coeff_mul_monomial — Mathlib

English

The coefficient of a monomial is given by a Kronecker delta: coeff m (monomial n a) = if n = m then a else 0.

Русский

Коэффициент мономиала — дельта Кронекке: coeff m (monomial n a) = if n = m then a иначе 0.

LaTeX

$$$\mathrm{coeff}\ m (\mathrm{monomial}\ n\ a) = \text{if } n=m\ \text{then } a\ \text{else } 0$$$

Lean4

@[simp]
theorem coeff_mul_monomial (m) (s : σ →₀ ℕ) (r : R) (p : MvPolynomial σ R) :
    coeff (m + s) (p * monomial s r) = coeff m p * r :=
  AddMonoidAlgebra.mul_single_apply_aux fun _a _ => add_left_inj _

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