Theorems · Theorem · commutative algebra

Algebra.PreSubmersivePresentation.jacobian_eq_jacobiMatrix_det

∀ {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 : Fintype σ] [inst_4 : DecidableEq σ],
  P.jacobian = (algebraMap P.Ring S) P.jacobiMatrix.det

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

12 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFintypeDecidableEq