Theorems · Theorem · field theory
Polynomial.aeval_comp
∀ {R : Type u} [inst : CommSemiring R] {p q : Polynomial R} {A : Type u_3} [inst_1 : Semiring A] [inst_2 : Algebra R A]
(x : A), (Polynomial.aeval x) (p.comp q) = (Polynomial.aeval ((Polynomial.aeval x) q)) p- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 14 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
- AlgHomstatement · cited by 3,236
- Polynomial.aevalstatement · cited by 615
- Polynomial.compstatement · cited by 193
- Polynomial.eval₂_comp'proof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- minpoly.add_algebraMapproof · cited by 4
- Ideal.IsFractionRing.normalproof · cited by 3
- IsAlgebraic.of_smul_isIntegralproof · cited by 2
- minpoly.negproof · cited by 2
- Transcendental.aeval_of_transcendentalproof · cited by 2
- IsAlgebraic.of_smulproof · cited by 1
- bernoulliFun_eval_one_subproof · cited by 1
- solvableByRad_le_algClosureproof · cited by 1
- Polynomial.irreducible_compproof · cited by 1
- IsAlgebraic.negproof · cited by 1
- Transcendental.of_aevalproof · cited by 1
- IsAlgebraic.of_aevalproof · cited by 1