Package edu.jas.application
Class ResidueRing<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.application.ResidueRing<C>
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- All Implemented Interfaces:
AbelianGroupFactory<Residue<C>>
,ElemFactory<Residue<C>>
,MonoidFactory<Residue<C>>
,RingFactory<Residue<C>>
,java.io.Serializable
public class ResidueRing<C extends GcdRingElem<C>> extends java.lang.Object implements RingFactory<Residue<C>>
Residue ring factory based on GenPolynomial with RingFactory interface. Objects of this class are immutable.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected GreatestCommonDivisor<C>
engine
Greatest common divisor engine for coefficient content and primitive parts.Ideal<C>
ideal
Polynomial ideal for the reduction.protected int
isField
Indicator if this ring is a field.GenPolynomialRing<C>
ring
Polynomial ring of the factory.
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Constructor Summary
Constructors Constructor Description ResidueRing(Ideal<C> i)
The constructor creates a ResidueRing object from an Ideal.ResidueRing(Ideal<C> i, boolean isMaximal)
The constructor creates a ResidueRing object from an Ideal.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.math.BigInteger
characteristic()
Characteristic of this ring.Residue<C>
copy(Residue<C> c)
Copy Residue element c.boolean
equals(java.lang.Object b)
Comparison with any other object.Residue<C>
fromInteger(long a)
Get a Residue element from a long value.Residue<C>
fromInteger(java.math.BigInteger a)
Get a Residue element from a BigInteger value.java.util.List<Residue<C>>
generators()
Get a list of the generating elements.Residue<C>
getONE()
Get the one element.Residue<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.Residue<C>
parse(java.io.Reader r)
Parse Residue from Reader.Residue<C>
parse(java.lang.String s)
Parse Residue from String.Residue<C>
random(int n)
Residue random.Residue<C>
random(int k, int l, int d, float q)
Generate a random residum polynomial.Residue<C>
random(int n, java.util.Random rnd)
Residue 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
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Methods inherited from interface edu.jas.structure.ElemFactory
valueOf
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Field Detail
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engine
protected final GreatestCommonDivisor<C extends GcdRingElem<C>> engine
Greatest common divisor engine for coefficient content and primitive parts.
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ideal
public final Ideal<C extends GcdRingElem<C>> ideal
Polynomial ideal for the reduction.
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ring
public final GenPolynomialRing<C extends GcdRingElem<C>> ring
Polynomial ring of the factory. Shortcut to ideal.list.ring.
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isField
protected int isField
Indicator if this ring is a field.
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Constructor Detail
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ResidueRing
public ResidueRing(Ideal<C> i)
The constructor creates a ResidueRing object from an Ideal.- Parameters:
i
- polynomial ideal.
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ResidueRing
public ResidueRing(Ideal<C> i, boolean isMaximal)
The constructor creates a ResidueRing object from an Ideal.- Parameters:
i
- polynomial ideal.isMaximal
- true, if ideal is maxmal.
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Method Detail
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isFinite
public boolean isFinite()
Is this structure finite or infinite.- Specified by:
isFinite
in interfaceElemFactory<C extends GcdRingElem<C>>
- Returns:
- true if this structure is finite, else false.
- See Also:
ElemFactory.isFinite()
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copy
public Residue<C> copy(Residue<C> c)
Copy Residue element c.- Specified by:
copy
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
c
-- Returns:
- a copy of c.
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getZERO
public Residue<C> getZERO()
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C>>
- Returns:
- 0 as Residue.
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getONE
public Residue<C> getONE()
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- 1 as Residue.
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generators
public java.util.List<Residue<C>> generators()
Get a list of the generating elements.- Specified by:
generators
in interfaceElemFactory<C extends GcdRingElem<C>>
- Returns:
- list of generators for the algebraic structure.
- See Also:
ElemFactory.generators()
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isCommutative
public boolean isCommutative()
Query if this ring is commutative.- Specified by:
isCommutative
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- true if this ring is commutative, else false.
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isAssociative
public boolean isAssociative()
Query if this ring is associative.- Specified by:
isAssociative
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- true if this ring is associative, else false.
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isField
public boolean isField()
Query if this ring is a field.- Specified by:
isField
in interfaceRingFactory<C extends GcdRingElem<C>>
- Returns:
- false.
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characteristic
public java.math.BigInteger characteristic()
Characteristic of this ring.- Specified by:
characteristic
in interfaceRingFactory<C extends GcdRingElem<C>>
- Returns:
- characteristic of this ring.
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fromInteger
public Residue<C> fromInteger(java.math.BigInteger a)
Get a Residue element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a Residue.
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fromInteger
public Residue<C> fromInteger(long a)
Get a Residue element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- long.- Returns:
- a Residue.
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toString
public java.lang.String toString()
Get the String representation as RingFactory.- Overrides:
toString
in classjava.lang.Object
- See Also:
Object.toString()
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toScript
public java.lang.String toScript()
Get a scripting compatible string representation.- Specified by:
toScript
in interfaceElemFactory<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
ElemFactory.toScript()
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equals
public boolean equals(java.lang.Object b)
Comparison with any other object.- Overrides:
equals
in classjava.lang.Object
- See Also:
Object.equals(java.lang.Object)
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hashCode
public int hashCode()
Hash code for this residue ring.- Overrides:
hashCode
in classjava.lang.Object
- See Also:
Object.hashCode()
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random
public Residue<C> random(int n)
Residue random.- Specified by:
random
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).- Returns:
- a random residue element.
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random
public Residue<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.
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random
public Residue<C> random(int n, java.util.Random rnd)
Residue random.- Specified by:
random
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).rnd
- is a source for random bits.- Returns:
- a random residue element.
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parse
public Residue<C> parse(java.lang.String s)
Parse Residue from String.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
s
- String.- Returns:
- Residue from s.
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parse
public Residue<C> parse(java.io.Reader r)
Parse Residue from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
r
- Reader.- Returns:
- next Residue from r.
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