numeric-prelude-0.4.4: 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

Instances details
Functor T Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

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

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

C T Source # 
Instance details

Defined in MathObj.PowerSeries2

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 # 
Instance details

Defined in MathObj.PowerSeries2

Methods

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

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

(C a, Ord a) => Ord (T a) Source # 
Instance details

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) Source # 
Instance details

Defined in MathObj.PowerSeries2

Methods

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

show :: T a -> String #

showList :: [T a] -> ShowS #

C a => C (T a) Source # 
Instance details

Defined in MathObj.PowerSeries2

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 # 
Instance details

Defined in MathObj.PowerSeries2

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 # 
Instance details

Defined in MathObj.PowerSeries2

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 # 
Instance details

Defined in MathObj.PowerSeries2

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 #