factory-0.3.0.0: Rational arithmetic in an irrational world.

Factory.Data.Ring

Description

AUTHOR
Dr. Alistair Ward
DESCRIPTION

Synopsis

Type-classes

class Ring r where Source #

Minimal complete definition

Methods

(=+=) :: r -> r -> r infixl 6 Source #

(=*=) :: r -> r -> r infixl 7 Source #

additiveInverse :: r -> r Source #

(=-=) :: r -> r -> r infixl 6 Source #

square :: r -> r Source #

Instances

 (Eq c, Num c, Num e, Ord e) => Ring (Polynomial c e) Source # Makes Polynomial a Ring, over the field composed from all possible coefficients; https://en.wikipedia.org/wiki/Polynomial_ring. Methods(=+=) :: Polynomial c e -> Polynomial c e -> Polynomial c e Source #(=*=) :: Polynomial c e -> Polynomial c e -> Polynomial c e Source #additiveInverse :: Polynomial c e -> Polynomial c e Source #(=-=) :: Polynomial c e -> Polynomial c e -> Polynomial c e Source #square :: Polynomial c e -> Polynomial c e Source # (Eq c, Num c, Num e, Ord e, Show c, Show e) => Ring (MonicPolynomial c e) Source # Methods(=+=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e Source #(=*=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e Source #(=-=) :: MonicPolynomial c e -> MonicPolynomial c e -> MonicPolynomial c e Source #square :: MonicPolynomial c e -> MonicPolynomial c e Source #

Functions

product' :: Ring r => BisectionRatio -> MinLength -> [r] -> r Source #

Returns the product of the list of ring-members.

sum' :: Ring r => BisectionRatio -> MinLength -> [r] -> r Source #

Returns the sum of the list of ring-members.

Operators

(=^) :: (Eq r, Integral power, Ring r, Show power) => r -> power -> r infixr 8 Source #