `irreducible_def`, and we have to add a missing `intCast` customization for `RingQuot`. In order to prevent diamonds in the `smul` fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the `smul` definition as an `irreducible_def`. We already had to make a similar refactor to prevent diamonds for `Algebra R (Polynomial A)`.
If we backport any of this to mathlib3, we'd additionally have to change the `smul` definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.
These diamonds are tested with inline `examples`.
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This is pre-work towards a base-change of clifford algebras.
The main result here is
Note that strictly the
IsScalarTower R A Margument isn't needed, but I'd claim the instance doesn't make any sense without it.In order to prevent diamonds in the
algebraMapfields of theIntandNatalgebra instances, we have stop havingnatCastas anirreducible_def, and we have to add a missingintCastcustomization forRingQuot. In order to prevent diamonds in thesmulfields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having thesmuldefinition as anirreducible_def. We already had to make a similar refactor to prevent diamonds forAlgebra R (Polynomial A).If we backport any of this to mathlib3, we'd additionally have to change the
smuldefinition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.These diamonds are tested with inline
examples.RingQuotandBilinForm#6066