Package edu.jas.application
Class Residue<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.application.Residue<C>
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- All Implemented Interfaces:
AbelianGroupElem<Residue<C>>
,Element<Residue<C>>
,GcdRingElem<Residue<C>>
,MonoidElem<Residue<C>>
,RingElem<Residue<C>>
,java.io.Serializable
,java.lang.Comparable<Residue<C>>
public class Residue<C extends GcdRingElem<C>> extends java.lang.Object implements GcdRingElem<Residue<C>>
Residue ring element based on GenPolynomial with RingElem interface. Objects of this class are (nearly) 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 residue element is a unit. -1 is unknown, 1 is unit, 0 not a unit.ResidueRing<C>
ring
Residue class factory data structure.GenPolynomial<C>
val
Value part of the element data structure.
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Constructor Summary
Constructors Constructor Description Residue(ResidueRing<C> r)
The constructor creates a Residue object from a ring factory.Residue(ResidueRing<C> r, GenPolynomial<C> a)
The constructor creates a Residue object from a ring factory and a polynomial.Residue(ResidueRing<C> r, GenPolynomial<C> a, int u)
The constructor creates a Residue object from a ring factory, a polynomial and an indicator if a is a unit.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description Residue<C>
abs()
Residue absolute value.int
compareTo(Residue<C> b)
Residue comparison.Residue<C>
copy()
Clone this.Residue<C>
divide(Residue<C> S)
Residue division.Residue<C>[]
egcd(Residue<C> b)
Extended greatest common divisor.boolean
equals(java.lang.Object b)
Comparison with any other object.ResidueRing<C>
factory()
Get the corresponding element factory.Residue<C>
gcd(Residue<C> b)
Greatest common divisor.int
hashCode()
Hash code for this residue.Residue<C>
inverse()
Residue inverse.boolean
isConstant()
Is Residue a constant.boolean
isONE()
Is Residue one.boolean
isUnit()
Is Residue unit.boolean
isZERO()
Is Residue zero.Residue<C>
monic()
Residue monic.Residue<C>
multiply(Residue<C> S)
Residue multiplication.Residue<C>
negate()
Residue negate.Residue<C>
remainder(Residue<C> S)
Residue remainder.int
signum()
Residue signum.Residue<C>
subtract(Residue<C> S)
Residue subtraction.Residue<C>
sum(Residue<C> S)
Residue 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, quotientRemainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder
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Field Detail
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ring
public final ResidueRing<C extends GcdRingElem<C>> ring
Residue class factory data structure.
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val
public final GenPolynomial<C extends GcdRingElem<C>> val
Value part of the element data structure.
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isunit
protected int isunit
Flag to remember if this residue element is a unit. -1 is unknown, 1 is unit, 0 not a unit.
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Constructor Detail
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Residue
public Residue(ResidueRing<C> r)
The constructor creates a Residue object from a ring factory.- Parameters:
r
- residue ring factory.
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Residue
public Residue(ResidueRing<C> r, GenPolynomial<C> a)
The constructor creates a Residue object from a ring factory and a polynomial.- Parameters:
r
- residue ring factory.a
- polynomial.
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Residue
public Residue(ResidueRing<C> r, GenPolynomial<C> a, int u)
The constructor creates a Residue object from a ring factory, a polynomial and an indicator if a is a unit.- Parameters:
r
- residue ring factory.a
- polynomial.u
- isunit indicator, -1, 0, 1.
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Method Detail
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factory
public ResidueRing<C> factory()
Get the corresponding element factory.- Specified by:
factory
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- factory for this Element.
- See Also:
Element.factory()
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copy
public Residue<C> copy()
Clone this.- Specified by:
copy
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- Creates and returns a copy of this Element.
- See Also:
Object.clone()
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isZERO
public boolean isZERO()
Is Residue zero.- Specified by:
isZERO
in interfaceAbelianGroupElem<C extends GcdRingElem<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 Residue one.- Specified by:
isONE
in interfaceMonoidElem<C extends GcdRingElem<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 Residue unit.- Specified by:
isUnit
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- If this is a unit then true is returned, else false.
- See Also:
MonoidElem.isUnit()
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isConstant
public boolean isConstant()
Is Residue a constant.- Returns:
- true if this.val is a constant polynomial, 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.- Specified by:
toScript
in interfaceElement<C extends GcdRingElem<C>>
- Returns:
- script compatible representation for this Element.
- See Also:
Element.toScript()
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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 GcdRingElem<C>>
- Returns:
- script compatible representation for this ElemFactory.
- See Also:
Element.toScriptFactory()
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compareTo
public int compareTo(Residue<C> b)
Residue comparison.- Specified by:
compareTo
in interfacejava.lang.Comparable<C extends GcdRingElem<C>>
- Specified by:
compareTo
in interfaceElement<C extends GcdRingElem<C>>
- Parameters:
b
- Residue.- Returns:
- sign(this-b), 0 means that this and b are equivalent in this residue class ring.
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equals
public boolean equals(java.lang.Object b)
Comparison with any other object.- Specified by:
equals
in interfaceElement<C extends GcdRingElem<C>>
- Overrides:
equals
in classjava.lang.Object
- Returns:
- true means that this and b are equivalent in this residue class ring.
- See Also:
Object.equals(java.lang.Object)
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hashCode
public int hashCode()
Hash code for this residue.- Specified by:
hashCode
in interfaceElement<C extends GcdRingElem<C>>
- Overrides:
hashCode
in classjava.lang.Object
- Returns:
- the hashCode.
- See Also:
Object.hashCode()
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abs
public Residue<C> abs()
Residue absolute value.- Specified by:
abs
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- the absolute value of this.
- See Also:
AbelianGroupElem.abs()
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sum
public Residue<C> sum(Residue<C> S)
Residue summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Residue.- Returns:
- this+S.
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negate
public Residue<C> negate()
Residue negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- -this.
- See Also:
AbelianGroupElem.negate()
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signum
public int signum()
Residue signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- signum(this).
- See Also:
AbelianGroupElem.signum()
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subtract
public Residue<C> subtract(Residue<C> S)
Residue subtraction.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Residue.- Returns:
- this-S.
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divide
public Residue<C> divide(Residue<C> S)
Residue division.- Specified by:
divide
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Residue.- Returns:
- this/S.
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inverse
public Residue<C> inverse()
Residue inverse.- Specified by:
inverse
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- S with S = 1/this if defined.
- See Also:
MonoidElem.inverse()
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remainder
public Residue<C> remainder(Residue<C> S)
Residue remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Residue.- Returns:
- this - (this/S)*S.
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multiply
public Residue<C> multiply(Residue<C> S)
Residue multiplication.- Specified by:
multiply
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Residue.- Returns:
- this*S.
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gcd
public Residue<C> gcd(Residue<C> b)
Greatest common divisor.- Specified by:
gcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- gcd(this,b).
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egcd
public Residue<C>[] egcd(Residue<C> b)
Extended greatest common divisor. Note: Not implemented, throws UnsupportedOperationException.- Specified by:
egcd
in interfaceRingElem<C extends GcdRingElem<C>>
- Parameters:
b
- other element.- Returns:
- [ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).
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