Package edu.jas.application
Class LocalRing<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.application.LocalRing<C>
- All Implemented Interfaces:
AbelianGroupFactory<Local<C>>
,ElemFactory<Local<C>>
,MonoidFactory<Local<C>>
,QuotPairFactory<GenPolynomial<C>,
,Local<C>> RingFactory<Local<C>>
,Serializable
public class LocalRing<C extends GcdRingElem<C>>
extends Object
implements RingFactory<Local<C>>, QuotPairFactory<GenPolynomial<C>,Local<C>>
Local ring class based on GenPolynomial with RingElem interface. Objects of
this class are effective immutable.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected final GreatestCommonDivisor
<C> Greatest common divisor engine for coefficient content and primitive parts.Polynomial ideal for localization.protected int
Indicator if this ring is a field.private static final org.apache.logging.log4j.Logger
final GenPolynomialRing
<C> Polynomial ring of the factory. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionCharacteristic of this ring.Copy Local element c.create
(GenPolynomial<C> n) Create from numerator.create
(GenPolynomial<C> n, GenPolynomial<C> d) Create from numerator, denominator pair.boolean
Comparison with any other object.fromInteger
(long a) Get a Local element from a long value.Get a Local element from a BigInteger value.Get a list of the generating elements.getONE()
Get the one element.getZERO()
Get the zero element.int
hashCode()
Hash code for this local ring.boolean
Query if this ring is associative.boolean
Query if this ring is commutative.boolean
isField()
Query if this ring is a field.boolean
isFinite()
Is this structure finite or infinite.Factory for base elements.Parse Local from Reader.Parse Local from String.random
(int n) Local random.random
(int k, int l, int d, float q) Generate a random residum polynomial.Local random.toScript()
Get a scripting compatible string representation.toString()
Get the String representation as RingFactory.Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait
Methods inherited from interface edu.jas.structure.ElemFactory
valueOf
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
engine
Greatest common divisor engine for coefficient content and primitive parts. -
ideal
Polynomial ideal for localization. -
ring
Polynomial ring of the factory. -
isField
protected int isFieldIndicator if this ring is a field.
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Constructor Details
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LocalRing
The constructor creates a LocalRing object from an Ideal.- Parameters:
i
- localization polynomial ideal.
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Method Details
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pairFactory
Factory for base elements.- Specified by:
pairFactory
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,
Local<C extends GcdRingElem<C>>>
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create
Create from numerator.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,
Local<C extends GcdRingElem<C>>>
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create
Create from numerator, denominator pair.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,
Local<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:
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copy
Copy Local element c.- Specified by:
copy
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
c
-- Returns:
- a copy of c.
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getZERO
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C>>
- Returns:
- 0 as Local.
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getONE
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- 1 as Local.
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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:
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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
Characteristic of this ring.- Specified by:
characteristic
in interfaceRingFactory<C extends GcdRingElem<C>>
- Returns:
- characteristic of this ring.
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fromInteger
Get a Local element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a Local.
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fromInteger
Get a Local element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- long.- Returns:
- a Local.
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toString
Get the String representation as RingFactory. -
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:
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equals
Comparison with any other object. -
hashCode
public int hashCode()Hash code for this local ring. -
random
Local 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
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
Local 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
Parse Local from String.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
s
- String.- Returns:
- Local from s.
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parse
Parse Local from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
r
- Reader.- Returns:
- next Local from r.
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