Mathlib Map

Theorems · Definition · field theory

Polynomial.roots

{R : Type u} → [inst : CommRing R] → [IsDomain R] → Polynomial R → Multiset R

roots p noncomputably gives a multiset containing all the roots of p, including their multiplicities.

Defined in
Mathlib.Algebra.Polynomial.Roots
Cited by
264 results in Mathlib
Foundations
Depth 129 from the axioms, rests on 3,039 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDomain

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

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

Cited by272

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 272.