edu.jas.arith

Class ProductRing<C extends RingElem<C>>

java.lang.Object

edu.jas.arith.ProductRing<C>

All Implemented Interfaces:

AbelianGroupFactory<Product<C>>, ElemFactory<Product<C>>, MonoidFactory<Product<C>>, RingFactory<Product<C>>, java.io.Serializable

public class ProductRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<Product<C>>

Direct product ring factory based on RingElem and RingFactory module. Objects of this class are mutable.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ProductRing(java.util.List<RingFactory<C>> l) The constructor creates a ProductRing object from an ring factory and a modul.
ProductRing(RingFactory<C> r, int n) The constructor creates a ProductRing object from an ring factory and a modul.

Method Summary

Modifier and Type	Method and Description
void	addFactory(RingFactory<C> rf) Add a ring factory.
java.math.BigInteger	characteristic() Characteristic of this ring.
boolean	containsFactory(RingFactory<C> rf) Contains a ring factory.
Product<C>	copy(Product<C> c) Copy Product element c.
boolean	equals(java.lang.Object b) Comparison with any other object.
Product<C>	fromInteger(java.math.BigInteger a) Get a Product element from a BigInteger value.
Product<C>	fromInteger(long a) Get a Product element from a long value.
java.util.List<Product<C>>	generators() Get a list of the generating elements.
Product<C>	getAtomic(int i) Get an atomic element.
RingFactory<C>	getFactory(int i) Get ring factory at index i.
Product<C>	getONE() Get the one element.
Product<C>	getZERO() Get the zero element.
int	hashCode() Hash code for this product ring.
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.
int	length() Get the number of factors of this ring.
boolean	onlyFields() Query if this ring consists only of fields.
Product<C>	parse(java.io.Reader r) Parse Product from Reader.
Product<C>	parse(java.lang.String s) Parse Product from String.
Product<C>	random(int n) Product random.
Product<C>	random(int n, float q) Product random.
Product<C>	random(int n, float q, java.util.Random rnd) Product random.
Product<C>	random(int n, java.util.Random rnd) Product random.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() Get the String representation as RingFactory.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

ProductRing

public ProductRing(RingFactory<C> r,
                   int n)

The constructor creates a ProductRing object from an ring factory and a modul.

Parameters:

r - ring factory.

n - number of copies.

ProductRing

public ProductRing(java.util.List<RingFactory<C>> l)

The constructor creates a ProductRing object from an ring factory and a modul.

Parameters:

l - list of ring factories.

Method Detail

getFactory

public RingFactory<C> getFactory(int i)

Get ring factory at index i.

Parameters:

i - index.

Returns:

RingFactory_i.

addFactory

public void addFactory(RingFactory<C> rf)

Add a ring factory.

Parameters:

rf - new ring factory.

containsFactory

public boolean containsFactory(RingFactory<C> rf)

Contains a ring factory.

Parameters:

rf - ring factory.

Returns:

true, if rf is contained in this, else false.

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<Product<C extends RingElem<C>>>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

public Product<C> copy(Product<C> c)

Copy Product element c.

Specified by:

copy in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

c -

Returns:

a copy of c.

getZERO

public Product<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<Product<C extends RingElem<C>>>

Returns:

0 as Product.

getONE

public Product<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<Product<C extends RingElem<C>>>

Returns:

1 as Product.

generators

public java.util.List<Product<C>> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<Product<C extends RingElem<C>>>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

getAtomic

public Product<C> getAtomic(int i)

Get an atomic element.

Parameters:

i - index.

Returns:

e_i as Product.

length

public int length()

Get the number of factors of this ring.

Returns:

nCopies or ringList.size().

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<Product<C extends RingElem<C>>>

Returns:

true if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<Product<C extends RingElem<C>>>

Returns:

true if this ring is associative, else false.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<Product<C extends RingElem<C>>>

Returns:

true or false.

onlyFields

public boolean onlyFields()

Query if this ring consists only of fields.

Returns:

true or false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<Product<C extends RingElem<C>>>

Returns:

minimal characteristic of ring component.

fromInteger

public Product<C> fromInteger(java.math.BigInteger a)

Get a Product element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

a - BigInteger.

Returns:

a Product.

fromInteger

public Product<C> fromInteger(long a)

Get a Product element from a long value.

Specified by:

fromInteger in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

a - long.

Returns:

a Product.

toString

public java.lang.String toString()

Get the String representation as RingFactory.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<Product<C extends RingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

ElemFactory.toScript()

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this product ring.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public Product<C> random(int n)

Product random.

Specified by:

random in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random product element v.

random

public Product<C> random(int n,
                         float q)

Product random.

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

q - density of nozero entries.

Returns:

a random product element v.

random

public Product<C> random(int n,
                         java.util.Random rnd)

Product random.

Specified by:

random in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random product element v.

random

public Product<C> random(int n,
                         float q,
                         java.util.Random rnd)

Product random.

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

q - density of nozero entries.

rnd - is a source for random bits.

Returns:

a random product element v.

parse

public Product<C> parse(java.lang.String s)

Parse Product from String.

Specified by:

parse in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

s - String.

Returns:

Product from s.

parse

public Product<C> parse(java.io.Reader r)

Parse Product from Reader. Syntax: p1 ... pn (no commas)

Specified by:

parse in interface ElemFactory<Product<C extends RingElem<C>>>

Parameters:

r - Reader.

Returns:

next Product from r.