Theorems · Theorem · field theory
Polynomial.aeval_mul
∀ {R : Type u} {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {p q : Polynomial R}
(x : A), (Polynomial.aeval x) (p * q) = (Polynomial.aeval x) p * (Polynomial.aeval x) q- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 16 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.
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
- 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
- map_mulproof · cited by 1,137
- Polynomial.aevalstatement and proof · cited by 615
Cited by16
Results whose statement or proof uses this declaration.
- minpoly.irreducibleproof · cited by 26
- minpoly.eq_of_irreducibleproof · cited by 8
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- Algebra.isIntegral_normproof · cited by 4
- spectrum.subset_polynomial_aevalproof · cited by 4
- Ideal.IsFractionRing.normalproof · cited by 3
- spectrum.map_polynomial_aeval_of_degree_posproof · cited by 2
- AnalyticWithinAt.aeval_polynomialproof · cited by 2
- Polynomial.sup_ker_aeval_le_ker_aeval_mulproof · cited by 1
- Polynomial.X_pow_sub_X_sub_one_irreducibleproof · cited by 1
- minpoly.prime_of_isIntegrallyClosedproof · cited by 1
- Polynomial.IsUnitTrinomial.irreducible_of_coprime'proof · cited by 1