edu.jas.application

Class SolvableResidueRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<SolvableResidue<C>>, ElemFactory<SolvableResidue<C>>, MonoidFactory<SolvableResidue<C>>, RingFactory<SolvableResidue<C>>, java.io.Serializable

public class SolvableResidueRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<SolvableResidue<C>>

SolvableResidue ring factory based on GenSolvablePolynomial with RingFactory interface. Objects of this class are immutable.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
SolvableIdeal<C>	ideal Solvable polynomial ideal for the reduction.
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

Modifier and Type	Method and Description
java.math.BigInteger	characteristic() Characteristic of this ring.
SolvableResidue<C>	copy(SolvableResidue<C> c) Copy SolvableResidue element c.
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.
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.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Field Detail

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.

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

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.