Theorems · Theorem · commutative algebra
MvPolynomial.aeval_X
∀ {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) (s : σ), (MvPolynomial.aeval f) (MvPolynomial.X s) = f s- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 1,882 definitions · 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 · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement · cited by 2,140
- MvPolynomial.Xstatement · cited by 552
- MvPolynomial.aevalstatement · cited by 298
- MvPolynomial.eval₂_Xproof · cited by 36
Cited by105
Results whose statement or proof uses this declaration.
- MvPolynomial.bind₁_X_rightproof · cited by 26
- Algebra.Generators.Hom.toAlgHom_Xproof · cited by 12
- WittVector.coeff_frobenius_charPproof · cited by 9
- Algebra.adjoin_range_eq_range_aevalproof · cited by 6
- Algebra.FormallySmooth.comp_surjectiveproof · cited by 6
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Algebra.Generators.Hom.algebraMap_toAlgHomproof · cited by 6
- MvPolynomial.aeval_uniqueproof · cited by 5
- Algebra.Generators.toAlgHom_ofComp_surjectiveproof · cited by 5
- MvPolynomial.rename_eq_aevalproof · cited by 5
- MvPolynomial.comp_aevalproof · cited by 5
- MvPolynomial.transcendental_supported_polynomial_aeval_Xproof · cited by 4