org.spaceroots.rkcheck

Class QuadraticSurd

java.lang.Object

org.spaceroots.rkcheck.QuadraticSurd

public class QuadraticSurd
extends java.lang.Object

This class implements quadratic irrational numbers (which are also called quadratic surds).

Quadratic irrational numbers are roots of quadratic polynoms with integer coefficients. They can be written:

         p1 + p2 sqrt (d)
   z =  ------------------
               q
   

where p1 and p2 are integers, d is a square free strictly positive integer and q is a strictly positive integer. This number is a root of:

     2  2                2       2
    q  X  - 2 q p1 X + p1  - d p2  = 0
   

The set of quadratic irrational numbers associated with a given number d is a field denoted F[sqrt(d)]. This class implements computation within such a field.

Constructor Summary

Constructors

Constructor and Description
QuadraticSurd() Simple constructor.
QuadraticSurd(java.math.BigDecimal r, java.math.BigDecimal tolerance) Simple constructor.
QuadraticSurd(java.math.BigInteger l) Simple constructor.
QuadraticSurd(java.math.BigInteger numerator, java.math.BigInteger denominator) Simple constructor.
QuadraticSurd(java.math.BigInteger p1, java.math.BigInteger p2, java.math.BigInteger d, java.math.BigInteger q) Simple constructor.
QuadraticSurd(long l) Simple constructor.
QuadraticSurd(long numerator, long denominator) Simple constructor.
QuadraticSurd(long p1, long p2, long d, long q) Simple constructor.
QuadraticSurd(QuadraticSurd qs) Copy-constructor.

Method Summary

Modifier and Type	Method and Description
static QuadraticSurd	add(QuadraticSurd qs1, QuadraticSurd qs2) Add two quadratic surds.
void	addToSelf(QuadraticSurd qs) Add a quadratic surd to the instance.
java.math.BigDecimal	bigDecimalValue(int scale) Returns the value of the underlying number as a BigDecimal.
static QuadraticSurd	divide(QuadraticSurd qs, long l) Divide a quadratic surd by an integer
static QuadraticSurd	divide(QuadraticSurd qs1, QuadraticSurd qs2) Divide two quadratic surds.
void	divideSelf(long l) Divide the instance by an integer.
void	divideSelf(QuadraticSurd qs) Divide the instance by a quadratic surd.
double	doubleValue() Returns the value of the underlying number as a double.
boolean	equals(java.lang.Object o) Check if the instance is equal to another quadratic surd.
java.math.BigInteger	getDenominator() Get the denominator.
java.math.BigInteger	getRationalNumerator() Get the numerator of the rational part.
java.math.BigInteger	getRootCoefficient() Get the coefficient of the irrational part.
java.math.BigInteger	getRootElement() Get the root element of the irrational part.
int	hashCode() Returns a hash code value for the object.
static QuadraticSurd	invert(QuadraticSurd qs) Invert a quadratic surd.
void	invertSelf() Invert the instance.
boolean	isInteger() Check if the number is integer.
boolean	isOne() Check if the instance is equal to 1.
boolean	isRational() Check if the instance holds a rational number.
boolean	isZero() Check if the instance is equal to 0.
static QuadraticSurd	multiply(QuadraticSurd qs, long l) Multiply a quadratic surd by an integer.
static QuadraticSurd	multiply(QuadraticSurd qs1, QuadraticSurd qs2) Multiply two quadratic surds.
void	multiplySelf(long l) Multiply the instance by an integer.
void	multiplySelf(QuadraticSurd qs) Multiply the instance by a quadratic surd.
static QuadraticSurd	negate(QuadraticSurd qs) Negate a quadratic surd.
void	negateSelf() Negate the instance
boolean	sameField(QuadraticSurd qs) Check if a quadratic surd belong to the same field as the instance.
static QuadraticSurd	subtract(QuadraticSurd qs1, QuadraticSurd qs2) Subtract two quadratic surds.
void	subtractFromSelf(QuadraticSurd qs) Subtract a quadratic surd to the instance.
java.lang.String	toString() Returns a string representation of the underlying number.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

QuadraticSurd

public QuadraticSurd()

Simple constructor. Build a null quadratic surd

QuadraticSurd

public QuadraticSurd(long l)

Simple constructor. Build a quadratic surd from a single integer

Parameters:

l - value of the quadratic surd

QuadraticSurd

public QuadraticSurd(java.math.BigInteger l)

Simple constructor. Build a quadratic surd from a single integer

Parameters:

l - value of the quadratic surd

QuadraticSurd

public QuadraticSurd(long numerator,
                     long denominator)

Simple constructor. Build a quadratic surd from a numerator and a denominator. This is a simple rational number.

Parameters:

numerator - numerator of the quadratic surd

denominator - denominator of the quadratic surd

Throws:

java.lang.ArithmeticException - if the denominator is zero

QuadraticSurd

public QuadraticSurd(java.math.BigInteger numerator,
                     java.math.BigInteger denominator)

Simple constructor. Build a quadratic surd from a numerator and a denominator. This is a simple rational number.

Parameters:

numerator - numerator of the quadratic surd

denominator - denominator of the quadratic surd

Throws:

java.lang.ArithmeticException - if the denominator is zero

QuadraticSurd

public QuadraticSurd(long p1,
                     long p2,
                     long d,
                     long q)

Simple constructor. Build a quadratic surd from its coordinates

Parameters:

p1 - integer part of the numerator

p2 - coefficient of the root part of the numerator

d - root

q - denominator

Throws:

java.lang.ArithmeticException - if the root is negative

java.lang.ArithmeticException - if the denominator is zero

QuadraticSurd

public QuadraticSurd(java.math.BigInteger p1,
                     java.math.BigInteger p2,
                     java.math.BigInteger d,
                     java.math.BigInteger q)

Simple constructor. Build a quadratic surd from its coordinates

Parameters:

p1 - integer part of the numerator

p2 - coefficient of the root part of the numerator

d - root

q - denominator

Throws:

java.lang.ArithmeticException - if the root is negative

java.lang.ArithmeticException - if the denominator is zero

QuadraticSurd

public QuadraticSurd(java.math.BigDecimal r,
                     java.math.BigDecimal tolerance)

Simple constructor. Build a quadratic surd by approximating a BigDecimal to a given tolerance using continued fractions

Parameters:

r - real number to approximate

tolerance - tolerance allowed for the approximation

QuadraticSurd

public QuadraticSurd(QuadraticSurd qs)

Copy-constructor.

Parameters:

qs - quadratic surd to copy

Method Detail

sameField

public boolean sameField(QuadraticSurd qs)

Check if a quadratic surd belong to the same field as the instance.

Parameters:

qs - quadratic surd to check against the instance

Returns:

true if the specified quadratic surd belong to the same field as the instance

negateSelf

public void negateSelf()

Negate the instance

negate

public static QuadraticSurd negate(QuadraticSurd qs)

Negate a quadratic surd.

Parameters:

qs - quadratic surd to negate

Returns:

a new quadratic surd which is the opposite of r

addToSelf

public void addToSelf(QuadraticSurd qs)
               throws java.lang.ArithmeticException

Add a quadratic surd to the instance.

Parameters:

qs - quadratic surd to add.

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

add

public static QuadraticSurd add(QuadraticSurd qs1,
                                QuadraticSurd qs2)
                         throws java.lang.ArithmeticException

Add two quadratic surds.

Parameters:

qs1 - first quadratic surd

qs2 - second quadratic surd

Returns:

a new quadratic surd which is the sum of qs1 and qs2

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

subtractFromSelf

public void subtractFromSelf(QuadraticSurd qs)
                      throws java.lang.ArithmeticException

Subtract a quadratic surd to the instance.

Parameters:

qs - quadratic surd to subtract.

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

subtract

public static QuadraticSurd subtract(QuadraticSurd qs1,
                                     QuadraticSurd qs2)
                              throws java.lang.ArithmeticException

Subtract two quadratic surds.

Parameters:

qs1 - first quadratic surd

qs2 - second quadratic surd

Returns:

a new quadratic surd which is the difference qs1 minus qs2

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

multiplySelf

public void multiplySelf(long l)

Multiply the instance by an integer.

Parameters:

l - integer to multiply by

multiply

public static QuadraticSurd multiply(QuadraticSurd qs,
                                     long l)

Multiply a quadratic surd by an integer.

Parameters:

qs - quadratic surd

l - integer to multiply by

multiplySelf

public void multiplySelf(QuadraticSurd qs)
                  throws java.lang.ArithmeticException

Multiply the instance by a quadratic surd.

Parameters:

qs - quadratic surd to multiply by

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

multiply

public static QuadraticSurd multiply(QuadraticSurd qs1,
                                     QuadraticSurd qs2)
                              throws java.lang.ArithmeticException

Multiply two quadratic surds.

