Safe Haskell	None
Language	Haskell2010

Math.Algebra.Polynomial.Univariate

Contents

Univariate polynomials

Description

Univariate polynomials

Synopsis

newtype Univariate (coeff :: *) (var :: Symbol) = Uni (FreeMod coeff (U var))
newtype U (var :: Symbol) = U Int
unUni :: Univariate c v -> FreeMod c (U v)
uniVar :: KnownSymbol var => Univariate c var -> String
renameUniVar :: Univariate c var1 -> Univariate c var2
type ZUni var = Univariate Integer var
type QUni var = Univariate Rational var
fromZUni :: (Ring c, KnownSymbol v) => Univariate Integer v -> Univariate c v
fromQUni :: (Field c, KnownSymbol v) => Univariate Rational v -> Univariate c v
differentiateUni :: (Ring c, KnownSymbol var) => Univariate c var -> Univariate c var
integrateUni :: (Field c, KnownSymbol var) => Univariate c var -> Univariate c var
integrateUni' :: (Field c, KnownSymbol var) => c -> Univariate c var -> Univariate c var

Univariate polynomials

newtype Univariate (coeff :: *) (var :: Symbol) Source #

A univariate polynomial with the given coefficient ring. Note: this is also indexed by the name of the variable.

Constructors

Uni (FreeMod coeff (U var))

Instances

Eq coeff => Eq (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods (==) :: Univariate coeff var -> Univariate coeff var -> Bool # (/=) :: Univariate coeff var -> Univariate coeff var -> Bool #
(Ring c, KnownSymbol v) => Num (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods (+) :: Univariate c v -> Univariate c v -> Univariate c v # (-) :: Univariate c v -> Univariate c v -> Univariate c v # (*) :: Univariate c v -> Univariate c v -> Univariate c v # negate :: Univariate c v -> Univariate c v # abs :: Univariate c v -> Univariate c v # signum :: Univariate c v -> Univariate c v # fromInteger :: Integer -> Univariate c v #
Ord coeff => Ord (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods compare :: Univariate coeff var -> Univariate coeff var -> Ordering # (<) :: Univariate coeff var -> Univariate coeff var -> Bool # (<=) :: Univariate coeff var -> Univariate coeff var -> Bool # (>) :: Univariate coeff var -> Univariate coeff var -> Bool # (>=) :: Univariate coeff var -> Univariate coeff var -> Bool # max :: Univariate coeff var -> Univariate coeff var -> Univariate coeff var # min :: Univariate coeff var -> Univariate coeff var -> Univariate coeff var #
Show coeff => Show (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods showsPrec :: Int -> Univariate coeff var -> ShowS # show :: Univariate coeff var -> String # showList :: [Univariate coeff var] -> ShowS #
FreeModule (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Associated Types type BaseF (Univariate c v) :: Type Source # type CoeffF (Univariate c v) :: Type Source # Methods toFreeModule :: Univariate c v -> FreeMod (CoeffF (Univariate c v)) (BaseF (Univariate c v)) Source # fromFreeModule :: FreeMod (CoeffF (Univariate c v)) (BaseF (Univariate c v)) -> Univariate c v Source #
IsSigned (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods signOf :: Univariate c v -> Maybe Sign Source #
(Ring c, KnownSymbol v) => Pretty (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods pretty :: Univariate c v -> String Source # prettyInParens :: Univariate c v -> String Source #
(Ring coeff, KnownSymbol var) => Polynomial (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods evalP :: Num d => (CoeffP (Univariate coeff var) -> d) -> (VarP (Univariate coeff var) -> d) -> Univariate coeff var -> d Source # varSubsP :: (VarP (Univariate coeff var) -> VarP (Univariate coeff var)) -> Univariate coeff var -> Univariate coeff var Source # coeffSubsP :: (VarP (Univariate coeff var) -> Maybe (CoeffP (Univariate coeff var))) -> Univariate coeff var -> Univariate coeff var Source # subsP :: (VarP (Univariate coeff var) -> Univariate coeff var) -> Univariate coeff var -> Univariate coeff var Source #
(Ring coeff, KnownSymbol var) => AlmostPolynomial (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Associated Types type CoeffP (Univariate coeff var) :: Type Source # type MonomP (Univariate coeff var) :: Type Source # type VarP (Univariate coeff var) :: Type Source # Methods fromListP :: [(MonomP (Univariate coeff var), CoeffP (Univariate coeff var))] -> Univariate coeff var Source # toListP :: Univariate coeff var -> [(MonomP (Univariate coeff var), CoeffP (Univariate coeff var))] Source # zeroP :: Univariate coeff var Source # isZeroP :: Univariate coeff var -> Bool Source # oneP :: Univariate coeff var Source # variableP :: VarP (Univariate coeff var) -> Univariate coeff var Source # singletonP :: VarP (Univariate coeff var) -> Int -> Univariate coeff var Source # monomP :: MonomP (Univariate coeff var) -> Univariate coeff var Source # monomP' :: MonomP (Univariate coeff var) -> CoeffP (Univariate coeff var) -> Univariate coeff var Source # scalarP :: CoeffP (Univariate coeff var) -> Univariate coeff var Source # addP :: Univariate coeff var -> Univariate coeff var -> Univariate coeff var Source # subP :: Univariate coeff var -> Univariate coeff var -> Univariate coeff var Source # negP :: Univariate coeff var -> Univariate coeff var Source # sumP :: [Univariate coeff var] -> Univariate coeff var Source # mulP :: Univariate coeff var -> Univariate coeff var -> Univariate coeff var Source # productP :: [Univariate coeff var] -> Univariate coeff var Source # coeffOfP :: MonomP (Univariate coeff var) -> Univariate coeff var -> CoeffP (Univariate coeff var) Source # mulByMonomP :: MonomP (Univariate coeff var) -> Univariate coeff var -> Univariate coeff var Source # scaleP :: CoeffP (Univariate coeff var) -> Univariate coeff var -> Univariate coeff var Source #
(Ring c, KnownSymbol v) => Ring (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate Methods isZeroR :: Univariate c v -> Bool Source # signumR :: Univariate c v -> Maybe Sign Source # absR :: Univariate c v -> Univariate c v Source # isSignedR :: Proxy (Univariate c v) -> Bool Source # isAtomicR :: Proxy (Univariate c v) -> Bool Source #
type BaseF (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate type BaseF (Univariate c v) = U v
type CoeffF (Univariate c v) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate type CoeffF (Univariate c v) = c
type CoeffP (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate type CoeffP (Univariate coeff var) = coeff
type MonomP (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate type MonomP (Univariate coeff var) = U var
type VarP (Univariate coeff var) Source #
Instance details Defined in Math.Algebra.Polynomial.Univariate type VarP (Univariate coeff var) = ()

