coeff_rTensorAlgHom_monomial_tmul

English

A repeat of the TMul-coefficient formula for rTensorAlgHom, emphasizing that the coefficient at d is coeff d p ⊗ n.

Русский

Повторение формулы коэффициента по d для rTensorAlgHom(p ⊗ n): coeff d = coeff d p ⊗ n.

LaTeX

$$$coeff d (rTensorAlgHom (p \\otimes n)) = (coeff d p) \\otimes n$$$

Lean4

theorem coeff_rTensorAlgHom_monomial_tmul (e : σ →₀ ℕ) (s : S) (n : N) (d : σ →₀ ℕ) :
    coeff d (rTensorAlgHom (monomial e s ⊗ₜ[R] n)) = if e = d then s ⊗ₜ[R] n else 0 := by simp [ite_tmul]

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