Theorems · Theorem · commutative algebra

Algebra.PreSubmersivePresentation.aevalDifferential_single

∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  (P : Algebra.PreSubmersivePresentation R S ι σ) [inst_3 : Finite σ] [inst_4 : DecidableEq σ] (i j : σ),
  P.aevalDifferential (Pi.single i 1) j = (MvPolynomial.aeval P.val) ((MvPolynomial.pderiv (P.map j)) (P.relation i))

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

3 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteDecidableEq