Theorems · Theorem · complex analysis
Complex.exists_root
- #2 of the 100 theorems: Fundamental Theorem of Algebra
∀ {f : Polynomial ℂ}, 0 < f.degree → ∃ z, f.IsRoot zFundamental theorem of algebra: every nonconstant complex polynomial has a root.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 294 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Polynomialstatement and proof · cited by 5,681
- Complexstatement and proof · cited by 5,565
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- WithBotstatement · cited by 1,498
- Polynomial.evalproof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Filter.Tendsto.compproof · cited by 560
- inv_zeroproof · cited by 184
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.eval_zeroproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.IsUnitTrinomial.irreducible_of_coprime'proof · cited by 1