[Merged by Bors] - refactor(Analysis/LocallyConvex/AbsConvex): Redefine AbsConvex to use a single ring of scalars#29342
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PR summary 724a6cb9d7Import changes for modified filesNo significant changes to the import graph Import changes for all files
Declarations diffNo declarations were harmed in the making of this PR! 🐙 You can run this locally as follows## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for No changes to technical debt.You can run this locally as
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I'd venture that this is the most controversial part of this PR. I think this PR is a good change, but in the past many people have been resistant to letting ℂ (and hence also RCLike 𝕜) have a PartialOrder instance.
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| open ComplexOrder | |
| open scoped ComplexOrder | |
I think this PR likely warrants a Zulip discussion.
Co-authored-by: Jireh Loreaux <[email protected]>
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… a single ring of scalars (#29342) Currently the definition of Absolutely Convex in Mathlib is a little unexpected: ``` def AbsConvex (s : Set E) : Prop := Balanced 𝕜 s ∧ Convex ℝ s ``` At the time this definition was formulated, Mathlib's definition of `Convex` required the scalars to be an `OrderedSemiring` whereas the definition of `Balanced` required the scalars to be a `SeminormedRing`. Mathlib didn't have a concept of a semi-normed ordered ring, so a set was defined as `AbsConvex` if it is balanced over a `SeminormedRing` `𝕜` and convex over `ℝ`. Recently the requirements for the definition of `Convex` have been relaxed (#24392, #20595) so it is now possible to use a single scalar ring in common with the literature. Previous discussion: - #17029 (comment) - #26345 (comment)
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… a single ring of scalars (leanprover-community#29342) Currently the definition of Absolutely Convex in Mathlib is a little unexpected: ``` def AbsConvex (s : Set E) : Prop := Balanced 𝕜 s ∧ Convex ℝ s ``` At the time this definition was formulated, Mathlib's definition of `Convex` required the scalars to be an `OrderedSemiring` whereas the definition of `Balanced` required the scalars to be a `SeminormedRing`. Mathlib didn't have a concept of a semi-normed ordered ring, so a set was defined as `AbsConvex` if it is balanced over a `SeminormedRing` `𝕜` and convex over `ℝ`. Recently the requirements for the definition of `Convex` have been relaxed (leanprover-community#24392, leanprover-community#20595) so it is now possible to use a single scalar ring in common with the literature. Previous discussion: - leanprover-community#17029 (comment) - leanprover-community#26345 (comment)
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… a single ring of scalars (leanprover-community#29342) Currently the definition of Absolutely Convex in Mathlib is a little unexpected: ``` def AbsConvex (s : Set E) : Prop := Balanced 𝕜 s ∧ Convex ℝ s ``` At the time this definition was formulated, Mathlib's definition of `Convex` required the scalars to be an `OrderedSemiring` whereas the definition of `Balanced` required the scalars to be a `SeminormedRing`. Mathlib didn't have a concept of a semi-normed ordered ring, so a set was defined as `AbsConvex` if it is balanced over a `SeminormedRing` `𝕜` and convex over `ℝ`. Recently the requirements for the definition of `Convex` have been relaxed (leanprover-community#24392, leanprover-community#20595) so it is now possible to use a single scalar ring in common with the literature. Previous discussion: - leanprover-community#17029 (comment) - leanprover-community#26345 (comment)
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Currently the definition of Absolutely Convex in Mathlib is a little unexpected:
At the time this definition was formulated, Mathlib's definition of
Convexrequired the scalars to be anOrderedSemiringwhereas the definition ofBalancedrequired the scalars to be aSeminormedRing. Mathlib didn't have a concept of a semi-normed ordered ring, so a set was defined asAbsConvexif it is balanced over aSeminormedRing𝕜and convex overℝ.Recently the requirements for the definition of
Convexhave been relaxed (#24392, #20595) so it is now possible to use a single scalar ring in common with the literature.Previous discussion: