Package edu.jas.poly
Class Quotient<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.poly.Quotient<C>
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- All Implemented Interfaces:
AbelianGroupElem<Quotient<C>>
,Element<Quotient<C>>
,MonoidElem<Quotient<C>>
,QuotPair<C>
,RingElem<Quotient<C>>
,java.io.Serializable
,java.lang.Comparable<Quotient<C>>
public class Quotient<C extends RingElem<C>> extends java.lang.Object implements RingElem<Quotient<C>>, QuotPair<C>
Quotient element based on RingElem pairs. Objects of this class are immutable.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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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, C n)
The constructor creates a Quotient object from a ring factory and a numerator element.Quotient(QuotientRing<C> r, C n, C d)
The constructor creates a Quotient object from a ring factory and a numerator and denominator element.protected
Quotient(QuotientRing<C> r, C n, C d, boolean isred)
The constructor creates a Quotient object from a ring factory and a numerator and denominator element.
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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.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 local.Quotient<C>
inverse()
Quotient inverse.boolean
isConstant()
Is Quotient a constant.boolean
isONE()
Is Quotient one.boolean
isUnit()
Is Quotient unit.boolean
isZERO()
Is Quotient zero.Quotient<C>
monic()
Quotient monic.Quotient<C>
multiply(Quotient<C> S)
Quotient multiplication.Quotient<C>
negate()
Quotient negate.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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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, C n)
The constructor creates a Quotient object from a ring factory and a numerator element. The denominator is assumed to be 1.- Parameters:
r
- ring factory.n
- numerator.
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Quotient
public Quotient(QuotientRing<C> r, C n, C d)
The constructor creates a Quotient object from a ring factory and a numerator and denominator element.- Parameters:
r
- ring factory.n
- numerator.d
- denominator.
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Quotient
protected Quotient(QuotientRing<C> r, C n, C d, boolean isred)
The constructor creates a Quotient object from a ring factory and a numerator and denominator element.- Parameters:
r
- ring factory.n
- numerator.d
- denominator.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.
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denominator
public C denominator()
Denominator.- Specified by:
denominator
in interfaceQuotPair<C extends RingElem<C>>
- See Also:
QuotPair.denominator()
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isConstant
public boolean isConstant()
Is Quotient a constant. Not implemented.- Specified by:
isConstant
in interfaceQuotPair<C extends RingElem<C>>
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isZERO
public boolean isZERO()
Is Quotient 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 Quotient 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 Quotient 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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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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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 local.
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abs
public Quotient<C> abs()
Quotient 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 Quotient<C> sum(Quotient<C> S)
Quotient summation.- Specified by:
sum
in interfaceAbelianGroupElem<C extends RingElem<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 RingElem<C>>
- Returns:
- -this.
- See Also:
AbelianGroupElem.negate()
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signum
public int signum()
Quotient signum.- Specified by:
signum
in interfaceAbelianGroupElem<C extends RingElem<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 RingElem<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 RingElem<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 RingElem<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 RingElem<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 RingElem<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 RingElem<C>>
- Parameters:
S
- Quotient.- Returns:
- this*S.
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gcd
public Quotient<C> gcd(Quotient<C> b)
Greatest common divisor. Note: If not defined, throws UnsupportedOperationException.
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