Theorems · Theorem · field theory
Polynomial.aeval_sub
∀ {R : Type u} {A : Type z} [inst : CommRing R] {p q : Polynomial R} [inst_1 : Ring A] [inst_2 : Algebra R A] (x : A),
(Polynomial.aeval x) (p - q) = (Polynomial.aeval x) p - (Polynomial.aeval x) q- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement and proof · cited by 615
- map_subproof · cited by 565
Cited by27
Results whose statement or proof uses this declaration.
- minpoly.uniqueproof · cited by 7
- Polynomial.aeval_modByMonic_eq_self_of_rootproof · cited by 6
- minpoly.add_algebraMapproof · cited by 4
- IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_oneproof · cited by 4
- isSeparable_algebraMapproof · cited by 3
- IsCyclotomicExtension.isSeparableproof · cited by 3
- Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iffproof · cited by 3
- IsLocalization.isAlgebraicproof · cited by 2
- IsIntegrallyClosed.minpoly.uniqueproof · cited by 2
- GaloisField.finrankproof · cited by 2
- minpoly_algEquiv_toLinearMapproof · cited by 2
- RatFunc.minpolyX_aeval_Xproof · cited by 2