Package edu.jas.ufd
Class QuotientRing<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.ufd.QuotientRing<C>
- All Implemented Interfaces:
AbelianGroupFactory<Quotient<C>>
,ElemFactory<Quotient<C>>
,MonoidFactory<Quotient<C>>
,QuotPairFactory<GenPolynomial<C>,
,Quotient<C>> RingFactory<Quotient<C>>
,Serializable
public class QuotientRing<C extends GcdRingElem<C>>
extends Object
implements RingFactory<Quotient<C>>, QuotPairFactory<GenPolynomial<C>,Quotient<C>>
Quotient ring factory based on GenPolynomial with RingElem interface. Objects
of this class are immutable.
- See Also:
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionstatic enum
Quotient polynomial normalization, simplification. -
Field Summary
FieldsModifier and TypeFieldDescriptionfinal GreatestCommonDivisor
<C> GCD engine of the factory.private static final org.apache.logging.log4j.Logger
static final QuotientRing.QuoNorm
Default quotient polynomial normalization, simplification.final GenPolynomialRing
<C> Polynomial ring of the factory.final boolean
Use GCD of package edu.jas.ufd. -
Constructor Summary
ConstructorsConstructorDescriptionThe constructor creates a QuotientRing object from a GenPolynomialRing.QuotientRing
(GenPolynomialRing<C> r, boolean ufdGCD) The constructor creates a QuotientRing object from a GenPolynomialRing. -
Method Summary
Modifier and TypeMethodDescriptionCharacteristic of this ring.Copy Quotient element c.create
(GenPolynomial<C> n) Create from numerator.create
(GenPolynomial<C> n, GenPolynomial<C> d) Create from numerator, denominator pair.protected GenPolynomial
<C> divide
(GenPolynomial<C> n, GenPolynomial<C> d) Divide.boolean
Comparison with any other object.long
Degree of extension field.fromInteger
(long a) Get a Quotient element from a long value.Get a Quotient element from a BigInteger value.protected GenPolynomial
<C> gcd
(GenPolynomial<C> n, GenPolynomial<C> d) Greatest common divisor.Get a list of the generating elements.getONE()
Get the one element.getZERO()
Get the zero element.int
hashCode()
Hash code for this quotient 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 Quotient from Reader.Parse Quotient from String.random
(int n) Quotient random.random
(int k, int l, int d, float q) Generate a random quotient polynomial.Quotient 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 -
quoNorm
Default quotient polynomial normalization, simplification. -
ring
Polynomial ring of the factory. -
engine
GCD engine of the factory. -
ufdGCD
public final boolean ufdGCDUse GCD of package edu.jas.ufd.
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Constructor Details
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QuotientRing
The constructor creates a QuotientRing object from a GenPolynomialRing.- Parameters:
r
- polynomial ring.
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QuotientRing
The constructor creates a QuotientRing object from a GenPolynomialRing.- Parameters:
r
- polynomial ring.ufdGCD
- flag, if syzygy or gcd based algorithm used for engine.
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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>>,
Quotient<C extends GcdRingElem<C>>>
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create
Create from numerator.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,
Quotient<C extends GcdRingElem<C>>>
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create
Create from numerator, denominator pair.- Specified by:
create
in interfaceQuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,
Quotient<C extends GcdRingElem<C>>>
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divide
Divide.- Parameters:
n
- first polynomial.d
- second polynomial.- Returns:
- divide(n,d)
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gcd
Greatest common divisor.- Parameters:
n
- first polynomial.d
- second polynomial.- Returns:
- gcd(n,d)
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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 Quotient 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 Quotient.
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getONE
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C>>
- Returns:
- 1 as Quotient.
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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:
- true.
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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 Quotient element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a Quotient.
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fromInteger
Get a Quotient element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
a
- long.- Returns:
- a Quotient.
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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 quotient ring. -
random
Quotient 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 quotient 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 quotient polynomial.
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random
Quotient 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 quotient element.
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parse
Parse Quotient from String. Syntax: "{ polynomial | polynomial }" or "{ polynomial }" or " polynomial | polynomial " or " polynomial "- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
s
- String.- Returns:
- Quotient from s.
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parse
Parse Quotient from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C>>
- Parameters:
r
- Reader.- Returns:
- next Quotient from r.
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extensionDegree
public long extensionDegree()Degree of extension field.- Returns:
- degree of this extension field, -1 for transcendental extension.
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