Safe Haskell	None
Language	Haskell2010

Algebra.Ring.Polynomial.Homogenised

Documentation

data Homogenised poly Source #

Instances

Instances details

IsOrderedPolynomial poly => RightModule Integer (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (*.) :: Homogenised poly -> Integer -> Homogenised poly #
IsOrderedPolynomial poly => RightModule Natural (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (*.) :: Homogenised poly -> Natural -> Homogenised poly #
IsOrderedPolynomial poly => LeftModule Integer (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (.*) :: Integer -> Homogenised poly -> Homogenised poly #
IsOrderedPolynomial poly => LeftModule Natural (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (.*) :: Natural -> Homogenised poly -> Homogenised poly #
IsOrderedPolynomial poly => Eq (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (==) :: Homogenised poly -> Homogenised poly -> Bool # (/=) :: Homogenised poly -> Homogenised poly -> Bool #
IsOrderedPolynomial poly => Num (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (+) :: Homogenised poly -> Homogenised poly -> Homogenised poly # (-) :: Homogenised poly -> Homogenised poly -> Homogenised poly # (*) :: Homogenised poly -> Homogenised poly -> Homogenised poly # negate :: Homogenised poly -> Homogenised poly # abs :: Homogenised poly -> Homogenised poly # signum :: Homogenised poly -> Homogenised poly # fromInteger :: Integer -> Homogenised poly #
(IsOrderedPolynomial poly, PrettyCoeff (Coefficient poly)) => Show (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods showsPrec :: Int -> Homogenised poly -> ShowS # show :: Homogenised poly -> String # showList :: [Homogenised poly] -> ShowS #
(Field (Coefficient poly), IsOrderedPolynomial poly) => UFD (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised
(Field (Coefficient poly), IsOrderedPolynomial poly) => PID (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods egcd :: Homogenised poly -> Homogenised poly -> (Homogenised poly, Homogenised poly, Homogenised poly) #
(Field (Coefficient poly), IsOrderedPolynomial poly) => GCDDomain (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods gcd :: Homogenised poly -> Homogenised poly -> Homogenised poly # reduceFraction :: Homogenised poly -> Homogenised poly -> (Homogenised poly, Homogenised poly) # lcm :: Homogenised poly -> Homogenised poly -> Homogenised poly #
(Field (Coefficient poly), IsOrderedPolynomial poly) => IntegralDomain (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods divides :: Homogenised poly -> Homogenised poly -> Bool # maybeQuot :: Homogenised poly -> Homogenised poly -> Maybe (Homogenised poly) #
(Field (Coefficient poly), IsOrderedPolynomial poly) => Euclidean (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods degree :: Homogenised poly -> Maybe Natural # divide :: Homogenised poly -> Homogenised poly -> (Homogenised poly, Homogenised poly) # quot :: Homogenised poly -> Homogenised poly -> Homogenised poly # rem :: Homogenised poly -> Homogenised poly -> Homogenised poly #
IsOrderedPolynomial poly => ZeroProductSemiring (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised
(Field (Coefficient poly), IsOrderedPolynomial poly) => UnitNormalForm (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods splitUnit :: Homogenised poly -> (Homogenised poly, Homogenised poly) #
IsOrderedPolynomial poly => Ring (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods fromInteger :: Integer -> Homogenised poly
IsOrderedPolynomial poly => Rig (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods fromNatural :: Natural -> Homogenised poly #
IsOrderedPolynomial poly => DecidableZero (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods isZero :: Homogenised poly -> Bool #
(Field (Coefficient poly), IsOrderedPolynomial poly) => DecidableUnits (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods recipUnit :: Homogenised poly -> Maybe (Homogenised poly) # isUnit :: Homogenised poly -> Bool # (^?) :: Integral n => Homogenised poly -> n -> Maybe (Homogenised poly) #
(Field (Coefficient poly), IsOrderedPolynomial poly) => DecidableAssociates (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods isAssociate :: Homogenised poly -> Homogenised poly -> Bool #
IsOrderedPolynomial poly => Unital (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods one :: Homogenised poly # pow :: Homogenised poly -> Natural -> Homogenised poly # productWith :: Foldable f => (a -> Homogenised poly) -> f a -> Homogenised poly #
IsOrderedPolynomial poly => Commutative (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised
IsOrderedPolynomial poly => Semiring (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised
IsOrderedPolynomial poly => Multiplicative (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (*) :: Homogenised poly -> Homogenised poly -> Homogenised poly # pow1p :: Homogenised poly -> Natural -> Homogenised poly # productWith1 :: Foldable1 f => (a -> Homogenised poly) -> f a -> Homogenised poly #
IsOrderedPolynomial poly => Monoidal (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods zero :: Homogenised poly # sinnum :: Natural -> Homogenised poly -> Homogenised poly # sumWith :: Foldable f => (a -> Homogenised poly) -> f a -> Homogenised poly #
IsOrderedPolynomial poly => Group (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (-) :: Homogenised poly -> Homogenised poly -> Homogenised poly # negate :: Homogenised poly -> Homogenised poly # subtract :: Homogenised poly -> Homogenised poly -> Homogenised poly # times :: Integral n => n -> Homogenised poly -> Homogenised poly #
