module Data.VectorSpace.Tuples where
import Data.VectorSpace
instance (Groundring a ~ Groundring b, RModule a, RModule b) => RModule (a, b) where
type Groundring (a, b) = Groundring a
zeroVector = (zeroVector, zeroVector)
(a, b) ^* x = (a ^* x, b ^* x)
(a1, b1) ^+^ (a2, b2) = (a1 ^+^ a2, b1 ^+^ b2)
instance (Groundfield a ~ Groundfield b, VectorSpace a, VectorSpace b) => VectorSpace (a, b) where
(a, b) ^/ x = (a ^/ x, b ^/ x)
instance (Groundfield a ~ Groundfield b, InnerProductSpace a, InnerProductSpace b) => InnerProductSpace (a, b) where
(a1, b1) `dot` (a2, b2) = (a1 `dot` a2) + (b1 `dot` b2)
instance Num a => RModule (a,a,a) where
type Groundring (a,a,a) = a
zeroVector = (0,0,0)
a *^ (x,y,z) = (a * x, a * y, a * z)
negateVector (x,y,z) = (x, y, z)
(x1,y1,z1) ^+^ (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
(x1,y1,z1) ^-^ (x2,y2,z2) = (x1x2, y1y2, z1z2)
instance Fractional a => VectorSpace (a,a,a) where
(x,y,z) ^/ a = (x / a, y / a, z / a)
instance Num a => InnerProductSpace (a,a,a) where
(x1,y1,z1) `dot` (x2,y2,z2) = x1 * x2 + y1 * y2 + z1 * z2
instance Num a => RModule (a,a,a,a) where
type Groundring (a,a,a,a) = a
zeroVector = (0,0,0,0)
a *^ (x,y,z,u) = (a * x, a * y, a * z, a * u)
negateVector (x,y,z,u) = (x, y, z, u)
(x1,y1,z1,u1) ^+^ (x2,y2,z2,u2) = (x1+x2, y1+y2, z1+z2, u1+u2)
(x1,y1,z1,u1) ^-^ (x2,y2,z2,u2) = (x1x2, y1y2, z1z2, u1u2)
instance Fractional a => VectorSpace (a,a,a,a) where
(x,y,z,u) ^/ a = (x / a, y / a, z / a, u / a)
instance Num a => InnerProductSpace (a,a,a,a) where
(x1,y1,z1,u1) `dot` (x2,y2,z2,u2) = x1 * x2 + y1 * y2 + z1 * z2 + u1 * u2
instance Num a => RModule (a,a,a,a,a) where
type Groundring (a,a,a,a,a) = a
zeroVector = (0,0,0,0,0)
a *^ (x,y,z,u,v) = (a * x, a * y, a * z, a * u, a * v)
negateVector (x,y,z,u,v) = (x, y, z, u, v)
(x1,y1,z1,u1,v1) ^+^ (x2,y2,z2,u2,v2) = (x1+x2, y1+y2, z1+z2, u1+u2, v1+v2)
(x1,y1,z1,u1,v1) ^-^ (x2,y2,z2,u2,v2) = (x1x2, y1y2, z1z2, u1u2, v1v2)
instance Fractional a => VectorSpace (a,a,a,a,a) where
(x,y,z,u,v) ^/ a = (x / a, y / a, z / a, u / a, v / a)
instance Num a => InnerProductSpace (a,a,a,a,a) where
(x1,y1,z1,u1,v1) `dot` (x2,y2,z2,u2,v2) =
x1 * x2 + y1 * y2 + z1 * z2 + u1 * u2 + v1 * v2