Safe Haskell	None
Language	Haskell2010

Algebra.Ring.Polynomial.Labeled

Synopsis

class UniqueList xs => IsUniqueList (xs :: [Symbol])
data LabPolynomial poly (vars :: [Symbol]) where
- pattern LabelPolynomial :: Wraps vars poly => Wraps vars poly => poly -> LabPolynomial poly vars
type family LabPolynomial' r ord vars where ...
type LabUnipol r sym = LabPolynomial (Unipol r) '[sym]
type Wraps vars poly = (IsUniqueList vars, Arity poly ~ Length vars)
canonicalMap :: forall xs ys poly poly'. (SingI xs, SingI ys, IsSubsetOf xs ys, Wraps xs poly, Wraps ys poly', IsPolynomial poly, IsPolynomial poly', Coefficient poly ~ Coefficient poly') => LabPolynomial poly xs -> LabPolynomial poly' ys
canonicalMap' :: (SingI xs, SingI ys, IsSubsetOf xs ys, Wraps xs poly, Wraps ys poly', IsPolynomial poly, IsPolynomial poly', Coefficient poly ~ Coefficient poly') => proxy poly' -> proxy' ys -> LabPolynomial poly xs -> LabPolynomial poly' ys
renameVars :: (SingI ys, SingI xs, Length xs ~ Length ys, IsPolynomial poly) => LabPolynomial poly xs -> LabPolynomial poly ys
renameVars' :: (SingI ys, SingI xs, Length xs ~ Length ys, IsPolynomial poly) => proxy ys -> LabPolynomial poly xs -> LabPolynomial poly ys
class All ((FlipSym0 @@ ElemSym0) @@ ys) xs ~ 'True => IsSubsetOf (xs :: [a]) (ys :: [a])

Documentation

class UniqueList xs => IsUniqueList (xs :: [Symbol]) Source #

Instances

Instances details

UniqueList xs => IsUniqueList xs Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled

data LabPolynomial poly (vars :: [Symbol]) where Source #

Bundled Patterns

pattern LabelPolynomial :: Wraps vars poly => Wraps vars poly => poly -> LabPolynomial poly vars

