MathObj.PowerSeries2

Two-variate power series.

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

Fields

• coeffs :: T a

Instances

Functor T

Defined in MathObj.PowerSeries2

Methods

fmap :: (a -> b) -> T a -> T b

(<$) :: a -> T b -> T a

C T

Defined in MathObj.PowerSeries2

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

(*>) :: C a => a -> T a -> T a

(Eq a, C a) => Eq (T a)

Defined in MathObj.PowerSeries2

Methods

(==) :: T a -> T a -> Bool

(/=) :: T a -> T a -> Bool

(Ord a, C a) => Ord (T a)

Defined in MathObj.PowerSeries2

Methods

compare :: T a -> T a -> Ordering

(<) :: T a -> T a -> Bool

(<=) :: T a -> T a -> Bool

(>) :: T a -> T a -> Bool

(>=) :: T a -> T a -> Bool

max :: T a -> T a -> T a

min :: T a -> T a -> T a

Show a => Show (T a)

Defined in MathObj.PowerSeries2

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

C a => C (T a)

Defined in MathObj.PowerSeries2

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

Defined in MathObj.PowerSeries2

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

C a => C (T a)

Defined in MathObj.PowerSeries2

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational' :: Rational -> T a

(^-) :: T a -> Integer -> T a

C a => C (T a)

Defined in MathObj.PowerSeries2

Methods

sqrt :: T a -> T a

root :: Integer -> T a -> T a

(^/) :: T a -> Rational -> T 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 :: T a -> T a

lift1 :: (T a -> T a) -> T a -> T a

lift2 :: (T a -> T a -> T a) -> T a -> T a -> T a

const :: a -> T a

truncate :: Int -> T a -> T a

appPrec :: Int