Theorems · Theorem · field theory
Polynomial.aroots_X_pow
∀ {S : Type v} {T : Type w} [inst : CommRing T] [inst_1 : CommRing S] [inst_2 : IsDomain S] [inst_3 : Algebra T S]
(n : ℕ), (Polynomial.X ^ n).aroots S = n • {0}- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Polynomialstatement · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.arootsstatement · cited by 89
- Polynomial.aroots_Xproof · cited by 2
- Polynomial.aroots_powproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.aroots_C_mul_X_powproof · cited by 1