safe-tensor-0.2.1.0: Dependently typed tensor algebra

Math.Tensor.Basic.Area

Description

Definitions of area-symmetric tensors.

Synopsis

# 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 #

# 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 #

# 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 #