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[Merged by Bors] - feat(ContinuousMultilinearMap): add lemmas about .prod #20462

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[Merged by Bors] - feat(ContinuousMultilinearMap): add lemmas about .prod #20462

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@urkud urkud commented Jan 4, 2025

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@urkud urkud added the t-analysis Analysis (normed *, calculus) label Jan 4, 2025
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PR summary f48f3adaff

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ add_prod_add
+ eq_prod_iff
+ neg_prod_neg
+ prodEquiv
+ prod_ext
+ prod_ext_iff
+ smul_prod_smul
+ sub_prod_sub
+ zero_prod_zero

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 script/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

eric-wieser
eric-wieser reviewed Jan 4, 2025
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Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean
/-- `ContinuousMultilinearMap.prod` as an `Equiv`. -/
@[simps apply symm_apply_fst symm_apply_snd, simps (config := .lemmasOnly) symm_apply]
def prodEquiv :
(ContinuousMultilinearMap R M₁ M₂ × ContinuousMultilinearMap R M₁ M₃) ≃
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Should this be a linear equiv?

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A LinearEquiv needs more typeclass assumptions, e.g., ContinuousAdd and ContinuousSMul.

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Weird, I'm surpised that ContinuousMultilinearMap is legal without those assumptions! Either way, that's a convincing enough reason to have the Equiv.

eric-wieser
eric-wieser reviewed Jan 4, 2025
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Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean
Comment on lines +334 to +337
theorem add_prod_add [ContinuousAdd M₂] [ContinuousAdd M₃]
(f₁ f₂ : ContinuousMultilinearMap R M₁ M₂) (g₁ g₂ : ContinuousMultilinearMap R M₁ M₃) :
(f₁ + f₂).prod (g₁ + g₂) = f₁.prod g₁ + f₂.prod g₂ :=
rfl
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Could you add smul_prod_smul too, where the same scalar is used twice?

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(Ideally with the scalar belonging to an unrelated semiring S, but R with a TODO comment about generalizing is ok)

eric-wieser
eric-wieser approved these changes Jan 4, 2025
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bors d+

Thanks!

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mathlib-bors bot commented Jan 4, 2025

✌️ urkud can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@urkud urkud added the auto-merge-after-CI Please do not add manually. Requests for a bot to merge automatically once CI is done. label Jan 6, 2025
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As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the ready-to-merge This PR has been sent to bors. label Jan 6, 2025
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As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

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mathlib-bors bot commented Jan 6, 2025

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mathlib-bors bot pushed a commit that referenced this pull request Jan 6, 2025
@urkud
feat(ContinuousMultilinearMap): add lemmas about .prod (#20462)
f0c7c5c
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Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(ContinuousMultilinearMap): add lemmas about .prod [Merged by Bors] - feat(ContinuousMultilinearMap): add lemmas about .prod Jan 6, 2025
@mathlib-bors mathlib-bors bot closed this Jan 6, 2025
@mathlib-bors mathlib-bors bot deleted the YK-cmm-prod branch January 6, 2025 14:44
Julian added a commit that referenced this pull request Jan 6, 2025
@Julian
Merge remote-tracking branch 'origin/master' into nat-ideal-eq-top
ca07f7f 
* origin/master: (189 commits)
  chore(Algebra): make more names consistent (#20449)
  feat: Polynomial FLT (#18882)
  feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty (#20457)
  fix: linkfix in 100.yaml (#20517)
  feat(1000): fill in more entries (#20470)
  feat(Combinatorics/SimpleGraph/Walk): add `penultimate` and `snd` (#16769)
  feat(ContinuousMultilinearMap): add lemmas about `.prod` (#20462)
  feat(RingTheory): classification of etale algebras over fields (#20324)
  fix: Allow multiple builds on staging branch (#20515)
  feat(CategoryTheory/Shift/Adjunction): properties of `Adjunction.CommShift` (#20337)
  chore(Data/Multiset/Basic): move the `sub`, `union`, `inter` sections lower (#19863)
  chore(Topology/UniformSpace/Completion): make coe' argument implicit (#20514)
  refactor(Algebra/Category/Grp/Colimits): change the construction of colimits in `AddCommGrp` (#20474)
  feat(Topology/Algebra/InfiniteSum/NatInt): Add pnat lems (#16544)
  chore(RingTheory/Finiteness): rename Module.Finite.out (#20506)
  refactor(CategoryTheory/Limits/Preserves/Ulift): simplify the proof that the universe lifting functor for types preserves all colimits (#20508)
  feat(CategoryTheory): products in the category of Ind-objects (#20507)
  chore: remove >9 month old deprecations (#20505)
  chore(FieldTheory/Galois): small cleanup (#20217)
  chore(LinearIndependent): generalize to semirings (#20480)
  chore(NumberTheory/NumberField/AdeleRing): refactor adele rings (#20500)
  chore: replace `aesop` with `simp` where possible (#20483)
  chore(1000): remove nonexistent fields (#20493)
  chore(CategoryTheory/Adjunction.Basic, CategoryTheory/Equivalence): change definition of `Adjunction.comp` and `Equivalence.trans` (#20490)
  feat(Asymptotics): add `Asymptotics.*.*Prod` lemmas (#20458)
  feat: a conditional kernel is almost everywhere a probability measure (#20430)
  feat: if `f` is a measurable group hom, then every point has a neighborhood `s` such that `f '' s` is bounded (#20304)
  feat: `Ico`, `Ioc`, and `Ioo` are not closed or compact (#20479)
  chore: drop redundant hypothesis in `Module.Dual.eq_of_preReflection_mapsTo` (#20492)
  feat(FaaDiBruno): derive `DecidableEq` (#20482)
  chore(SetTheory/Ordinal/Basic): `{x // x < y}` → `Iio y` (#20413)
  chore: generalize `FormalMultilinearSeries.ofScalars_norm` to `Seminormed` (#20351)
  chore(MvPolynomial/Localization): golf using TensorProduct (#20309)
  chore(Combinatorics/Enumerative/Partition): auto-derive DecidableEq (#20277)
  chore(CategoryTheory): make relevant parameters explicit in `Arrow.homMk`. (#20259)
  feat: add `IsStarNormal (↑x⁻¹ : R)` instance for `x : Rˣ` (#20091)
  fix: Stop cancelling builds of master (#20435)
  chore: update Mathlib dependencies 2025-01-05 (#20485)
  feat(SetTheory/Cardinal/Arithmetic): miscellaneous cardinality lemmas (#18933)
  chore: bump toolchain to v4.16.0-rc1, and merge bump/v4.16.0 (#20464)
  chore: bot validates lean-toolchain on bump/v4.X.0 branches (#20478)
  feat: shorthand lemmas for the L1 norm (#20383)
  chore: remove unnecessary adaptation notes (#20467)
  chore(Algebra/Category/MonCat/Colimits): remove smallness condition (#20473)
  chore(SetTheory/Ordinal/Arithmetic): `IsLeftCancelAdd Ordinal` (#19888)
  feat(Algebra): more on `OrthogonalIdempotents` (#18195)
  feat(Radical): `(radical a).natDegree ≤ a.natDegree` (#20468)
  feat(Polynomial): `(a^n)' = 0` iff `a' = 0` when `n` doesn't divide the characteristic (#20190)
  feat(Algebra/Lie): add Lie's theorem (#13480)
  chore(RingTheory/Generators): make algebra instance a def (#14265)
  ...
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