Theorems · Theorem · commutative algebra
MvPolynomial.comp_aeval
∀ {R : Type u} {S₁ : Type v} {σ : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S₁] [inst_2 : Algebra R S₁]
(f : σ → S₁) {B : Type u_2} [inst_3 : CommSemiring B] [inst_4 : Algebra R B] (φ : S₁ →ₐ[R] B),
φ.comp (MvPolynomial.aeval f) = MvPolynomial.aeval fun i => φ (f i)- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- AlgHomstatement and proof · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- AlgHom.compstatement · cited by 501
- MvPolynomial.aevalstatement · cited by 298
- MvPolynomial.aeval_Xproof · cited by 105
- MvPolynomial.algHom_extproof · cited by 55
Cited by5
Results whose statement or proof uses this declaration.
- MvPolynomial.comp_aeval_applyproof · cited by 3
- Algebra.Generators.ofComp_kerCompPreimageproof · cited by 2
- PolynomialLaw.isCompat_applyproof · cited by 2
- LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_evalproof · cited by 1
- Algebra.Generators.ker_ofAlgEquivproof · cited by 0