Theorems · Theorem · commutative algebra

Polynomial.gaussNorm_coe_powerSeries

∀ {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], 0 ≤ c → PowerSeries.gaussNorm (⇑v) c ↑p = Polynomial.gaussNorm v c p

If v is a nonnegative function with v 0 = 0 and c is nonnegative, the Gauss norm of a polynomial is equal to its Gauss norm as a power series.

Defined in

Mathlib.RingTheory.Polynomial.GaussNorm

Cited by

4 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringFunLikeZeroHomClassNonnegHomClass