Theorems · Theorem · real analysis
Polynomial.isBigO_cobounded_of_degree_le
∀ {R : Type u_2} [inst : NormedRing R] [NormMulClass R] {P Q : Polynomial R},
P.degree ≤ Q.degree → (fun x => Polynomial.eval x P) =O[Bornology.cobounded R] fun x => Polynomial.eval x Q- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingNormMulClass
Around this declaration
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Polynomialstatement and proof · cited by 5,681
- Filter.EventuallyEqproof · cited by 1,912
- WithBotstatement · cited by 1,498
- NormedRingstatement and proof · cited by 924
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Asymptotics.IsBigOstatement and proof · cited by 506
- Polynomial.leadingCoeffproof · cited by 498
- Bornology.coboundedstatement and proof · cited by 162
- Filter.EventuallyEq.reflproof · cited by 108
- NormMulClassstatement and proof · cited by 66
- Polynomial.eval_zeroproof · cited by 36
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