Instances

Instances details

(KnownSymbol symb, SingI vars, UniqueList vars, IsPolynomial poly, Wraps vars poly, Elem symb vars ~ 'True) => IsLabel symb (LabPolynomial poly vars) Source #	This instance allows something like `#x :: LabPolynomial (OrderedPolynomial Integer Grevlex 3) '["x", "y", "z"]`.
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromLabel :: LabPolynomial poly vars #
(Wraps vars poly, RightModule Integer poly) => RightModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Integer -> LabPolynomial poly vars #
(Wraps vars poly, RightModule Natural poly) => RightModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule Integer poly) => LeftModule Integer (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Integer -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule Natural poly) => LeftModule Natural (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Wraps vars poly, RightModule (Scalar r) poly) => RightModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*.) :: LabPolynomial poly vars -> Scalar r -> LabPolynomial poly vars #
(Wraps vars poly, LeftModule (Scalar r) poly) => LeftModule (Scalar r) (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (.*) :: Scalar r -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Wraps vars poly, Eq poly) => Eq (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (==) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (/=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool #
(Wraps vars poly, Num poly) => Num (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (+) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # (-) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # (*) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # negate :: LabPolynomial poly vars -> LabPolynomial poly vars # abs :: LabPolynomial poly vars -> LabPolynomial poly vars # signum :: LabPolynomial poly vars -> LabPolynomial poly vars # fromInteger :: Integer -> LabPolynomial poly vars #
(Wraps vars poly, Ord poly) => Ord (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods compare :: LabPolynomial poly vars -> LabPolynomial poly vars -> Ordering # (<) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (<=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (>) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # (>=) :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # max :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # min :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
(PrettyCoeff (Coefficient poly), IsOrderedPolynomial poly, Wraps vars poly, SingI vars) => Show (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods showsPrec :: Int -> LabPolynomial poly vars -> ShowS # show :: LabPolynomial poly vars -> String # showList :: [LabPolynomial poly vars] -> ShowS #
(UFD poly, Wraps vars poly) => UFD (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(PID poly, Wraps vars poly) => PID (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods egcd :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars, LabPolynomial poly vars) #
(GCDDomain poly, Wraps vars poly) => GCDDomain (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods gcd :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # reduceFraction :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) # lcm :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
(IntegralDomain poly, Wraps vars poly) => IntegralDomain (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods divides :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool # maybeQuot :: LabPolynomial poly vars -> LabPolynomial poly vars -> Maybe (LabPolynomial poly vars) #
(Euclidean poly, Wraps vars poly) => Euclidean (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods degree :: LabPolynomial poly vars -> Maybe Natural # divide :: LabPolynomial poly vars -> LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) # quot :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # rem :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars #
(ZeroProductSemiring poly, Wraps vars poly) => ZeroProductSemiring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(UnitNormalForm poly, Wraps vars poly) => UnitNormalForm (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods splitUnit :: LabPolynomial poly vars -> (LabPolynomial poly vars, LabPolynomial poly vars) #
(Wraps vars poly, Ring poly) => Ring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromInteger :: Integer -> LabPolynomial poly vars
(Wraps vars poly, Rig poly) => Rig (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods fromNatural :: Natural -> LabPolynomial poly vars #
(Wraps vars poly, DecidableZero poly) => DecidableZero (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods isZero :: LabPolynomial poly vars -> Bool #
(DecidableUnits poly, Wraps vars poly) => DecidableUnits (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods recipUnit :: LabPolynomial poly vars -> Maybe (LabPolynomial poly vars) # isUnit :: LabPolynomial poly vars -> Bool # (^?) :: Integral n => LabPolynomial poly vars -> n -> Maybe (LabPolynomial poly vars) #
(DecidableAssociates poly, Wraps vars poly) => DecidableAssociates (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods isAssociate :: LabPolynomial poly vars -> LabPolynomial poly vars -> Bool #
(Wraps vars poly, Unital poly) => Unital (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods one :: LabPolynomial poly vars # pow :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars # productWith :: Foldable f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Wraps vars poly, Commutative poly) => Commutative (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Wraps vars poly, Semiring poly) => Semiring (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
(Wraps vars poly, Multiplicative poly) => Multiplicative (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (*) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # pow1p :: LabPolynomial poly vars -> Natural -> LabPolynomial poly vars # productWith1 :: Foldable1 f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Wraps vars poly, Monoidal poly) => Monoidal (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods zero :: LabPolynomial poly vars # sinnum :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars # sumWith :: Foldable f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Wraps vars poly, Group poly) => Group (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (-) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # negate :: LabPolynomial poly vars -> LabPolynomial poly vars # subtract :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # times :: Integral n => n -> LabPolynomial poly vars -> LabPolynomial poly vars #
(Wraps vars poly, Additive poly) => Additive (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods (+) :: LabPolynomial poly vars -> LabPolynomial poly vars -> LabPolynomial poly vars # sinnum1p :: Natural -> LabPolynomial poly vars -> LabPolynomial poly vars # sumWith1 :: Foldable1 f => (a -> LabPolynomial poly vars) -> f a -> LabPolynomial poly vars #
(Wraps vars poly, Abelian poly) => Abelian (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled
NFData poly => NFData (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods rnf :: LabPolynomial poly vars -> () #
(IsPolynomial poly, Wraps vars poly) => IsPolynomial (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Associated Types type Coefficient (LabPolynomial poly vars) # type Arity (LabPolynomial poly vars) :: Nat # Methods liftMap :: (Module (Scalar (Coefficient (LabPolynomial poly vars))) alg, Ring alg, Commutative alg) => (Ordinal (Arity (LabPolynomial poly vars)) -> alg) -> LabPolynomial poly vars -> alg # subst :: (Ring alg, Commutative alg, Module (Scalar (Coefficient (LabPolynomial poly vars))) alg) => Sized (Arity (LabPolynomial poly vars)) alg -> LabPolynomial poly vars -> alg # substWith :: Ring m => (Coefficient (LabPolynomial poly vars) -> m -> m) -> Sized (Arity (LabPolynomial poly vars)) m -> LabPolynomial poly vars -> m # sArity' :: LabPolynomial poly vars -> SNat (Arity (LabPolynomial poly vars)) # sArity :: proxy (LabPolynomial poly vars) -> SNat (Arity (LabPolynomial poly vars)) # arity :: proxy (LabPolynomial poly vars) -> Integer # injectCoeff :: Coefficient (LabPolynomial poly vars) -> LabPolynomial poly vars # injectCoeff' :: proxy (LabPolynomial poly vars) -> Coefficient (LabPolynomial poly vars) -> LabPolynomial poly vars # monomials :: LabPolynomial poly vars -> HashSet (Monomial (Arity (LabPolynomial poly vars))) # terms' :: LabPolynomial poly vars -> Map (Monomial (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars)) # coeff' :: Monomial (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars -> Coefficient (LabPolynomial poly vars) # constantTerm :: LabPolynomial poly vars -> Coefficient (LabPolynomial poly vars) # fromMonomial :: Monomial (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars # toPolynomial' :: (Coefficient (LabPolynomial poly vars), Monomial (Arity (LabPolynomial poly vars))) -> LabPolynomial poly vars # polynomial' :: Map (Monomial (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars)) -> LabPolynomial poly vars # totalDegree' :: LabPolynomial poly vars -> Int # var :: Ordinal (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars # mapCoeff' :: (Coefficient (LabPolynomial poly vars) -> Coefficient (LabPolynomial poly vars)) -> LabPolynomial poly vars -> LabPolynomial poly vars # (>\|) :: Monomial (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars -> LabPolynomial poly vars # (\|<) :: LabPolynomial poly vars -> Monomial (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars # (!*) :: Coefficient (LabPolynomial poly vars) -> LabPolynomial poly vars -> LabPolynomial poly vars # _Terms' :: Iso' (LabPolynomial poly vars) (Map (Monomial (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars))) # mapMonomial :: (Monomial (Arity (LabPolynomial poly vars)) -> Monomial (Arity (LabPolynomial poly vars))) -> LabPolynomial poly vars -> LabPolynomial poly vars #
(IsOrderedPolynomial poly, Wraps vars poly) => IsOrderedPolynomial (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Associated Types type MOrder (LabPolynomial poly vars) # Methods coeff :: OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars -> Coefficient (LabPolynomial poly vars) # terms :: LabPolynomial poly vars -> Map (OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars)) # leadingTerm :: LabPolynomial poly vars -> (Coefficient (LabPolynomial poly vars), OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) # leadingMonomial :: LabPolynomial poly vars -> OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) # leadingCoeff :: LabPolynomial poly vars -> Coefficient (LabPolynomial poly vars) # splitLeadingTerm :: LabPolynomial poly vars -> (Term (LabPolynomial poly vars), LabPolynomial poly vars) # orderedMonomials :: LabPolynomial poly vars -> Set (OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) # fromOrderedMonomial :: OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars # toPolynomial :: (Coefficient (LabPolynomial poly vars), OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) -> LabPolynomial poly vars # polynomial :: Map (OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars)) -> LabPolynomial poly vars # (>) :: OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars -> LabPolynomial poly vars # (<) :: LabPolynomial poly vars -> OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars # _Terms :: Iso' (LabPolynomial poly vars) (Map (OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) (Coefficient (LabPolynomial poly vars))) # diff :: Ordinal (Arity (LabPolynomial poly vars)) -> LabPolynomial poly vars -> LabPolynomial poly vars # mapMonomialMonotonic :: (OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars)) -> OrderedMonomial (MOrder (LabPolynomial poly vars)) (Arity (LabPolynomial poly vars))) -> LabPolynomial poly vars -> LabPolynomial poly vars #
type Arity (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled type Arity (LabPolynomial poly vars) = Arity poly
type Coefficient (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled type Coefficient (LabPolynomial poly vars) = Coefficient poly
type MOrder (LabPolynomial poly vars) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled type MOrder (LabPolynomial poly vars) = MOrder poly

