[Merged by Bors] - feat(AlgebraicGeometry/EllipticCurve/Jacobian): implement equations and nonsingularity for Jacobian coordinates #9432
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
Multramate
added
awaiting-review
This was referenced Jan 4, 2024
Open
5 tasks
jcommelin
reviewed
Jan 6, 2024
alreadydone
reviewed
Feb 14, 2024
Comment on lines
221
to
228
| lemma nonsingular_zero [Nontrivial R] : W.nonsingular ![1, 1, 0] := | ||
| (W.nonsingular_iff ![1, 1, 0]).mpr ⟨W.equation_zero, | ||
| by simp; by_contra! h; exact one_ne_zero <| by linear_combination -h.1 - h.2.1⟩ | ||
|
|
||
| lemma nonsingular_zero' [NoZeroDivisors R] {Y : R} (hy : Y ≠ 0) : | ||
| W.nonsingular ![Y ^ 2, Y ^ 3, 0] := | ||
| (W.nonsingular_iff ![Y ^ 2, Y ^ 3, 0]).mpr ⟨W.equation_zero' Y, | ||
| by simp [hy]; by_contra! h; exact pow_ne_zero 3 hy <| by linear_combination Y ^ 3 * h.1 - h.2.1⟩ |
There was a problem hiding this comment.
Some nonterminal simps here and the behavior is a bit nonpredictable; the first simp results in ¬0 = 3 ∨ ¬1 = -1 ∨ ¬W.a₁ = 0 while the second results in ¬3 = 0 ∨ ¬Y ^ 3 = -Y ^ 3 ∨ ¬W.a₁ = 0 (the order of 3 and 0 is changed). However, if this breaks it's probably not hard to figure out what linear combination to use by inspecting the simp'd expressions. Here's a slight generalization to the second proof:
Suggested change
| lemma nonsingular_zero [Nontrivial R] : W.nonsingular ![1, 1, 0] := | |
| (W.nonsingular_iff ![1, 1, 0]).mpr ⟨W.equation_zero, | |
| by simp; by_contra! h; exact one_ne_zero <| by linear_combination -h.1 - h.2.1⟩ | |
| lemma nonsingular_zero' [NoZeroDivisors R] {Y : R} (hy : Y ≠ 0) : | |
| W.nonsingular ![Y ^ 2, Y ^ 3, 0] := | |
| (W.nonsingular_iff ![Y ^ 2, Y ^ 3, 0]).mpr ⟨W.equation_zero' Y, | |
| by simp [hy]; by_contra! h; exact pow_ne_zero 3 hy <| by linear_combination Y ^ 3 * h.1 - h.2.1⟩ | |
| lemma nonsingular_zero [Nontrivial R] : W.nonsingular ![1, 1, 0] := | |
| (W.nonsingular_iff ![1, 1, 0]).mpr ⟨W.equation_zero, | |
| by simp; by_contra! h; exact one_ne_zero <| by linear_combination -h.1 - h.2.1⟩ | |
| lemma nonsingular_zero' [IsReduced R] {Y : R} (hy : Y ≠ 0) : | |
| W.nonsingular ![Y ^ 2, Y ^ 3, 0] := | |
| (W.nonsingular_iff ![Y ^ 2, Y ^ 3, 0]).mpr ⟨W.equation_zero' Y, by | |
| simp; contrapose! hy; exact IsNilpotent.eq_zero ⟨4, by linear_combination -hy.1 - Y * hy.2.1⟩⟩ |
There was a problem hiding this comment.
Similar to the projective file, I think we can relegate this to a future PR.
jcommelin
added
awaiting-author
Multramate
added
awaiting-review
leanprover-community-mathlib4-bot
added
the
merge-conflict
leanprover-community-mathlib4-bot
removed
the
merge-conflict
|
Thanks! |
|
🚀 Pull request has been placed on the maintainer queue by alreadydone. |
|
Thanks! bors merge |
github-actions
bot
added
ready-to-merge
mathlib-bors bot
pushed a commit
that referenced
this pull request
Feb 23, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
|
Pull request successfully merged into master. Build succeeded: |
mathlib-bors
bot
changed the title
thorimur
pushed a commit
that referenced
this pull request
Feb 24, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
thorimur
pushed a commit
that referenced
this pull request
Feb 26, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
riccardobrasca
pushed a commit
that referenced
this pull request
Mar 1, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
dagurtomas
pushed a commit
that referenced
this pull request
Mar 22, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
Louddy
pushed a commit
that referenced
this pull request
Apr 15, 2024
…nd nonsingularity for Jacobian coordinates (#9432) Define a Jacobian point representative over a ring `R` as the type `Fin 3 -> R`, and its equivalence class `PointClass` as a quotient by the usual weighted scaling relation. Define the analogous `equation` and `nonsingular` predicates on `Fin 3 -> F` over a field `F`, and lift `nonsingular` to `PointClass`. This also has minimal API (e.g. it's missing many of the `equation` lemmas) as most computations should ideally be done using the affine API. This is the first in a series of four PRs leading to #9405 and is analogous to #9416
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.
Define a Jacobian point representative over a ring
Ras the typeFin 3 -> R, and its equivalence classPointClassas a quotient by the usual weighted scaling relation. Define the analogousequationandnonsingularpredicates onFin 3 -> Fover a fieldF, and liftnonsingulartoPointClass. This also has minimal API (e.g. it's missing many of theequationlemmas) as most computations should ideally be done using the affine API.This is the first in a series of four PRs leading to #9405 and is analogous to #9416