feat: port RingTheory.Polynomial.Quotient#3292
Closed
Ruben-VandeVelde wants to merge 17 commits intomasterfrom
Closed
feat: port RingTheory.Polynomial.Quotient#3292Ruben-VandeVelde wants to merge 17 commits intomasterfrom
Ruben-VandeVelde wants to merge 17 commits intomasterfrom
Conversation
Contributor
Ruben-VandeVelde
commented
Apr 5, 2023
Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
Collaborator
noncomputable def quotientSpanXSubCAlgEquivAux2 (x : R) :
(R[X] ⧸ (RingHom.ker (aeval x).toRingHom : Ideal R[X])) ≃ₐ[R] R :=
let e := RingHom.quotientKerEquivOfRightInverse (by
intro x; exact eval_C : Function.RightInverse (fun a : R => (C a : R[X])) (@aeval R R _ _ _ x))
{ e with commutes' := fun r => e.apply_symm_apply r }
noncomputable def quotientSpanXSubCAlgEquivAux1 (x : R) :
(R[X] ⧸ Ideal.span {X - C x}) ≃ₐ[R] (R[X] ⧸ (RingHom.ker (aeval x).toRingHom : Ideal R[X])) :=
@Ideal.quotientEquivAlgOfEq R R[X] _ _ _ _ _ (ker_evalRingHom x).symm
noncomputable def quotientSpanXSubCAlgEquiv (x : R) :
(R[X] ⧸ Ideal.span ({X - C x} : Set R[X])) ≃ₐ[R] R :=
(quotientSpanXSubCAlgEquivAux1 x).trans (quotientSpanXSubCAlgEquivAux2 x)This works but introduces two sub definitions, so I am not sure if I should push it? |
Contributor
Author
|
Feel free to push |
jjaassoonn
reviewed
May 10, 2023
| (R[X] ⧸ Ideal.span {X - C x}) ≃ₐ[R] (R[X] ⧸ (RingHom.ker (aeval x).toRingHom : Ideal R[X])) := | ||
| @Ideal.quotientEquivAlgOfEq R R[X] _ _ _ _ _ (ker_evalRingHom x).symm | ||
|
|
||
| noncomputable def quotientSpanXSubCAlgEquiv (x : R) : |
Collaborator
There was a problem hiding this comment.
As mentioned above, this has been splited into two sub-constructions which may or may not be ideal
1 task
1 task
Contributor
|
Closing in favour of #3932. |
bors bot
pushed a commit
that referenced
this pull request
May 17, 2023
Coming from #3292 - [x] depends on: #3414 [](https://gitpod.io/from-referrer/) Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
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 join this conversation on GitHub.
Already have an account?
Sign in to comment
5 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.