Theorems · Definition · complex analysis
Complex.canonicalFactor
ℝ → ℂ → ℂ → ℂ
Given R : ℝ and w : ℂ, the canonical factor is the function
fun z ↦ (R ^ 2 - (conj w) * z) / (R * (z - w)). In applications, one will typically consider a
setting where w ∈ ball 0 R.
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Complex.ofRealproof · cited by 1,654
- starRingEndproof · cited by 671
Cited by24
Results whose statement or proof uses this declaration.
- Complex.canonicalFactor_ne_zerostatement · cited by 6
- Complex.meromorphic_canonicalFactorstatement · cited by 5
- Complex.analyticOnNhd_canonicalFactorstatement · cited by 4
- Complex.meromorphicOrderAt_canonicalFactorstatement · cited by 3
- Complex.canonicalFactor_apply_selfstatement · cited by 2
- Complex.CanonicalDecomp.eventuallyEqstatement · cited by 2
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtstatement and proof · cited by 1
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt_of_meromorphicOrderAtstatement and proof · cited by 1
- Complex.ECanonicalDecomp.eventuallyEqstatement · cited by 1
- Complex.meromorphicNFOn_canonicalFactorstatement · cited by 1
- Complex.meromorphicOrderAt_canonicalFactor_ne_topstatement and proof · cited by 1
- MeromorphicOn.exists_canonicalDecompproof · cited by 1