Theorems · Definition · complex analysis
Polynomial.cauchyBound
{K : Type u_1} → [inst : NormedDivisionRing K] → Polynomial K → NNRealCauchy's bound on the roots of a given polynomial.
See IsRoot.norm_lt_cauchyBound for the proof that the roots satisfy this bound.
- Defined in
- Mathlib.Analysis.Polynomial.CauchyBound
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- NNRealstatement · cited by 4,310
- Finset.rangeproof · cited by 1,341
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- NNNorm.nnnormproof · cited by 952
- Finset.supproof · cited by 530
- Polynomial.leadingCoeffproof · cited by 498
- NormedDivisionRingstatement and proof · cited by 360
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.cauchyBound_Cstatement · cited by 1
- Polynomial.IsRoot.norm_lt_cauchyBoundstatement and proof · cited by 0
- Polynomial.one_le_cauchyBoundstatement · cited by 0
- Polynomial.cauchyBound_Xstatement · cited by 0
- Polynomial.cauchyBound_X_add_Cstatement · cited by 0
- Polynomial.cauchyBound_X_sub_Cstatement · cited by 0
- Polynomial.cauchyBound_onestatement · cited by 0
- Polynomial.cauchyBound_smulstatement · cited by 0
- Polynomial.cauchyBound_zerostatement · cited by 0