Theorems · Theorem · field theory
IsAlgClosed.roots_eq_zero_iff_degree_nonpos
∀ {k : Type u} [inst : Field k] [IsAlgClosed k] {p : Polynomial k}, p.roots = 0 ↔ p.degree ≤ 0- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsAlgClosed
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Polynomial.rootsstatement · cited by 264
- IsAlgClosedstatement and proof · cited by 150
- Polynomial.natDegree_eq_zero_iff_degree_le_zeroproof · cited by 12
- IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zeroproof · cited by 2
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