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

Math.Tensor.Basic.Area

Contents

Area metric tensor induced from flat Lorentzian metric
Injections from \(AS(V)\) into \(V\times V\times V\times V\)
Surjections from \(V\times V\times V\times V\) onto \(AS(V)\)
Vertical coefficients for functions on \(AS(V)\)
Kronecker delta on \(AS(V)\)
Internals

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 #

someFlatAreaCon :: Num v => Demote Symbol -> Demote Symbol -> T 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 #

Kronecker delta on \(AS(V)\)

someDeltaArea :: Num v => Demote Symbol -> Demote Symbol -> Demote Symbol -> T v Source #

Internals

trianMapArea :: Map (Vec ('S ('S ('S ('S 'Z)))) Int) Int Source #

facMapArea :: forall b. Num b => Map (Vec ('S ('S ('S ('S 'Z)))) Int) b Source #

areaSign :: (Ord a, Num v) => a -> a -> a -> a -> Maybe v Source #

sortArea :: Ord a => a -> a -> a -> a -> Vec ('S ('S ('S ('S 'Z)))) a Source #