Theorems · Theorem · field theory
Polynomial.roots_C_mul_X_sub_C_of_IsUnit
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (b : R) (a : Rˣ),
(Polynomial.C ↑a * Polynomial.X - Polynomial.C b).roots = {↑a⁻¹ * b}- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Unitsstatement and proof · cited by 2,804
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.roots_C_mul_X_add_C_of_IsUnitproof · cited by 1
- Polynomial.roots_C_mul_X_sub_Cproof · cited by 0