Theorems · Theorem · field theory
Polynomial.aeval_def
∀ {R : Type u} {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (x : A)
(p : Polynomial R), (Polynomial.aeval x) p = Polynomial.eval₂ (algebraMap R A) x p- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 51 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.
Cites9
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 and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement · cited by 615
- Polynomial.eval₂statement · cited by 267
Cited by51
Results whose statement or proof uses this declaration.
- Polynomial.eval_map_algebraMapproof · cited by 49
- Polynomial.aeval_map_algebraMapproof · cited by 31
- IsIntegral.tower_topproof · cited by 30
- Polynomial.aeval_algebraMap_applyproof · cited by 24
- Polynomial.map_aeval_eq_aeval_mapproof · cited by 14
- IsIntegral.fg_adjoin_singletonproof · cited by 13
- isAlgebraic_iff_isIntegralproof · cited by 12
- AdjoinRoot.eval₂_rootproof · cited by 10
- Algebra.isIntegral_traceproof · cited by 7
- IsPrimitiveRoot.minpoly_eq_cyclotomic_of_irreducibleproof · cited by 4
- IsIntegral.of_powproof · cited by 4
- Submodule.span_range_natDegree_eq_adjoinproof · cited by 3