Algebra.Ring.Polynomial.Monomorphic

Documentation

data Variable

Constructors

Variable

Fields

varName :: Char

varIndex :: Maybe Int

Instances

Eq Variable

Ord Variable

Show Variable

type Monomial = Map Variable Integer

newtype Polynomial k

Constructors

Polynomial

Fields

unPolynomial :: Map Monomial k

Instances

(Eq r, NoetherianRing r) => LeftModule Integer (Polynomial r)

(Eq r, NoetherianRing r) => LeftModule Natural (Polynomial r)

(Eq r, NoetherianRing r) => RightModule Integer (Polynomial r)

(Eq r, NoetherianRing r) => RightModule Natural (Polynomial r)

Eq k => Eq (Polynomial k)

(Eq r, NoetherianRing r, Num r) => Num (Polynomial r)

Ord k => Ord (Polynomial k)

(Integral a, Show a) => Show (Polynomial (Ratio a))

(Eq r, NoetherianRing r, Show r) => Show (Polynomial r)

(Eq r, NoetherianRing r) => Commutative (Polynomial r)

(Eq r, NoetherianRing r) => Ring (Polynomial r)

(Eq r, NoetherianRing r) => Rig (Polynomial r)

(Eq r, NoetherianRing r) => Unital (Polynomial r)

(Eq r, NoetherianRing r) => Group (Polynomial r)

(Eq r, NoetherianRing r) => Multiplicative (Polynomial r)

(Eq r, NoetherianRing r) => Semiring (Polynomial r)

(Eq r, NoetherianRing r) => Monoidal (Polynomial r)

(Eq r, NoetherianRing r) => Additive (Polynomial r)

(Eq r, NoetherianRing r) => Abelian (Polynomial r)

(Eq r, NoetherianRing r) => NoetherianRing (Polynomial r)

normalize :: (Eq k, Monoidal k) => Polynomial k -> Polynomial k

normalizeMonom :: Monomial -> Monomial

buildVarsList :: Polynomial r -> [Variable]

encodeMonomList :: [Variable] -> Monomial -> [Int]

encodeMonomial :: [Variable] -> Monomial -> Monomorphic (Vector Int)

encodePolynomial :: Monomorphicable (Polynomial r) => Polynomial r -> Monomorphic (Polynomial r)

toPolynomialSetting :: Polynomial r -> PolynomialSetting r

data PolynomialSetting r

Constructors

PolySetting

Fields

dimension :: Monomorphic (Sing :: Nat -> *)

polyn :: Polynomial r

uniformlyPromoteWithDim :: (Eq r, NoetherianRing r) => IsMonomialOrder ord => Int -> [Polynomial r] -> Monomorphic (Ideal :.: OrderedPolynomial r ord)

uniformlyPromote :: (Eq r, NoetherianRing r, IsMonomialOrder ord) => [Polynomial r] -> Monomorphic (Ideal :.: OrderedPolynomial r ord)

promoteList :: (Eq r, NoetherianRing r, IsMonomialOrder ord) => [Polynomial r] -> Monomorphic ([] :.: OrderedPolynomial r ord)

promoteListWithVarOrder :: (Eq r, NoetherianRing r, IsMonomialOrder ord) => [Variable] -> [Polynomial r] -> Monomorphic ([] :.: OrderedPolynomial r ord)

promoteListWithDim :: (NoetherianRing r, Eq r, IsMonomialOrder ord) => Int -> [Polynomial r] -> Monomorphic ([] :.: OrderedPolynomial r ord)

renameVars :: [Variable] -> Polynomial r -> Polynomial r

showPolynomial :: (Show r, Eq r, NoetherianRing r) => Polynomial r -> String

showRatPolynomial :: (Integral a, Show a) => Polynomial (Ratio a) -> String

injectVar :: Unital r => Variable -> Polynomial r

injectCoeff :: r -> Polynomial r