Theorems · Theorem · field theory
Polynomial.aeval_X
∀ {R : Type u} {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A),
(Polynomial.aeval x) Polynomial.X = x- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 120 results in Mathlib
- Foundations
- Depth 110 from the axioms, rests on 2,018 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- Polynomial.Xstatement · cited by 1,639
- RingHomClass.toRingHomproof · cited by 746
- Polynomial.aevalstatement · cited by 615
- Algebra.ofIdproof · cited by 166
- Polynomial.eval₂_Xproof · cited by 34
Cited by120
Results whose statement or proof uses this declaration.
- Polynomial.aeval_algHom_applyproof · cited by 31
- isAlgebraic_algebraMapproof · cited by 19
- Polynomial.aeval_algHomproof · cited by 14
- Algebra.adjoin_singleton_eq_range_aevalproof · cited by 12
- Polynomial.aeval_X_leftproof · cited by 7
- IsAlgClosed.algebraMap_bijective_of_isIntegralproof · cited by 6
- IsAdjoinRoot.aeval_root_eq_mapproof · cited by 5
- IsAlgebraic.exists_nonzero_dvdproof · cited by 5
- Polynomial.expand_aevalproof · cited by 4
- IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_oneproof · cited by 4
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4
- spectrum.subset_polynomial_aevalproof · cited by 4