Base change (and complexification) of quadratic forms #31
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
had a problem deploying
to
documentation
GitHub Actions
Failure
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
3 tasks
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
But not trivially proven!
eric-wieser
had a problem deploying
to
documentation
GitHub Actions
Failure
eric-wieser
had a problem deploying
to
documentation
GitHub Actions
Failure
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
bors bot
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Aug 17, 2023
…ar forms (#6306) This generalizes the existing `BilinForm.tensorDistrib` to be heterogenous in the rings it uses, such that a base change, ```lean protected def baseChange (B : BilinForm R M₂) : BilinForm A (A ⊗[R] M₂) := ``` falls out as a special case. I do not attempt to generalize `BilinForm.tensorDistribEquiv`. Unfortunately, this changes the defeq as ```diff -(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' +(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₂ m₂ m₂' • B₁ m₁ m₁' ``` We could fix this by using the right action instead, but that's a lot of work for a very minorly annoying defeq. This also breaks the defeq of `tensorDistribEquiv B = tensorDistrib B`; though the reason is more complicated than the scalar action issue above. It would be fixed if we defined all the homogenous operations on tensor products as special cases of the heterogenous ones, but that's also a lot of work for a very small win. This is a port of work from pygae/lean-ga#31, and almost at the end of the path to a base change of quadratic forms and clifford algebras. This was independently developed at the Leiden workshop as [`BilinForm.baseChange`](https://github.com/alexjbest/ant-lorentz/blob/1f97add294b2d50f99537c15583666d78b0d7e24/AntLorentz/BaseChange.lean#L75-L85), though the results there are not sorry-free.
bors bot
pushed a commit
to leanprover-community/mathlib4
that referenced
this pull request
Aug 17, 2023
…ar forms (#6306) This generalizes the existing `BilinForm.tensorDistrib` to be heterogenous in the rings it uses, such that a base change, ```lean protected def baseChange (B : BilinForm R M₂) : BilinForm A (A ⊗[R] M₂) := ``` falls out as a special case. I do not attempt to generalize `BilinForm.tensorDistribEquiv`. Unfortunately, this changes the defeq as ```diff -(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' +(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₂ m₂ m₂' • B₁ m₁ m₁' ``` We could fix this by using the right action instead, but that's a lot of work for a very minorly annoying defeq. This also breaks the defeq of `tensorDistribEquiv B = tensorDistrib B`; though the reason is more complicated than the scalar action issue above. It would be fixed if we defined all the homogenous operations on tensor products as special cases of the heterogenous ones, but that's also a lot of work for a very small win. This is a port of work from pygae/lean-ga#31, and almost at the end of the path to a base change of quadratic forms and clifford algebras. This was independently developed at the Leiden workshop as [`BilinForm.baseChange`](https://github.com/alexjbest/ant-lorentz/blob/1f97add294b2d50f99537c15583666d78b0d7e24/AntLorentz/BaseChange.lean#L75-L85), though the results there are not sorry-free.
eric-wieser
temporarily deployed
to
documentation
GitHub Actions
Inactive
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
This is now fully covered by leanprover-community/mathlib4#6778