Class BigQuaternionRing

java.lang.Object

edu.jas.arith.BigQuaternionRing

All Implemented Interfaces:

AbelianGroupFactory<BigQuaternion>, ElemFactory<BigQuaternion>, MonoidFactory<BigQuaternion>, RingFactory<BigQuaternion>, Serializable

public final class BigQuaternionRing
extends Object
implements RingFactory<BigQuaternion>

BigQuaternion ring class based on BigRational implementing the RingElem interface.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final BigQuaternion	I	The constant i.
protected boolean	integral	Flag to signal if this ring is integral.
final BigQuaternion	J	The constant j.
final BigQuaternion	K	The constant k.
final BigQuaternion	ONE	The constant 1.
protected static final Random	random
final BigQuaternion	ZERO	The constant 0.

Constructor Summary

Constructors

Constructor	Description
BigQuaternionRing()	Constructor for a BigQuaternion ring.
BigQuaternionRing(boolean i)	Constructor for a BigQuaternion ring.

Method Summary

Modifier and Type	Method	Description
BigInteger	characteristic()	Characteristic of this ring.
BigQuaternion	copy(BigQuaternion c)	Copy BigQuaternion element c.
boolean	equals(Object b)	Comparison with any other object.
BigQuaternion	fromInteger(long a)	Get a BigQuaternion element from a long.
BigQuaternion	fromInteger(long[] a)	Get a BigQuaternion element from a long vector.
BigQuaternion	fromInteger(BigInteger a)	Get a BigQuaternion element from a BigInteger.
List<BigQuaternion>	generators()	Get a list of the generating elements.
BigQuaternion	getONE()	Get the one element.
BigQuaternion	getZERO()	Get the zero element.
int	hashCode()	Hash code for this BigQuaternionRing.
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Query if this ring is commutative.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
BigQuaternion	parse(Reader r)	Parse quaternion number from Reader.
BigQuaternion	parse(String s)	Parse quaternion number from String.
BigQuaternion	random(int n)	BigQuaternion random.
BigQuaternion	random(int n, Random rnd)	BigQuaternion random.
String	toScript()	Get a scripting compatible string representation.
String	toString()	Get the string representation.
List<BigQuaternion>	unitsOfHurwitzian()	BigQuaternion units of the Hurwitzian integers.

Methods inherited from class Object

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

Methods inherited from interface ElemFactory

valueOf

Field Details

integral

protected boolean integral

Flag to signal if this ring is integral.

random

protected static final Random random

ZERO

public final BigQuaternion ZERO

The constant 0.

ONE

public final BigQuaternion ONE

The constant 1.

I

public final BigQuaternion I

The constant i.

J

public final BigQuaternion J

The constant j.

K

public final BigQuaternion K

The constant k.

Constructor Details

BigQuaternionRing

public BigQuaternionRing()

Constructor for a BigQuaternion ring.

BigQuaternionRing

public BigQuaternionRing(boolean i)

Constructor for a BigQuaternion ring.

Method Details

generators

public List<BigQuaternion> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<BigQuaternion>

Returns:

list of generators for the algebraic structure.

See Also:

• ElemFactory.generators()

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<BigQuaternion>

Returns:

true if this structure is finite, else false.

See Also:

• ElemFactory.isFinite()

copy

public BigQuaternion copy(BigQuaternion c)

Copy BigQuaternion element c.

Specified by:

copy in interface ElemFactory<BigQuaternion>

Parameters:

c - BigQuaternion.

Returns:

a copy of c.

getZERO

public BigQuaternion getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<BigQuaternion>

Returns:

0 as BigQuaternion.

getONE

public BigQuaternion getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<BigQuaternion>

Returns:

q as BigQuaternion.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<BigQuaternion>

Returns:

false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<BigQuaternion>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<BigQuaternion>

Returns:

true.

characteristic

public BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<BigQuaternion>

Returns:

characteristic of this ring.

fromInteger

public BigQuaternion fromInteger(BigInteger a)

Get a BigQuaternion element from a BigInteger.

Specified by:

fromInteger in interface ElemFactory<BigQuaternion>

Parameters:

a - BigInteger.

Returns:

a BigQuaternion.

fromInteger

public BigQuaternion fromInteger(long a)

Get a BigQuaternion element from a long.

Specified by:

fromInteger in interface ElemFactory<BigQuaternion>

Parameters:

a - long.

Returns:

a BigQuaternion.

fromInteger

public BigQuaternion fromInteger(long[] a)

Get a BigQuaternion element from a long vector.

Parameters:

a - long vector.

Returns:

a BigQuaternion.

toString

public String toString()

Get the string representation. Is compatible with the string constructor.

Overrides:

toString in class Object

See Also:

• Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<BigQuaternion>

Returns:

script compatible representation for this Element.

See Also:

• Element.toScript()

equals

public boolean equals(Object b)

Comparison with any other object.

Overrides:

equals in class Object

See Also:

• Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this BigQuaternionRing.

Overrides:

hashCode in class Object

See Also:

• Object.hashCode()

unitsOfHurwitzian

public List<BigQuaternion> unitsOfHurwitzian()

BigQuaternion units of the Hurwitzian integers. BigQuaternion units with all integer or all 1/2 times integer components.

Returns:

list of all 24 units.

random

public BigQuaternion random(int n)

BigQuaternion random. Random rational numbers A, B, C and D are generated using random(n). Then R is the quaternion number with real part A and imaginary parts B, C and D.

Specified by:

random in interface ElemFactory<BigQuaternion>

Parameters:

n - such that 0 ≤ A, B, C, D ≤ (2ⁿ-1).

Returns:

R, a random BigQuaternion.

random

public BigQuaternion random(int n,
 Random rnd)

BigQuaternion random. Random rational numbers A, B, C and D are generated using RNRAND(n). Then R is the quaternion number with real part A and imaginary parts B, C and D.

Specified by:

random in interface ElemFactory<BigQuaternion>

Parameters:

n - such that 0 ≤ A, B, C, D ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

R, a random BigQuaternion.

parse

public BigQuaternion parse(String s)

Parse quaternion number from String.

Specified by:

parse in interface ElemFactory<BigQuaternion>

Parameters:

s - String.

Returns:

BigQuaternion from s.

parse

public BigQuaternion parse(Reader r)

Parse quaternion number from Reader.

Specified by:

parse in interface ElemFactory<BigQuaternion>

Parameters:

r - Reader.

Returns:

next BigQuaternion from r.