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

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 Fieldscoeffs :: T a

Instances

 Source # Methodsfmap :: (a -> b) -> T a -> T b #(<\$) :: a -> T b -> T a # Source # Methodszero :: 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 # Methodscompare :: 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 # MethodsshowsPrec :: Int -> T a -> ShowS #show :: T a -> String #showList :: [T a] -> ShowS # C a => C (T a) Source # Methodszero :: 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 #(^) :: 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 #(^-) :: T a -> Integer -> T a Source # C a => C (T a) Source # Methodssqrt :: 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 #