edu.jas.arith
Class BigQuaternion

java.lang.Object
  edu.jas.arith.BigQuaternion

All Implemented Interfaces:

Coefficient, java.io.Serializable, java.lang.Comparable

public class BigQuaternion
extends java.lang.Object
implements Coefficient, java.lang.Comparable, java.io.Serializable

BigQuaternion class based on BigRational implementing the Coefficient interface and with the familiar SAC method names.

See Also:

Serialized Form

Field Summary

static BigQuaternion	I
static BigQuaternion	J
static BigQuaternion	K
static BigQuaternion	ONE
static BigQuaternion	ZERO constants: 1, 0 und i

Constructor Summary

BigQuaternion()

BigQuaternion(BigRational r)

BigQuaternion(BigRational r, BigRational i)

BigQuaternion(BigRational r, BigRational i, BigRational j)

BigQuaternion(BigRational r, BigRational i, BigRational j, BigRational k)
The constructors create a BigQuaternion object from two BigRational objects real and imaginary parts.

BigQuaternion(int r)

BigQuaternion(java.lang.String s)
The BigQuaternion string constructor accepts the following formats: empty string, "rational", or "rat i rat j rat k rat"

Method Summary

Coefficient	abs()
Coefficient	add(Coefficient b) arithmetic operations: +, -, -
int	compareTo(java.lang.Object b) since quaternion numbers are unordered, there is no compareTo method.
BigQuaternion	conjugate() arithmetic operations: conjugate, absolut value
Coefficient	divide(Coefficient b)
boolean	equals(java.lang.Object b) comparison of two BigQuaternion numbers
Coefficient	fromInteger(java.math.BigInteger a)
Coefficient	fromInteger(long a)
BigRational	getIm()
BigRational	getJm()
BigRational	getKm()
BigRational	getRe() get the real and imaginary part
Coefficient	inverse()
static boolean	isCONE(BigQuaternion A) Quaternion number one.
static boolean	isCZERO(BigQuaternion A) Quaternion number zero.
boolean	isIMAG()
boolean	isONE()
boolean	isZERO()
Coefficient	multiply(Coefficient b) arithmetic operations: *, inverse, /
Coefficient	negate()
static BigRational	QABS(BigQuaternion A) Quaternion number absolute value.
static BigQuaternion	QCON(BigQuaternion A) Quaternion number conjugate.
static BigQuaternion	QDIF(BigQuaternion A, BigQuaternion B) Quaternion number difference.
static BigQuaternion	QINV(BigQuaternion A) Quaternion number inverse.
static BigQuaternion	QNEG(BigQuaternion A) Quaternion number negative.
static BigQuaternion	QPROD(BigQuaternion A, BigQuaternion B) Quaternion number product.
static BigQuaternion	QQ(BigQuaternion A, BigQuaternion B) Quaternion number quotient.
static BigQuaternion	QRAND(int n) Quaternion number, random.
static BigQuaternion	QSUM(BigQuaternion A, BigQuaternion B) Quaternion number sum.
Coefficient	random(int n) random quaternion number
int	signum()
Coefficient	subtract(Coefficient b)
java.lang.String	toString() string representation compatible with string constructor

Methods inherited from class java.lang.Object

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

Field Detail

ZERO

public static final BigQuaternion ZERO

constants: 1, 0 und i

ONE

public static final BigQuaternion ONE

I

public static final BigQuaternion I

J

public static final BigQuaternion J

K

public static final BigQuaternion K

Constructor Detail

BigQuaternion

public BigQuaternion(BigRational r,
                     BigRational i,
                     BigRational j,
                     BigRational k)

The constructors create a BigQuaternion object from two BigRational objects real and imaginary parts.

