Theorems · Theorem · field theory
Polynomial.aroots_X
∀ {S : Type v} {T : Type w} [inst : CommRing T] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra T S],
Polynomial.X.aroots S = {0}- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Algebrastatement and proof · cited by 11,388
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.rootsproof · cited by 264
- Polynomial.map_Xproof · cited by 122
- Polynomial.arootsstatement · cited by 89
- Polynomial.aroots_defproof · cited by 17
- Polynomial.roots_Xproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.aroots_X_powproof · cited by 1
- Polynomial.natSepDegree_Xproof · cited by 1