Theorems · Theorem · real analysis
Polynomial.isEquivalent_cobounded_leading_monomial
∀ {R : Type u_2} [inst : NormedRing R] [NormMulClass R] {P : Polynomial R},
Asymptotics.IsEquivalent (Bornology.cobounded R) (fun x => Polynomial.eval x P) fun x =>
P.leadingCoeff * x ^ P.natDegree- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRingNormMulClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- mul_oneproof · cited by 3,885
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- pow_zeroproof · cited by 1,094
- Polynomial.coeffproof · cited by 1,045
- NormedRingstatement and proof · cited by 924
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Bornology.coboundedstatement and proof · cited by 162
- Finset.mem_rangeproof · cited by 140
- Finset.sum_range_succproof · cited by 121
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.isLittleO_cobounded_of_degree_ltproof · cited by 1
- Polynomial.isBigO_cobounded_of_degree_leproof · cited by 0