BigQuaternion

public BigQuaternion(BigRational r,
                     BigRational i,
                     BigRational j)

BigQuaternion

public BigQuaternion(BigRational r,
                     BigRational i)

BigQuaternion

public BigQuaternion(BigRational r)

BigQuaternion

public BigQuaternion(int r)

BigQuaternion

public BigQuaternion()

BigQuaternion

public BigQuaternion(java.lang.String s)
              throws java.lang.NumberFormatException

The BigQuaternion string constructor accepts the following formats: empty string, "rational", or "rat i rat j rat k rat"

Throws:

java.lang.NumberFormatException

Method Detail

fromInteger

public Coefficient fromInteger(java.math.BigInteger a)

Specified by:

fromInteger in interface Coefficient

fromInteger

public Coefficient fromInteger(long a)

Specified by:

fromInteger in interface Coefficient

getRe

public BigRational getRe()

get the real and imaginary part

getIm

public BigRational getIm()

getJm

public BigRational getJm()

getKm

public BigRational getKm()

toString

public java.lang.String toString()

string representation compatible with string constructor

Overrides:

toString in class java.lang.Object

isCZERO

public static boolean isCZERO(BigQuaternion A)

Quaternion number zero. A is a quaternion number. If A is 0 then true is returned, else false.

isZERO

public boolean isZERO()

Specified by:

isZERO in interface Coefficient

isCONE

public static boolean isCONE(BigQuaternion A)

Quaternion number one. A is a quaternion number. If A is 1 then true is returned, else false.

isONE

public boolean isONE()

Specified by:

isONE in interface Coefficient

isIMAG

public boolean isIMAG()

equals

public boolean equals(java.lang.Object b)

comparison of two BigQuaternion numbers

Overrides:

equals in class java.lang.Object

compareTo

public int compareTo(java.lang.Object b)

since quaternion numbers are unordered, there is no compareTo method. We define the result to be

Specified by:

compareTo in interface Coefficient

Specified by:

compareTo in interface java.lang.Comparable

Returns:

-1 if b is not a BigQuaternion object

signum

public int signum()

Specified by:

signum in interface Coefficient

add

public Coefficient add(Coefficient b)

arithmetic operations: +, -, -

Specified by:

add in interface Coefficient

QSUM

public static BigQuaternion QSUM(BigQuaternion A,
                                 BigQuaternion B)

Quaternion number sum. A and B are quaternion numbers.

Returns:

T=A+B.

QDIF

public static BigQuaternion QDIF(BigQuaternion A,
                                 BigQuaternion B)

Quaternion number difference. A and B are quaternion numbers.

Returns:

T=A-B.

subtract

public Coefficient subtract(Coefficient b)

Specified by:

subtract in interface Coefficient

QNEG

public static BigQuaternion QNEG(BigQuaternion A)

Quaternion number negative. A is a quaternion number.

Returns:

S=-A.

negate

public Coefficient negate()

Specified by:

negate in interface Coefficient

QCON

public static BigQuaternion QCON(BigQuaternion A)

Quaternion number conjugate. A is a quaternion number. S is the quaternion conjugate of A.

conjugate

public BigQuaternion conjugate()

arithmetic operations: conjugate, absolut value

abs

public Coefficient abs()

Specified by:

abs in interface Coefficient

QABS

public static BigRational QABS(BigQuaternion A)

Quaternion number absolute value. R is a quaternion number. S is the absolute value of R, a rational number.

QPROD

public static BigQuaternion QPROD(BigQuaternion A,
                                  BigQuaternion B)

Quaternion number product. A and B are quaternion numbers.

Returns:

T=A*B.

multiply

public Coefficient multiply(Coefficient b)

arithmetic operations: *, inverse, /

Specified by:

multiply in interface Coefficient

QINV

public static BigQuaternion QINV(BigQuaternion A)

Quaternion number inverse. A is a non-zero quaternion number. S A=1.

inverse

public Coefficient inverse()

Specified by:

inverse in interface Coefficient

QQ

public static BigQuaternion QQ(BigQuaternion A,
                               BigQuaternion B)

Quaternion number quotient. A and B are quaternion numbers, B non-zero.

Returns:

T=R/S.

divide

public Coefficient divide(Coefficient b)

Specified by:

divide in interface Coefficient

QRAND

public static BigQuaternion QRAND(int n)

Quaternion number, random. n is a positive beta-integer. Random rational numbers A and B are generated using RNRAND(n). Then R is the quaternion number with real part A and imaginary part B.

random

public Coefficient random(int n)

random quaternion number

Specified by:

random in interface Coefficient