Package edu.jas.application
Class RealAlgebraicRing<C extends GcdRingElem<C> & Rational>
- java.lang.Object
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- edu.jas.application.RealAlgebraicRing<C>
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- All Implemented Interfaces:
AbelianGroupFactory<RealAlgebraicNumber<C>>
,ElemFactory<RealAlgebraicNumber<C>>
,MonoidFactory<RealAlgebraicNumber<C>>
,RingFactory<RealAlgebraicNumber<C>>
,java.io.Serializable
public class RealAlgebraicRing<C extends GcdRingElem<C> & Rational> extends java.lang.Object implements RingFactory<RealAlgebraicNumber<C>>
Real algebraic number factory class based on bi-variate real algebraic numbers. Objects of this class are immutable with the exception of the isolating intervals. Bi-variate ideal implementation is in version 3614 2011-04-28 09:20:34Z.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected BigRational
eps
Epsilon of the isolating rectangle for a complex root.int
PRECISION
Precision of the isolating rectangle for a complex root.RealAlgebraicRing<RealAlgebraicNumber<C>>
realRing
Recursive real root ring.
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Constructor Summary
Constructors Constructor Description RealAlgebraicRing(IdealWithUniv<C> m, ResidueRing<C> a, RealRootTuple<C> r)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv, ResidueRing and a root tuple.RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root, boolean isField)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.
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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.RealAlgebraicNumber<C>
copy(RealAlgebraicNumber<C> c)
Copy RealAlgebraicNumber element c.boolean
equals(java.lang.Object b)
Comparison with any other object.RealAlgebraicNumber<C>
fromInteger(long a)
Get a RealAlgebraicNumber element from a long value.RealAlgebraicNumber<C>
fromInteger(java.math.BigInteger a)
Get a RealAlgebraicNumber element from a BigInteger value.java.util.List<RealAlgebraicNumber<C>>
generators()
Get a list of the generating elements.BigRational
getEps()
Get epsilon.RealAlgebraicNumber<C>
getONE()
Get the one element.RealRootTuple<C>
getRoot()
Get rectangle for the complex root.RealAlgebraicNumber<C>
getZERO()
Get the zero element.int
hashCode()
Hash code for this RealAlgebraicNumber.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.RealAlgebraicNumber<C>
parse(java.io.Reader r)
Parse RealAlgebraicNumber from Reader.RealAlgebraicNumber<C>
parse(java.lang.String s)
Parse RealAlgebraicNumber from String.RealAlgebraicNumber<C>
random(int n)
RealAlgebraicNumber random.RealAlgebraicNumber<C>
random(int n, java.util.Random rnd)
RealAlgebraicNumber random.void
refineRoot(BigRational e)
Refine root.void
setEps(C e)
Set a new epsilon.void
setEps(BigRational e)
Set a new epsilon.void
setField(boolean isField)
Assert that this ring is a field.void
setRoot(RealRootTuple<C> v)
Set a refined rectangle for the complex root.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
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Methods inherited from interface edu.jas.structure.ElemFactory
valueOf
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Field Detail
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realRing
public final RealAlgebraicRing<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>> realRing
Recursive real root ring.
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eps
protected BigRational eps
Epsilon of the isolating rectangle for a complex root.
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PRECISION
public final int PRECISION
Precision of the isolating rectangle for a complex root.- See Also:
- Constant Field Values
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Constructor Detail
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RealAlgebraicRing
public RealAlgebraicRing(IdealWithUniv<C> m, ResidueRing<C> a, RealRootTuple<C> r)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv, ResidueRing and a root tuple.- Parameters:
m
- module IdealWithUniv<C>.a
- module ResidueRing<C>.r
- isolating rectangle for a complex root.
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RealAlgebraicRing
public RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.- Parameters:
m
- module IdealWithUniv<C>.root
- isolating rectangle for a complex root.
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RealAlgebraicRing
public RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root, boolean isField)
The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.- Parameters:
m
- module IdealWithUniv<C>.root
- isolating rectangle for a complex root.isField
- indicator if m is maximal.
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Method Detail
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setRoot
public void setRoot(RealRootTuple<C> v)
Set a refined rectangle for the complex root. Note: rectangle may shrink eventually.- Parameters:
v
- rectangle.
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getRoot
public RealRootTuple<C> getRoot()
Get rectangle for the complex root.- Returns:
- v rectangle.
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getEps
public BigRational getEps()
Get epsilon.- Returns:
- epsilon.
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setEps
public void setEps(BigRational e)
Set a new epsilon.- Parameters:
e
- epsilon.
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refineRoot
public void refineRoot(BigRational e)
Refine root.- Parameters:
e
- epsilon.
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isFinite
public boolean isFinite()
Is this structure finite or infinite.- Specified by:
isFinite
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- true if this structure is finite, else false.
- See Also:
ElemFactory.isFinite()
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copy
public RealAlgebraicNumber<C> copy(RealAlgebraicNumber<C> c)
Copy RealAlgebraicNumber element c.- Specified by:
copy
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
c
-- Returns:
- a copy of c.
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getZERO
public RealAlgebraicNumber<C> getZERO()
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- 0 as RealAlgebraicNumber.
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getONE
public RealAlgebraicNumber<C> getONE()
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- 1 as RealAlgebraicNumber.
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generators
public java.util.List<RealAlgebraicNumber<C>> generators()
Get a list of the generating elements.- Specified by:
generators
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- 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> & Rational>
- 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> & Rational>
- 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> & Rational>
- Returns:
- true if algebraic is prime, else false.
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setField
public void setField(boolean isField)
Assert that this ring is a field.- Parameters:
isField
- true if this ring is a field, else false.
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characteristic
public java.math.BigInteger characteristic()
Characteristic of this ring.- Specified by:
characteristic
in interfaceRingFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- characteristic of this ring.
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fromInteger
public RealAlgebraicNumber<C> fromInteger(java.math.BigInteger a)
Get a RealAlgebraicNumber element from a BigInteger value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
a
- BigInteger.- Returns:
- a RealAlgebraicNumber.
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fromInteger
public RealAlgebraicNumber<C> fromInteger(long a)
Get a RealAlgebraicNumber element from a long value.- Specified by:
fromInteger
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
a
- long.- Returns:
- a RealAlgebraicNumber.
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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> & Rational>
- 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 RealAlgebraicNumber.- Overrides:
hashCode
in classjava.lang.Object
- See Also:
Object.hashCode()
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random
public RealAlgebraicNumber<C> random(int n)
RealAlgebraicNumber random.- Specified by:
random
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).- Returns:
- a random integer mod modul.
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random
public RealAlgebraicNumber<C> random(int n, java.util.Random rnd)
RealAlgebraicNumber random.- Specified by:
random
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
n
- such that 0 ≤ v ≤ (2n-1).rnd
- is a source for random bits.- Returns:
- a random integer mod modul.
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parse
public RealAlgebraicNumber<C> parse(java.lang.String s)
Parse RealAlgebraicNumber from String.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
s
- String.- Returns:
- RealAlgebraicNumber from s.
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parse
public RealAlgebraicNumber<C> parse(java.io.Reader r)
Parse RealAlgebraicNumber from Reader.- Specified by:
parse
in interfaceElemFactory<C extends GcdRingElem<C> & Rational>
- Parameters:
r
- Reader.- Returns:
- next RealAlgebraicNumber from r.
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