org.jscience.mathematics.algebraic.numbers
Class ExactQuaternion

java.lang.Object
  java.lang.Number
      org.jscience.mathematics.algebraic.numbers.ExactQuaternion

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Field.Member, Ring.Member, AbelianGroup.Member, Module.Member, VectorSpace.Member, Member

public final class ExactQuaternion
extends java.lang.Number
implements java.lang.Cloneable, java.io.Serializable, Field.Member, CStarAlgebra.Member

The ExactQuaternion class encapsulates quaternions.

See Also:

Serialized Form

Field Summary

static ExactQuaternion	I
static ExactQuaternion	J
static ExactQuaternion	K
static ExactQuaternion	ONE
static java.lang.Class	TYPE
static ExactQuaternion	ZERO

Constructor Summary

ExactQuaternion(double real, Double3Vector imag)
Constructs a quaternion.

ExactQuaternion(double q0, double q1, double q2, double q3)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion(ExactQuaternion quaternion)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion(ExactReal q0, ExactReal q1, ExactReal q2, ExactReal q3)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion(Quaternion quaternion)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Method Summary

AbelianGroup.Member	add(AbelianGroup.Member x) Returns the addition of this number and another.
ExactQuaternion	add(ExactQuaternion q) Returns the addition of this quaternion and another.
ExactQuaternion	add(Quaternion q) Returns the addition of this quaternion and another.
ExactQuaternion	addImag(RingVector imag) Returns the addition of this quaternion with an imaginary part.
ExactQuaternion	addReal(double real) Returns the addition of this quaternion with a real part.
ExactQuaternion	addReal(ExactReal real) Returns the addition of this quaternion with a real part.
java.lang.Object	clone()
ExactQuaternion	conjugate() Returns the conjugate of this quaternion.
ExactQuaternion	divide(double x) Returns the division of this quaternion by a scalar.
ExactQuaternion	divide(ExactQuaternion q) Returns the division of this quaternion by another.
ExactQuaternion	divide(ExactReal x) Returns the division of this quaternion by a scalar.
Field.Member	divide(Field.Member x) Returns the division of this number and another.
double	doubleValue()
boolean	equals(java.lang.Object obj) Compares two quaternions for equality.
float	floatValue()
int	hashCode() Returns a hashcode for this quaternion.
RingVector	imag() Returns the imaginary part of this quaternion as a Vector of length 3.
int	intValue()
Field.Member	inverse() Returns the inverse of this quaternion.
CStarAlgebra.Member	involution() Returns the involution of this quaternion.
boolean	isInfinite() Returns true if either the real or imaginary part is infinite.
boolean	isNaN() Returns true if either the real or imaginary part is NaN.
long	longValue()
ExactQuaternion	multiply(double x) Returns the multiplication of this quaternion by a scalar.
ExactQuaternion	multiply(ExactQuaternion q) Returns the multiplication of this quaternion and another.
ExactQuaternion	multiply(ExactReal x) Returns the multiplication of this quaternion by a scalar.
ExactQuaternion	multiply(Quaternion q) Returns the multiplication of this quaternion and another.
Ring.Member	multiply(Ring.Member x) Returns the multiplication of this number and another.
AbelianGroup.Member	negate() Returns the negative of this quaternion.
double	norm() Returns the l2-norm (magnitude), which is also the C* norm.
ExactReal	real() Returns the real part of this quaternion.
VectorSpace.Member	scalarDivide(Field.Member x) Returns the division of this number by a real scalar.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this number by a real scalar.
AbelianGroup.Member	subtract(AbelianGroup.Member x) Returns the subtraction of this number and another.
ExactQuaternion	subtract(ExactQuaternion q) Returns the subtraction of this quaternion and another.
ExactQuaternion	subtract(Quaternion q) Returns the subtraction of this quaternion and another.
ExactQuaternion	subtractImag(RingVector imag) Returns the subtraction of this quaternion with an imaginary part.
ExactQuaternion	subtractReal(double real) Returns the subtraction of this quaternion with a real part.
ExactQuaternion	subtractReal(ExactReal real) Returns the subtraction of this quaternion with a real part.
ExactReal	sumSquares() Returns the sum of the squares of the components.
java.lang.String	toString() Returns a string representing the value of this quaternion.

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

ZERO

public static final ExactQuaternion ZERO

ONE

public static final ExactQuaternion ONE

I

public static final ExactQuaternion I

J

public static final ExactQuaternion J

K

public static final ExactQuaternion K

TYPE

public static final java.lang.Class TYPE

Constructor Detail

ExactQuaternion

public ExactQuaternion(double real,
                       Double3Vector imag)

Constructs a quaternion.

ExactQuaternion

public ExactQuaternion(double q0,
                       double q1,
                       double q2,
                       double q3)

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion

public ExactQuaternion(ExactReal q0,
                       ExactReal q1,
                       ExactReal q2,
                       ExactReal q3)

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion

public ExactQuaternion(Quaternion quaternion)

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

ExactQuaternion

public ExactQuaternion(ExactQuaternion quaternion)

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Method Detail

equals

public boolean equals(java.lang.Object obj)

Compares two quaternions for equality.

Overrides:

equals in class java.lang.Object

Parameters:

obj - a quaternion

toString

public java.lang.String toString()

Returns a string representing the value of this quaternion.

Overrides:

toString in class java.lang.Object

hashCode

public int hashCode()

Returns a hashcode for this quaternion.

