Polynomial.Monomial

• - Module : Data.Massiv.Array
• - Copyright :
• - License : BSD3
• - Maintainer : Jose Seraquive [e-mail]
• - Stability : experimental
• - Portability : non-portable

Documentation

newtype Mon ord

A wrapper for monomials with a certain (monomial) order

Constructors

Mon (Array P Ix1 Int)

Instances

LeftModule Integer (Mon ord)

Defined in Polynomial.Monomial

Methods

(.*) :: Integer -> Mon ord -> Mon ord

LeftModule Natural (Mon ord)

Defined in Polynomial.Monomial

Methods

(.*) :: Natural -> Mon ord -> Mon ord

RightModule Integer (Mon ord)

Defined in Polynomial.Monomial

Methods

(*.) :: Mon ord -> Integer -> Mon ord

RightModule Natural (Mon ord)

Defined in Polynomial.Monomial

Methods

(*.) :: Mon ord -> Natural -> Mon ord

Eq (Mon ord)

Defined in Polynomial.Monomial

Methods

(==) :: Mon ord -> Mon ord -> Bool

(/=) :: Mon ord -> Mon ord -> Bool

Ord (Mon Revlex)

Defined in Polynomial.Monomial

Methods

compare :: Mon Revlex -> Mon Revlex -> Ordering

(<) :: Mon Revlex -> Mon Revlex -> Bool

(<=) :: Mon Revlex -> Mon Revlex -> Bool

(>) :: Mon Revlex -> Mon Revlex -> Bool

(>=) :: Mon Revlex -> Mon Revlex -> Bool

max :: Mon Revlex -> Mon Revlex -> Mon Revlex

min :: Mon Revlex -> Mon Revlex -> Mon Revlex

Ord (Mon Lex)

Defined in Polynomial.Monomial

Methods

compare :: Mon Lex -> Mon Lex -> Ordering

(<) :: Mon Lex -> Mon Lex -> Bool

(<=) :: Mon Lex -> Mon Lex -> Bool

(>) :: Mon Lex -> Mon Lex -> Bool

(>=) :: Mon Lex -> Mon Lex -> Bool

max :: Mon Lex -> Mon Lex -> Mon Lex

min :: Mon Lex -> Mon Lex -> Mon Lex

Show (Mon ord)

Defined in Polynomial.Monomial

Methods

showsPrec :: Int -> Mon ord -> ShowS

show :: Mon ord -> String

showList :: [Mon ord] -> ShowS

Generic (Mon ord)

Defined in Polynomial.Monomial

Associated Types

type Rep (Mon ord) :: Type -> Type

Methods

from :: Mon ord -> Rep (Mon ord) x

to :: Rep (Mon ord) x -> Mon ord

NFData (Mon ord)

Defined in Polynomial.Monomial

Methods

rnf :: Mon ord -> ()

Division (Mon ord)

Defined in Polynomial.Monomial

Methods

recip :: Mon ord -> Mon ord

(/) :: Mon ord -> Mon ord -> Mon ord

(\\) :: Mon ord -> Mon ord -> Mon ord

(^) :: Integral n => Mon ord -> n -> Mon ord

Unital (Mon ord)

Defined in Polynomial.Monomial

Methods

one :: Mon ord

pow :: Mon ord -> Natural -> Mon ord

productWith :: Foldable f => (a -> Mon ord) -> f a -> Mon ord

Group (Mon ord)

Defined in Polynomial.Monomial

Methods

(-) :: Mon ord -> Mon ord -> Mon ord

negate :: Mon ord -> Mon ord

subtract :: Mon ord -> Mon ord -> Mon ord

times :: Integral n => n -> Mon ord -> Mon ord

Multiplicative (Mon ord)

Defined in Polynomial.Monomial

Methods

(*) :: Mon ord -> Mon ord -> Mon ord

pow1p :: Mon ord -> Natural -> Mon ord

productWith1 :: Foldable1 f => (a -> Mon ord) -> f a -> Mon ord

Semiring (Mon ord)

Defined in Polynomial.Monomial

Monoidal (Mon ord)

Defined in Polynomial.Monomial

Methods

zero :: Mon ord

sinnum :: Natural -> Mon ord -> Mon ord

sumWith :: Foldable f => (a -> Mon ord) -> f a -> Mon ord

Additive (Mon ord)

Defined in Polynomial.Monomial

Methods

(+) :: Mon ord -> Mon ord -> Mon ord

sinnum1p :: Natural -> Mon ord -> Mon ord

sumWith1 :: Foldable1 f => (a -> Mon ord) -> f a -> Mon ord

Abelian (Mon ord)

Defined in Polynomial.Monomial

type Rep (Mon ord)

Defined in Polynomial.Monomial

type Rep (Mon ord) = D1 (MetaData "Mon" "Polynomial.Monomial" "Ritt-Wu-0.1.0.0-HkN3umTPbNu5vlsngcCGAk" True) (C1 (MetaCons "Mon" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Array P Ix1 Int))))

data Lex

Lexicographical order

Constructors

Lex

Instances

Ord (Mon Lex)

Defined in Polynomial.Monomial

Methods

compare :: Mon Lex -> Mon Lex -> Ordering

(<) :: Mon Lex -> Mon Lex -> Bool

(<=) :: Mon Lex -> Mon Lex -> Bool

(>) :: Mon Lex -> Mon Lex -> Bool

(>=) :: Mon Lex -> Mon Lex -> Bool

max :: Mon Lex -> Mon Lex -> Mon Lex

min :: Mon Lex -> Mon Lex -> Mon Lex

data Revlex

Reverse lexicographical order

Constructors

Revlex

Instances

(NFData t, Num t, Eq t) => LeftModule Integer (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(.*) :: Integer -> Poly t Revlex -> Poly t Revlex

(NFData t, Num t, Eq t) => LeftModule Natural (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(.*) :: Natural -> Poly t Revlex -> Poly t Revlex

(NFData t, Num t, Eq t) => RightModule Integer (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(*.) :: Poly t Revlex -> Integer -> Poly t Revlex

(NFData t, Num t, Eq t) => RightModule Natural (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(*.) :: Poly t Revlex -> Natural -> Poly t Revlex

Ord (Mon Revlex)

Defined in Polynomial.Monomial

Methods

compare :: Mon Revlex -> Mon Revlex -> Ordering

(<) :: Mon Revlex -> Mon Revlex -> Bool

(<=) :: Mon Revlex -> Mon Revlex -> Bool

(>) :: Mon Revlex -> Mon Revlex -> Bool

(>=) :: Mon Revlex -> Mon Revlex -> Bool

max :: Mon Revlex -> Mon Revlex -> Mon Revlex

min :: Mon Revlex -> Mon Revlex -> Mon Revlex

Eq k => Ord (Term k Revlex)

Defined in Polynomial.Terms

Methods

compare :: Term k Revlex -> Term k Revlex -> Ordering

(<) :: Term k Revlex -> Term k Revlex -> Bool

(<=) :: Term k Revlex -> Term k Revlex -> Bool

(>) :: Term k Revlex -> Term k Revlex -> Bool

(>=) :: Term k Revlex -> Term k Revlex -> Bool

max :: Term k Revlex -> Term k Revlex -> Term k Revlex

min :: Term k Revlex -> Term k Revlex -> Term k Revlex

(NFData t, Num t, Eq t) => Group (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(-) :: Poly t Revlex -> Poly t Revlex -> Poly t Revlex

negate :: Poly t Revlex -> Poly t Revlex

subtract :: Poly t Revlex -> Poly t Revlex -> Poly t Revlex

times :: Integral n => n -> Poly t Revlex -> Poly t Revlex

(NFData t, Num t, Eq t) => Multiplicative (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(*) :: Poly t Revlex -> Poly t Revlex -> Poly t Revlex

pow1p :: Poly t Revlex -> Natural -> Poly t Revlex

productWith1 :: Foldable1 f => (a -> Poly t Revlex) -> f a -> Poly t Revlex

(NFData t, Num t, Eq t) => Semiring (Poly t Revlex)

Defined in Polynomial.Polynomial

(NFData t, Num t, Eq t) => Monoidal (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

zero :: Poly t Revlex

sinnum :: Natural -> Poly t Revlex -> Poly t Revlex

sumWith :: Foldable f => (a -> Poly t Revlex) -> f a -> Poly t Revlex

(NFData t, Num t, Eq t) => Additive (Poly t Revlex)

Defined in Polynomial.Polynomial

Methods

(+) :: Poly t Revlex -> Poly t Revlex -> Poly t Revlex

sinnum1p :: Natural -> Poly t Revlex -> Poly t Revlex

sumWith1 :: Foldable1 f => (a -> Poly t Revlex) -> f a -> Poly t Revlex

(NFData t, Num t, Eq t) => Abelian (Poly t Revlex)

Defined in Polynomial.Polynomial

m :: [Int] -> Mon ord

Monomial with terms

mp :: [Int] -> [Int] -> Mon ord

Monomial with the term position