Package edu.jas.application
Class SolvableResidueRing<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.application.SolvableResidueRing<C>
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- 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
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Field Summary
Fields Modifier and Type Field 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.
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Constructor Summary
Constructors Constructor 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.
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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.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(long a)
Get a SolvableResidue element from a long value.SolvableResidue<C>
fromInteger(java.math.BigInteger a)
Get a SolvableResidue element from a BigInteger 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
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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 SolvableGroebnerBaseAbstract<C extends GcdRingElem<C>> bb
Groebner base engine.
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ideal
public final SolvableIdeal<C extends GcdRingElem<C>> ideal
Solvable polynomial ideal for the reduction.
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ring
public final GenSolvablePolynomialRing<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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SolvableResidueRing
public SolvableResidueRing(SolvableIdeal<C> i)
The constructor creates a SolvableResidueRing object from an Ideal.- Parameters:
i
- polynomial ideal.
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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.
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Method Detail
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pairFactory
public GenSolvablePolynomialRing<C> pairFactory()
Factory for base elements.- Specified by:
pairFactory
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
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valueFactory
public GenSolvablePolynomialRing<C> valueFactory()
Factory for base elements.- Specified by:
valueFactory
in interfaceValueFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
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create
public SolvableResidue<C> create(GenPolynomial<C> n)
Create from numerator.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
- Specified by:
create
in interfaceValueFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<C extends GcdRingElem<C>>>
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create
public SolvableResidue<C> create(GenPolynomial<C> n, GenPolynomial<C> d)
Create from numerator, denominator pair.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableResidue<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 SolvableResidue<C> copy(SolvableResidue<C> c)
Copy SolvableResidue element c.- Specified by:
copy
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
c
-- Returns:
- a copy of c.
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getZERO
public SolvableResidue<C> getZERO()
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C>>
- Returns:
- 0 as SolvableResidue.
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getONE
public SolvableResidue<C> getONE()
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- 1 as SolvableResidue.
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generators
public java.util.List<SolvableResidue<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 SolvableResidue<C> fromInteger(java.math.BigInteger a)
Get a SolvableResidue element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a SolvableResidue.
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fromInteger
public SolvableResidue<C> fromInteger(long a)
Get a SolvableResidue element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- long.- Returns:
- a SolvableResidue.
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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 SolvableResidue<C> random(int n)
SolvableResidue 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 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.
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random
public SolvableResidue<C> random(int n, java.util.Random rnd)
SolvableResidue 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 SolvableResidue<C> parse(java.lang.String s)
Parse SolvableResidue from String.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
s
- String.- Returns:
- SolvableResidue from s.
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parse
public SolvableResidue<C> parse(java.io.Reader r)
Parse SolvableResidue from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
r
- Reader.- Returns:
- next SolvableResidue from r.
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