Copyright	(c) Nils Alex 2020
License	MIT
Maintainer	nils.alex@fau.de
Safe Haskell	None
Language	Haskell2010

Math.Tensor.Basic.Delta

Contents

Kronecker delta

Description

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

Synopsis

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

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 Source #

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 Source #

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 Source #

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.