Package edu.jas.poly
Class AlgebraicNumber<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.poly.AlgebraicNumber<C>
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- All Implemented Interfaces:
AbelianGroupElem<AlgebraicNumber<C>>
,Element<AlgebraicNumber<C>>
,GcdRingElem<AlgebraicNumber<C>>
,MonoidElem<AlgebraicNumber<C>>
,RingElem<AlgebraicNumber<C>>
,java.io.Serializable
,java.lang.Comparable<AlgebraicNumber<C>>
public class AlgebraicNumber<C extends RingElem<C>> extends java.lang.Object implements GcdRingElem<AlgebraicNumber<C>>
Algebraic number class. Based on GenPolynomial with RingElem interface. Objects of this class are immutable.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected int
isunit
Flag to remember if this algebraic number is a unit. -1 is unknown, 1 is unit, 0 not a unit.AlgebraicNumberRing<C>
ring
Ring part of the data structure.GenPolynomial<C>
val
Value part of the element data structure.
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Constructor Summary
Constructors Constructor Description AlgebraicNumber(AlgebraicNumberRing<C> r)
The constructor creates a AlgebraicNumber object from a GenPolynomial object module.AlgebraicNumber(AlgebraicNumberRing<C> r, GenPolynomial<C> a)
The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description AlgebraicNumber<C>
abs()
AlgebraicNumber absolute value.int
compareTo(AlgebraicNumber<C> b)
AlgebraicNumber comparison.AlgebraicNumber<C>
copy()
Copy this.AlgebraicNumber<C>
divide(AlgebraicNumber<C> S)
AlgebraicNumber division.AlgebraicNumber<C>[]
egcd(AlgebraicNumber<C> S)
AlgebraicNumber extended greatest common divisor.boolean
equals(java.lang.Object b)
Comparison with any other object.AlgebraicNumberRing<C>
factory()
Get the corresponding element factory.AlgebraicNumber<C>
gcd(AlgebraicNumber<C> S)
AlgebraicNumber greatest common divisor.GenPolynomial<C>
getVal()
Get the value part.int
hashCode()
Hash code for this AlgebraicNumber.AlgebraicNumber<C>
inverse()
AlgebraicNumber inverse.boolean
isONE()
Is AlgebraicNumber one.boolean
isRootOfUnity()
Is AlgebraicNumber a root of unity.boolean
isUnit()
Is AlgebraicNumber unit.boolean
isZERO()
Is AlgebraicNumber zero.AlgebraicNumber<C>
monic()
AlgebraicNumber monic.AlgebraicNumber<C>
multiply(C c)
AlgebraicNumber multiplication.AlgebraicNumber<C>
multiply(AlgebraicNumber<C> S)
AlgebraicNumber multiplication.AlgebraicNumber<C>
multiply(GenPolynomial<C> c)
AlgebraicNumber multiplication.AlgebraicNumber<C>
negate()
AlgebraicNumber negate.AlgebraicNumber<C>[]
quotientRemainder(AlgebraicNumber<C> S)
Quotient and remainder by division of this by S.AlgebraicNumber<C>
remainder(AlgebraicNumber<C> S)
AlgebraicNumber remainder.int
signum()
AlgebraicNumber signum.AlgebraicNumber<C>
subtract(AlgebraicNumber<C> S)
AlgebraicNumber subtraction.AlgebraicNumber<C>
sum(C c)
AlgebraicNumber summation.AlgebraicNumber<C>
sum(AlgebraicNumber<C> S)
AlgebraicNumber summation.AlgebraicNumber<C>
sum(GenPolynomial<C> c)
AlgebraicNumber summation.java.lang.String
toScript()
Get a scripting compatible string representation.java.lang.String
toScriptFactory()
Get a scripting compatible string representation of the factory.java.lang.String
toString()
Get the String representation as RingElem.-
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.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Field Detail
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ring
public final AlgebraicNumberRing<C extends RingElem<C>> ring
Ring part of the data structure.
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val
public final GenPolynomial<C extends RingElem<C>> val
Value part of the element data structure.
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isunit
protected int isunit
Flag to remember if this algebraic number is a unit. -1 is unknown, 1 is unit, 0 not a unit.
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Constructor Detail
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AlgebraicNumber
public AlgebraicNumber(AlgebraicNumberRing<C> r, GenPolynomial<C> a)
The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.- Parameters:
r
- ring AlgebraicNumberRing. a
- value GenPolynomial.
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AlgebraicNumber
public AlgebraicNumber(AlgebraicNumberRing<C> r)
The constructor creates a AlgebraicNumber object from a GenPolynomial object module.- Parameters:
r
- ring AlgebraicNumberRing.
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Method Detail
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getVal
public GenPolynomial<C> getVal()
Get the value part.- Returns:
- val.
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factory
public AlgebraicNumberRing<C> factory()
Get the corresponding element factory.
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copy
public AlgebraicNumber<C> copy()
Copy this.
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isZERO
public boolean isZERO()
Is AlgebraicNumber zero.- Specified by:
isZERO
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- If this is 0 then true is returned, else false.
- See Also:
AbelianGroupElem.isZERO()
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isONE
public boolean isONE()
Is AlgebraicNumber one.- Specified by:
isONE
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- If this is 1 then true is returned, else false.
- See Also:
MonoidElem.isONE()
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isUnit
public boolean isUnit()
Is AlgebraicNumber unit.- Specified by:
isUnit
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- If this is a unit then true is returned, else false.
- See Also:
MonoidElem.isUnit()
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isRootOfUnity
public boolean isRootOfUnity()
Is AlgebraicNumber a root of unity.- Returns:
- true if |this**i| == 1, for some 0 < i ≤ deg(modul), else false.
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toString
public java.lang.String toString()
Get the String representation as RingElem.- 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.
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toScriptFactory
public java.lang.String toScriptFactory()
Get a scripting compatible string representation of the factory.- Specified by:
toScriptFactory
in interfaceElement<C extends RingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
Element.toScriptFactory()
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compareTo
public int compareTo(AlgebraicNumber<C> b)
AlgebraicNumber comparison.
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equals
public boolean equals(java.lang.Object b)
Comparison with any other object.
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hashCode
public int hashCode()
Hash code for this AlgebraicNumber.
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abs
public AlgebraicNumber<C> abs()
AlgebraicNumber absolute value.- Specified by:
abs
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- the absolute value of this.
- See Also:
AbelianGroupElem.abs()
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sum
public AlgebraicNumber<C> sum(AlgebraicNumber<C> S)
AlgebraicNumber summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Parameters:
S
- AlgebraicNumber.- Returns:
- this+S.
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sum
public AlgebraicNumber<C> sum(GenPolynomial<C> c)
AlgebraicNumber summation.- Parameters:
c
- coefficient.- Returns:
- this+c.
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sum
public AlgebraicNumber<C> sum(C c)
AlgebraicNumber summation.- Parameters:
c
- polynomial.- Returns:
- this+c.
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negate
public AlgebraicNumber<C> negate()
AlgebraicNumber negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- -this.
- See Also:
AbelianGroupElem.negate()
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signum
public int signum()
AlgebraicNumber signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Returns:
- signum(this).
- See Also:
AbelianGroupElem.signum()
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subtract
public AlgebraicNumber<C> subtract(AlgebraicNumber<C> S)
AlgebraicNumber subtraction.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends RingElem<C>>
- Parameters:
S
- AlgebraicNumber.- Returns:
- this-S.
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divide
public AlgebraicNumber<C> divide(AlgebraicNumber<C> S)
AlgebraicNumber division.- Specified by:
divide
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
S
- AlgebraicNumber.- Returns:
- this/S.
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inverse
public AlgebraicNumber<C> inverse()
AlgebraicNumber inverse.- Specified by:
inverse
in interfaceMonoidElem<C extends RingElem<C>>
- Returns:
- S with S = 1/this if defined.
- Throws:
NotInvertibleException
- if the element is not invertible.- See Also:
MonoidElem.inverse()
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remainder
public AlgebraicNumber<C> remainder(AlgebraicNumber<C> S)
AlgebraicNumber remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
S
- AlgebraicNumber.- Returns:
- this - (this/S)*S.
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quotientRemainder
public AlgebraicNumber<C>[] quotientRemainder(AlgebraicNumber<C> S)
Quotient and remainder by division of this by S.- Specified by:
quotientRemainder
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
S
- a AlgebraicNumber- Returns:
- [this/S, this - (this/S)*S].
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multiply
public AlgebraicNumber<C> multiply(AlgebraicNumber<C> S)
AlgebraicNumber multiplication.- Specified by:
multiply
in interfaceMonoidElem<C extends RingElem<C>>
- Parameters:
S
- AlgebraicNumber.- Returns:
- this*S.
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multiply
public AlgebraicNumber<C> multiply(C c)
AlgebraicNumber multiplication.- Parameters:
c
- coefficient.- Returns:
- this*c.
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multiply
public AlgebraicNumber<C> multiply(GenPolynomial<C> c)
AlgebraicNumber multiplication.- Parameters:
c
- polynomial.- Returns:
- this*c.
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monic
public AlgebraicNumber<C> monic()
AlgebraicNumber monic.- Returns:
- this with monic value part.
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gcd
public AlgebraicNumber<C> gcd(AlgebraicNumber<C> S)
AlgebraicNumber greatest common divisor.
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egcd
public AlgebraicNumber<C>[] egcd(AlgebraicNumber<C> S)
AlgebraicNumber extended greatest common divisor.
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