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

Number.Root

Synopsis

# Documentation

data T a Source #

The root degree must be positive. This way we can implement multiplication using only multiplication from type a.

Constructors

 Cons Integer a

Instances

 Source # When you use fmap you must assert that forall n. fmap f (Cons d x) == fmap f (Cons (n*d) (x^n)) Methodsfmap :: (a -> b) -> T a -> T b #(<\$) :: a -> T b -> T a # (Eq a, C a) => Eq (T a) Source # Methods(==) :: T a -> T a -> Bool #(/=) :: T a -> T a -> Bool # (Ord a, C 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 #

fromNumber :: a -> T a Source #

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

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

commonDegree :: C a => T a -> T a -> T (a, a) Source #

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

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

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

cardinalPower :: C a => Integer -> T a -> T a Source #

exponent must be non-negative

integerPower :: C a => Integer -> T a -> T a Source #

exponent can be negative

rationalPower :: C a => Rational -> T a -> T a Source #

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

exponent must be positive

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