This repository was archived by the owner on Jul 24, 2024. It is now read-only.
feat(algebra/add_torsor, linear_algebra/affine_space/affine_equiv, analysis/normed_space/affine_isometry): base_at construction#8837
Open
hrmacbeth wants to merge 14 commits into
Open
feat(algebra/add_torsor, linear_algebra/affine_space/affine_equiv, analysis/normed_space/affine_isometry): base_at construction#8837hrmacbeth wants to merge 14 commits into
base_at construction#8837hrmacbeth wants to merge 14 commits into
Conversation
hrmacbeth
added
the
awaiting-review
github-actions
Bot
added
the
merge-conflict
github-actions
Bot
removed
the
merge-conflict
urkud
reviewed
Sep 11, 2021
Comment on lines
+414
to
+415
| def _root_.add_equiv.base_at (f : G ≃+ G) (x : P) : perm P := | ||
| ((vadd_const x).symm.trans f.to_equiv).trans (vadd_const x) |
Member
There was a problem hiding this comment.
A few other reasonable definitions:
Suggested change
| def _root_.add_equiv.base_at (f : G ≃+ G) (x : P) : perm P := | |
| ((vadd_const x).symm.trans f.to_equiv).trans (vadd_const x) | |
| def _root_.equiv.base_at {G' P' : Type*} [add_group G'] [add_torsor G' P'] (f : G ≃ G') (x : P) (y : P') : | |
| P ≃ P':= | |
| ((vadd_const x).symm.trans f).trans (vadd_const y) | |
| def _root_.add_equiv.base_at {G' P' : Type*} [add_group G'] [add_torsor G' P'] (f : G ≃+ G') (x : P) (y : P') : | |
| P ≃ P':= | |
| f.to_equiv.base_at x y | |
| def _root_.add_aut.base_at (f : add_aut G) (x : P) : | |
| perm P := | |
| f.base_at x x |
Member
Author
There was a problem hiding this comment.
You're right that one could introduce a more general base_at construction which constructs, from an isomorphism of model spaces, an isomorphism of the add_torsors according to a fixed basepoint x, y of each. It would double the size of the PR, though, so I'd rather not add it until someone needs it for something. (The version with a single add_torsor, constructing an automorphism, is more immediately useful -- it allows one to talk sensibly to talk about rotations in affine space.)
On your other point, I'd be happy to change the definition here to
Suggested change
| def _root_.add_equiv.base_at (f : G ≃+ G) (x : P) : perm P := | |
| ((vadd_const x).symm.trans f.to_equiv).trans (vadd_const x) | |
| def _root_.equiv.base_at (f : G ≃ G) (x : P) : perm P := | |
| ((vadd_const x).symm.trans f).trans (vadd_const x) |
if you prefer, or include both.
urkud
reviewed
Sep 11, 2021
|
|
||
| @[simp] lemma linear_isometry_equiv_symm : | ||
| e.linear_isometry_equiv.symm = e.symm.linear_isometry_equiv := | ||
| rfl |
Member
There was a problem hiding this comment.
jcommelin
approved these changes
Sep 30, 2021
Comment on lines
+414
to
+415
| def _root_.add_equiv.base_at (f : G ≃+ G) (x : P) : perm P := | ||
| ((vadd_const x).symm.trans f.to_equiv).trans (vadd_const x) |
eric-wieser
reviewed
Sep 30, 2021
| ((vadd_const x).symm.trans f.to_equiv).trans (vadd_const x) | ||
|
|
||
| @[simp] lemma _root_.add_equiv.base_at_apply (f : G ≃+ G) (x y : P) : | ||
| f.base_at x y = f (y -ᵥ x) +ᵥ x := |
Member
There was a problem hiding this comment.
Can @[simps apply] generate this? If not, are we missing some lemmas?
eric-wieser
reviewed
Sep 30, 2021
| ← f.map_add, vadd_vsub_assoc], | ||
| end | ||
|
|
||
| @[simp] lemma _root_.add_equiv.base_at_symm (f : G ≃+ G) (x : P) : |
Member
There was a problem hiding this comment.
Can you add the refl variant of this lemma too?
eric-wieser
reviewed
Sep 30, 2021
| variables {G : Type*} {P : Type*} [add_comm_group G] [add_torsor G P] | ||
| include G | ||
|
|
||
| lemma base_at_neg (x : P) : (add_equiv.neg G).base_at x = point_reflection x := |
Member
There was a problem hiding this comment.
Should this be in the add_equiv namespace?
eric-wieser
reviewed
Sep 30, 2021
| ..equiv.inv G} | ||
|
|
||
| @[simp, to_additive] lemma mul_equiv.coe_inv (G : Type*) [comm_group G] : | ||
| ⇑(mul_equiv.inv G) = λ a, a⁻¹ := |
Member
There was a problem hiding this comment.
Suggested change
| ⇑(mul_equiv.inv G) = λ a, a⁻¹ := | |
| ⇑(mul_equiv.inv G) = has_inv.inv := |
Member
There was a problem hiding this comment.
Alternately, can @[simps {fully_applied := ff}] generate this?
kim-em
added
the
awaiting-author
sgouezel
removed
the
awaiting-review
github-actions
Bot
added
the
merge-conflict
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
Sign up for free
to subscribe to this conversation on GitHub.
Already have an account?
Sign in.
6 participants
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.
Add constructions
add_equiv.base_at(of typeperm),linear_equiv.base_at(of typeaffine_equiv), andlinear_isometry_equiv.base_at(of typeaffine_isometry_equiv), to describe the automorphism of anadd_torsor/normed_add_torsorobtained by fixing a basepoint, temporarily identifying theadd_torsorwith its model space using this basepoint, and applying theadd_equiv/linear_equiv/linear_isometry_equivto the space under this identification.Also API for these constructions and a few more missing lemmas.