Theorems · Theorem · commutative algebra

Polynomial.isNonarchimedean_gaussNorm

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

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

Defined in

Mathlib.RingTheory.Polynomial.GaussNorm

Cited by

0 results in Mathlib

Foundations

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

Assumes

SemiringFunLikeZeroHomClassNonnegHomClass