algebra-4.3: Constructive abstract algebra

Numeric.Coalgebra.Geometric

Synopsis

Constructors

Instances

# Operations over an eigenbasis

class Eigenbasis m where Source #

Minimal complete definition

Methods

euclidean :: proxy m -> Bool Source #

antiEuclidean :: proxy m -> Bool Source #

v :: m -> BasisCoblade m Source #

e :: Int -> m Source #

Instances

 Source # Methodseuclidean :: proxy Euclidean -> Bool Source #antiEuclidean :: proxy Euclidean -> Bool Source #

class (Ring r, Eigenbasis m) => Eigenmetric r m where Source #

Minimal complete definition

metric

Methods

metric :: m -> r Source #

Instances

 Source # Methodsmetric :: Euclidean -> r Source #

newtype Euclidean Source #

Constructors

 Euclidean Int

Instances

 Source # MethodsenumFrom :: Euclidean -> [Euclidean] # Source # Methods Source # Methods Source # Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Euclidean -> c Euclidean #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Euclidean #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Euclidean) #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Euclidean) #gmapT :: (forall b. Data b => b -> b) -> Euclidean -> Euclidean #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Euclidean -> r #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Euclidean -> r #gmapQ :: (forall d. Data d => d -> u) -> Euclidean -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Euclidean -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Euclidean -> m Euclidean #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Euclidean -> m Euclidean #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Euclidean -> m Euclidean # Source # Methods Source # Methods Source # Methods Source # Methods Source # MethodsshowList :: [Euclidean] -> ShowS # Source # Methodsrange :: (Euclidean, Euclidean) -> [Euclidean] #index :: (Euclidean, Euclidean) -> Euclidean -> Int #unsafeIndex :: (Euclidean, Euclidean) -> Euclidean -> IntinRange :: (Euclidean, Euclidean) -> Euclidean -> Bool #rangeSize :: (Euclidean, Euclidean) -> Int #unsafeRangeSize :: (Euclidean, Euclidean) -> Int Source # Source # MethodssumWith1 :: Foldable1 f => (a -> Euclidean) -> f a -> Euclidean Source # Source # MethodssumWith :: Foldable f => (a -> Euclidean) -> f a -> Euclidean Source # Source # Source # MethodsproductWith1 :: Foldable1 f => (a -> Euclidean) -> f a -> Euclidean Source # Source # Methodstimes :: Integral n => n -> Euclidean -> Euclidean Source # Source # MethodsproductWith :: Foldable f => (a -> Euclidean) -> f a -> Euclidean Source # Source # Methods Source # Methods Source # Source # Source # Source # Methods Source # Methodseuclidean :: proxy Euclidean -> Bool Source #antiEuclidean :: proxy Euclidean -> Bool Source # Source # Methods Source # Methods Source # Methods Source # Methods Source # Methodsmetric :: Euclidean -> r Source #