Theorems · Theorem · field theory
Polynomial.roots_def
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : DecidableEq R] (p : Polynomial R)
[inst_3 : Decidable (p = 0)], p.roots = if h : p = 0 then ∅ else Classical.choose ⋯- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement · cited by 643
- Multiset.cardstatement · cited by 375
- Multiset.countstatement · cited by 302
- Polynomial.rootsstatement and proof · cited by 264
- Classical.decEqproof · cited by 134
- Polynomial.rootMultiplicitystatement · cited by 79
- Classical.decproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.count_rootsproof · cited by 19