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feat: multiplication of intervals in rings #20636

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feat: multiplication of intervals in rings #20636

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PR summary ad349f59d1

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ NonemptyInterval.instMul
+ fst_mul'
+ instMulOfSemiring
+ instance : MulZeroOneClass (NonemptyInterval α)
+ snd_mul'
- instance : Mul (NonemptyInterval α)

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).

@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Jan 10, 2025
YaelDillies
YaelDillies reviewed Jan 14, 2025
View reviewed changes
Mathlib/Algebra/Order/Interval/Basic.lean
Comment on lines +536 to +547
instance instMulOfSemiring : Mul (NonemptyInterval α) where
mul a b :=
{ fst := a.fst * b.fst ⊓ a.fst * b.snd ⊓ a.snd * b.fst ⊓ a.snd * b.snd
snd := a.fst * b.fst ⊔ a.fst * b.snd ⊔ a.snd * b.fst ⊔ a.snd * b.snd
fst_le_snd := by
dsimp
apply inf_le_sup.trans ?_
gcongr
apply inf_le_sup.trans ?_
gcongr
apply inf_le_sup.trans ?_
rfl }
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This generalises the existing multiplication, right? Maybe we can merge both instances

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I think only under certain assumptions. Right now I don't think either satisfies the requirements of the other.

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Really? The existing one has [MulLeftMono α] [MulRightMono α], which implies a.fst * b.fst ⊓ a.fst * b.snd ⊓ a.snd * b.fst ⊓ a.snd * b.snd = a.fst * b.fst ⊓ a.snd * b.snd and similarly for ⊔

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@eric-wieser @YaelDillies