NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classesContentsIndex
MathObj.PowerSeries2
Contents
Series arithmetic
Description
Two-variate power series.
Synopsis
newtype T a = Cons {
coeffs :: (Core a)
}
type Core a = [[a]]
isValid :: [[a]] -> Bool
check :: [[a]] -> [[a]]
fromCoeffs :: [[a]] -> T a
fromPowerSeries0 :: C a => T a -> T a
fromPowerSeries1 :: C a => T a -> T a
lift0 :: Core a -> T a
lift1 :: (Core a -> Core a) -> T a -> T a
lift2 :: (Core a -> Core a -> Core a) -> T a -> T a -> T a
lift0fromPowerSeries :: [T a] -> Core a
lift1fromPowerSeries :: ([T a] -> [T a]) -> Core a -> Core a
lift2fromPowerSeries :: ([T a] -> [T a] -> [T a]) -> Core a -> Core a -> Core a
const :: a -> T a
appPrec :: Int
add :: C a => Core a -> Core a -> Core a
sub :: C a => Core a -> Core a -> Core a
negate :: C a => Core a -> Core a
scale :: C a => a -> Core a -> Core a
mul :: C a => Core a -> Core a -> Core a
divide :: C a => Core a -> Core a -> Core a
sqrt :: C a => (a -> a) -> Core a -> Core a
swapVariables :: Core a -> Core a
differentiate0 :: C a => Core a -> Core a
differentiate1 :: C a => Core a -> Core a
integrate0 :: C a => [a] -> Core a -> Core a
integrate1 :: C a => [a] -> Core a -> Core a
comp :: C a => [a] -> Core a -> Core a
Documentation
newtype T a

In order to handle both variables equivalently we maintain a list of coefficients for terms of the same total degree. That is 

 eval [[a], [b,c], [d,e,f]] (x,y) ==
    a + b*x+c*y + d*x^2+e*x*y+f*y^2

Although the sub-lists are always finite and thus are more like polynomials than power series, division and square root computation are easier to implement for power series.

Constructors
Cons
coeffs :: (Core a)
show/hide Instances
C T
Functor T
C a => C (T a)
C a => C (T a)
C a => C (T a)
C a => C (T a)
(Eq a, C a) => Eq (T a)
??? a => Ord (T a)
Show a => Show (T a)
type Core a = [[a]]
isValid :: [[a]] -> Bool
check :: [[a]] -> [[a]]
fromCoeffs :: [[a]] -> T a
fromPowerSeries0 :: C a => T a -> T a
fromPowerSeries1 :: C a => T a -> T a
lift0 :: Core a -> T a
lift1 :: (Core a -> Core a) -> T a -> T a
lift2 :: (Core a -> Core a -> Core a) -> T a -> T a -> T a
lift0fromPowerSeries :: [T a] -> Core a
lift1fromPowerSeries :: ([T a] -> [T a]) -> Core a -> Core a
lift2fromPowerSeries :: ([T a] -> [T a] -> [T a]) -> Core a -> Core a -> Core a
const :: a -> T a
appPrec :: Int
Series arithmetic
add :: C a => Core a -> Core a -> Core a
sub :: C a => Core a -> Core a -> Core a
negate :: C a => Core a -> Core a
scale :: C a => a -> Core a -> Core a
mul :: C a => Core a -> Core a -> Core a
divide :: C a => Core a -> Core a -> Core a
sqrt :: C a => (a -> a) -> Core a -> Core a
swapVariables :: Core a -> Core a
differentiate0 :: C a => Core a -> Core a
differentiate1 :: C a => Core a -> Core a
integrate0 :: C a => [a] -> Core a -> Core a
integrate1 :: C a => [a] -> Core a -> Core a
comp :: C a => [a] -> Core a -> Core a
Since the inner series must start with a zero, the first term is omitted in y.
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