IsOrderedPolynomial poly => Additive (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (+) :: Homogenised poly -> Homogenised poly -> Homogenised poly # sinnum1p :: Natural -> Homogenised poly -> Homogenised poly # sumWith1 :: Foldable1 f => (a -> Homogenised poly) -> f a -> Homogenised poly #
IsOrderedPolynomial poly => Abelian (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised
IsOrderedPolynomial poly => IsPolynomial (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Associated Types type Coefficient (Homogenised poly) # type Arity (Homogenised poly) :: Nat # Methods liftMap :: (Module (Scalar (Coefficient (Homogenised poly))) alg, Ring alg, Commutative alg) => (Ordinal (Arity (Homogenised poly)) -> alg) -> Homogenised poly -> alg # subst :: (Ring alg, Commutative alg, Module (Scalar (Coefficient (Homogenised poly))) alg) => Sized (Arity (Homogenised poly)) alg -> Homogenised poly -> alg # substWith :: Ring m => (Coefficient (Homogenised poly) -> m -> m) -> Sized (Arity (Homogenised poly)) m -> Homogenised poly -> m # sArity' :: Homogenised poly -> SNat (Arity (Homogenised poly)) # sArity :: proxy (Homogenised poly) -> SNat (Arity (Homogenised poly)) # arity :: proxy (Homogenised poly) -> Integer # injectCoeff :: Coefficient (Homogenised poly) -> Homogenised poly # injectCoeff' :: proxy (Homogenised poly) -> Coefficient (Homogenised poly) -> Homogenised poly # monomials :: Homogenised poly -> HashSet (Monomial (Arity (Homogenised poly))) # terms' :: Homogenised poly -> Map (Monomial (Arity (Homogenised poly))) (Coefficient (Homogenised poly)) # coeff' :: Monomial (Arity (Homogenised poly)) -> Homogenised poly -> Coefficient (Homogenised poly) # constantTerm :: Homogenised poly -> Coefficient (Homogenised poly) # fromMonomial :: Monomial (Arity (Homogenised poly)) -> Homogenised poly # toPolynomial' :: (Coefficient (Homogenised poly), Monomial (Arity (Homogenised poly))) -> Homogenised poly # polynomial' :: Map (Monomial (Arity (Homogenised poly))) (Coefficient (Homogenised poly)) -> Homogenised poly # totalDegree' :: Homogenised poly -> Int # var :: Ordinal (Arity (Homogenised poly)) -> Homogenised poly # mapCoeff' :: (Coefficient (Homogenised poly) -> Coefficient (Homogenised poly)) -> Homogenised poly -> Homogenised poly # (>\|) :: Monomial (Arity (Homogenised poly)) -> Homogenised poly -> Homogenised poly # (\|<) :: Homogenised poly -> Monomial (Arity (Homogenised poly)) -> Homogenised poly # (!*) :: Coefficient (Homogenised poly) -> Homogenised poly -> Homogenised poly # _Terms' :: Iso' (Homogenised poly) (Map (Monomial (Arity (Homogenised poly))) (Coefficient (Homogenised poly))) # mapMonomial :: (Monomial (Arity (Homogenised poly)) -> Monomial (Arity (Homogenised poly))) -> Homogenised poly -> Homogenised poly #
IsOrderedPolynomial poly => IsOrderedPolynomial (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Associated Types type MOrder (Homogenised poly) # Methods coeff :: OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) -> Homogenised poly -> Coefficient (Homogenised poly) # terms :: Homogenised poly -> Map (OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) (Coefficient (Homogenised poly)) # leadingTerm :: Homogenised poly -> (Coefficient (Homogenised poly), OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) # leadingMonomial :: Homogenised poly -> OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) # leadingCoeff :: Homogenised poly -> Coefficient (Homogenised poly) # splitLeadingTerm :: Homogenised poly -> (Term (Homogenised poly), Homogenised poly) # orderedMonomials :: Homogenised poly -> Set (OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) # fromOrderedMonomial :: OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) -> Homogenised poly # toPolynomial :: (Coefficient (Homogenised poly), OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) -> Homogenised poly # polynomial :: Map (OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) (Coefficient (Homogenised poly)) -> Homogenised poly # (>) :: OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) -> Homogenised poly -> Homogenised poly # (<) :: Homogenised poly -> OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) -> Homogenised poly # _Terms :: Iso' (Homogenised poly) (Map (OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) (Coefficient (Homogenised poly))) # diff :: Ordinal (Arity (Homogenised poly)) -> Homogenised poly -> Homogenised poly # mapMonomialMonotonic :: (OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly)) -> OrderedMonomial (MOrder (Homogenised poly)) (Arity (Homogenised poly))) -> Homogenised poly -> Homogenised poly #
(IsOrderedPolynomial poly, k ~ Coefficient poly) => RightModule (Scalar k) (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (*.) :: Homogenised poly -> Scalar k -> Homogenised poly #
(IsOrderedPolynomial poly, k ~ Coefficient poly) => LeftModule (Scalar k) (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised Methods (.*) :: Scalar k -> Homogenised poly -> Homogenised poly #
type Arity (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised type Arity (Homogenised poly) = Arity poly + 1
type Coefficient (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised type Coefficient (Homogenised poly) = Coefficient poly
type MOrder (Homogenised poly) Source #
Instance details Defined in Algebra.Ring.Polynomial.Homogenised type MOrder (Homogenised poly) = HomogOrder (Arity poly) (MOrder poly)

homogenise :: IsOrderedPolynomial poly => poly -> Homogenised poly Source #

unhomogenise :: IsOrderedPolynomial poly => Homogenised poly -> poly Source #

tryHomogenise :: IsOrderedPolynomial poly => poly -> Either poly (Homogenised poly) Source #

type HomogOrder n ord = ProductOrder n 1 ord Lex Source #