Package edu.jas.poly
Class QuotientRing<C extends RingElem<C>>
- java.lang.Object
-
- edu.jas.poly.QuotientRing<C>
-
- All Implemented Interfaces:
AbelianGroupFactory<Quotient<C>>
,ElemFactory<Quotient<C>>
,MonoidFactory<Quotient<C>>
,QuotPairFactory<C,Quotient<C>>
,RingFactory<Quotient<C>>
,java.io.Serializable
public class QuotientRing<C extends RingElem<C>> extends java.lang.Object implements RingFactory<Quotient<C>>, QuotPairFactory<C,Quotient<C>>
Quotient ring factory using RingElem and RingFactory. Objects of this class are immutable.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
-
-
Field Summary
Fields Modifier and Type Field Description RingFactory<C>
ring
Ring factory of this factory.
-
Constructor Summary
Constructors Constructor Description QuotientRing(RingFactory<C> r)
The constructor creates a QuotientRing object from a RingFactory.
-
Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.math.BigInteger
characteristic()
Characteristic of this ring.Quotient<C>
copy(Quotient<C> c)
Copy Quotient element c.Quotient<C>
create(C n)
Create from numerator.Quotient<C>
create(C n, C d)
Create from numerator, denominator pair.boolean
equals(java.lang.Object b)
Comparison with any other object.Quotient<C>
fromInteger(long a)
Get a Quotient element from a long value.Quotient<C>
fromInteger(java.math.BigInteger a)
Get a Quotient element from a BigInteger value.java.util.List<Quotient<C>>
generators()
Get a list of the generating elements.Quotient<C>
getONE()
Get the one element.Quotient<C>
getZERO()
Get the zero element.int
hashCode()
Hash code for this quotient 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.RingFactory<C>
pairFactory()
Factory for base elements.Quotient<C>
parse(java.io.Reader r)
Parse Quotient from Reader.Quotient<C>
parse(java.lang.String s)
Parse Quotient from String.Quotient<C>
random(int n)
Quotient random.Quotient<C>
random(int n, java.util.Random rnd)
Quotient 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
-
Methods inherited from interface edu.jas.structure.ElemFactory
valueOf
-
-
-
-
Field Detail
-
ring
public final RingFactory<C extends RingElem<C>> ring
Ring factory of this factory.
-
-
Constructor Detail
-
QuotientRing
public QuotientRing(RingFactory<C> r)
The constructor creates a QuotientRing object from a RingFactory.- Parameters:
r
- ring factory.
-
-
Method Detail
-
pairFactory
public RingFactory<C> pairFactory()
Factory for base elements.- Specified by:
pairFactory
in interfaceQuotPairFactory<C extends RingElem<C>,Quotient<C extends RingElem<C>>>
-
isFinite
public boolean isFinite()
Is this structure finite or infinite.- Specified by:
isFinite
in interfaceElemFactory<C extends RingElem<C>>
- Returns:
- true if this structure is finite, else false.
- See Also:
ElemFactory.isFinite()
-
copy
public Quotient<C> copy(Quotient<C> c)
Copy Quotient element c.- Specified by:
copy
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
c
-- Returns:
- a copy of c.
-
getZERO
public Quotient<C> getZERO()
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends RingElem<C>>
- Returns:
- 0 as Quotient.
-
getONE
public Quotient<C> getONE()
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends RingElem<C>>
- Returns:
- 1 as Quotient.
-
generators
public java.util.List<Quotient<C>> generators()
Get a list of the generating elements.- Specified by:
generators
in interfaceElemFactory<C extends RingElem<C>>
- Returns:
- list of generators for the algebraic structure.
- See Also:
ElemFactory.generators()
-
isCommutative
public boolean isCommutative()
Query if this ring is commutative.- Specified by:
isCommutative
in interfaceMonoidFactory<C extends RingElem<C>>
- Returns:
- true if this ring is commutative, else false.
-
isAssociative
public boolean isAssociative()
Query if this ring is associative.- Specified by:
isAssociative
in interfaceMonoidFactory<C extends RingElem<C>>
- Returns:
- true if this ring is associative, else false.
-
isField
public boolean isField()
Query if this ring is a field.- Specified by:
isField
in interfaceRingFactory<C extends RingElem<C>>
- Returns:
- true.
-
characteristic
public java.math.BigInteger characteristic()
Characteristic of this ring.- Specified by:
characteristic
in interfaceRingFactory<C extends RingElem<C>>
- Returns:
- characteristic of this ring.
-
fromInteger
public Quotient<C> fromInteger(java.math.BigInteger a)
Get a Quotient element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
a
- BigInteger.- Returns:
- a Quotient.
-
fromInteger
public Quotient<C> fromInteger(long a)
Get a Quotient element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
a
- long.- Returns:
- a Quotient.
-
toString
public java.lang.String toString()
Get the String representation as RingFactory.- Overrides:
toString
in classjava.lang.Object
- See Also:
Object.toString()
-
toScript
public java.lang.String toScript()
Get a scripting compatible string representation.- Specified by:
toScript
in interfaceElemFactory<C extends RingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
ElemFactory.toScript()
-
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)
-
hashCode
public int hashCode()
Hash code for this quotient ring.- Overrides:
hashCode
in classjava.lang.Object
- See Also:
Object.hashCode()
-
random
public Quotient<C> random(int n)
Quotient random.- Specified by:
random
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).- Returns:
- a random residue element.
-
random
public Quotient<C> random(int n, java.util.Random rnd)
Quotient random.- Specified by:
random
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).rnd
- is a source for random bits.- Returns:
- a random residue element.
-
parse
public Quotient<C> parse(java.lang.String s)
Parse Quotient from String.- Specified by:
parse
in interfaceElemFactory<C extends RingElem<C>>
- Parameters:
s
- String.- Returns:
- Quotient from s.
-
-