Theorems · Theorem · field theory
IsAlgClosed.roots_eq_zero_iff
∀ {k : Type u} [inst : Field k] [IsAlgClosed k] {p : Polynomial k}, p.roots = 0 ↔ p = Polynomial.C (p.coeff 0)- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsAlgClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Polynomial.Cstatement and proof · cited by 1,598
- LT.lt.ne'proof · cited by 1,417
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreeproof · cited by 643
- le_or_gtproof · cited by 269
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.IsRootproof · cited by 152
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zeroproof · cited by 2