Package edu.jas.ufd
Class Quotient<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.ufd.Quotient<C>
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- All Implemented Interfaces:
AbelianGroupElem<Quotient<C>>
,Element<Quotient<C>>
,GcdRingElem<Quotient<C>>
,MonoidElem<Quotient<C>>
,QuotPair<GenPolynomial<C>>
,RingElem<Quotient<C>>
,java.io.Serializable
,java.lang.Comparable<Quotient<C>>
public class Quotient<C extends GcdRingElem<C>> extends java.lang.Object implements GcdRingElem<Quotient<C>>, QuotPair<GenPolynomial<C>>
Quotient, that is a rational function, 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 GenPolynomial<C>
den
Denominator part of the element data structure.GenPolynomial<C>
num
Numerator part of the element data structure.QuotientRing<C>
ring
Quotient class factory data structure.
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Constructor Summary
Constructors Modifier Constructor Description Quotient(QuotientRing<C> r)
The constructor creates a Quotient object from a ring factory.Quotient(QuotientRing<C> r, GenPolynomial<C> n)
The constructor creates a Quotient object from a ring factory and a numerator polynomial.Quotient(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d)
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.protected
Quotient(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d, boolean isred)
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description Quotient<C>
abs()
Quotient absolute value.int
compareTo(Quotient<C> b)
Quotient comparison.Quotient<C>
copy()
Clone this.GenPolynomial<C>
denominator()
Denominator.Quotient<C>
divide(Quotient<C> S)
Quotient division.Quotient<C>[]
egcd(Quotient<C> b)
Extended greatest common divisor.boolean
equals(java.lang.Object b)
Comparison with any other object.QuotientRing<C>
factory()
Get the corresponding element factory.Quotient<C>
gcd(Quotient<C> b)
Greatest common divisor.int
hashCode()
Hash code for this quotient.Quotient<C>
inverse()
Quotient inverse.boolean
isConstant()
Is Qoutient a constant.boolean
isONE()
Is Quotient one.boolean
isUnit()
Is Quotient a unit.boolean
isZERO()
Is Quotient zero.Quotient<C>
monic()
Quotient monic.Quotient<C>
multiply(C b)
Quotient multiplication by coefficient.Quotient<C>
multiply(GenPolynomial<C> b)
Quotient multiplication by GenPolynomial.Quotient<C>
multiply(Quotient<C> S)
Quotient multiplication.Quotient<C>
negate()
Quotient negate.GenPolynomial<C>
numerator()
Numerator.Quotient<C>[]
quotientRemainder(Quotient<C> S)
Quotient and remainder by division of this by S.Quotient<C>
remainder(Quotient<C> S)
Quotient remainder.int
signum()
Quotient signum.Quotient<C>
subtract(Quotient<C> S)
Quotient subtraction.Quotient<C>
sum(Quotient<C> S)
Quotient 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 QuotientRing<C extends GcdRingElem<C>> ring
Quotient class factory data structure.
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num
public final GenPolynomial<C extends GcdRingElem<C>> num
Numerator part of the element data structure.
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den
public final GenPolynomial<C extends GcdRingElem<C>> den
Denominator part of the element data structure.
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Constructor Detail
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Quotient
public Quotient(QuotientRing<C> r)
The constructor creates a Quotient object from a ring factory.- Parameters:
r
- ring factory.
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Quotient
public Quotient(QuotientRing<C> r, GenPolynomial<C> n)
The constructor creates a Quotient object from a ring factory and a numerator polynomial. The denominator is assumed to be 1.- Parameters:
r
- ring factory.n
- numerator polynomial.
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Quotient
public Quotient(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d)
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.
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Quotient
protected Quotient(QuotientRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d, boolean isred)
The constructor creates a Quotient object from a ring factory and a numerator and denominator polynomial.- Parameters:
r
- ring factory.n
- numerator polynomial.d
- denominator polynomial.isred
- true if gcd(n,d) == 1, else false.
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Method Detail
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factory
public QuotientRing<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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numerator
public GenPolynomial<C> numerator()
Numerator.- Specified by:
numerator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
QuotPair.numerator()
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denominator
public GenPolynomial<C> denominator()
Denominator.- Specified by:
denominator
in interfaceQuotPair<C extends GcdRingElem<C>>
- See Also:
QuotPair.denominator()
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copy
public Quotient<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 Quotient 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 Quotient 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 Quotient a 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 Qoutient a constant.- Specified by:
isConstant
in interfaceQuotPair<C extends GcdRingElem<C>>
- Returns:
- true, if this has constant numerator and denominator, 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(Quotient<C> b)
Quotient comparison.- Specified by:
compareTo
in interfacejava.lang.Comparable<C extends GcdRingElem<C>>
- Specified by:
compareTo
in interfaceElement<C extends GcdRingElem<C>>
- Parameters:
b
- Quotient.- Returns:
- sign(this-b).
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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 if this is equal to b, else false.
- See Also:
Object.equals(java.lang.Object)
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hashCode
public int hashCode()
Hash code for this quotient.- 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 Quotient<C> abs()
Quotient 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 Quotient<C> sum(Quotient<C> S)
Quotient summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this+S.
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negate
public Quotient<C> negate()
Quotient negate.- Specified by:
negate
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- -this.
- See Also:
AbelianGroupElem.negate()
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signum
public int signum()
Quotient signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Returns:
- signum(this).
- See Also:
AbelianGroupElem.signum()
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subtract
public Quotient<C> subtract(Quotient<C> S)
Quotient subtraction.- Specified by:
subtract
in interfaceAbelianGroupElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this-S.
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divide
public Quotient<C> divide(Quotient<C> S)
Quotient division.- Specified by:
divide
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this/S.
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inverse
public Quotient<C> inverse()
Quotient inverse.- Specified by:
inverse
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Returns:
- S with S = 1/this.
- See Also:
MonoidElem.inverse()
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remainder
public Quotient<C> remainder(Quotient<C> S)
Quotient remainder.- Specified by:
remainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this - (this/S)*S.
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quotientRemainder
public Quotient<C>[] quotientRemainder(Quotient<C> S)
Quotient and remainder by division of this by S.- Specified by:
quotientRemainder
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- a Quotient- Returns:
- [this/S, this - (this/S)*S].
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multiply
public Quotient<C> multiply(Quotient<C> S)
Quotient multiplication.- Specified by:
multiply
in interfaceMonoidElem<C extends GcdRingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this*S.
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multiply
public Quotient<C> multiply(GenPolynomial<C> b)
Quotient multiplication by GenPolynomial.- Parameters:
b
- GenPolynomial. - Returns:
- this*b.
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multiply
public Quotient<C> multiply(C b)
Quotient multiplication by coefficient.- Parameters:
b
- coefficient.- Returns:
- this*b.
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gcd
public Quotient<C> gcd(Quotient<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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