Overrides:

hashCode in class java.lang.Object

isNaN

public boolean isNaN()

Returns true if either the real or imaginary part is NaN.

isInfinite

public boolean isInfinite()

Returns true if either the real or imaginary part is infinite.

real

public ExactReal real()

Returns the real part of this quaternion.

imag

public RingVector imag()

Returns the imaginary part of this quaternion as a Vector of length 3.

norm

public double norm()

Returns the l²-norm (magnitude), which is also the C^* norm.

Specified by:

norm in interface BanachSpace.Member

Returns:

DOCUMENT ME!

sumSquares

public ExactReal sumSquares()

Returns the sum of the squares of the components.

intValue

public int intValue()

Specified by:

intValue in class java.lang.Number

longValue

public long longValue()

Specified by:

longValue in class java.lang.Number

floatValue

public float floatValue()

Specified by:

floatValue in class java.lang.Number

doubleValue

public double doubleValue()

Specified by:

doubleValue in class java.lang.Number

negate

public AbelianGroup.Member negate()

Returns the negative of this quaternion.

Specified by:

negate in interface AbelianGroup.Member

Returns:

DOCUMENT ME!

inverse

public Field.Member inverse()

Returns the inverse of this quaternion.

Specified by:

inverse in interface Field.Member

Returns:

DOCUMENT ME!

involution

public CStarAlgebra.Member involution()

Returns the involution of this quaternion.

Specified by:

involution in interface CStarAlgebra.Member

Returns:

DOCUMENT ME!

conjugate

public ExactQuaternion conjugate()

Returns the conjugate of this quaternion.

add

public AbelianGroup.Member add(AbelianGroup.Member x)

Returns the addition of this number and another.

Specified by:

add in interface AbelianGroup.Member

Parameters:

x - a group member

Returns:

DOCUMENT ME!

add

public ExactQuaternion add(ExactQuaternion q)

Returns the addition of this quaternion and another.

Parameters:

q - a quaternion

add

public ExactQuaternion add(Quaternion q)

Returns the addition of this quaternion and another.

Parameters:

q - a quaternion

addReal

public ExactQuaternion addReal(double real)

Returns the addition of this quaternion with a real part.

Parameters:

real - a real part

addReal

public ExactQuaternion addReal(ExactReal real)

Returns the addition of this quaternion with a real part.

Parameters:

real - a real part

addImag

public ExactQuaternion addImag(RingVector imag)

Returns the addition of this quaternion with an imaginary part.

Parameters:

imag - an imaginary part

subtract

public AbelianGroup.Member subtract(AbelianGroup.Member x)

Returns the subtraction of this number and another.

Specified by:

subtract in interface AbelianGroup.Member

Parameters:

x - a group member

Returns:

DOCUMENT ME!

subtract

public ExactQuaternion subtract(ExactQuaternion q)

Returns the subtraction of this quaternion and another.

Parameters:

q - a quaternion

subtract

public ExactQuaternion subtract(Quaternion q)

Returns the subtraction of this quaternion and another.

Parameters:

q - a quaternion

subtractReal

public ExactQuaternion subtractReal(double real)

Returns the subtraction of this quaternion with a real part.

Parameters:

real - a real part

subtractReal

public ExactQuaternion subtractReal(ExactReal real)

Returns the subtraction of this quaternion with a real part.

Parameters:

real - a real part

subtractImag

public ExactQuaternion subtractImag(RingVector imag)

Returns the subtraction of this quaternion with an imaginary part.

Parameters:

imag - an imaginary part

scalarMultiply

public Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this number by a real scalar.

Specified by:

scalarMultiply in interface Module.Member

Parameters:

x - a ring member

Returns:

DOCUMENT ME!

multiply

public Ring.Member multiply(Ring.Member x)

Returns the multiplication of this number and another.

Specified by:

multiply in interface Ring.Member

Parameters:

x - a ring member

Returns:

DOCUMENT ME!

multiply

public ExactQuaternion multiply(ExactQuaternion q)

Returns the multiplication of this quaternion and another.

Parameters:

q - a quaternion

multiply

public ExactQuaternion multiply(Quaternion q)

Returns the multiplication of this quaternion and another.

Parameters:

q - a real number

multiply

public ExactQuaternion multiply(double x)

Returns the multiplication of this quaternion by a scalar.

Parameters:

x - a real number

multiply

public ExactQuaternion multiply(ExactReal x)

Returns the multiplication of this quaternion by a scalar.

Parameters:

x - a real number

scalarDivide

public VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this number by a real scalar.

Specified by:

scalarDivide in interface VectorSpace.Member

Parameters:

x - a field member

Returns:

DOCUMENT ME!

divide

public Field.Member divide(Field.Member x)

Returns the division of this number and another.

Specified by:

divide in interface Field.Member

Parameters:

x - a field member

Returns:

DOCUMENT ME!

divide

public ExactQuaternion divide(ExactQuaternion q)

Returns the division of this quaternion by another.

Parameters:

q - a quaternion

Throws:

java.lang.ArithmeticException - If divide by zero.

divide

public ExactQuaternion divide(double x)

Returns the division of this quaternion by a scalar.

Parameters:

x - a real number

Throws:

java.lang.ArithmeticException - If divide by zero.

divide

public ExactQuaternion divide(ExactReal x)

Returns the division of this quaternion by a scalar.

Parameters:

x - a real number

Throws:

java.lang.ArithmeticException - If divide by zero.

clone

public java.lang.Object clone()

Overrides:

clone in class java.lang.Object