map — Mathlib

English

There is a natural additive-monoid homomorphism Behrend map(d) from Fin n → ℕ to ℕ given by applying the d-adic weight sum: map(d)(a) = ∑ i a(i) d^i.

Русский

СуществуетNaturally определённый односторонний гомоморфизм от Fin n → ℕ в ℕ, называемый Behrend map(d), определяемый по формуле: map(d)(a) = ∑ i a(i) d^i.

LaTeX

$$$ map(d)(a) = \\sum_{i} a(i) \\cdot d^{\,i} $$$

Lean4

/-- The map that appears in Behrend's bound on Roth numbers. -/
@[simps]
def map (d : ℕ) : (Fin n → ℕ) →+ ℕ where
  toFun a := ∑ i, a i * d ^ (i : ℕ)
  map_zero' := by simp_rw [Pi.zero_apply, zero_mul, sum_const_zero]
  map_add' a b := by simp_rw [Pi.add_apply, add_mul, sum_add_distrib]

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