[Merged by Bors] - refactor(ring_theory/class_group): redefine class_group without fraction field #16727
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
…coercions There are a bunch of random specific versions of these lemmas floating around, which can be made generic to apply to all `one_hom_class`/`mul_hom_class`/`monoid_hom_class` instances. Compare existing `ring_hom.coe_coe`.
…quiv`
This PR adds more lemmas for the coercion of `refl` and `trans` of `{mul,add,ring}_equiv` to other types of maps. In particular, it ensures these types come with:
* `coe_{type}_refl` and `coe_{type}_trans` where `type` ranges over the types of bundled maps that the equivs inherit from
* `self_trans_symm` and `symm_trans_self`
* `coe_trans`
Of course, it would be great if we figured out some generic way of stating all these results so we wouldn't have to go through and add all these lemmas.
Vierkantor
added
awaiting-review
4 tasks
…quiv`
This PR adds more lemmas for the coercion of `refl` and `trans` of `{mul,add,ring}_equiv` to other types of maps. In particular, it ensures these types come with:
* `coe_{type}_refl` and `coe_{type}_trans` where `type` ranges over the types of bundled maps that the equivs inherit from
* `self_trans_symm` and `symm_trans_self`
* `coe_trans`
Of course, it would be great if we figured out some generic way of stating all these results so we wouldn't have to go through and add all these lemmas.
…to subgroup isomorphism
Vierkantor
force-pushed
the
redefine-class-group
branch
from
942d3bb
to
bda9673
Compare
github-actions
bot
removed
the
awaiting-CI
mathlib-dependent-issues-bot
removed
the
blocked-by-other-PR
leanprover-community-bot-assistant
added
ready-to-merge
bors bot
pushed a commit
that referenced
this pull request
Oct 8, 2022
…ion field (#16727) Although the definition of the class group of a ring `R` involves the field of fractions, the definition does not depend (up to isomorphism) on the choice of field of fractions. This PR proposes to always choose `fraction_ring R` as that field, so that we don't need to carry around the mathematically unnecessary parameters `(K) [field K] [algebra R K] [is_fraction_ring R K]`. Instead, we insert the isomorphism between the definitions of class group at the API boundaries. This was inspired by our work on quadratic rings: it gets even more annoying when you need to start carrying around a proof that the field of fractions of `ℤ[1/2√-7]` is `ℚ(√-7)`. Co-authored-by: Anne Baanen <t.baanen@vu.nl> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
|
Pull request successfully merged into master. Build succeeded: |
bors
bot
changed the title
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.
Although the definition of the class group of a ring
Rinvolves the field of fractions, the definition does not depend (up to isomorphism) on the choice of field of fractions. This PR proposes to always choosefraction_ring Ras that field, so that we don't need to carry around the mathematically unnecessary parameters(K) [field K] [algebra R K] [is_fraction_ring R K]. Instead, we insert the isomorphism between the definitions of class group at the API boundaries.This was inspired by our work on quadratic rings: it gets even more annoying when you need to start carrying around a proof that the field of fractions of
ℤ[1/2√-7]isℚ(√-7).simplemmas for applying generic morphism coercions #16700simplemmas forunits.map_equiv#16701simplemmas forfractional_ideal.canonical_equiv#16702simplemmas forquotient_group.map#16703{mul,add,ring}_equiv#16725