Copyright	Joe Jevnik 2013
License	GPL-2
Maintainer	joejev@gmail.org
Stability	stable
Portability	GHC
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Diophantine.Internal

Contents

Data
Equation Solving

Description

WARNING: The internal workings of solve. These functions use error, and should only be called directly if you know the type of the equation ahead of time. For example, solveLinear will try to resolve a GeneralEquation into a linear one if possible, but if you pass a GeneralEquation of a parabolic form, then it will error.

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.
LinearEquation Z Z Z	dx + ey + f = 0
SimpleHyperbolicEquation Z Z Z Z	bxy + dx +ey + f = 0
ElipticalEquation Z Z Z Z Z Z	Eliptical equations.
ParabolicEquation Z Z Z Z Z Z	Parabolic equations.
HyperbolicEquation Z Z Z Z Z Z	Hyperbolic equations.

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.

Equation Solving

mergeSolutions :: Solution -> Solution -> Solution Source

Merges two Solutions into one.

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.

solveLinear :: Equation -> Solution Source

Solves for Equations in the form of dx + ey + f = 0

WARNING: This expects that the Equation is actually a LinearEquation; it is safer to just call solve unless you have already verified that the equation is linear.

solveSimpleHyperbolic :: Equation -> Solution Source

Solves for Equations in the form of bxy + dx + ey + f = 0

WARNING: This expects that the Equation is actually a SimpleHyperbolicEquation; it is safer to just call solve unless you have already verified that the equation is simple hyperbolic.

solveEliptical :: Equation -> Solution Source

Solves for Equations in the form of ax^2 + bxy + cy^2 + dx + ey + f = 0 when b^2 - 4ac < 0

WARNING: This expects that the Equation is actually an ElipticalEquation; it is safer to just call solve unless you have already verified that the equation is eliptical.

solveParabolic :: Equation -> Solution Source

Solves for Equations in the form of ax^2 + bxy + cy^2 + dx + ey + f = 0 when b^2 - 4ac = 0

WARNING: This expects that the Equation is actually a ParabolicEquation; it is safer to just call solve unless you have already verified that the equation is parabolic.