Parameters:

qs1 - first quadratic surd

qs2 - second quadratic surd

Returns:

a new quadratic surd which is the product of qs1 and qs2

Throws:

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

divideSelf

public void divideSelf(long l)
                throws java.lang.ArithmeticException

Divide the instance by an integer.

Parameters:

l - integer to divide by

Throws:

java.lang.ArithmeticException - if l is zero

divide

public static QuadraticSurd divide(QuadraticSurd qs,
                                   long l)
                            throws java.lang.ArithmeticException

Divide a quadratic surd by an integer

Parameters:

qs - quadratic surd

l - integer

Returns:

a new quadratic surd which is the quotient of qs by l

Throws:

java.lang.ArithmeticException - if l is zero

divideSelf

public void divideSelf(QuadraticSurd qs)
                throws java.lang.ArithmeticException

Divide the instance by a quadratic surd.

Parameters:

qs - quadratic surd to divide by

Throws:

java.lang.ArithmeticException - if qs is zero

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

divide

public static QuadraticSurd divide(QuadraticSurd qs1,
                                   QuadraticSurd qs2)

Divide two quadratic surds.

Parameters:

qs1 - first quadratic surd

qs2 - second quadratic surd

Returns:

a new quadratic surd which is the quotient of qs1 by qs2

Throws:

java.lang.ArithmeticException - if qs2 is zero

java.lang.ArithmeticException - if the two quadratic surds do not belong to the same field (i.e. if they do not share the same root)

invertSelf

public void invertSelf()
                throws java.lang.ArithmeticException

Invert the instance. Replace the instance by its inverse.

Throws:

java.lang.ArithmeticException - if the instance is zero

invert

public static QuadraticSurd invert(QuadraticSurd qs)
                            throws java.lang.ArithmeticException

Invert a quadratic surd.

Parameters:

qs - quadratic surd to invert

Returns:

a new quadratic surd which is the inverse of qs

Throws:

java.lang.ArithmeticException - if qs is zero

isZero

public boolean isZero()

Check if the instance is equal to 0.

Returns:

true if the instance is equal to 0

isOne

public boolean isOne()

Check if the instance is equal to 1.

Returns:

true if the instance is equal to 1

isInteger

public boolean isInteger()

Check if the number is integer.

Returns:

true if the number is an integer

isRational

public boolean isRational()

Check if the instance holds a rational number.

Returns:

true if the instance holds a rational number

equals

public boolean equals(java.lang.Object o)

Check if the instance is equal to another quadratic surd. Equality here is having the same value.

Overrides:

equals in class java.lang.Object

Returns:

true if the object is a quadratic surd which has the same value as the instance

hashCode

public int hashCode()

Returns a hash code value for the object. The hash code value is computed from the reduced coefficents, hence equal quadratic surds have the same hash code, as required by the method specification.

Overrides:

hashCode in class java.lang.Object

Returns:

a hash code value for this object.

getRationalNumerator

public java.math.BigInteger getRationalNumerator()

Get the numerator of the rational part.

If the instance is a number of the form:

         p1 + p2 sqrt (d)
   z =  ------------------
               q
 

then this method returns p1

Returns:

numerator of the rational part

getRootCoefficient

public java.math.BigInteger getRootCoefficient()

Get the coefficient of the irrational part.

If the instance is a number of the form:

         p1 + p2 sqrt (d)
   z =  ------------------
               q
 

then this method returns p2

Returns:

coefficient of the irrational part

getRootElement

public java.math.BigInteger getRootElement()

Get the root element of the irrational part.

If the instance is a number of the form:

         p1 + p2 sqrt (d)
   z =  ------------------
               q
 

then this method returns d

Returns:

root element of the irrational part

getDenominator

public java.math.BigInteger getDenominator()

Get the denominator.

If the instance is a number of the form:

         p1 + p2 sqrt (d)
   z =  ------------------
               q
 

then this method returns q

Returns:

denominator

doubleValue

public double doubleValue()

Returns the value of the underlying number as a double.

Returns:

the numeric value represented by this object after conversion to type double.

bigDecimalValue

public java.math.BigDecimal bigDecimalValue(int scale)

Returns the value of the underlying number as a BigDecimal.

Parameters:

scale - scale of the BigDecimal to return

Returns:

the numeric value represented by this object after conversion to type BigDecimal.

toString

public java.lang.String toString()

Returns a string representation of the underlying number.

Overrides:

toString in class java.lang.Object

Returns:

a string representation of the underlying number