Safe Haskell	Safe-Inferred
Language	Haskell98

Factory.Data.Monomial

Contents

Types
- Type-synonyms
Functions

Description

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.

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.

mod' Source

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.

shiftCoefficient Source

Arguments

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

Shift the coefficient, by the specified amount.

shiftExponent Source

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 Monomials.

(</>) 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 Monomials.

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

Multiply the two specified Monomials.

(=~) :: 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.