Package edu.jas.root
Class RealAlgebraicRing<C extends GcdRingElem<C> & Rational>
java.lang.Object
edu.jas.root.RealAlgebraicRing<C>
- All Implemented Interfaces:
AbelianGroupFactory<RealAlgebraicNumber<C>>
,ElemFactory<RealAlgebraicNumber<C>>
,MonoidFactory<RealAlgebraicNumber<C>>
,RingFactory<RealAlgebraicNumber<C>>
,Serializable
public class RealAlgebraicRing<C extends GcdRingElem<C> & Rational>
extends Object
implements RingFactory<RealAlgebraicNumber<C>>
Real algebraic number factory class based on AlgebraicNumberRing with
RingFactory interface. Objects of this class are immutable with the exception
of the isolating intervals.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionfinal AlgebraicNumberRing
<C> Representing AlgebraicNumberRing.final RealRootsSturm
<C> Real root computation engine.protected BigRational
Precision of the isolating interval for a real root.static final int
Precision of the isolating rectangle for a complex root.Isolating interval for a real root. -
Constructor Summary
ConstructorsConstructorDescriptionRealAlgebraicRing
(GenPolynomial<C> m, Interval<C> root) The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.RealAlgebraicRing
(GenPolynomial<C> m, Interval<C> root, boolean isField) The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module. -
Method Summary
Modifier and TypeMethodDescriptionCharacteristic of this ring.copy()
Copy this RealAlgebraicRing.copy
(RealAlgebraicNumber<C> c) Copy RealAlgebraicNumber element c.boolean
Comparison with any other object.fromInteger
(long a) Get a RealAlgebraicNumber element from a long value.Get a RealAlgebraicNumber element from a BigInteger value.Get a RealAlgebraicNumber element from a BigRational value.Get a list of the generating elements.getEps()
Get the epsilon.Get the generating element.getONE()
Get the one element.getRoot()
Get the interval for the real root.getZERO()
Get the zero element.void
RealAlgebraicRing half interval.int
hashCode()
Hash code for this RealAlgebraicNumber.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.Parse RealAlgebraicNumber from Reader.Parse RealAlgebraicNumber from String.random
(int n) RealAlgebraicNumber random.RealAlgebraicNumber random.void
Refine root.void
Refine root.void
Set a new epsilon.void
Set a new epsilon.void
setField
(boolean isField) Assert that this ring is a field.void
Set a refined interval for the real root.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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algebraic
Representing AlgebraicNumberRing. -
root
Interval<C extends GcdRingElem<C> & Rational> rootIsolating interval for a real root. Note: interval may shrink eventually. -
PRECISION
public static final int PRECISIONPrecision of the isolating rectangle for a complex root. -
eps
Precision of the isolating interval for a real root. -
engine
Real root computation engine.
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Constructor Details
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RealAlgebraicRing
The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.- Parameters:
m
- module GenPolynomial. root
- isolating interval for a real root.
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RealAlgebraicRing
The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.- Parameters:
m
- module GenPolynomial.root
- isolating interval for a real root.isField
- indicator if m is prime.
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Method Details
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getRoot
Get the interval for the real root. Note: interval may shrink later.- Returns:
- real root isolating interval
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setRoot
Set a refined interval for the real root. Note: interval may shrink eventually.- Parameters:
v
- interval.
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getEps
Get the epsilon.- Returns:
- eps.
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setEps
Set a new epsilon.- Parameters:
e
- epsilon.
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setEps
Set a new epsilon.- Parameters:
e
- epsilon.
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refineRoot
public void refineRoot()Refine root. -
refineRoot
Refine root.- Parameters:
e
- epsilon.
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halfInterval
public void halfInterval()RealAlgebraicRing half interval. -
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:
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copy
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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copy
Copy this RealAlgebraicRing.- Returns:
- a copy of this.
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getZERO
Get the zero element.- Specified by:
getZERO
in interfaceAbelianGroupFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- 0 as RealAlgebraicNumber.
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getONE
Get the one element.- Specified by:
getONE
in interfaceMonoidFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- 1 as RealAlgebraicNumber.
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getGenerator
Get the generating element.- Returns:
- alpha as RealAlgebraicNumber.
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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:
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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
Characteristic of this ring.- Specified by:
characteristic
in interfaceRingFactory<C extends GcdRingElem<C> & Rational>
- Returns:
- characteristic of this ring.
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fromInteger
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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fromRational
Get a RealAlgebraicNumber element from a BigRational value.- Parameters:
a
- BigRational.- Returns:
- a RealAlgebraicNumber.
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fromInteger
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
Get the String representation as RingFactory. -
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:
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equals
Comparison with any other object. -
hashCode
public int hashCode()Hash code for this RealAlgebraicNumber. -
random
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
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
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
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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