Theorems · Theorem · linear algebra

MultilinearMap.fromDFinsuppEquiv_apply

∀ {ι : Type uι} {κ : ι → Type uκ} {R : Type uR} {M : (i : ι) → κ i → Type uM} [inst : DecidableEq ι]
  [inst_1 : Fintype ι] [inst_2 : CommSemiring R] [inst_3 : (i : ι) → (k : κ i) → AddCommMonoid (M i k)]
  [inst_4 : (i : ι) → (k : κ i) → Module R (M i k)] {N : Type u_1} [inst_5 : AddCommMonoid N] [inst_6 : Module R N]
  [inst_7 : (i : ι) → DecidableEq (κ i)] [inst_8 : (i : ι) → (j : κ i) → (x : M i j) → Decidable (x ≠ 0)]
  (f : (p : (i : ι) → κ i) → MultilinearMap R (fun i => M i (p i)) N) (x : (i : ι) → Π₀ (j : κ i), M i j),
  ((MultilinearMap.fromDFinsuppEquiv κ R) f) x =
    ∑ p ∈ Fintype.piFinset fun i => (x i).support, (f p) fun i => (x i) (p i)

Defined in

Mathlib.LinearAlgebra.Multilinear.DFinsupp

Cited by

3 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqFintypeCommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEqDecidable