Polynomial.Monomial

Types

newtype Monomial ord n

Monomial is defined as an array of exponents

Constructors

Monomial

Fields

• getMonomial :: Mon n

Instances

Eq (Monomial ord n)

Defined in Polynomial.Monomial

Methods

(==) :: Monomial ord n -> Monomial ord n -> Bool

(/=) :: Monomial ord n -> Monomial ord n -> Bool

IsMonomialOrder ord => Ord (Monomial ord n)

Defined in Polynomial.Monomial

Methods

compare :: Monomial ord n -> Monomial ord n -> Ordering

(<) :: Monomial ord n -> Monomial ord n -> Bool

(<=) :: Monomial ord n -> Monomial ord n -> Bool

(>) :: Monomial ord n -> Monomial ord n -> Bool

(>=) :: Monomial ord n -> Monomial ord n -> Bool

max :: Monomial ord n -> Monomial ord n -> Monomial ord n

min :: Monomial ord n -> Monomial ord n -> Monomial ord n

Show (Monomial ord n)

Defined in Polynomial.Monomial

Methods

showsPrec :: Int -> Monomial ord n -> ShowS

show :: Monomial ord n -> String

showList :: [Monomial ord n] -> ShowS

(IsMonomialOrder ord, KnownNat n) => Unital (Monomial ord n)

Defined in Polynomial.Monomial

Methods

one :: Monomial ord n

pow :: Monomial ord n -> Natural -> Monomial ord n

productWith :: Foldable f => (a -> Monomial ord n) -> f a -> Monomial ord n

(IsMonomialOrder ord, KnownNat n) => Multiplicative (Monomial ord n)

Defined in Polynomial.Monomial

Methods

(*) :: Monomial ord n -> Monomial ord n -> Monomial ord n

pow1p :: Monomial ord n -> Natural -> Monomial ord n

productWith1 :: Foldable1 f => (a -> Monomial ord n) -> f a -> Monomial ord n

Wrapped (Monomial ord n)

Defined in Polynomial.Monomial

Associated Types

type Unwrapped (Monomial ord n) :: *

Methods

_Wrapped' :: Iso' (Monomial ord n) (Unwrapped (Monomial ord n))

Monomial ord1 n1 ~ t => Rewrapped (Monomial ord2 n2) t

Defined in Polynomial.Monomial

type Unwrapped (Monomial ord n)

Defined in Polynomial.Monomial

type Unwrapped (Monomial ord n) = Mon n

type Mon n = Sized' n Int

type SNat (n :: Nat) = Sing n

data Lex

Instances

IsMonomialOrder Lex

Defined in Polynomial.Monomial

Methods

compareMonomial :: Monomial Lex n -> Monomial Lex n -> Ordering

(Unital k, Show k, Eq k) => Show (Polynomial k Lex n)

Defined in Polynomial.Prelude

Methods

showsPrec :: Int -> Polynomial k Lex n -> ShowS

show :: Polynomial k Lex n -> String

showList :: [Polynomial k Lex n] -> ShowS

data Revlex

Instances

IsMonomialOrder Revlex

Defined in Polynomial.Monomial

Methods

compareMonomial :: Monomial Revlex n -> Monomial Revlex n -> Ordering

(KnownNat n, Unital k, Show k, Eq k) => Show (Polynomial k Revlex n)

Defined in Polynomial.Prelude

Methods

showsPrec :: Int -> Polynomial k Revlex n -> ShowS

show :: Polynomial k Revlex n -> String

showList :: [Polynomial k Revlex n] -> ShowS

Classes

class IsMonomialOrder (ord :: *)

Definition of what a monomial order must meet

Minimal complete definition

compareMonomial

Instances

IsMonomialOrder Revlex

Defined in Polynomial.Monomial

Methods

compareMonomial :: Monomial Revlex n -> Monomial Revlex n -> Ordering

IsMonomialOrder Lex

Defined in Polynomial.Monomial

Methods

compareMonomial :: Monomial Lex n -> Monomial Lex n -> Ordering

Functions

toMonomial :: (IsMonomialOrder ord, KnownNat n) => [Int] -> Monomial ord n