SolvableResidueRing

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

All Implemented Interfaces:

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

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

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

Constructor Summary

Constructors
Constructor and Description
`SolvableResidueRing(SolvableIdeal<C> i)` The constructor creates a SolvableResidueRing object from an Ideal.
`SolvableResidueRing(SolvableIdeal<C> i, boolean isMaximal)` The constructor creates a SolvableResidueRing object from an SolvableIdeal.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`SolvableResidue<C>`	`copy(SolvableResidue<C> c)` Copy SolvableResidue element c.
`SolvableResidue<C>`	`create(GenPolynomial<C> n)` Create from numerator.
`SolvableResidue<C>`	`create(GenPolynomial<C> n, GenPolynomial<C> d)` Create from numerator, denominator pair.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`SolvableResidue<C>`	`fromInteger(java.math.BigInteger a)` Get a SolvableResidue element from a BigInteger value.
`SolvableResidue<C>`	`fromInteger(long a)` Get a SolvableResidue element from a long value.
`java.util.List<SolvableResidue<C>>`	`generators()` Get a list of the generating elements.
`SolvableResidue<C>`	`getONE()` Get the one element.
`SolvableResidue<C>`	`getZERO()` Get the zero element.
`int`	`hashCode()` Hash code for this residue 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.
`SolvableResidue<C>`	`parse(java.io.Reader r)` Parse SolvableResidue from Reader.
`SolvableResidue<C>`	`parse(java.lang.String s)` Parse SolvableResidue from String.
`SolvableResidue<C>`	`random(int n)` SolvableResidue random.
`SolvableResidue<C>`	`random(int k, int l, int d, float q)` Generate a random residum polynomial.
`SolvableResidue<C>`	`random(int n, java.util.Random rnd)` SolvableResidue random.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toString()` Get the String representation as RingFactory.
`GenSolvablePolynomialRing<C>`	`valueFactory()` Factory for base elements.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - bb
```
protected final SolvableGroebnerBaseAbstract<C extends GcdRingElem<C>> bb
```
    Groebner base engine.
  - ideal
```
public final SolvableIdeal<C extends GcdRingElem<C>> ideal
```
    Solvable polynomial ideal for the reduction.
  - ring
```
public final GenSolvablePolynomialRing<C extends GcdRingElem<C>> ring
```
    Polynomial ring of the factory. Shortcut to ideal.list.ring.
  - isField
```
protected int isField
```
    Indicator if this ring is a field.
- Constructor Detail
  - SolvableResidueRing
```
public SolvableResidueRing(SolvableIdeal<C> i)
```
    The constructor creates a SolvableResidueRing object from an Ideal.
    
    Parameters:
    
    i - polynomial ideal.
  - SolvableResidueRing
```
public SolvableResidueRing(SolvableIdeal<C> i,
                           boolean isMaximal)
```
    The constructor creates a SolvableResidueRing object from an SolvableIdeal.
    
    Parameters:
    
    i - solvable polynomial ideal.
    
    isMaximal - true, if ideal is maxmal.
- Method Detail
  - pairFactory
```
public GenSolvablePolynomialRing<C> pairFactory()
```
    Factory for base elements.
    
    Specified by:
    
    pairFactory in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
  - valueFactory
```
public GenSolvablePolynomialRing<C> valueFactory()
```
    Factory for base elements.
    
    Specified by:
    
    valueFactory in interface ValueFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
  - create
```
public SolvableResidue<C> create(GenPolynomial<C> n)
```
    Create from numerator.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
    
    Specified by:
    
    create in interface ValueFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
  - create
```
public SolvableResidue<C> create(GenPolynomial<C> n,
                                 GenPolynomial<C> d)
```
    Create from numerator, denominator pair.
    
    Specified by:
    
    create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    true if this structure is finite, else false.
    
    See Also:
    
    ElemFactory.isFinite()
  - copy
```
public SolvableResidue<C> copy(SolvableResidue<C> c)
```
    Copy SolvableResidue element c.
    
    Specified by:
    
    copy in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    c -
    
    Returns:
    
    a copy of c.
  - getZERO
```
public SolvableResidue<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    0 as SolvableResidue.
  - getONE
```
public SolvableResidue<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    1 as SolvableResidue.
  - generators
```
public java.util.List<SolvableResidue<C>> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<SolvableResidue<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<SolvableResidue<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<SolvableResidue<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<SolvableResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    false.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Returns:
    
    characteristic of this ring.
  - fromInteger
```
public SolvableResidue<C> fromInteger(java.math.BigInteger a)
```
    Get a SolvableResidue element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - BigInteger.
    
    Returns:
    
    a SolvableResidue.
  - fromInteger
```
public SolvableResidue<C> fromInteger(long a)
```
    Get a SolvableResidue element from a long value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    a - long.
    
    Returns:
    
    a SolvableResidue.
  - 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<SolvableResidue<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 residue ring.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    See Also:
    
    Object.hashCode()
  - random
```
public SolvableResidue<C> random(int n)
```
    SolvableResidue random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    Returns:
    
    a random residue element.
  - random
```
public SolvableResidue<C> random(int k,
                                 int l,
                                 int d,
                                 float q)
```
    Generate a random residum 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 residue polynomial.
  - random
```
public SolvableResidue<C> random(int n,
                                 java.util.Random rnd)
```
    SolvableResidue random.
    
    Specified by:
    
    random in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    rnd - is a source for random bits.
    
    Returns:
    
    a random residue element.
  - parse
```
public SolvableResidue<C> parse(java.lang.String s)
```
    Parse SolvableResidue from String.
    
    Specified by:
    
    parse in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    s - String.
    
    Returns:
    
    SolvableResidue from s.
  - parse
```
public SolvableResidue<C> parse(java.io.Reader r)
```
    Parse SolvableResidue from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<SolvableResidue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    r - Reader.
    
    Returns:
    
    next SolvableResidue from r.

Class SolvableResidueRing<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

bb

ideal

ring

isField

Constructor Detail

SolvableResidueRing

SolvableResidueRing

Method Detail

pairFactory

valueFactory

create

create

isFinite

copy

getZERO

getONE

generators

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

toString

toScript

equals

hashCode

random

random

random

parse

parse