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[Merged by Bors] - feat: port LinearAlgebra.SesquilinearForm #2607

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[Merged by Bors] - feat: port LinearAlgebra.SesquilinearForm #2607

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ocfnash
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@ocfnash ocfnash commented Mar 3, 2023

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@ocfnash ocfnash added WIP Work in progress mathlib-port This is a port of a theory file from mathlib. labels Mar 3, 2023
ocfnash
ocfnash commented Mar 3, 2023
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Mathlib/LinearAlgebra/SesquilinearForm.lean Outdated
/-- A set of vectors `v` is orthogonal with respect to some bilinear form `B` if and only
if for all `i ≠ j`, `B (v i) (v j) = 0`. For orthogonality between two elements, use
`bilin_form.is_ortho` -/
def IsOrthoCat (B : M₁ →ₛₗ[I₁] M₁ →ₛₗ[I₁'] R) (v : n → M₁) : Prop :=
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@ocfnash ocfnash Mar 3, 2023 •
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Unfortunately the original Mathlib3 source commits the sin of having two definitions with names distinguished only by case:

  • linear_map.is_ortho
  • linear_map.is_Ortho

It seems Mathport deals with this by naming them LinearMap.IsOrtho and LinearMap.IsOrthoCat respectively. I'm not sure if we should first rename in Mathlib3 or just rename on the fly.

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I have taken the liberty of simply renaming these on the fly to LinearMap.IsOrtho and LinearMap.IsOrthoᵢ so as to match other things that have binary and indexed versions (like sup and supᵢ or union and unionᵢ).

@ocfnash ocfnash added help-wanted The author needs attention to resolve issues and removed WIP Work in progress labels Mar 4, 2023
@semorrison semorrison added the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Mar 13, 2023
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@ocfnash The errors here are definitely caused by lean4#2074 because the file compiles with set_option synthInstance.etaExperiment true. However, I had trouble finding a complete set of workarounds.

  1. The failure to find the AddCommMonoid instance can be fixed by attribute [-instance] Ring.toNonAssocRing (although that caused the proof to fail if I used etaExperiment, so maybe it's not a good approach).
  2. The Module K₁ V₁ instance is a bit tricky, because it can be found as a standalone instance without issue. One solution for this is the _ vs (_) hack. So @Submodule.orthogonalBilin _ _ _ _ _ _ (_) _ _ (K₁ ∙ x) B succeeds.

Unfortunately I have to stop working on this for now though. I didn't push any fixes yet, just wanted to document them here.

ocfnash and others added 14 commits March 21, 2023 16:08
@ocfnash @j-loreaux
feat: port LinearAlgebra.SesquilinearForm
a934fa7
@ocfnash @j-loreaux
Initial file copy from mathport
5be601e
@ocfnash @j-loreaux
automated fixes
b34e305 
Mathbin -> Mathlib

fix certain import statements

move "by" to end of line

add import to Mathlib.lean
@ocfnash @j-loreaux
Trivial fixes
da1fc49
@ocfnash @j-loreaux
Minor fixes
787c067 
That's is for today
@ocfnash @j-loreaux
Some more fixes
95c55cf 
This is horrible. I think it's better to wait and see if we solve these issues
more generally before putting more time into this file.
@mo271 @j-loreaux
small fixes
73c0cdd
@ocfnash @j-loreaux
Some more easy fixes
f5f7975
@ocfnash @j-loreaux
A few more easy fixes
4529631
@ocfnash @j-loreaux
Further fixes
7ad35d2 
I still need `set_option synthInstance.etaExperiment true` to get things
to work but hopefully we can solve this next.
@ocfnash @j-loreaux
Trivial fixes
13b156f 
With these changes, this will now build provided we add:
`set_option synthInstance.etaExperiment true`
Unfortunately I haven't found a way to avoid using this yet.
@j-loreaux
error free
21c9a65
@j-loreaux
rename IsOrthoCat to IsOrthoᵢ
514f376
@j-loreaux
lint
4811df5
@j-loreaux j-loreaux force-pushed the port/LinearAlgebra.SesquilinearForm branch from 8d478b1 to 4811df5 Compare March 21, 2023 21:10
@j-loreaux j-loreaux added awaiting-review The author would like community review of the PR and removed help-wanted The author needs attention to resolve issues merge-conflict The PR has a merge conflict with master, and needs manual merging. labels Mar 21, 2023
jcommelin
jcommelin approved these changes Mar 22, 2023
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Thanks 🎉

bors merge

@semorrison semorrison added ready-to-merge This PR has been sent to bors. and removed awaiting-review The author would like community review of the PR labels Mar 22, 2023
bors bot pushed a commit that referenced this pull request Mar 22, 2023
@ocfnash @mo271 @j-loreaux
feat: port LinearAlgebra.SesquilinearForm (#2607)
accbdce 
Co-authored-by: Moritz Firsching <firsching@google.com>
Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>
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bors bot commented Mar 22, 2023

Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat: port LinearAlgebra.SesquilinearForm [Merged by Bors] - feat: port LinearAlgebra.SesquilinearForm Mar 22, 2023
@bors bors bot closed this Mar 22, 2023
@bors bors bot deleted the port/LinearAlgebra.SesquilinearForm branch March 22, 2023 14:44
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