edu.princeton.repeatedgames.rgsolve.utilities
Class Fraction

java.lang.Object
  edu.princeton.repeatedgames.rgsolve.utilities.Fraction

public class Fraction
extends java.lang.Object

A class for converting doubles to rationals, and the reverse. See http://shreevatsa.wordpress.com/2011/01/10/not-all-best- rational-approximations-are-the-convergents-of-the-continued-fraction/

Field Summary

private long	denominator the denominator of this fraction
static int	MAX_CONVERGENTS default Maximum number of convergents in series to calculate
private long	numerator the numerator of this fraction
static Fraction	ONE 1/1
static double	TOLERANCE default approximation tolerance of fraction to inputed double
static Fraction	ZERO 0/1

Constructor Summary

Fraction(double value)
Constructs a rational approximation to the double value

Fraction(long numerator, long denominator)
Constructor.

Method Summary

Fraction	add(Fraction f)
static long	gcd(long A, long B) The greatest common divisor of integers A and B
static Fraction	getFraction(double x) Finds rational approximation to reals (doubles) x, using default parameters.
static Fraction	getFraction(double x, double tolerance, int maxConvergents) Finds rational approximation to reals (doubles) x.
java.lang.String	getLatexString()
Fraction	getReciprocal() Gets the reciprocal.
double	getValue() Returns this fraction as a double value
Fraction	multiply(Fraction f)
Fraction	over(Fraction f) Returns this / f
static void	setMaxConvergents(int max)
Fraction	subtract(Fraction f)
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

ONE

public static final Fraction ONE

1/1

ZERO

public static final Fraction ZERO

0/1

TOLERANCE

public static final double TOLERANCE

default approximation tolerance of fraction to inputed double

See Also:

Constant Field Values

MAX_CONVERGENTS

public static int MAX_CONVERGENTS

default Maximum number of convergents in series to calculate

numerator

private long numerator

the numerator of this fraction

denominator

private long denominator

the denominator of this fraction

Constructor Detail

Fraction

public Fraction(long numerator,
                long denominator)

Constructor. Throws exception for denominator = 0

Parameters:

numerator -

denominator -

Fraction

public Fraction(double value)

Constructs a rational approximation to the double value

Parameters:

value -

Method Detail

add

public Fraction add(Fraction f)

subtract

public Fraction subtract(Fraction f)

multiply

public Fraction multiply(Fraction f)

over

public Fraction over(Fraction f)

Returns this / f

Parameters:

f -

Returns:

this/ / f

getReciprocal

public Fraction getReciprocal()

Gets the reciprocal. Throws exception if numerator is zero

Returns:

1 / this

getValue

public double getValue()

Returns this fraction as a double value

Returns:

the double value of this fraction

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

gcd

public static long gcd(long A,
                       long B)

The greatest common divisor of integers A and B

Parameters:

A -

B -

Returns:

The greatest common divisor of integers A and B

getFraction

public static Fraction getFraction(double x)

Finds rational approximation to reals (doubles) x, using default parameters.

Parameters:

x - the real to be approximated

Returns:

a rational approximation to x

getFraction

public static Fraction getFraction(double x,
                                   double tolerance,
                                   int maxConvergents)

Finds rational approximation to reals (doubles) x.

Parameters:

x - the real to be approximated

tolerance - distance between approximation and x prompting termination

maxConvergents - maximum number of convergents in series to calculate

Returns:

a rational approximation to x

getLatexString

public java.lang.String getLatexString()

setMaxConvergents

public static void setMaxConvergents(int max)