instMulActionForallFinOfNatNat — Mathlib

English

The scalar action is compatible with the Jacobian's three-coordinate representation: (f ∘ ![a,b,c]) = ![f a, f b, f c] under a suitable ring homomorphism.

Русский

Скалярное действие совместимо с тройной координатной записью Джейкобия: f ∘ ![a,b,c] = ![f a, f b, f c], при подходящем кольцевом гомоморфизме.

LaTeX

$$f ∘ ![a,b,c] = ![f a, f b, f c]$$

Lean4

/-- The multiplicative action for a Jacobian point representative on a Weierstrass curve. -/
scoped instance : MulAction R <| Fin 3 → R
    where
  one_smul _ := by simp only [smul_fin3, one_pow, one_mul, fin3_def]
  mul_smul _ _ _ := by simp only [smul_fin3, mul_pow, mul_assoc, fin3_def_ext]

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