Theorems · Definition · field theory
Polynomial.roots
{R : Type u} → [inst : CommRing R] → [IsDomain R] → Polynomial R → Multiset Rroots 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
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.
- Polynomial.arootsproof · cited by 89
- Polynomial.roots.congr_simpstatement and proof · cited by 31
- Polynomial.mem_rootsstatement · cited by 30
- Polynomial.roots_zerostatement · cited by 19
- Polynomial.nthRootsproof · cited by 19
- Polynomial.count_rootsstatement and proof · cited by 19
- Polynomial.aroots_defstatement · cited by 17
- Polynomial.Splits.natDegree_eq_card_rootsstatement and proof · cited by 16
- Polynomial.Splits.eq_prod_rootsstatement and proof · cited by 16
- Polynomial.roots_X_sub_Cstatement · cited by 14
- Cubic.rootsproof · cited by 14
- Polynomial.roots_mulstatement and proof · cited by 12
Showing the 200 most cited of 272.