Theorems · Definition · commutative algebra

Algebra.PreSubmersivePresentation.jacobiMatrix

{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) → [Fintype σ] → [DecidableEq σ] → Matrix σ σ P.Ring

If σ has a Fintype and DecidableEq instance, the differential of P can be expressed in matrix form.

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

21 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFintypeDecidableEq