Theorems · Theorem · field theory
Polynomial.exists_multiset_roots
∀ {R : Type u} [inst : CommRing R] [IsDomain R] [inst_2 : DecidableEq R] {p : Polynomial R},
p ≠ 0 → ∃ s, ↑s.card ≤ p.degree ∧ ∀ (a : R), Multiset.count a s = Polynomial.rootMultiplicity a p- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDomainDecidableEq
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
- 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.rootMultiplicitystatement · cited by 79
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.count_rootsproof · cited by 19
- Polynomial.card_rootsproof · cited by 7
- Polynomial.roots_defstatement · cited by 1