Package edu.jas.application
Class WordResidueRing<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.application.WordResidueRing<C>
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- All Implemented Interfaces:
AbelianGroupFactory<WordResidue<C>>
,ElemFactory<WordResidue<C>>
,MonoidFactory<WordResidue<C>>
,QuotPairFactory<GenWordPolynomial<C>,WordResidue<C>>
,RingFactory<WordResidue<C>>
,ValueFactory<GenWordPolynomial<C>,WordResidue<C>>
,java.io.Serializable
public class WordResidueRing<C extends GcdRingElem<C>> extends java.lang.Object implements RingFactory<WordResidue<C>>, QuotPairFactory<GenWordPolynomial<C>,WordResidue<C>>, ValueFactory<GenWordPolynomial<C>,WordResidue<C>>
WordResidue ring factory based on GenWordPolynomialRing with GcdRingFactory 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 WordGroebnerBaseAbstract<C>
bb
Groebner base engine.WordIdeal<C>
ideal
Word polynomial ideal for the reduction.protected int
isField
Indicator if this ring is a field.GenWordPolynomialRing<C>
ring
Polynomial ring of the factory.
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Constructor Summary
Constructors Constructor Description WordResidueRing(WordIdeal<C> i)
The constructor creates a WordResidueRing object from an Ideal.WordResidueRing(WordIdeal<C> i, boolean isMaximal)
The constructor creates a WordResidueRing object from an WordIdeal.
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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.WordResidue<C>
copy(WordResidue<C> c)
Copy WordResidue element c.WordResidue<C>
create(GenWordPolynomial<C> n)
Create from numerator.WordResidue<C>
create(GenWordPolynomial<C> n, GenWordPolynomial<C> d)
Create from numerator, denominator pair.boolean
equals(java.lang.Object b)
Comparison with any other object.WordResidue<C>
fromInteger(long a)
Get a WordResidue element from a long value.WordResidue<C>
fromInteger(java.math.BigInteger a)
Get a WordResidue element from a BigInteger value.java.util.List<WordResidue<C>>
generators()
Get a list of the generating elements.WordResidue<C>
getONE()
Get the one element.WordResidue<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.GenWordPolynomialRing<C>
pairFactory()
Factory for base elements.WordResidue<C>
parse(java.io.Reader r)
Parse WordResidue from Reader.WordResidue<C>
parse(java.lang.String s)
Parse WordResidue from String.WordResidue<C>
random(int n)
WordResidue random.WordResidue<C>
random(int k, int l, int d)
Generate a random residum polynomial.WordResidue<C>
random(int n, java.util.Random rnd)
WordResidue random.java.lang.String
toScript()
Get a scripting compatible string representation.java.lang.String
toString()
Get the String representation as RingFactory.GenWordPolynomialRing<C>
valueFactory()
Factory for base elements.-
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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bb
protected final WordGroebnerBaseAbstract<C extends GcdRingElem<C>> bb
Groebner base engine.
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ideal
public final WordIdeal<C extends GcdRingElem<C>> ideal
Word polynomial ideal for the reduction.
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ring
public final GenWordPolynomialRing<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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WordResidueRing
public WordResidueRing(WordIdeal<C> i)
The constructor creates a WordResidueRing object from an Ideal.- Parameters:
i
- polynomial ideal.
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WordResidueRing
public WordResidueRing(WordIdeal<C> i, boolean isMaximal)
The constructor creates a WordResidueRing object from an WordIdeal.- Parameters:
i
- solvable polynomial ideal.isMaximal
- true, if ideal is maxmal.
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Method Detail
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pairFactory
public GenWordPolynomialRing<C> pairFactory()
Factory for base elements.- Specified by:
pairFactory
in interfaceQuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>
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valueFactory
public GenWordPolynomialRing<C> valueFactory()
Factory for base elements.- Specified by:
valueFactory
in interfaceValueFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>
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create
public WordResidue<C> create(GenWordPolynomial<C> n)
Create from numerator.- Specified by:
create
in interfaceQuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>
- Specified by:
create
in interfaceValueFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>
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create
public WordResidue<C> create(GenWordPolynomial<C> n, GenWordPolynomial<C> d)
Create from numerator, denominator pair.- Specified by:
create
in interfaceQuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>
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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 WordResidue<C> copy(WordResidue<C> c)
Copy WordResidue element c.- Specified by:
copy
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
c
-- Returns:
- a copy of c.
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getZERO
public WordResidue<C> getZERO()
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C>>
- Returns:
- 0 as WordResidue.
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getONE
public WordResidue<C> getONE()
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- 1 as WordResidue.
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generators
public java.util.List<WordResidue<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 WordResidue<C> fromInteger(java.math.BigInteger a)
Get a WordResidue element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a WordResidue.
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fromInteger
public WordResidue<C> fromInteger(long a)
Get a WordResidue element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- long.- Returns:
- a WordResidue.
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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 WordResidue<C> random(int n)
WordResidue 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 WordResidue<C> random(int k, int l, int d)
Generate a random residum polynomial.- Parameters:
k
- bitsize of random coefficients.l
- number of terms.d
- maximal degree in each variable.- Returns:
- a random residue polynomial.
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random
public WordResidue<C> random(int n, java.util.Random rnd)
WordResidue 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 WordResidue<C> parse(java.lang.String s)
Parse WordResidue from String.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
s
- String.- Returns:
- WordResidue from s.
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parse
public WordResidue<C> parse(java.io.Reader r)
Parse WordResidue from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
r
- Reader.- Returns:
- next WordResidue from r.
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