Theorems · Theorem · field theory
Polynomial.aeval_C
∀ {R : Type u} {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A) (r : R),
(Polynomial.aeval x) (Polynomial.C r) = (algebraMap R A) r- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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 · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement · cited by 3,236
- Polynomial.Cstatement · cited by 1,598
- RingHomClass.toRingHomproof · cited by 746
- Polynomial.aevalstatement · cited by 615
- Algebra.ofIdproof · cited by 166
Cited by81
Results whose statement or proof uses this declaration.
- Polynomial.aeval_algHom_applyproof · cited by 31
- isAlgebraic_algebraMapproof · cited by 19
- IsAlgClosed.algebraMap_bijective_of_isIntegralproof · cited by 6
- IsAlgebraic.exists_nonzero_dvdproof · cited by 5
- Polynomial.expand_aevalproof · cited by 4
- spectrum.subset_polynomial_aevalproof · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- minpoly.add_algebraMapproof · cited by 4
- minpoly.eq_X_sub_C_of_algebraMap_injproof · cited by 4
- minpoly.natSepDegree_eq_one_iff_pow_memproof · cited by 4
- isSeparable_algebraMapproof · cited by 3
- Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iffproof · cited by 3