Theorems · Theorem · field theory
Polynomial.map_roots_le
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : IsDomain A] [inst_3 : IsDomain B]
{p : Polynomial A} {f : A →+* B}, Polynomial.map f p ≠ 0 → Multiset.map (⇑f) p.roots ≤ (Polynomial.map f p).roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 3 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Multiset.mapstatement and proof · cited by 876
- Polynomial.mapstatement and proof · cited by 806
- Multiset.countproof · cited by 302
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.count_rootsproof · cited by 19
- Multiset.le_iff_countproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegreeproof · cited by 1
- Polynomial.map_roots_le_of_injectiveproof · cited by 1
- Polynomial.card_roots_le_mapproof · cited by 1