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Theorems · Theorem · commutative algebra

KaehlerDifferential.mvPolynomialBasis_repr_apply

∀ (R : Type u) [inst : CommRing R] (σ : Type u_1) (x : MvPolynomial σ R) (i : σ),
  ((KaehlerDifferential.mvPolynomialBasis R σ).repr ((KaehlerDifferential.D R (MvPolynomial σ R)) x)) i =
    (MvPolynomial.pderiv i) x
Defined in
Mathlib.RingTheory.Kaehler.Polynomial
Cited by
2 results in Mathlib
Foundations
Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
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Around this declaration

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Algebra.Generators.cotangentSpaceBasis_repr_tmul · cited by 4Generators.cotangentSpace…Algebra.Presentation.differentials.comm₁₂_single · cited by 1differentials.comm₁₂_sing…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingFinsupp · cited by 5255FinsuppLinearEquiv · cited by 3317LinearEquivMvPolynomial · cited by 2140MvPolynomialLinearMap.comp · cited by 1642LinearMap.compLinearEquiv.toLinearMap · cited by 1171LinearEquiv.toLinearMapModule.Basis.repr · cited by 498Basis.reprDerivation · cited by 293DerivationKaehlerDifferential · cited by 204KaehlerDifferentialFinsupp.single_apply · cited by 99Finsupp.single_applyKaehlerDifferential.D · cited by 92KaehlerDifferential.DPi.single_apply · cited by 78Pi.single_applyMvPolynomial.pderiv · cited by 71MvPolynomial.pderivKaehlerDifferential.mvPolynom…CITED BYCITES

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