numeric-prelude-0.4.3: An experimental alternative hierarchy of numeric type classes

Safe HaskellNone
LanguageHaskell98

MathObj.PowerSeries2

Description

Two-variate power series.

Synopsis

Documentation

newtype T a Source #

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

Instances

Functor T Source # 

Methods

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

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

C T Source # 

Methods

zero :: C a => T a Source #

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

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

(Eq a, C a) => Eq (T a) Source # 

Methods

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

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

(C a, Ord a) => Ord (T a) Source # 

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) Source # 

Methods

showsPrec :: Int -> T a -> ShowS #

show :: T a -> String #

showList :: [T a] -> ShowS #

C a => C (T a) Source # 

Methods

zero :: T a Source #

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

(-) :: T a -> T a -> T a Source #

negate :: T a -> T a Source #

C a => C (T a) Source # 

Methods

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

one :: T a Source #

fromInteger :: Integer -> T a Source #

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

C a => C (T a) Source # 

Methods

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

recip :: T a -> T a Source #

fromRational' :: Rational -> T a Source #

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

C a => C (T a) Source # 

Methods

sqrt :: T a -> T a Source #

root :: Integer -> T a -> T a Source #

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

isValid :: [[a]] -> Bool Source #

check :: [[a]] -> [[a]] Source #

fromCoeffs :: [[a]] -> T a Source #

fromPowerSeries0 :: C a => T a -> T a Source #

fromPowerSeries1 :: C a => T a -> T a Source #

lift0 :: T a -> T a Source #

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

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

const :: a -> T a Source #

truncate :: Int -> T a -> T a Source #