Use ⟪x, y⟫_ℝ instead of Matrix.dotProduct
#233
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lean4/src/putnam_1998_a6.lean
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| @@ -13,6 +14,6 @@ theorem putnam_1998_a6 | |||
| (hint : ∀ i : Fin 2, ∃ a b c : ℤ, A i = a ∧ B i = b ∧ C i = c) | |||
| (htriangle : A ≠ B ∧ A ≠ C ∧ B ≠ C) | |||
| (harea : (dist A B + dist B C) ^ 2 < 8 * (MeasureTheory.volume (convexHull ℝ {A, B, C})).toReal + 1) | |||
| (threesquare : (EuclideanSpace ℝ (Fin 2)) → (EuclideanSpace ℝ (Fin 2)) → (EuclideanSpace ℝ (Fin 2)) → Prop := fun P Q R ↦ dist Q P = dist Q R ∧ Matrix.dotProduct (P - Q) (R - Q) = 0) | |||
| (threesquare : EuclideanSpace ℝ (Fin 2) → EuclideanSpace ℝ (Fin 2) → EuclideanSpace ℝ (Fin 2) → Prop := fun P Q R ↦ dist Q P = dist Q R ∧ ⟪P - Q, R - Q⟫_ℝ = 0) | |||
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Could you clarify why using Matrix.dotProduct is error free? Also, looks like this is also an optParam, must have missed it earlier. Could you modify that?
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Nice catch, this is indeed an optParam!
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#236 finds two other stray optParams
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Could you clarify why using Matrix.dotProduct is error free?
I've expanded the PR description.
GeorgeTsoukalas
approved these changes
Oct 22, 2024
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Strictly
dotProductis for plain functions, not for elements ofEuclideanSpace.The original phrasing was still mathematically correct, as shown by
EuclideanSpace.inner_eq_star_dotProduct(andstar x = xon the real numbers); but it is using "evil" casting betweenEuclideanSpaceandFunction.