Theorems · Definition · several complex variables

FormalMultilinearSeries.applyComposition

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : CommRing 𝕜] →
        [inst_1 : AddCommGroup E] →
          [inst_2 : AddCommGroup F] →
            [inst_3 : Module 𝕜 E] →
              [inst_4 : Module 𝕜 F] →
                [inst_5 : TopologicalSpace E] →
                  [inst_6 : TopologicalSpace F] →
                    [inst_7 : IsTopologicalAddGroup E] →
                      [inst_8 : ContinuousConstSMul 𝕜 E] →
                        [inst_9 : IsTopologicalAddGroup F] →
                          [inst_10 : ContinuousConstSMul 𝕜 F] →
                            FormalMultilinearSeries 𝕜 E F →
                              {n : ℕ} → (c : Composition n) → (Fin n → E) → Fin c.length → F

Given a formal multilinear series p, a composition c of n and the index i of a block of c, we may define a function on Fin n → E by picking the variables in the i-th block of n, and applying the corresponding coefficient of p to these variables. This function is called p.applyComposition c v i for v : Fin n → E and i : Fin c.length.

Defined in

Mathlib.Analysis.Analytic.Composition

Cited by

24 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupAddCommGroupModuleModuleTopologicalSpaceTopologicalSpaceIsTopologicalAddGroupContinuousConstSMulIsTopologicalAddGroupContinuousConstSMul