newtype U (var :: Symbol) Source #

A monomial in a univariate polynomial, indexed by its name, eg U "x"

Constructors

U Int

Instances

Eq (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods (==) :: U var -> U var -> Bool # (/=) :: U var -> U var -> Bool #
Ord (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods compare :: U var -> U var -> Ordering # (<) :: U var -> U var -> Bool # (<=) :: U var -> U var -> Bool # (>) :: U var -> U var -> Bool # (>=) :: U var -> U var -> Bool # max :: U var -> U var -> U var # min :: U var -> U var -> U var #
Show (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods showsPrec :: Int -> U var -> ShowS # show :: U var -> String # showList :: [U var] -> ShowS #
Semigroup (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods (<>) :: U var -> U var -> U var # sconcat :: NonEmpty (U var) -> U var # stimes :: Integral b => b -> U var -> U var #
Monoid (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods mempty :: U var # mappend :: U var -> U var -> U var # mconcat :: [U var] -> U var #
KnownSymbol var => Pretty (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Methods pretty :: U var -> String Source # prettyInParens :: U var -> String Source #
KnownSymbol var => Monomial (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate Associated Types type VarM (U var) :: Type Source # Methods normalizeM :: U var -> U var Source # isNormalM :: U var -> Bool Source # fromListM :: [(VarM (U var), Int)] -> U var Source # toListM :: U var -> [(VarM (U var), Int)] Source # emptyM :: U var Source # isEmptyM :: U var -> Bool Source # variableM :: VarM (U var) -> U var Source # singletonM :: VarM (U var) -> Int -> U var Source # mulM :: U var -> U var -> U var Source # productM :: [U var] -> U var Source # powM :: U var -> Int -> U var Source # divM :: U var -> U var -> Maybe (U var) Source # diffM :: Num c => VarM (U var) -> Int -> U var -> Maybe (U var, c) Source # maxDegM :: U var -> Int Source # totalDegM :: U var -> Int Source # evalM :: Num c => (VarM (U var) -> c) -> U var -> c Source # varSubsM :: (VarM (U var) -> VarM (U var)) -> U var -> U var Source # termSubsM :: Num c => (VarM (U var) -> Maybe c) -> (U var, c) -> (U var, c) Source #
type VarM (U var) Source #
Instance details Defined in Math.Algebra.Polynomial.Monomial.Univariate type VarM (U var) = ()

unUni :: Univariate c v -> FreeMod c (U v) Source #

uniVar :: KnownSymbol var => Univariate c var -> String Source #

Name of the variable

renameUniVar :: Univariate c var1 -> Univariate c var2 Source #

Rename the variable (zero cost)

type ZUni var = Univariate Integer var Source #

An univariate polynomial integer coefficients

type QUni var = Univariate Rational var Source #

An univariate polynomial with rational coefficients

fromZUni :: (Ring c, KnownSymbol v) => Univariate Integer v -> Univariate c v Source #

Change the coefficient ring

fromQUni :: (Field c, KnownSymbol v) => Univariate Rational v -> Univariate c v Source #

Change the coefficient ring

differentiateUni :: (Ring c, KnownSymbol var) => Univariate c var -> Univariate c var Source #

Differentiation

integrateUni :: (Field c, KnownSymbol var) => Univariate c var -> Univariate c var Source #

Integration

integrateUni' :: (Field c, KnownSymbol var) => c -> Univariate c var -> Univariate c var Source #