QuotientRing

java.lang.Object
- edu.jas.ufd.QuotientRing<C>

All Implemented Interfaces:

AbelianGroupFactory<Quotient<C>>, ElemFactory<Quotient<C>>, MonoidFactory<Quotient<C>>, QuotPairFactory<GenPolynomial<C>,Quotient<C>>, RingFactory<Quotient<C>>, java.io.Serializable
```
public class QuotientRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<Quotient<C>>, QuotPairFactory<GenPolynomial<C>,Quotient<C>>
```
Quotient ring factory based on GenPolynomial with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`GreatestCommonDivisor<C>`	`engine` GCD engine of the factory.
`GenPolynomialRing<C>`	`ring` Polynomial ring of the factory.
`boolean`	`ufdGCD` Use GCD of package edu.jas.ufd.

Constructor Summary

Constructors
Constructor and Description
`QuotientRing(GenPolynomialRing<C> r)` The constructor creates a QuotientRing object from a GenPolynomialRing.
`QuotientRing(GenPolynomialRing<C> r, boolean ufdGCD)` The constructor creates a QuotientRing object from a GenPolynomialRing.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`Quotient<C>`	`copy(Quotient<C> c)` Copy Quotient element c.
`Quotient<C>`	`create(GenPolynomial<C> n)` Create from numerator.
`Quotient<C>`	`create(GenPolynomial<C> n, GenPolynomial<C> d)` Create from numerator, denominator pair.
`protected GenPolynomial<C>`	`divide(GenPolynomial<C> n, GenPolynomial<C> d)` Divide.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`long`	`extensionDegree()` Degree of extension field.
`Quotient<C>`	`fromInteger(java.math.BigInteger a)` Get a Quotient element from a BigInteger value.
`Quotient<C>`	`fromInteger(long a)` Get a Quotient element from a long value.
`protected GenPolynomial<C>`	`gcd(GenPolynomial<C> n, GenPolynomial<C> d)` Greatest common divisor.
`java.util.List<Quotient<C>>`	`generators()` Get a list of the generating elements.
`Quotient<C>`	`getONE()` Get the one element.
`Quotient<C>`	`getZERO()` Get the zero element.
`int`	`hashCode()` Hash code for this quotient 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.
`GenPolynomialRing<C>`	`pairFactory()` Factory for base elements.
`Quotient<C>`	`parse(java.io.Reader r)` Parse Quotient from Reader.
`Quotient<C>`	`parse(java.lang.String s)` Parse Quotient from String.
`Quotient<C>`	`random(int n)` Quotient random.
`Quotient<C>`	`random(int k, int l, int d, float q)` Generate a random quotient polynomial.
`Quotient<C>`	`random(int n, java.util.Random rnd)` Quotient 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
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ring
```
public final GenPolynomialRing<C extends GcdRingElem<C>> ring
```
    Polynomial ring of the factory.
  - engine
```
public final GreatestCommonDivisor<C extends GcdRingElem<C>> engine
```
    GCD engine of the factory.
  - ufdGCD
```
public final boolean ufdGCD
```
    Use GCD of package edu.jas.ufd.
- Constructor Detail
  - QuotientRing
```
public QuotientRing(GenPolynomialRing<C> r)
```
    The constructor creates a QuotientRing object from a GenPolynomialRing.
    
    Parameters:
    
    r - polynomial ring.
  - QuotientRing
```
public QuotientRing(GenPolynomialRing<C> r,
                    boolean ufdGCD)
```
    The constructor creates a QuotientRing object from a GenPolynomialRing.
    
    Parameters:
    
    r - polynomial ring.
    
    ufdGCD - flag, if syzygy or gcd based algorithm used for engine.
- Method Detail
  - pairFactory
```
public GenPolynomialRing<C> pairFactory()
```
    Factory for base elements.
    
    Specified by:
    
    pairFactory in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,Quotient<C extends GcdRingElem<C>>>
  - create
```
public Quotient<C> create(GenPolynomial<C> n)
```
    Create from numerator.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,Quotient<C extends GcdRingElem<C>>>
  - create
```
public Quotient<C> create(GenPolynomial<C> n,
                          GenPolynomial<C> d)
```
    Create from numerator, denominator pair.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,Quotient<C extends GcdRingElem<C>>>
  - divide
```
protected GenPolynomial<C> divide(GenPolynomial<C> n,
                                  GenPolynomial<C> d)
```
    Divide.
    
    Parameters:
    
    n - first polynomial.
    
    d - second polynomial.
    
    Returns:
    
    divide(n,d)
  - gcd
```
protected GenPolynomial<C> gcd(GenPolynomial<C> n,
                               GenPolynomial<C> d)
```
    Greatest common divisor.
    
    Parameters:
    
    n - first polynomial.
    
    d - second polynomial.
    
    Returns:
    
    gcd(n,d)
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    true if this structure is finite, else false.
    
    See Also:
    
    ElemFactory.isFinite()
  - copy
```
public Quotient<C> copy(Quotient<C> c)
```
    Copy Quotient element c.
    
    Specified by:
    
    copy in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - getZERO
```
public Quotient<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    0 as Quotient.
  - getONE
```
public Quotient<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    1 as Quotient.
  - generators
```
public java.util.List<Quotient<C>> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    list of generators for the algebraic structure.
    
    See Also:
    
    ElemFactory.generators()
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<Quotient<C extends GcdRingElem<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<Quotient<C extends GcdRingElem<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<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    true.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<Quotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    characteristic of this ring.
  - fromInteger
```
public Quotient<C> fromInteger(java.math.BigInteger a)
```
    Get a Quotient element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a Quotient.
  - fromInteger
```
public Quotient<C> fromInteger(long a)
```
    Get a Quotient element from a long value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a Quotient.
  - 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<Quotient<C extends GcdRingElem<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 quotient ring.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    See Also:
    
    Object.hashCode()
  - random
```
public Quotient<C> random(int n)
```
    Quotient random.
    
    Specified by:
    
    random in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    Returns:
    
    a random residue element.
  - random
```
public Quotient<C> random(int k,
                          int l,
                          int d,
                          float q)
```
    Generate a random quotient polynomial.
    
    Parameters:
    
    k - bitsize of random coefficients.
    
    l - number of terms.
    
    d - maximal degree in each variable.
    
    q - density of nozero exponents.
    
    Returns:
    
    a random quotient polynomial.
  - random
```
public Quotient<C> random(int n,
                          java.util.Random rnd)
```
    Quotient random.
    
    Specified by:
    
    random in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    rnd - is a source for random bits.
    
    Returns:
    
    a random quotient element.
  - parse
```
public Quotient<C> parse(java.lang.String s)
```
    Parse Quotient from String. Syntax: "{ polynomial | polynomial }" or "{ polynomial }" or " polynomial | polynomial " or " polynomial "
    
    Specified by:
    
    parse in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    s - String.
    
    Returns:
    
    Quotient from s.
  - parse
```
public Quotient<C> parse(java.io.Reader r)
```
    Parse Quotient from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<Quotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    r - Reader.
    
    Returns:
    
    next Quotient from r.
  - extensionDegree
```
public long extensionDegree()
```
    Degree of extension field.
    
    Returns:
    
    degree of this extension field, -1 for transcendental extension.

Class QuotientRing<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

engine

ufdGCD

Constructor Detail

QuotientRing

QuotientRing

Method Detail

pairFactory

create

create

divide

gcd

isFinite

copy

getZERO

getONE

generators

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

toString

toScript

equals

hashCode

random

random

random

parse

parse

extensionDegree