Theorems · Theorem · real analysis
Polynomial.isEquivalent_atTop_lead
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] (P : Polynomial 𝕜)
[OrderTopology 𝕜],
Asymptotics.IsEquivalent Filter.atTop (fun x => Polynomial.eval x P) fun x => P.leadingCoeff * x ^ P.natDegree- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- OrderTopologystatement and proof · cited by 1,355
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- NormedFieldstatement and proof · cited by 1,084
- Polynomial.coeffproof · cited by 1,045
- Polynomial.evalstatement and proof · cited by 796
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.isEquivalent_atTop_divproof · cited by 5
- Polynomial.tendsto_atTop_of_leadingCoeff_nonnegproof · cited by 3
- Polynomial.isEquivalent_atBot_leadproof · cited by 1
- Polynomial.tendsto_atTop_iff_leadingCoeff_nonnegproof · cited by 0
- Polynomial.tendsto_nhds_iffproof · cited by 0