Theorems · Theorem · field theory
Polynomial.Splits.roots_ne_zero
∀ {R : Type u_1} [inst : CommRing R] {f : Polynomial R} [inst_1 : IsDomain R], f.Splits → f.natDegree ≠ 0 → f.roots ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.rootsstatement · cited by 264
- Polynomial.Splits.natDegree_eq_card_rootsproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.sum_derivRootWeight_posproof · cited by 2