Theorems · Theorem · commutative algebra

MvPolynomial.pderiv_sumAlgEquiv

∀ {R : Type u_1} {S₁ : Type u_2} {S₂ : Type u_3} [inst : CommSemiring R] (b : S₁) (p : MvPolynomial (S₁ ⊕ S₂) R),
  (MvPolynomial.pderiv b) ((MvPolynomial.sumAlgEquiv R S₁ S₂) p) =
    (MvPolynomial.sumAlgEquiv R S₁ S₂) ((MvPolynomial.pderiv (Sum.inl b)) p)

Defined in: Mathlib.Algebra.MvPolynomial.PDeriv
Cited by: 1 results in Mathlib
Foundations: Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring

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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
CommSemiringstatement and proof · cited by 10,911
Finsuppstatement · cited by 5,255
MvPolynomialstatement and proof · cited by 2,140
AlgEquivstatement · cited by 1,681
Derivationstatement · cited by 293
MvPolynomial.pderivstatement · cited by 71
MvPolynomial.sumAlgEquivstatement · cited by 17
MvPolynomial.pderiv_sumRingEquivproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomialproof · cited by 1