SubHask.Category.Polynomial

Documentation

type Polynomial a = Polynomial_ a a

The type of polynomials over an arbitrary ring.

See wikipedia for more detail.

data Polynomial_ a b where

FIXME: Polynomial_ takes two type parameters in order to be compatible with the Category hierarchy of classes. But currently, both types must match each other. Can/Should we generalize this to allow polynomials between types?

Constructors

Polynomial_ :: (ValidLogic a, Ring a, a ~ b) => ![a] -> Polynomial_ a b

Instances

Category * Polynomial_

(Eq r, Show r) => Show (Polynomial_ r r)

IsMutable (Polynomial_ a b)

IsScalar r => FreeModule (Polynomial_ r r)

IsScalar r => Module (Polynomial_ r r)

(ValidLogic r, Ring r) => Ring (Polynomial_ r r)

(ValidLogic r, Ring r) => Rig (Polynomial_ r r)

(ValidLogic r, Ring r) => Rg (Polynomial_ r r)

(Ring r, Abelian r) => Abelian (Polynomial_ r r)

(ValidLogic r, Ring r) => Group (Polynomial_ r r)

(ValidLogic r, Ring r) => Cancellative (Polynomial_ r r)

(ValidLogic r, Ring r) => Monoid (Polynomial_ r r)

Ring r => Semigroup (Polynomial_ r r)

Eq b => Eq_ (Polynomial_ a b)

(<:) (* -> * -> *) Polynomial_ Hask

Sup (* -> * -> *) Hask Polynomial_ Hask

Sup (* -> * -> *) Polynomial_ Hask Hask

IsMutable (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Ring (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Rig (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Rg (ProofOf * Polynomial_ a)

(Ring a, Abelian a) => Abelian (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Group (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Cancellative (ProofOf * Polynomial_ a)

(ValidLogic a, Ring a) => Monoid (ProofOf * Polynomial_ a)

Ring a => Semigroup (ProofOf * Polynomial_ a)

data ProofOf * Polynomial_ = ProofOf {

• unProofOf :: Polynomial_ a a

}

type ValidCategory * Polynomial_ a = (ValidLogic a, Ring a)

type (><) * * (Polynomial_ r r) r = Polynomial_ r r

data Mutable m (Polynomial_ a0 b0) = Mutable_AppT__AppT__ConT_SubHask_Category_Polynomial_Polynomial____VarT_a_1627677154____VarT_b_1627677155_ (PrimRef m (Polynomial_ a b))

data Mutable m (ProofOf * Polynomial_ a0) = Mutable_AppT__AppT__ConT_SubHask_Category_ProofOf___ConT_SubHask_Category_Polynomial_Polynomial_____VarT_a_1627677543_ (PrimRef m (ProofOf * Polynomial_ a))

type Scalar (Polynomial_ a b) = Scalar b

type Logic (Polynomial_ a b) = Logic b

provePolynomial :: (ValidLogic a, Ring a) => (ProofOf Polynomial_ a -> ProofOf Polynomial_ a) -> Polynomial_ a a

sumList :: (t -> t -> t) -> [t] -> [t] -> [t]

pow :: Rig r => r -> Int -> r

evalPolynomial_ :: Polynomial_ a b -> a -> b