Theorems · Theorem · commutative algebra

Polynomial.gaussNorm_mul_le

∀ {R : Type u_1} {F : Type u_2} [inst : Semiring R] [inst_1 : FunLike F R ℝ] (v : F) {c : ℝ} [ZeroHomClass F R ℝ]
  [NonnegHomClass F R ℝ] [MulHomClass F R ℝ],
  IsNonarchimedean ⇑v →
    ∀ (p q : Polynomial R),
      0 ≤ c → Polynomial.gaussNorm v c (p * q) ≤ Polynomial.gaussNorm v c p * Polynomial.gaussNorm v c q

If v is a nonnegative nonarchimedean multiplicative function with v 0 = 0 and c is nonnegative, then the Gauss norm is submultiplicative.

Defined in

Mathlib.RingTheory.Polynomial.GaussNorm

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringFunLikeZeroHomClassNonnegHomClassMulHomClass