Theorems · Theorem · commutative algebra

Polynomial.gaussNorm_eq_zero_iff

∀ {R : Type u_1} {F : Type u_2} [inst : Semiring R] [inst_1 : FunLike F R ℝ] (v : F) {c : ℝ} (p : Polynomial R)
  [ZeroHomClass F R ℝ] [NonnegHomClass F R ℝ],
  (∀ (x : R), v x = 0 → x = 0) → 0 < c → (Polynomial.gaussNorm v c p = 0 ↔ p = 0)

If v x = 0 → x = 0 for all x : R and v is nonnegative, then the Gauss norm is zero if and only if the polynomial is zero.

Defined in

Mathlib.RingTheory.Polynomial.GaussNorm

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringFunLikeZeroHomClassNonnegHomClass