Math.Tensor.Basic.Delta

Definitions of Kronecker deltas \(\delta^{a}_{\hphantom ab}\) (identity automorphisms) for arbitrary vector spaces.

Kronecker delta

delta :: forall (id :: Symbol) (n :: Nat) (a :: Symbol) (b :: Symbol) (r :: Rank) v. ('['(VSpace id n, ConCov (a :| '[]) (b :| '[]))] ~ r, TailR (TailR r) ~ '[], Sane (TailR r) ~ True, SingI n, Num v) => Tensor r v

The Kronecker delta \(\delta^a_{\hphantom ab} \) for a given VSpace id n with contravariant index label a and covariant index label b.

delta' :: forall (id :: Symbol) (n :: Nat) (a :: Symbol) (b :: Symbol) (r :: Rank) v. (KnownNat n, Num v, '['(VSpace id n, ConCov (a :| '[]) (b :| '[]))] ~ r, TailR (TailR r) ~ '[], Sane (TailR r) ~ True) => Sing id -> Sing n -> Sing a -> Sing b -> Tensor r v

The Kronecker delta \(\delta^a_{\hphantom ab} \) for a given VSpace id n with contravariant index label a and covariant index label b. Labels and dimension are passed explicitly as singletons.

someDelta :: Num v => Demote Symbol -> Demote Nat -> Demote Symbol -> Demote Symbol -> T v

The Kronecker delta \(\delta^a_{\hphantom ab} \) for a given VSpace id n with contravariant index label a and covariant index label b. Labels and dimension are passed as values. Result is existentially quantified.