Theorems · Theorem · commutative algebra

Algebra.SubmersivePresentation.basisDeriv_apply

∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (i j : σ),
  P.basisDeriv i j = (MvPolynomial.aeval P.val) ((MvPolynomial.pderiv (P.map j)) (P.relation i))

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

2 results in Mathlib

Foundations

Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFinite