Theorems · Theorem · field theory
Polynomial.Monic.roots_map_of_card_eq_natDegree
∀ {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},
p.Monic → ∀ (f : A →+* B), p.roots.card = p.natDegree → Multiset.map (⇑f) p.roots = (Polynomial.map f p).roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Polynomial.natDegreestatement and proof · cited by 1,105
- Multiset.mapstatement · cited by 876
- Polynomial.mapstatement · cited by 806
- Polynomial.Monicstatement and proof · cited by 461
- Multiset.cardstatement and proof · cited by 375
- Polynomial.rootsstatement and proof · cited by 264
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