Theorems · Theorem · field theory
IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero
∀ {k : Type u} [inst : Field k] [IsAlgClosed k] {p : Polynomial k}, p.roots = 0 ↔ p.natDegree = 0- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 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.
Cites8
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
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.rootsstatement · cited by 264
- IsAlgClosedstatement and proof · cited by 150
- IsAlgClosed.roots_eq_zero_iffproof · cited by 1
- Polynomial.eq_C_coeff_zero_iff_natDegree_eq_zeroproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsAlgClosed.card_roots_eq_natDegreeproof · cited by 4
- IsAlgClosed.roots_eq_zero_iff_degree_nonposproof · cited by 0