| Copyright | (c) Nils Alex 2020 |
|---|---|
| License | MIT |
| Maintainer | nils.alex@fau.de |
| Safe Haskell | None |
| Language | Haskell2010 |
Math.Tensor.Basic.Area
Description
Definitions of area-symmetric tensors.
Synopsis
- flatAreaCon :: forall (id :: Symbol) (a :: Symbol) (r :: Rank) v. ('['('VSpace (id <> "Area") 21, 'Con (a :| '[]))] ~ r, Num v) => Sing id -> Sing a -> Tensor r v
- someFlatAreaCon :: Num v => Demote Symbol -> Demote Symbol -> T v
- injAreaCon' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (InjAreaConRank id a b c d i ~ 'Just r, SingI r, Num v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v
- injAreaCov' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (InjAreaCovRank id a b c d i ~ 'Just r, SingI r, Num v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v
- someInjAreaCon :: forall v m. (Num v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v)
- someInjAreaCov :: forall v m. (Num v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v)
- surjAreaCon' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (SurjAreaConRank id a b c d i ~ 'Just r, SingI r, Fractional v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v
- surjAreaCov' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (SurjAreaCovRank id a b c d i ~ 'Just r, SingI r, Fractional v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v
- someSurjAreaCon :: forall v m. (Fractional v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v)
- someSurjAreaCov :: forall v m. (Fractional v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v)
- someInterAreaCon :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> T v
- someInterAreaCov :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> T v
- someDeltaArea :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> T v
- trianMapArea :: Map (Vec ('S ('S ('S ('S 'Z)))) Int) Int
- facMapArea :: forall b. Num b => Map (Vec ('S ('S ('S ('S 'Z)))) Int) b
- areaSign :: (Ord a, Num v) => a -> a -> a -> a -> Maybe v
- sortArea :: Ord a => a -> a -> a -> a -> Vec ('S ('S ('S ('S 'Z)))) a
Area metric tensor induced from flat Lorentzian metric
flatAreaCon :: forall (id :: Symbol) (a :: Symbol) (r :: Rank) v. ('['('VSpace (id <> "Area") 21, 'Con (a :| '[]))] ~ r, Num v) => Sing id -> Sing a -> Tensor r v Source #
Injections from \(AS(V)\) into \(V\times V\times V\times V\)
injAreaCon' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (InjAreaConRank id a b c d i ~ 'Just r, SingI r, Num v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v Source #
injAreaCov' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (InjAreaCovRank id a b c d i ~ 'Just r, SingI r, Num v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v Source #
someInjAreaCon :: forall v m. (Num v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v) Source #
someInjAreaCov :: forall v m. (Num v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v) Source #
Surjections from \(V\times V\times V\times V\) onto \(AS(V)\)
surjAreaCon' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (SurjAreaConRank id a b c d i ~ 'Just r, SingI r, Fractional v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v Source #
surjAreaCov' :: forall (id :: Symbol) (a :: Symbol) (b :: Symbol) (c :: Symbol) (d :: Symbol) (i :: Symbol) (r :: Rank) v. (SurjAreaCovRank id a b c d i ~ 'Just r, SingI r, Fractional v) => Sing id -> Sing a -> Sing b -> Sing c -> Sing d -> Sing i -> Tensor r v Source #
someSurjAreaCon :: forall v m. (Fractional v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v) Source #
someSurjAreaCov :: forall v m. (Fractional v, MonadError String m) => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> m (T v) Source #
Vertical coefficients for functions on \(AS(V)\)
someInterAreaCon :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> T v Source #
someInterAreaCov :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> Demote Symbol -> T v Source #