Factory.Data.Monomial

AUTHOR

Dr. Alistair Ward

DESCRIPTION

• Describes a http://en.wikipedia.org/wiki/Monomial and operations on it.
• A monomial is merely a polynomial with a single non-zero term; cf. Binomial.

Types

Type-synonyms

type Monomial coefficient exponent = (coefficient, exponent)

• 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

Double the specified Monomial.

mod'

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

Negate the coefficient.

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

Convert the type of the coefficient.

shiftCoefficient

Arguments

:: Num c

=> Monomial c e

-> c

The magnitude of the shift.

-> Monomial c e

Shift the coefficient, by the specified amount.

shiftExponent

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

Square the specified Monomial.

Accessors

getExponent :: Monomial c e -> e

Accessor.

getCoefficient :: Monomial c e -> c

Accessor.

Operators

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

Compares the exponents of the specified Monomials.

(</>)

Arguments

:: (Eq c, Fractional c, Num e)

=> Monomial c e

Numerator.

-> Monomial c e

Denominator.

-> Monomial c e

Divide the two specified Monomials.

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

Multiply the two specified Monomials.

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

True if the exponents are equal.

Predicates

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

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