Theorems · Theorem · commutative algebra
MvPolynomial.aeval_def
∀ {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) (p : MvPolynomial σ R), (MvPolynomial.aeval f) p = MvPolynomial.eval₂ (algebraMap R S₁) f p- Defined in
- Mathlib.Algebra.MvPolynomial.Eval
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapstatement · cited by 4,706
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.aevalstatement · cited by 298
- MvPolynomial.eval₂statement · cited by 103
Cited by7
Results whose statement or proof uses this declaration.
- MvPolynomial.aeval_map_algebraMapproof · cited by 8
- MvPolynomial.aeval_algebraMap_applyproof · cited by 6
- Algebra.Generators.ofComp_kerCompPreimageproof · cited by 2
- MvPowerSeries.aeval_uniqueproof · cited by 2
- MvPowerSeries.subst_coeproof · cited by 1
- MvPolynomial.aeval_natDegree_leproof · cited by 1
- MvPowerSeries.aeval_coeproof · cited by 1