Theorems · Theorem · field theory
Polynomial.roots_comp_C_mul_X_add_C
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (p : Polynomial R) (a b : R),
IsUnit a →
(p.comp (Polynomial.C a * Polynomial.X + Polynomial.C b)).roots =
Multiset.map (fun x => Ring.inverse a * (x - b)) p.roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites20
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 · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xstatement and proof · cited by 1,639
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.mapstatement and proof · cited by 876
- Polynomial.rootsstatement and proof · cited by 264
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