[Merged by Bors] - feat(analysis/quaternion): add complete_space, module.free, and module.finite instances
#18347
Conversation
This file contains 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
… its coefficients
eric-wieser
added
the
awaiting-review
6 tasks
eric-wieser
changed the title
complete_space, module.free, and module.finite instances
YaelDillies
reviewed
Feb 8, 2023
src/algebra/quaternion.lean
Outdated
Comment on lines
227
to
233
| def linear_equiv_tuple : ℍ[R,c₁,c₂] ≃ₗ[R] (fin 4 → R) := | ||
| linear_equiv.symm | ||
| { to_fun := (equiv_tuple c₁ c₂).symm, | ||
| inv_fun := (equiv_tuple c₁ c₂), | ||
| map_add' := λ v₁ v₂, rfl, | ||
| map_smul' := λ v₁ v₂, rfl, | ||
| .. (equiv_tuple c₁ c₂).symm } |
There was a problem hiding this comment.
Sorry if I'm missing something obvious, but why do you need to symm everything?
Suggested change
| def linear_equiv_tuple : ℍ[R,c₁,c₂] ≃ₗ[R] (fin 4 → R) := | |
| linear_equiv.symm | |
| { to_fun := (equiv_tuple c₁ c₂).symm, | |
| inv_fun := (equiv_tuple c₁ c₂), | |
| map_add' := λ v₁ v₂, rfl, | |
| map_smul' := λ v₁ v₂, rfl, | |
| .. (equiv_tuple c₁ c₂).symm } | |
| def linear_equiv_tuple : ℍ[R,c₁,c₂] ≃ₗ[R] (fin 4 → R) := | |
| { map_add' := λ v₁ v₂, rfl, | |
| map_smul' := λ v₁ v₂, rfl, | |
| ..equiv_tuple c₁ c₂ } |
There was a problem hiding this comment.
I seem to remember that that didn't work as the proofs weren't rfl in that direction; but I can't test right now because the cache seems to be a corrupt tarball...
There was a problem hiding this comment.
Yep, I can confirm that rfl doesn't work in your code. I added a comment explaining the symm.
You could of course spend some effort proving the harder statements, but I don't see any reason to do so.
|
LGTM bors merge |
github-actions
bot
added
ready-to-merge
bors bot
pushed a commit
that referenced
this pull request
Feb 9, 2023
…module.finite` instances (#18347) The main trick here is showing that the quaternions are in isometric equivalence with 4D euclidean space.
|
Pull request successfully merged into master. Build succeeded: |
bors
bot
changed the title
complete_space, module.free, and module.finite instancescomplete_space, module.free, and module.finite instances
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.
The main trick here is showing that the quaternions are in isometric equivalence with 4D euclidean space.