Theorems · Theorem · complex analysis

Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zero

∀ (p : Polynomial ℝ) {z : ℂ},
  (Polynomial.aeval z) p = 0 →
    z.im ≠ 0 →
      (Polynomial.X - Polynomial.C ((starRingEnd ℂ) z)) * (Polynomial.X - Polynomial.C z) ∣
        Polynomial.map (algebraMap ℝ ℂ) p

Defined in: Mathlib.Analysis.Complex.Polynomial.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
RingHomstatement · cited by 10,189
Polynomialstatement and proof · cited by 5,681
Complexstatement and proof · cited by 5,565
Algebra.algebraMapstatement · cited by 4,706
AlgHomstatement · cited by 3,236
Polynomial.Xstatement · cited by 1,639
Polynomial.Cstatement · cited by 1,598
Polynomial.mapstatement · cited by 806
starRingEndstatement and proof · cited by 671
Polynomial.aevalstatement and proof · cited by 615

Cited by1

Results whose statement or proof uses this declaration.

Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zeroproof · cited by 0