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[Merged by Bors] - feat(linear_algebra/affine_space/affine_subspace/pointwise): Translations are an action on affine subspaces #14230

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[Merged by Bors] - feat(linear_algebra/affine_space/affine_subspace/pointwise): Translations are an action on affine subspaces #14230

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@winston-h-zhang winston-h-zhang commented May 18, 2022 •
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Defines instance : has_vadd V (affine_subspace k P) and instance : add_action V (affine_subspace k P) of the form p → v +ᵥ p.

I feel like this is really about sub-torsors, but that would require refactoring... :(
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@semorrison semorrison added the awaiting-review The author would like community review of the PR label May 18, 2022
@eric-wieser eric-wieser added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels May 18, 2022
@winston-h-zhang winston-h-zhang self-assigned this May 19, 2022
@winston-h-zhang winston-h-zhang added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels May 19, 2022
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eric-wieser commented May 22, 2022 •
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Note that with #14319 this is basically a one-liner if you put it in a new file where you can import map; S.map (affine_equiv.const_vadd k O x)

@eric-wieser eric-wieser added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels May 24, 2022
@winston-h-zhang winston-h-zhang added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels May 24, 2022
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Since we're spliting this off to a new pointwise file, why not reorganize affine_subspace entirely into something more like affine_subspace/{defs, lattice, basic, pointwise}? Then the usage of (s : set P).nonempty everywhere could be replaced with s ≠ ⊥.

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eric-wieser commented May 25, 2022 •
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Let's try to avoid making multiple refactors at once. That does sound like a reasonable idea for a follow-up PR.

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@YaelDillies @eric-wieser I've fixed the names, lmk if there's anything else

@YaelDillies YaelDillies changed the title feat(linear_algebra/affine_space/affine_subspace): Translations are an action on affine subspaces feat(linear_algebra/affine_space/affine_subspace/pointwise): Translations are an action on affine subspaces May 28, 2022
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@YaelDillies @eric-wieser When you guys have time please take a look at this again, thank you!

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Sorry, this might have to wait a week. This looks good overall but I don't have time to agree on the details.

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eric-wieser reviewed Jun 3, 2022
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Another good lemma to have would be that the affine span of a pointwise vadd on a set is the same as the pointwise vadd on the span of the set (which should follow immediately from affine_subspace.map_span)

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If it looks good overall, may I have merging permission? 👀

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eric-wieser reviewed Jun 4, 2022
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src/linear_algebra/affine_space/pointwise.lean Outdated Show resolved Hide resolved
src/linear_algebra/affine_space/pointwise.lean Outdated
exact submodule.map_id _,
end

lemma pointwise_vadd_span (v : V) {s : set P} :
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Suggested change
lemma pointwise_vadd_span (v : V) {s : set P} :
lemma pointwise_vadd_span (v : V) (s : set P) :

src/linear_algebra/affine_space/pointwise.lean Outdated Show resolved Hide resolved
src/linear_algebra/affine_space/pointwise.lean Outdated
@[simp] lemma coe_pointwise_vadd (v : V) (s : affine_subspace k P) :
((v +ᵥ s : affine_subspace k P) : set P) = v +ᵥ s := rfl

lemma vadd_mem_pointwise_vadd_iff (v : V) {s : affine_subspace k P} {p : P} :
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lemma vadd_mem_pointwise_vadd_iff (v : V) {s : affine_subspace k P} {p : P} :
lemma vadd_mem_pointwise_vadd_iff {v : V} {s : affine_subspace k P} {p : P} :

src/linear_algebra/affine_space/pointwise.lean Outdated
variables {V₁ P₁ V₂ P₂ V₃ P₃ : Type*}
variables [add_comm_group V₁] [module k V₁] [add_torsor V₁ P₁]
variables [add_comm_group V₂] [module k V₂] [add_torsor V₂ P₂]
variables [add_comm_group V₃] [module k V₃] [add_torsor V₃ P₃]
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Is V₃ used here? If not, can you remove all mentions of it?

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eric-wieser approved these changes Jun 8, 2022
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bors d+

Let's just wait for CI to pass.

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bors bot commented Jun 8, 2022

✌️ winston-h-zhang can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@eric-wieser eric-wieser added the awaiting-CI The author would like to see what CI has to say before doing more work. label Jun 8, 2022
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label Jun 8, 2022
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bors merge

@github-actions github-actions bot added the ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) label Jun 8, 2022
bors bot pushed a commit that referenced this pull request Jun 8, 2022
@winston-h-zhang @eric-wieser
feat(linear_algebra/affine_space/affine_subspace/pointwise): Translat…
c1faa2e 
…ions are an action on affine subspaces (#14230)

Co-authored-by: Hanting Zhang <hantingzhang03@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@winston-h-zhang winston-h-zhang removed the request for review from YaelDillies June 8, 2022 21:51
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Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(linear_algebra/affine_space/affine_subspace/pointwise): Translations are an action on affine subspaces [Merged by Bors] - feat(linear_algebra/affine_space/affine_subspace/pointwise): Translations are an action on affine subspaces Jun 8, 2022
@bors bors bot closed this Jun 8, 2022
@bors bors bot deleted the hzhang-affine_space_action branch June 8, 2022 21:55
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