SolvableLocalResidueRing

java.lang.Object
- edu.jas.application.SolvableLocalResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<SolvableLocalResidue<C>>, ElemFactory<SolvableLocalResidue<C>>, MonoidFactory<SolvableLocalResidue<C>>, QuotPairFactory<GenPolynomial<C>,SolvableLocalResidue<C>>, RingFactory<SolvableLocalResidue<C>>, java.io.Serializable
```
public class SolvableLocalResidueRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<SolvableLocalResidue<C>>, QuotPairFactory<GenPolynomial<C>,SolvableLocalResidue<C>>
```
SolvableLocalResidue ring factory for SolvableLocalResidue based on GenSolvablePolynomial with GcdRingElem interface. Objects of this class are immutable. It represents the "classical quotient ring modulo an ideal".

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`protected SolvableGroebnerBaseAbstract<C>`	`bb` Groebner base engine.
`SolvableSyzygyAbstract<C>`	`engine` Syzygy engine of the factory.
`SolvableIdeal<C>`	`ideal` Solvable polynomial ideal for the reduction.
`protected int`	`isField` Indicator if this ring is a field.
`GenSolvablePolynomialRing<C>`	`ring` Solvable polynomial ring of the factory.

Constructor Summary

Constructors
Constructor and Description

SolvableLocalResidueRing(SolvableIdeal<C> i)
The constructor creates a SolvableLocalResidueRing object from a SolvableIdeal.

Constructors
Constructor and Description
`SolvableLocalResidueRing(SolvableIdeal<C> i)` The constructor creates a SolvableLocalResidueRing object from a SolvableIdeal.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`SolvableLocalResidue<C>`	`copy(SolvableLocalResidue<C> c)` Copy SolvableLocalResidue element c.
`SolvableLocalResidue<C>`	`create(GenPolynomial<C> n)` Create from numerator.
`SolvableLocalResidue<C>`	`create(GenPolynomial<C> n, GenPolynomial<C> d)` Create from numerator, denominator pair.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`SolvableLocalResidue<C>`	`fromInteger(java.math.BigInteger a)` Get a SolvableLocalResidue element from a BigInteger value.
`SolvableLocalResidue<C>`	`fromInteger(long a)` Get a SolvableLocalResidue element from a long value.
`java.util.List<SolvableLocalResidue<C>>`	`generators()` Get a list of the generating elements.
`SolvableLocalResidue<C>`	`getONE()` Get the one element.
`SolvableLocalResidue<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.
`SolvableLocalResidue<C>`	`parse(java.io.Reader r)` Parse SolvableLocalResidue from Reader.
`SolvableLocalResidue<C>`	`parse(java.lang.String s)` Parse SolvableLocalResidue from String.
`SolvableLocalResidue<C>`	`random(int n)` SolvableLocalResidue random.
`SolvableLocalResidue<C>`	`random(int k, int l, int d, float q)` Generate a random quotient.
`SolvableLocalResidue<C>`	`random(int n, java.util.Random rnd)` SolvableLocalResidue 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.
  - ideal
```
public final SolvableIdeal<C extends GcdRingElem<C>> ideal
```
    Solvable polynomial ideal for the reduction.
  - engine
```
public final SolvableSyzygyAbstract<C extends GcdRingElem<C>> engine
```
    Syzygy engine of the factory.
  - bb
```
protected final SolvableGroebnerBaseAbstract<C extends GcdRingElem<C>> bb
```
    Groebner base engine.
  - isField
```
protected int isField
```
    Indicator if this ring is a field.
- Constructor Detail
  - SolvableLocalResidueRing
```
public SolvableLocalResidueRing(SolvableIdeal<C> i)
```
    The constructor creates a SolvableLocalResidueRing object from a SolvableIdeal.
    
    Parameters:
    
    i - ideal in 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>>,SolvableLocalResidue<C extends GcdRingElem<C>>>
  - create
```
public SolvableLocalResidue<C> create(GenPolynomial<C> n)
```
    Create from numerator.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableLocalResidue<C extends GcdRingElem<C>>>
  - create
```
public SolvableLocalResidue<C> create(GenPolynomial<C> n,
                                      GenPolynomial<C> d)
```
    Create from numerator, denominator pair.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableLocalResidue<C extends GcdRingElem<C>>>
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    true if this structure is finite, else false.
  - copy
```
public SolvableLocalResidue<C> copy(SolvableLocalResidue<C> c)
```
    Copy SolvableLocalResidue element c.
    
    Specified by:
    
    copy in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - getZERO
```
public SolvableLocalResidue<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    0 as SolvableLocalResidue.
  - getONE
```
public SolvableLocalResidue<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    1 as SolvableLocalResidue.
  - generators
```
public java.util.List<SolvableLocalResidue<C>> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<SolvableLocalResidue<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<SolvableLocalResidue<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<SolvableLocalResidue<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<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    true.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    characteristic of this ring.
  - fromInteger
```
public SolvableLocalResidue<C> fromInteger(java.math.BigInteger a)
```
    Get a SolvableLocalResidue element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a SolvableLocalResidue.
  - fromInteger
```
public SolvableLocalResidue<C> fromInteger(long a)
```
    Get a SolvableLocalResidue element from a long value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a SolvableLocalResidue.
  - 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<SolvableLocalResidue<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 SolvableLocalResidue<C> random(int n)
```
    SolvableLocalResidue random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    Returns:
    
    a random quotient element.
  - random
```
public SolvableLocalResidue<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 SolvableLocalResidue<C> random(int n,
                                      java.util.Random rnd)
```
    SolvableLocalResidue random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableLocalResidue<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 SolvableLocalResidue<C> parse(java.lang.String s)
```
    Parse SolvableLocalResidue from String. Syntax: "{ polynomial | polynomial }" or "{ polynomial }" or " polynomial | polynomial " or " polynomial "
    
    Specified by:
    
    parse in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    s - String.
    
    Returns:
    
    SolvableLocalResidue from s.
  - parse
```
public SolvableLocalResidue<C> parse(java.io.Reader r)
```
    Parse SolvableLocalResidue from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<SolvableLocalResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    r - Reader.
    
    Returns:
    
    next SolvableLocalResidue from r.

Class SolvableLocalResidueRing<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

ideal

engine

bb

isField

Constructor Detail

SolvableLocalResidueRing

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