Equation Class Reference

#include <Equation.h>

Public Member Functions
	Equation (int nGen, int nVar, const Word &eq)
bool	isGenerator (int g) const
	Determine if g is a letter in this equation.
bool	isVariable (int g) const
	Determine if g is a variable in this equation.
int	getTheNumberOfGenerators () const
	Get the number of the generators of the group.
int	getTheNumberOfVariables () const
	Get the number of variables in the formula.
const Word &	getTheEquation () const
	Get the word presentation of the equation.
bool	isQuadratic () const
	Determine if the equation is quadratic.
bool	trivialSolution () const
	Determine if the equation has trivial solution.
Static Public Member Functions
static Equation	randomQuadraticEquation (int nGen, int nVar, int len)
	Generate random (strictly) quadratic equation of length $len + 2 \cdot nVars$ with generators, variables.
Private Attributes
int	theNumberOfGenerators
	the number of the generators of the group
int	theNumberOfVariables
	the number of variables in the formula (the actual number of variables in the equation can be lesser)
Word	theEquation
	the presentation of the equation
Friends
ostream &	operator<< (ostream &os, const Equation &eq)

Detailed Description

Definition at line 27 of file Equation.h.

Constructor & Destructor Documentation

Equation::Equation	(	int	nGen,
		int	nVar,
		const Word &	eq
	)

Member Function Documentation

const Word& Equation::getTheEquation ( ) const [inline]

Get the word presentation of the equation.

Definition at line 66 of file Equation.h.

References theEquation.

int Equation::getTheNumberOfGenerators ( ) const [inline]

Get the number of the generators of the group.

Definition at line 58 of file Equation.h.

References theNumberOfGenerators.

int Equation::getTheNumberOfVariables ( ) const [inline]

Get the number of variables in the formula.

Definition at line 62 of file Equation.h.

References theNumberOfVariables.

bool Equation::isGenerator ( int g ) const

Determine if g is a letter in this equation.

bool Equation::isQuadratic ( ) const

Determine if the equation is quadratic.

bool Equation::isVariable ( int g ) const

Determine if g is a variable in this equation.

static Equation Equation::randomQuadraticEquation	(	int	nGen,
		int	nVar,
		int	len
	)			`[static]`

Generate random (strictly) quadratic equation of length $len + 2 \cdot nVars$ with $nGen$ generators, $nVar$ variables.

Routine "arranges" len generators and $2 \cdot nVars$ variables (each variable twice) into a reduced equation. The distribution is not uniform among equations of this type (even though for large values of len I think it will be close to uniform). For uniform distribution one has to construct a FSA accepting all equations of this type, then assign weights to edges using dynamic programming, and finally choose words from that FSA accoring to the weights.

bool Equation::trivialSolution ( ) const

Determine if the equation has trivial solution.

Friends And Related Function Documentation

ostream& operator<<	(	ostream &	os,
		const Equation &	eq
	)			`[friend]`

Member Data Documentation

Word Equation::theEquation [private]

the presentation of the equation

A word theEquation is a sequence of generators. Each generator $g$ is interpreted the following way:

if $|g| \le theNumberOfGenerators$ then is the corresponding generator of the group
if then is a variable with index raised in the power $\pm 1$ depending on the sign of .