factory-0.2.1.1: Rational arithmetic in an irrational world.

Factory.Data.Monomial

Description

`AUTHOR`
Dr. Alistair Ward
`DESCRIPTION`

Synopsis

# Types

## Type-synonyms

type Monomial coefficient exponent = (coefficient, exponent) Source

• The type of an arbitrary monomial.
• CAVEAT: though a monomial has an integral power, this contraint is only imposed at the function-level.

# Functions

double :: Num c => Monomial c e -> Monomial c e Source

Double the specified `Monomial`.

Arguments

 :: Integral c => Monomial c e -> c Modulus. -> Monomial c e

Reduce the coefficient using modular arithmetic.

negateCoefficient :: Num c => Monomial c e -> Monomial c e Source

Negate the coefficient.

realCoefficientToFrac :: (Real r, Fractional f) => Monomial r e -> Monomial f e Source

Convert the type of the coefficient.

Arguments

 :: Num c => Monomial c e -> c The magnitude of the shift. -> Monomial c e

Shift the coefficient, by the specified amount.

Arguments

 :: Num e => Monomial c e -> e The magnitude of the shift. -> Monomial c e

Shift the exponent, by the specified amount.

square :: (Num c, Num e) => Monomial c e -> Monomial c e Source

Square the specified `Monomial`.

## Accessors

getExponent :: Monomial c e -> e Source

Accessor.

getCoefficient :: Monomial c e -> c Source

Accessor.

## Operators

(<=>) :: Ord e => Monomial c e -> Monomial c e -> Ordering infix 4 Source

Compares the exponents of the specified `Monomial`s.

(</>) infixl 7 Source

Arguments

 :: (Eq c, Fractional c, Num e) => Monomial c e Numerator. -> Monomial c e Denominator. -> Monomial c e

Divide the two specified `Monomial`s.

(<*>) :: (Num c, Num e) => Monomial c e -> Monomial c e -> Monomial c e infixl 7 Source

Multiply the two specified `Monomial`s.

(=~) :: Eq e => Monomial c e -> Monomial c e -> Bool infix 4 Source

True if the exponents are equal.

## Predicates

isMonomial :: Integral e => Monomial c e -> Bool Source

• `True` if the exponent is both integral and non-negative.
• CAVEAT: one can't even call this function unless the exponent is integral.