Theorems · Theorem · field theory
Polynomial.roots_eq_of_degree_eq_card
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {p : Polynomial R} {S : Finset R},
(∀ x ∈ S, Polynomial.eval x p = 0) → ↑S.card = p.degree → p.roots = S.val- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 135 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
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- IsDomainstatement and proof · cited by 2,196
- WithBotstatement · cited by 1,498
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Finset.valstatement · cited by 438
- Polynomial.rootsstatement · cited by 264
- Polynomial.roots_eq_of_degree_le_card_of_ne_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.roots_T_realproof · cited by 2
- Polynomial.Chebyshev.roots_U_realproof · cited by 2