SolvableQuotient

Documentation of 'edu.jas.gbmod.SolvableQuotient' Java class SolvableQuotient

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Summary:
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Constr |
Method

Detail:
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java.lang.Object
- edu.jas.gbmod.SolvableQuotient<C>

All Implemented Interfaces:

AbelianGroupElem<SolvableQuotient<C>>, Element<SolvableQuotient<C>>, GcdRingElem<SolvableQuotient<C>>, MonoidElem<SolvableQuotient<C>>, QuotPair<GenPolynomial<C>>, RingElem<SolvableQuotient<C>>, java.io.Serializable, java.lang.Comparable<SolvableQuotient<C>>
```
public class SolvableQuotient<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<SolvableQuotient<C>>, QuotPair<GenPolynomial<C>>
```
SolvableQuotient, that is a (left) rational function, based on GenSolvablePolynomial with RingElem interface. Objects of this class are immutable.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`GenSolvablePolynomial<C>`	`den` Denominator part of the element data structure.
`GenSolvablePolynomial<C>`	`num` Numerator part of the element data structure.
`SolvableQuotientRing<C>`	`ring` SolvableQuotient class factory data structure.

Constructor Summary

Constructors
Constructor and Description
`SolvableQuotient(SolvableQuotientRing<C> r)` The constructor creates a SolvableQuotient object from a ring factory.
`SolvableQuotient(SolvableQuotientRing<C> r, GenSolvablePolynomial<C> n)` The constructor creates a SolvableQuotient object from a ring factory and a numerator polynomial.
`SolvableQuotient(SolvableQuotientRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)` The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator solvable polynomial.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`SolvableQuotient<C>`	`abs()` SolvableQuotient absolute value.
`int`	`compareTo(SolvableQuotient<C> b)` SolvableQuotient comparison.
`SolvableQuotient<C>`	`copy()` Clone this.
`GenSolvablePolynomial<C>`	`denominator()` Denominator.
`SolvableQuotient<C>`	`divide(SolvableQuotient<C> S)` SolvableQuotient division.
`SolvableQuotient<C>[]`	`egcd(SolvableQuotient<C> b)` Extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`SolvableQuotientRing<C>`	`factory()` Get the corresponding element factory.
`SolvableQuotient<C>`	`gcd(SolvableQuotient<C> b)` Greatest common divisor.
`int`	`hashCode()` Hash code for this element.
`SolvableQuotient<C>`	`inverse()` SolvableQuotient inverse.
`boolean`	`isConstant()` Is Qoutient a constant.
`boolean`	`isONE()` Is SolvableQuotient one.
`boolean`	`isRightFraction(SolvableQuotient<C> s)` Test if SolvableQuotient right fraction.
`boolean`	`isUnit()` Is SolvableQuotient a unit.
`boolean`	`isZERO()` Is SolvableQuotient zero.
`SolvableQuotient<C>`	`monic()` SolvableQuotient monic.
`SolvableQuotient<C>`	`multiply(C b)` SolvableQuotient multiplication by coefficient.
`SolvableQuotient<C>`	`multiply(ExpVector e)` SolvableQuotient multiplication by exponent.
`SolvableQuotient<C>`	`multiply(GenSolvablePolynomial<C> b)` SolvableQuotient multiplication by GenSolvablePolynomial.
`SolvableQuotient<C>`	`multiply(SolvableQuotient<C> S)` SolvableQuotient multiplication.
`SolvableQuotient<C>`	`negate()` SolvableQuotient negate.
`GenSolvablePolynomial<C>`	`numerator()` Numerator.
`SolvableQuotient<C>[]`	`quotientRemainder(SolvableQuotient<C> S)` Quotient and remainder by division of this by S.
`SolvableQuotient<C>`	`remainder(SolvableQuotient<C> S)` SolvableQuotient remainder.
`SolvableQuotient<C>`	`rightFraction()` SolvableQuotient right fraction.
`int`	`signum()` SolvableQuotient signum.
`SolvableQuotient<C>`	`subtract(SolvableQuotient<C> S)` SolvableQuotient subtraction.
`SolvableQuotient<C>`	`sum(SolvableQuotient<C> S)` SolvableQuotient 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
getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ring
```
public final SolvableQuotientRing<C extends GcdRingElem<C>> ring
```
    SolvableQuotient class factory data structure.
  - num
```
public final GenSolvablePolynomial<C extends GcdRingElem<C>> num
```
    Numerator part of the element data structure.
  - den
```
public final GenSolvablePolynomial<C extends GcdRingElem<C>> den
```
    Denominator part of the element data structure.
- Constructor Detail
  - SolvableQuotient
```
public SolvableQuotient(SolvableQuotientRing<C> r)
```
    The constructor creates a SolvableQuotient object from a ring factory.
    
