Factory.Data.MonicPolynomial

AUTHOR

Dr. Alistair Ward

DESCRIPTION

• Describes a monic polynomial; <https:en.wikipedia.orgwiki/Monic_polynomial#Classifications>; ie. in which the coefficient of the leading term is one.

Types

Data-types

data MonicPolynomial c e

A type of Polynomial, in which the leading term is required to have a coefficient of one.

Instances

(Eq c, Eq e) => Eq (MonicPolynomial c e)

Methods

(==) :: MonicPolynomial c e -> MonicPolynomial c e -> Bool

(/=) :: MonicPolynomial c e -> MonicPolynomial c e -> Bool

(Show c, Show e) => Show (MonicPolynomial c e)

Methods

showsPrec :: Int -> MonicPolynomial c e -> ShowS

show :: MonicPolynomial c e -> String

showList :: [MonicPolynomial c e] -> ShowS

(Eq c, Num c, Num e, Ord e, Show c, Show e) => Ring (MonicPolynomial c e)

Methods

(=+=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e

(=*=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e

additiveInverse :: MonicPolynomial c e -> MonicPolynomial c e

multiplicativeIdentity :: MonicPolynomial c e

additiveIdentity :: MonicPolynomial c e

(=-=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e

square :: MonicPolynomial c e -> MonicPolynomial c e

(Eq c, Num c, Num e, Ord e, Show c, Show e) => QuotientRing (MonicPolynomial c e)

Methods

quotRem' :: MonicPolynomial c e -> MonicPolynomial c e -> (MonicPolynomial c e, MonicPolynomial c e)

Functions

Constructor

mkMonicPolynomial :: (Eq c, Num c, Ord e, Show c, Show e) => Polynomial c e -> MonicPolynomial c e

Smart constructor. Constructs an arbitrary monic polynomial.