Theorems · Theorem · commutative algebra

MonomialOrder.sPolynomial_monomial_mul

∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommRing R] [NoZeroDivisors R] (p₁ p₂ : MvPolynomial σ R)
  (d₁ d₂ : σ →₀ ℕ) (c₁ c₂ : R),
  m.sPolynomial ((MvPolynomial.monomial d₁) c₁ * p₁) ((MvPolynomial.monomial d₂) c₂ * p₂) =
    (MvPolynomial.monomial ((d₁ + m.degree p₁) ⊔ (d₂ + m.degree p₂) - m.degree p₁ ⊔ m.degree p₂)) (c₁ * c₂) *
      m.sPolynomial p₁ p₂

Defined in

Mathlib.RingTheory.MvPolynomial.MonomialOrder

Cited by

3 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingNoZeroDivisors