-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Math and quantum mechanics
--   
--   List based linear algebra, similtaneous linear equations, eigenvalues
--   and eigenvectors, roots of polynomials, transcendent functions with
--   arbitrary precision implemented by continued fractions, quantum
--   operations, tensors
@package numeric-quest
@version 0.2.0.2

module Fraction
data Fraction
(:-:) :: Integer -> Integer -> Fraction
num :: Fraction -> Integer
den :: Fraction -> Integer
reduce :: Fraction -> Fraction
(//) :: Integer -> Integer -> Fraction
approx :: Fraction -> Fraction -> Fraction
numericEnumFrom :: Real a => a -> [a]
numericEnumFromThen :: Real a => a -> a -> [a]
numericEnumFromTo :: Real a => a -> a -> [a]
numericEnumFromThenTo :: Real a => a -> a -> a -> [a]
type CF = [(Fraction, Fraction)]
fromCF :: CF -> Fraction
toCF :: Fraction -> CF
approxCF :: Fraction -> CF -> Fraction
fromTaylorToCF :: (Fractional a) => [a] -> a -> [(a, a)]
fromFraction :: Fraction -> Double
fac :: Integer -> Integer
integerRoot2 :: Integer -> Integer
class Transcendental a
pi' :: Transcendental a => Fraction -> a
tan' :: Transcendental a => Fraction -> a -> a
sin' :: Transcendental a => Fraction -> a -> a
cos' :: Transcendental a => Fraction -> a -> a
atan' :: Transcendental a => Fraction -> a -> a
asin' :: Transcendental a => Fraction -> a -> a
acos' :: Transcendental a => Fraction -> a -> a
sqrt' :: Transcendental a => Fraction -> a -> a
root' :: Transcendental a => Fraction -> a -> Integer -> a
power' :: Transcendental a => Fraction -> a -> a -> a
exp' :: Transcendental a => Fraction -> a -> a
tanh' :: Transcendental a => Fraction -> a -> a
sinh' :: Transcendental a => Fraction -> a -> a
cosh' :: Transcendental a => Fraction -> a -> a
atanh' :: Transcendental a => Fraction -> a -> a
asinh' :: Transcendental a => Fraction -> a -> a
acosh' :: Transcendental a => Fraction -> a -> a
log' :: Transcendental a => Fraction -> a -> a
decimal :: Transcendental a => Integer -> a -> IO ()
instance GHC.Classes.Eq Fraction.Fraction
instance Fraction.Transcendental Fraction.Fraction
instance GHC.Read.Read Fraction.Fraction
instance GHC.Show.Show Fraction.Fraction
instance GHC.Classes.Ord Fraction.Fraction
instance GHC.Num.Num Fraction.Fraction
instance GHC.Real.Fractional Fraction.Fraction
instance GHC.Real.Real Fraction.Fraction
instance GHC.Real.RealFrac Fraction.Fraction
instance GHC.Enum.Enum Fraction.Fraction

module Orthogonals
bra_ket :: (Scalar a, Num a) => [a] -> [a] -> a
class Eq a => Scalar a
coupled :: Scalar a => a -> a
norm :: Scalar a => [a] -> a
almostZero :: Scalar a => a -> Bool
scaled :: Scalar a => [a] -> [a]
norm1 :: (Num a) => [a] -> a
norminf :: (Num a, Ord a) => [a] -> a
matnorm1 :: (Num a, Ord a) => [[a]] -> a
matnorminf :: (Num a, Ord a) => [[a]] -> a
sum_product :: Num a => [a] -> [a] -> a
normalized :: (Scalar a, Fractional a) => [a] -> [a]
scaled' :: (Fractional t, Ord t) => [t] -> [t]
transposed :: [[a]] -> [[a]]
adjoint :: Scalar a => [[a]] -> [[a]]
matrix_zipWith :: (a -> b -> c) -> [[a]] -> [[b]] -> [[c]]
add_matrices :: (Num a) => t -> t1 -> [[a]] -> [[a]] -> [[a]]
matrix_matrix :: Num a => [[a]] -> [[a]] -> [[a]]
matrix_matrix' :: (Num a) => [[a]] -> [[a]] -> [[a]]
triangle_matrix' :: Num a => [[a]] -> [[a]] -> [[a]]
matrix_ket :: Num a => [[a]] -> [a] -> [a]
bra_matrix :: (Scalar a, Num a) => [a] -> [[a]] -> [a]
bra_matrix_ket :: (Scalar a, Num a) => [a] -> [[a]] -> [a] -> a
scalar_matrix :: Num a => a -> [[a]] -> [[a]]
orthogonals :: (Scalar a, Fractional a) => [a] -> [[a]]
gram_schmidt :: (Scalar a, Fractional a) => [[a]] -> [a] -> [a]
one_ket_triangle :: (Scalar a, Fractional a) => [[a]] -> [a] -> [([a], a)]
one_ket_solution :: (Scalar a, Fractional a) => [[a]] -> [a] -> [a]
many_kets_triangle :: (Scalar a, Fractional a) => [[a]] -> [[a]] -> [([a], [a])]
many_kets_solution :: (Scalar a, Fractional a) => [[a]] -> [[a]] -> [[a]]
inverse :: (Scalar a, Fractional a) => [[a]] -> [[a]]
factors_QR :: (Scalar a, Fractional a) => [[a]] -> ([[a]], [[a]])
determinant :: (Scalar a, Fractional a) => [[a]] -> a
determinantNaive :: (Num a) => [[a]] -> a
determinantClow :: (Num a) => [[a]] -> a
newClow :: (Num a) => [[a]] -> [[a]] -> [a]
extendClow :: (Num a) => [[a]] -> [[a]] -> [[a]]
longerClow :: (Num a) => [[a]] -> [[a]] -> [[a]]

-- | Compositional power of a function, i.e. apply the function n times to
--   a value.
nest :: Int -> (a -> a) -> a -> a
removeEach :: [a] -> [[a]]
alternate :: (Num a) => [a] -> [a]
parityFlip :: Num a => Int -> a -> a

-- | Weight a list of numbers by a scalar.
scaleVec :: (Num a) => a -> [a] -> [a]

-- | Add corresponding numbers of two lists.
addVec :: (Num a) => [a] -> [a] -> [a]

-- | Add some lists.
sumVec :: (Num a) => [[a]] -> [a]
similar_to :: (Scalar a, Fractional a) => [[a]] -> [[a]]
iterated_eigenvalues :: (Scalar a1, Fractional a1, Eq a, Num a) => [[a1]] -> a -> [[a1]]
eigenvalues :: (Scalar a1, Fractional a1, Eq a, Num a) => [[a1]] -> a -> [a1]
add_to_diagonal :: Num a => a -> [[a]] -> [[a]]
eigenkets :: (Scalar a, Fractional a) => [[a]] -> [a] -> [[a]]
eigenket' :: (Scalar a, Fractional a) => [[a]] -> a -> a -> [a] -> [a]
unit_matrix :: Num a => Int -> [[a]]
unit_vector :: Num a => Int -> Int -> [a]
diagonals :: [[a]] -> [a]
instance Orthogonals.Scalar GHC.Types.Double
instance Orthogonals.Scalar GHC.Types.Float
instance GHC.Real.Integral a => Orthogonals.Scalar (GHC.Real.Ratio a)
instance GHC.Float.RealFloat a => Orthogonals.Scalar (Data.Complex.Complex a)

module LinearAlgorithms
triangular :: Int -> [[Scalar]] -> [[Scalar]]
triangular2 :: Int -> [[Scalar]] -> ([[Scalar]], [[Scalar]])
tridiagonal :: [[Scalar]] -> [[Scalar]]
tridiagonal2 :: [[Scalar]] -> ([[Scalar]], [[Scalar]])
type Scalar = Complex Double

module EigensystemNum
mult :: Num a => [[a]] -> [[a]] -> [[a]]
matSqr :: Num a => [[a]] -> [[a]]
powerIter :: (Fractional a, Ord a) => [[a]] -> [([[a]], [[a]])]
normalize :: (Fractional a, Ord a) => [[a]] -> [[a]]
getGrowth :: (Fractional a, Ord a) => ([[a]], [[a]]) -> a
specRadApprox :: (Fractional a, Ord a) => [[a]] -> [a]
eigenValuesApprox :: (Scalar a, Fractional a) => [[a]] -> [[a]]
limit :: (Num a, Ord a) => a -> [a] -> a

module QuantumVector
class DiracVector a
add :: DiracVector a => a -> a -> a
scale :: DiracVector a => Scalar -> a -> a
reduce :: DiracVector a => a -> a
basis :: DiracVector a => a -> [a]
components :: DiracVector a => a -> [Scalar]
compose :: DiracVector a => [Scalar] -> [a] -> a
dimension :: DiracVector a => a -> Int
norm :: DiracVector a => a -> Double
normalize :: DiracVector a => a -> a
type Scalar = Complex Double
data Ket a
KetZero :: Ket a
Ket :: a -> Ket a
(:|>) :: Scalar -> Ket a -> Ket a
(:+>) :: Ket a -> Ket a -> Ket a
(*>) :: (Ord a, Ord b) => Ket a -> Ket b -> Ket (Tuple a b)
infixl 7 *>
(|>) :: Ord a => Scalar -> Ket a -> Ket a
infix 6 |>
(+>) :: Ord a => Ket a -> Ket a -> Ket a
infixl 5 +>
reduceKet :: Ord a => Ket a -> Ket a
ketBasis :: Ord a => Ket a -> [Ket a]
toBra :: Ord a => Ket a -> Bra a
data Bra a
BraZero :: Bra a
Bra :: a -> Bra a
(:<|) :: Scalar -> Bra a -> Bra a
(:<+) :: Bra a -> Bra a -> Bra a
(<*) :: (Ord a, Ord b) => Bra a -> Bra b -> Bra (Tuple a b)
infixl 7 <*
(<|) :: Ord a => Scalar -> Bra a -> Bra a
infix 6 <|
(<+) :: Ord a => Bra a -> Bra a -> Bra a
infixl 5 <+
reduceBra :: Ord a => Bra a -> Bra a
braBasis :: Ord a => Bra a -> [Bra a]
toKet :: Ord a => Bra a -> Ket a
(<>) :: Ord a => Bra a -> Ket a -> Scalar
infix 4 <>
d :: Eq a => a -> a -> Scalar
closure :: (DiracVector a, DiracVector b) => (a -> b) -> a -> b
(><) :: (DiracVector b, DiracVector a) => (a -> b) -> a -> b
infix 5 ><
label :: t -> Ket t1 -> Ket (t, t1)
rot :: Ket Int -> Ket (Int, Int)
label' :: (Ord a, Ord b) => Ket (a, b) -> Ket b
rot' :: Ket (Int, Int) -> Ket (Int)
showsScalar :: (Show t, RealFloat t) => Int -> Complex t -> String -> String
data Tuple a b
(:*) :: a -> b -> Tuple a b
instance (GHC.Classes.Ord b, GHC.Classes.Ord a) => GHC.Classes.Ord (QuantumVector.Tuple a b)
instance (GHC.Classes.Eq b, GHC.Classes.Eq a) => GHC.Classes.Eq (QuantumVector.Tuple a b)
instance (GHC.Show.Show a, GHC.Show.Show b) => GHC.Show.Show (QuantumVector.Tuple a b)
instance (GHC.Classes.Eq a, GHC.Classes.Ord a) => GHC.Classes.Eq (QuantumVector.Bra a)
instance GHC.Classes.Ord a => QuantumVector.DiracVector (QuantumVector.Bra a)
instance (GHC.Show.Show a, GHC.Classes.Eq a, GHC.Classes.Ord a) => GHC.Show.Show (QuantumVector.Bra a)
instance (GHC.Classes.Eq a, GHC.Classes.Ord a) => GHC.Classes.Eq (QuantumVector.Ket a)
instance GHC.Classes.Ord a => QuantumVector.DiracVector (QuantumVector.Ket a)
instance (GHC.Show.Show a, GHC.Classes.Eq a, GHC.Classes.Ord a) => GHC.Show.Show (QuantumVector.Ket a)

module Eigensystem
eigenvalues :: Ord a => Bool -> Int -> [Ket a] -> (Ket a -> Ket a) -> [Scalar]
adjoint :: Ord a => [Ket a] -> (Ket a -> Ket a) -> (Ket a -> Ket a)

module Roots
roots :: RealFloat a => a -> Int -> [Complex a] -> [Complex a]
laguerre :: RealFloat a => a -> Int -> [Complex a] -> Complex a -> Complex a
polynomial_value :: Num a => [a] -> a -> a
polynomial_derivative :: Num a => [a] -> [a]

module Tensor
data Tensor
S :: Double -> Tensor
T :: [Tensor] -> Tensor
rank :: Tensor -> Int
dims :: Int
showList' :: (Show t) => Int -> [t] -> String -> String
tensor :: [Double] -> Tensor
(#) :: Tensor -> Int -> Tensor
infixl 9 #
(##) :: Tensor -> [Int] -> Tensor
infixl 9 ##
scalar :: Tensor -> Double
vector :: Tensor -> [Double]
epsilon' :: Int -> Int -> Int -> Double
delta' :: Int -> Int -> Double
delta :: Tensor
epsilon :: Tensor
dot :: Tensor -> Tensor -> Tensor
cross' :: Tensor -> Tensor -> Int -> Double
cross :: Tensor -> Tensor -> Tensor
contract :: Int -> Int -> Tensor -> Tensor
(<*>) :: Tensor -> Tensor -> Tensor
infixl 7 <*>
(<<*>>) :: Tensor -> Tensor -> Tensor
infixl 7 <<*>>
d_standard :: Tensor
d_simpler :: Tensor
instance GHC.Show.Show Tensor.Tensor
instance GHC.Classes.Eq Tensor.Tensor
instance GHC.Num.Num Tensor.Tensor