Portability	GHC
Stability	stable
Maintainer	joejev@gmail.org
Safe Haskell	Safe-Inferred

Math.Diophantine

Contents

Data
Utilities
Equation Solving

Description

A module for solving quadratic diophantine equations.

Synopsis

Data

data Equation Source

A way to setup an equation in the form of:

 ax^2 + bxy + cy^2 + dx + ey + f = 0

Constructors

GeneralEquation Z Z Z Z Z Z

A general quadratic diophantine equation.

Instances

Show Equation

data Solution Source

The results of attempting to solve an Equation.

Constructors

ZxZ	All Integer pairs satisfy the equation.
NoSolutions	For all (x,y) in ZxZ
SolutionSet [(Z, Z)]	The set of pairs (x,y) that satisfy the equation. These are not in any particular order, and may contain duplicates.

Instances

Eq Solution
Show Solution

type Z = Integer Source

An alias for Integer, used to shorten type signatures.

data SolveError Source

A way to report an error in solving.

Constructors

SolveError ReadError	Represents a read error when reading the equation from a string.
HyperbolicError	The error when you try to solve a hyperbolic equation.

Instances

Show SolveError

Utilities

readEquation :: String -> Either ReadError Equation Source

Reads an Equation as a String. Equations must be set equal to 0. Order of the terms does not matter expect for constant term, and = 0, which should come last if given. Returns 'Either ReadError Equation'

>>> readEquation "-5y + 2x - 3xy + 2"
-3xy + 2x + -5y + 2 = 0
>>> readEquation  "2xy + x + 1 = 0"
2xy + x + 1 = 0

specializeEquation :: Equation -> Equation Source

Detirmines what kind of equation form a GeneralEquation fits. If you pass a non GeneralEquation to this function, it is the same as id.

toMaybeList :: Solution -> Maybe [(Z, Z)]Source

Extracts the list of solution pairs from a Solution.

mergeSolutions :: Solution -> Solution -> Solution Source

Merges two Solutions into one.

Equation Solving

solve :: Equation -> Either SolveError Solution Source

Determines what type of equation to solve for, and then calls the appropriate solve function. Example:

>>> solve (GeneralEquation 1 2 3 3 5 0)
[(-3,0),(-2,-1),(0,0),(1,-1)]