Safe Haskell	Safe
Language	Haskell2010

Data.Semiring.V3

Synopsis

data V3 a = V3 !a !a !a
(<@>) :: Ring a => V3 a -> V3 a -> V3 a
triple :: Ring a => V3 a -> V3 a -> V3 a -> a
data I3
- = I31
- | I32
- | I33

Documentation

data V3 a Source #

Constructors

V3 !a !a !a

Instances

Functor V3 Source #
Instance details Defined in Data.Semiring.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
Foldable V3 Source #
Instance details Defined in Data.Semiring.V3 Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> m # foldr :: (a -> b -> b) -> b -> V3 a -> b # foldr' :: (a -> b -> b) -> b -> V3 a -> b # foldl :: (b -> a -> b) -> b -> V3 a -> b # foldl' :: (b -> a -> b) -> b -> V3 a -> b # foldr1 :: (a -> a -> a) -> V3 a -> a # foldl1 :: (a -> a -> a) -> V3 a -> a # toList :: V3 a -> [a] # null :: V3 a -> Bool # length :: V3 a -> Int # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # sum :: Num a => V3 a -> a # product :: Num a => V3 a -> a #
Distributive V3 Source #
Instance details Defined in Data.Semiring.V3 Methods distribute :: Functor f => f (V3 a) -> V3 (f a) # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) # distributeM :: Monad m => m (V3 a) -> V3 (m a) # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #
Representable V3 Source #
Instance details Defined in Data.Semiring.V3 Associated Types type Rep V3 :: Type # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Foldable1 V3 Source #
Instance details Defined in Data.Semiring.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
Eq a => Eq (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Ord a => Ord (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods compare :: V3 a -> V3 a -> Ordering # (<) :: V3 a -> V3 a -> Bool # (<=) :: V3 a -> V3 a -> Bool # (>) :: V3 a -> V3 a -> Bool # (>=) :: V3 a -> V3 a -> Bool # max :: V3 a -> V3 a -> V3 a # min :: V3 a -> V3 a -> V3 a #
Show a => Show (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Semigroup a => Semigroup (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods (<>) :: V3 a -> V3 a -> V3 a # sconcat :: NonEmpty (V3 a) -> V3 a # stimes :: Integral b => b -> V3 a -> V3 a #
Monoid a => Monoid (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods mempty :: V3 a # mappend :: V3 a -> V3 a -> V3 a # mconcat :: [V3 a] -> V3 a #
Prd a => Prd (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods (<~) :: V3 a -> V3 a -> Bool # (>~) :: V3 a -> V3 a -> Bool # (=~) :: V3 a -> V3 a -> Bool # (?~) :: V3 a -> V3 a -> Bool # pcompare :: V3 a -> V3 a -> Maybe Ordering #
Group a => Group (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods negate :: V3 a -> V3 a Source # (<<) :: V3 a -> V3 a -> V3 a Source #
Unital a => Semiring (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods (><) :: V3 a -> V3 a -> V3 a Source # fromBoolean :: Bool -> V3 a Source #
(Monoid a, Dioid a) => Dioid (V3 a) Source #
Instance details Defined in Data.Semiring.V3 Methods fromNatural :: Natural -> V3 a Source #
type Rep V3 Source #
Instance details Defined in Data.Semiring.V3 type Rep V3 = I3

(<@>) :: Ring a => V3 a -> V3 a -> V3 a infixl 7 Source #

Cross product.

>>> V3 1 1 1 <@> V3 (-2) 1 1
V3 0 (-3) 3

The cross product satisfies the following properties:

a <@> a = 0 
a <@> b = − ( b <@> a ) , 
a <@> ( b + c ) = ( a <@> b ) + ( a <@> c ) , 
( r a ) <@> b = a <@> ( r b ) = r ( a <@> b ) . 
a <@> ( b <@> c ) + b <@> ( c <@> a ) + c <@> ( a <@> b ) = 0 .

triple :: Ring a => V3 a -> V3 a -> V3 a -> a Source #

Scalar triple product.

data I3 Source #

Constructors

I31
I32
I33

Instances

Eq I3 Source #
Instance details Defined in Data.Semiring.V3 Methods (==) :: I3 -> I3 -> Bool # (/=) :: I3 -> I3 -> Bool #
Ord I3 Source #
Instance details Defined in Data.Semiring.V3 Methods compare :: I3 -> I3 -> Ordering # (<) :: I3 -> I3 -> Bool # (<=) :: I3 -> I3 -> Bool # (>) :: I3 -> I3 -> Bool # (>=) :: I3 -> I3 -> Bool # max :: I3 -> I3 -> I3 # min :: I3 -> I3 -> I3 #
Show I3 Source #
Instance details Defined in Data.Semiring.V3 Methods showsPrec :: Int -> I3 -> ShowS # show :: I3 -> String # showList :: [I3] -> ShowS #
Prd I3 Source #
Instance details Defined in Data.Semiring.V3 Methods (<~) :: I3 -> I3 -> Bool # (>~) :: I3 -> I3 -> Bool # (=~) :: I3 -> I3 -> Bool # (?~) :: I3 -> I3 -> Bool # pcompare :: I3 -> I3 -> Maybe Ordering #
Minimal I3 Source #
Instance details Defined in Data.Semiring.V3 Methods minimal :: I3 #
Maximal I3 Source #
Instance details Defined in Data.Semiring.V3 Methods maximal :: I3 #