SolvableQuotientRing

java.lang.Object
- edu.jas.gbufd.SolvableQuotientRing<C>

All Implemented Interfaces:

AbelianGroupFactory<SolvableQuotient<C>>, ElemFactory<SolvableQuotient<C>>, MonoidFactory<SolvableQuotient<C>>, QuotPairFactory<GenPolynomial<C>,SolvableQuotient<C>>, RingFactory<SolvableQuotient<C>>, java.io.Serializable
```
public class SolvableQuotientRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<SolvableQuotient<C>>, QuotPairFactory<GenPolynomial<C>,SolvableQuotient<C>>
```
SolvableQuotient 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

SolvableSyzygyAbstract<C> engine
Syzygy engine of the factory.

GenSolvablePolynomialRing<C> ring
Solvable polynomial ring of the factory.

Fields
Modifier and Type	Field and Description
`SolvableSyzygyAbstract<C>`	`engine` Syzygy engine of the factory.
`GenSolvablePolynomialRing<C>`	`ring` Solvable polynomial ring of the factory.

Constructor Summary

Constructors
Constructor and Description

SolvableQuotientRing(GenSolvablePolynomialRing<C> r)
The constructor creates a SolvableQuotientRing object from a GenSolvablePolynomialRing.

Constructors
Constructor and Description
`SolvableQuotientRing(GenSolvablePolynomialRing<C> r)` The constructor creates a SolvableQuotientRing object from a GenSolvablePolynomialRing.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`SolvableQuotient<C>`	`copy(SolvableQuotient<C> c)` Copy SolvableQuotient element c.
`SolvableQuotient<C>`	`create(GenPolynomial<C> n)` Create from numerator.
`SolvableQuotient<C>`	`create(GenPolynomial<C> n, GenPolynomial<C> d)` Create from numerator, denominator pair.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`SolvableQuotient<C>`	`fromInteger(java.math.BigInteger a)` Get a SolvableQuotient element from a BigInteger value.
`SolvableQuotient<C>`	`fromInteger(long a)` Get a SolvableQuotient element from a long value.
`java.util.List<SolvableQuotient<C>>`	`generators()` Get a list of the generating elements.
`SolvableQuotient<C>`	`getONE()` Get the one element.
`SolvableQuotient<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.
`GenSolvablePolynomialRing<C>`	`pairFactory()` Factory for base elements.
`SolvableQuotient<C>`	`parse(java.io.Reader r)` Parse SolvableQuotient from Reader.
`SolvableQuotient<C>`	`parse(java.lang.String s)` Parse SolvableQuotient from String.
`SolvableQuotient<C>`	`random(int n)` SolvableQuotient random.
`SolvableQuotient<C>`	`random(int k, int l, int d, float q)` Generate a random quotient.
`SolvableQuotient<C>`	`random(int n, java.util.Random rnd)` SolvableQuotient 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 GenSolvablePolynomialRing<C extends GcdRingElem<C>> ring
```
    Solvable polynomial ring of the factory.
  - engine
```
public final SolvableSyzygyAbstract<C extends GcdRingElem<C>> engine
```
    Syzygy engine of the factory.
- Constructor Detail
  - SolvableQuotientRing
```
public SolvableQuotientRing(GenSolvablePolynomialRing<C> r)
```
    The constructor creates a SolvableQuotientRing object from a GenSolvablePolynomialRing.
    
    Parameters:
    
    r - solvable polynomial ring.
- Method Detail
  - pairFactory
```
public GenSolvablePolynomialRing<C> pairFactory()
```
    Factory for base elements.
    
    Specified by:
    
    pairFactory in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableQuotient<C extends GcdRingElem<C>>>
  - create
```
public SolvableQuotient<C> create(GenPolynomial<C> n)
```
    Create from numerator.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableQuotient<C extends GcdRingElem<C>>>
  - create
```
public SolvableQuotient<C> create(GenPolynomial<C> n,
                                  GenPolynomial<C> d)
```
    Create from numerator, denominator pair.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableQuotient<C extends GcdRingElem<C>>>
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    true if this structure is finite, else false.
  - copy
```
public SolvableQuotient<C> copy(SolvableQuotient<C> c)
```
    Copy SolvableQuotient element c.
    
    Specified by:
    
    copy in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - getZERO
```
public SolvableQuotient<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    0 as SolvableQuotient.
  - getONE
```
public SolvableQuotient<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    1 as SolvableQuotient.
  - generators
```
public java.util.List<SolvableQuotient<C>> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    list of generators for the algebraic structure.
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<SolvableQuotient<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<SolvableQuotient<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<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    true.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    characteristic of this ring.
  - fromInteger
```
public SolvableQuotient<C> fromInteger(java.math.BigInteger a)
```
    Get a SolvableQuotient element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a SolvableQuotient.
  - fromInteger
```
public SolvableQuotient<C> fromInteger(long a)
```
    Get a SolvableQuotient element from a long value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a SolvableQuotient.
  - toString
```
public java.lang.String toString()
```
    Get the String representation as RingFactory.
    
    Overrides:
    
    toString in class java.lang.Object
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Hash code for this quotient ring.
    
    Overrides:
    
    hashCode in class java.lang.Object
  - random
```
public SolvableQuotient<C> random(int n)
```
    SolvableQuotient random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    Returns:
    
    a random quotient element.
  - random
```
public SolvableQuotient<C> random(int k,
                                  int l,
                                  int d,
                                  float q)
```
    Generate a random quotient.
    
    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.
  - random
```
public SolvableQuotient<C> random(int n,
                                  java.util.Random rnd)
```
    SolvableQuotient random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableQuotient<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 SolvableQuotient<C> parse(java.lang.String s)
```
    Parse SolvableQuotient from String. Syntax: "{ polynomial | polynomial }" or "{ polynomial }" or " polynomial | polynomial " or " polynomial "
    
    Specified by:
    
    parse in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    s - String.
    
    Returns:
    
    SolvableQuotient from s.
  - parse
```
public SolvableQuotient<C> parse(java.io.Reader r)
```
    Parse SolvableQuotient from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    r - Reader.
    
    Returns:
    
    next SolvableQuotient from r.

Class SolvableQuotientRing<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

engine

Constructor Detail

SolvableQuotientRing

Method Detail

pairFactory

create

create

isFinite

copy

getZERO

getONE

generators

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

toString

toScript

equals

hashCode

random

random

random

parse

parse