AlgebraicNumberRing

java.lang.Object
- edu.jas.poly.AlgebraicNumberRing<C>

All Implemented Interfaces:

AbelianGroupFactory<AlgebraicNumber<C>>, ElemFactory<AlgebraicNumber<C>>, MonoidFactory<AlgebraicNumber<C>>, RingFactory<AlgebraicNumber<C>>, java.io.Serializable, java.lang.Iterable<AlgebraicNumber<C>>
```
public class AlgebraicNumberRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<AlgebraicNumber<C>>, java.lang.Iterable<AlgebraicNumber<C>>
```
Algebraic number factory class 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
`protected int`	`isField` Indicator if this ring is a field
`GenPolynomial<C>`	`modul` Module part of the factory data structure.
`GenPolynomialRing<C>`	`ring` Ring part of the factory data structure.

Constructor Summary

Constructors
Constructor and Description
`AlgebraicNumberRing(GenPolynomial<C> m)` The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.
`AlgebraicNumberRing(GenPolynomial<C> m, boolean isField)` The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.

Method Summary

Methods
Modifier and Type	Method and Description
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`AlgebraicNumber<C>`	`chineseRemainder(AlgebraicNumber<C> c, AlgebraicNumber<C> ci, AlgebraicNumber<C> a)` AlgebraicNumber chinese remainder algorithm.
`AlgebraicNumber<C>`	`copy(AlgebraicNumber<C> c)` Copy AlgebraicNumber element c.
`int`	`depth()` Depth of extension field tower.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`long`	`extensionDegree()` Degree of extension field.
`AlgebraicNumber<C>`	`fillFromInteger(java.math.BigInteger a)` Get a AlgebraicNumber element from a BigInteger value.
`AlgebraicNumber<C>`	`fillFromInteger(long a)` Get a AlgebraicNumber element from a long value.
`AlgebraicNumber<C>`	`fromInteger(java.math.BigInteger a)` Get a AlgebraicNumber element from a BigInteger value.
`AlgebraicNumber<C>`	`fromInteger(long a)` Get a AlgebraicNumber element from a long value.
`java.util.List<AlgebraicNumber<C>>`	`generators()` Get a list of the generating elements.
`int`	`getField()` Get the internal field indicator.
`AlgebraicNumber<C>`	`getGenerator()` Get the generating element.
`GenPolynomial<C>`	`getModul()` Get the module part.
`AlgebraicNumber<C>`	`getONE()` Get the one element.
`AlgebraicNumber<C>`	`getZERO()` Get the zero element.
`int`	`hashCode()` Hash code for this AlgebraicNumber.
`AlgebraicNumber<C>`	`interpolate(AlgebraicNumber<C> c, C ci, C am, C a)` AlgebraicNumber interpolation algorithm.
`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.
`java.util.Iterator<AlgebraicNumber<C>>`	`iterator()` Get a AlgebraicNumber iterator.
`AlgebraicNumber<C>`	`parse(java.io.Reader r)` Parse AlgebraicNumber from Reader.
`AlgebraicNumber<C>`	`parse(java.lang.String s)` Parse AlgebraicNumber from String.
`AlgebraicNumber<C>`	`random(int n)` AlgebraicNumber random.
`AlgebraicNumber<C>`	`random(int n, java.util.Random rnd)` AlgebraicNumber random.
`void`	`setField(boolean field)` Set field property of this ring.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toString()` Get the String representation as RingFactory.
`long`	`totalExtensionDegree()` Total degree of nested extension fields.

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

- Field Detail
  - ring
```
public final GenPolynomialRing<C extends RingElem<C>> ring
```
    Ring part of the factory data structure.
  - modul
```
public final GenPolynomial<C extends RingElem<C>> modul
```
    Module part of the factory data structure.
  - isField
```
protected int isField
```
    Indicator if this ring is a field
- Constructor Detail
  - AlgebraicNumberRing
```
public AlgebraicNumberRing(GenPolynomial<C> m)
```
    The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.
    
    Parameters:
    m - module GenPolynomial.
  - AlgebraicNumberRing
```
public AlgebraicNumberRing(GenPolynomial<C> m,
                   boolean isField)
```
    The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.
    
    Parameters:
    m - module GenPolynomial.
    isField - indicator if m is prime.
- Method Detail
  - getModul
```
public GenPolynomial<C> getModul()
```
    Get the module part.
    
    Returns:
    modul.
  - copy
```
public AlgebraicNumber<C> copy(AlgebraicNumber<C> c)
```
    Copy AlgebraicNumber element c.
    
    Specified by:
    
    copy in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    c - algebraic number to copy.
    
    Returns:
    a copy of c.
  - getZERO
```
public AlgebraicNumber<C> getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    0 as AlgebraicNumber.
  - getONE
```
public AlgebraicNumber<C> getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    1 as AlgebraicNumber.
  - getGenerator
```
public AlgebraicNumber<C> getGenerator()
```
    Get the generating element.
    
    Returns:
    alpha as AlgebraicNumber.
  - generators
```
public java.util.List<AlgebraicNumber<C>> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    list of generators for the algebraic structure.
    See Also:
    ElemFactory.generators()
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    true if this structure is finite, else false.
    See Also:
    ElemFactory.isFinite()
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<AlgebraicNumber<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<AlgebraicNumber<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<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    true if modul is prime, else false.
  - setField
```
public void setField(boolean field)
```
    Set field property of this ring.
    
    Parameters:
    field - true, if this ring is determined to be a field, false, if it is determined that it is not a field.
  - getField
```
public int getField()
```
    Get the internal field indicator.
    
    Returns:
    internal field indicator.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    characteristic of this ring.
  - fillFromInteger
```
public AlgebraicNumber<C> fillFromInteger(java.math.BigInteger a)
```
    Get a AlgebraicNumber element from a BigInteger value.
    
    Parameters:
    a - BigInteger.
    
    Returns:
    a AlgebraicNumber.
  - fillFromInteger
```
public AlgebraicNumber<C> fillFromInteger(long a)
```
    Get a AlgebraicNumber element from a long value.
    
    Parameters:
    a - long.
    
    Returns:
    a AlgebraicNumber.
  - fromInteger
```
public AlgebraicNumber<C> fromInteger(java.math.BigInteger a)
```
    Get a AlgebraicNumber element from a BigInteger value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    a - BigInteger.
    
    Returns:
    a AlgebraicNumber.
  - fromInteger
```
public AlgebraicNumber<C> fromInteger(long a)
```
    Get a AlgebraicNumber element from a long value.
    
    Specified by:
    
    fromInteger in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    a - long.
    
    Returns:
    a AlgebraicNumber.
  - 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<AlgebraicNumber<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 AlgebraicNumber.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    See Also:
    Object.hashCode()
  - random
```
public AlgebraicNumber<C> random(int n)
```
    AlgebraicNumber random.
    
    Specified by:
    
    random in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    
    Returns:
    a random integer mod modul.
  - random
```
public AlgebraicNumber<C> random(int n,
                        java.util.Random rnd)
```
    AlgebraicNumber random.
    
    Specified by:
    
    random in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    n - such that 0 ≤ v ≤ (2ⁿ-1).
    rnd - is a source for random bits.
    
    Returns:
    a random integer mod modul.
  - parse
```
public AlgebraicNumber<C> parse(java.lang.String s)
```
    Parse AlgebraicNumber from String.
    
    Specified by:
    
    parse in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    s - String.
    
    Returns:
    AlgebraicNumber from s.
  - parse
```
public AlgebraicNumber<C> parse(java.io.Reader r)
```
    Parse AlgebraicNumber from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    r - Reader.
    
    Returns:
    next AlgebraicNumber from r.
  - chineseRemainder
```
public AlgebraicNumber<C> chineseRemainder(AlgebraicNumber<C> c,
                                  AlgebraicNumber<C> ci,
                                  AlgebraicNumber<C> a)
```
    AlgebraicNumber chinese remainder algorithm. Assert deg(c.modul) >= deg(a.modul) and c.modul * a.modul = this.modul.
    
    Parameters:
    c - AlgebraicNumber.
    ci - inverse of c.modul in ring of a.
    a - other AlgebraicNumber.
    
    Returns:
    S, with S mod c.modul == c and S mod a.modul == a.
  - interpolate
```
public AlgebraicNumber<C> interpolate(AlgebraicNumber<C> c,
                             C ci,
                             C am,
                             C a)
```
    AlgebraicNumber interpolation algorithm. Assert deg(c.modul) >= deg(A.modul) and c.modul * A.modul = this.modul. Special case with deg(A.modul) == 1. Similar algorithm as chinese remainder algortihm.
    
    Parameters:
    c - AlgebraicNumber.
    ci - inverse of (c.modul)(a) in ring of A.
    am - trailing base coefficient of modul of other AlgebraicNumber A.
    a - value of other AlgebraicNumber A.
    
    Returns:
    S, with S(c) == c and S(A) == a.
  - depth
```
public int depth()
```
    Depth of extension field tower.
    
    Returns:
    number of nested algebraic extension fields
  - extensionDegree
```
public long extensionDegree()
```
    Degree of extension field.
    
    Returns:
    degree of this algebraic extension field
  - totalExtensionDegree
```
public long totalExtensionDegree()
```
    Total degree of nested extension fields.
    
    Returns:
    degree of tower of algebraic extension fields
  - iterator
```
public java.util.Iterator<AlgebraicNumber<C>> iterator()
```
    Get a AlgebraicNumber iterator. Note: Only for finite field coefficients or fields which are iterable.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    a iterator over all algebraic numbers in this ring.

Class AlgebraicNumberRing<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

modul

isField

Constructor Detail

AlgebraicNumberRing

AlgebraicNumberRing

Method Detail

getModul

copy

getZERO

getONE

getGenerator

generators

isFinite

isCommutative

isAssociative

isField

setField

getField

characteristic

fillFromInteger

fillFromInteger

fromInteger

fromInteger

toString

toScript

equals

hashCode

random

random

parse

parse

chineseRemainder

interpolate

depth

extensionDegree

totalExtensionDegree

iterator