Theorems · Theorem · field theory
Polynomial.aeval_smul
∀ {R : Type u} {A : Type z} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (f : Polynomial R)
{G : Type u_3} [inst_3 : Monoid G] [inst_4 : MulSemiringAction G A] [SMulCommClass G R A] (g : G) (x : A),
(Polynomial.aeval (g • x)) f = g • (Polynomial.aeval x) f- Defined in
- Mathlib.Algebra.Polynomial.AlgebraMap
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · 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
- Monoidstatement and proof · cited by 3,887
- AlgHomstatement · cited by 3,236
- SMulCommClassstatement and proof · cited by 1,927
- Polynomial.aevalstatement and proof · cited by 615
- MulSemiringActionstatement and proof · cited by 423
- Polynomial.aeval_algHom_applyproof · cited by 31
- MulSemiringAction.toAlgHomproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.smul_mem_rootSetproof · cited by 1