type family LabPolynomial' r ord vars where ... Source #

Convenient type-synonym for LabPlynomial wrapping OrderedPolynomial and Unipol.

Equations

LabPolynomial' r ord '[x] = LabPolynomial (Unipol r) '[x]
LabPolynomial' r ord vars = LabPolynomial (OrderedPolynomial r ord (Length vars)) vars

type LabUnipol r sym = LabPolynomial (Unipol r) '[sym] Source #

Convenient type-synonym for LabPlynomial wrapping univariate polynomial Unipol.

type Wraps vars poly = (IsUniqueList vars, Arity poly ~ Length vars) Source #

canonicalMap :: forall xs ys poly poly'. (SingI xs, SingI ys, IsSubsetOf xs ys, Wraps xs poly, Wraps ys poly', IsPolynomial poly, IsPolynomial poly', Coefficient poly ~ Coefficient poly') => LabPolynomial poly xs -> LabPolynomial poly' ys Source #

canonicalMap' :: (SingI xs, SingI ys, IsSubsetOf xs ys, Wraps xs poly, Wraps ys poly', IsPolynomial poly, IsPolynomial poly', Coefficient poly ~ Coefficient poly') => proxy poly' -> proxy' ys -> LabPolynomial poly xs -> LabPolynomial poly' ys Source #

renameVars :: (SingI ys, SingI xs, Length xs ~ Length ys, IsPolynomial poly) => LabPolynomial poly xs -> LabPolynomial poly ys Source #

renameVars' :: (SingI ys, SingI xs, Length xs ~ Length ys, IsPolynomial poly) => proxy ys -> LabPolynomial poly xs -> LabPolynomial poly ys Source #

class All ((FlipSym0 @@ ElemSym0) @@ ys) xs ~ 'True => IsSubsetOf (xs :: [a]) (ys :: [a]) Source #

Instances

Instances details

All (((FlipSym0 :: TyFun (a ~> ([a] ~> Bool)) ([a] ~> (a ~> Bool)) -> Type) @@ (ElemSym0 :: TyFun a ([a] ~> Bool) -> Type)) @@ ys) xs ~ 'True => IsSubsetOf (xs :: [a]) (ys :: [a]) Source #
Instance details Defined in Algebra.Ring.Polynomial.Labeled Methods _suppress :: proxy xs -> proxy ys -> x -> x