Safe Haskell	Safe
Language	Haskell2010

Math.FreeModule.SortedList

Description

Free modules implemented as sorted lists of (base,coeff) pairs. The functions coeff, maxTerm, split, unsafeJoin are slow in this implementation.

Documentation

module Math.FreeModule.Class

baseMap :: Ord b => (a -> b) -> FreeMod a c -> FreeMod b c Source #

coeffMap :: (c -> d) -> FreeMod b c -> FreeMod b d Source #

data FreeMod b c Source #

Instances

Functor (FreeMod b) Source #
Methods fmap :: (a -> b) -> FreeMod b a -> FreeMod b b # (<$) :: a -> FreeMod b b -> FreeMod b a #
(Eq b, Eq c) => Eq (FreeMod b c) Source #
Methods (==) :: FreeMod b c -> FreeMod b c -> Bool # (/=) :: FreeMod b c -> FreeMod b c -> Bool #
(Ord b, Ord c) => Ord (FreeMod b c) Source #
Methods compare :: FreeMod b c -> FreeMod b c -> Ordering # (<) :: FreeMod b c -> FreeMod b c -> Bool # (<=) :: FreeMod b c -> FreeMod b c -> Bool # (>) :: FreeMod b c -> FreeMod b c -> Bool # (>=) :: FreeMod b c -> FreeMod b c -> Bool # max :: FreeMod b c -> FreeMod b c -> FreeMod b c # min :: FreeMod b c -> FreeMod b c -> FreeMod b c #
(Show b, Show c) => Show (FreeMod b c) Source #
Methods showsPrec :: Int -> FreeMod b c -> ShowS # show :: FreeMod b c -> String # showList :: [FreeMod b c] -> ShowS #
(Ord b, Eq c, Num c) => FreeModule (FreeMod b c) Source #
Associated Types type Base (FreeMod b c) :: * Source # type Coeff (FreeMod b c) :: * Source # Methods isZero :: FreeMod b c -> Bool Source # zero :: FreeMod b c Source # fromBase :: Base (FreeMod b c) -> FreeMod b c Source # fromTerm :: Base (FreeMod b c) -> Coeff (FreeMod b c) -> FreeMod b c Source # (^+^) :: FreeMod b c -> FreeMod b c -> FreeMod b c Source # (^-^) :: FreeMod b c -> FreeMod b c -> FreeMod b c Source # neg :: FreeMod b c -> FreeMod b c Source # scalarMul :: Coeff (FreeMod b c) -> FreeMod b c -> FreeMod b c Source # unionWith :: (Coeff (FreeMod b c) -> Coeff (FreeMod b c) -> Coeff (FreeMod b c)) -> FreeMod b c -> FreeMod b c -> FreeMod b c Source # coeff :: Base (FreeMod b c) -> FreeMod b c -> Coeff (FreeMod b c) Source # size :: FreeMod b c -> Int Source # minTerm :: FreeMod b c -> (Base (FreeMod b c), Coeff (FreeMod b c)) Source # maxTerm :: FreeMod b c -> (Base (FreeMod b c), Coeff (FreeMod b c)) Source # split :: FreeMod b c -> (FreeMod b c, FreeMod b c) Source # unsafeJoin :: FreeMod b c -> FreeMod b c -> FreeMod b c Source # toList :: FreeMod b c -> [(Base (FreeMod b c), Coeff (FreeMod b c))] Source # fromList :: [(Base (FreeMod b c), Coeff (FreeMod b c))] -> FreeMod b c Source # fromAscendingList :: [(Base (FreeMod b c), Coeff (FreeMod b c))] -> FreeMod b c Source #
(Pretty b, Ord b) => Pretty (FreeMod b Rational) Source #
Methods pretty :: FreeMod b Rational -> String Source #
(Pretty b, Ord b) => Pretty (FreeMod b Integer) Source #
Methods pretty :: FreeMod b Integer -> String Source #
(Pretty b, Ord b) => Pretty (FreeMod b Zp) Source #
Methods pretty :: FreeMod b Zp -> String Source #
type Base (FreeMod b c) Source #
type Base (FreeMod b c) = b
type Coeff (FreeMod b c) Source #
type Coeff (FreeMod b c) = c

type ZModule b = FreeMod b Integer Source #

type QModule b = FreeMod b Rational Source #