    Parameters:
    
    r - ring factory.
  - SolvableQuotient
```
public SolvableQuotient(SolvableQuotientRing<C> r,
                        GenSolvablePolynomial<C> n)
```
    The constructor creates a SolvableQuotient object from a ring factory and a numerator polynomial. The denominator is assumed to be 1.
    
    Parameters:
    
    r - ring factory.
    
    n - numerator solvable polynomial.
  - SolvableQuotient
```
public SolvableQuotient(SolvableQuotientRing<C> r,
                        GenSolvablePolynomial<C> n,
                        GenSolvablePolynomial<C> d)
```
    The constructor creates a SolvableQuotient object from a ring factory and a numerator and denominator solvable polynomial.
    
    Parameters:
    
    r - ring factory.
    
    n - numerator polynomial.
    
    d - denominator polynomial.
- Method Detail
  - factory
```
public SolvableQuotientRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - numerator
```
public GenSolvablePolynomial<C> numerator()
```
    Numerator.
    
    Specified by:
    
    numerator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    See Also:
    
    QuotPair.numerator()
  - denominator
```
public GenSolvablePolynomial<C> denominator()
```
    Denominator.
    
    Specified by:
    
    denominator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    See Also:
    
    QuotPair.denominator()
  - copy
```
public SolvableQuotient<C> copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Object.clone()
  - isZERO
```
public boolean isZERO()
```
    Is SolvableQuotient zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is SolvableQuotient one.
    
    Specified by:
    
    isONE in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is SolvableQuotient a unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    If this is a unit then true is returned, else false.
    
    See Also:
    
    MonoidElem.isUnit()
  - isConstant
```
public boolean isConstant()
```
    Is Qoutient a constant.
    
    Specified by:
    
    isConstant in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    Returns:
    
    true, if this has constant numerator and denominator, else false.
  - toString
```
public java.lang.String toString()
```
    Get the String representation as RingElem.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()
  - toScriptFactory
```
public java.lang.String toScriptFactory()
```
    Get a scripting compatible string representation of the factory.
    
    Specified by:
    
    toScriptFactory in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - compareTo
```
public int compareTo(SolvableQuotient<C> b)
```
    SolvableQuotient comparison.
    
    Specified by:
    
    compareTo in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    b - SolvableQuotient.
    
    Returns:
    
    sign(this-b).
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    
    true if this is equal to b, else false.
    
    See Also:
    
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this element.
    
    Specified by:
    
    hashCode in interface Element<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - rightFraction
```
public SolvableQuotient<C> rightFraction()
```
    SolvableQuotient right fraction. Note: It is not possible to distinguish right from left fractions in the current implementation. So it is not possible to compute with right fractions.
    
    Returns:
    
    SolvableQuotient(a,b), where den^-1 num = a b^-1
  - isRightFraction
```
public boolean isRightFraction(SolvableQuotient<C> s)
```
    Test if SolvableQuotient right fraction. Note: It is not possible to distinguish right from left fractions in the current implementation. So it is not possible to compute with right fractions.
    
    Parameters:
    
    s - = SolvableQuotient(a,b)
    
    Returns:
    
    true if s is a right fraction of this, i.e. den^-1 num = a b^-1
  - abs
```
public SolvableQuotient<C> abs()
```
    SolvableQuotient absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    the absolute value of this.
    
    See Also:
    
    AbelianGroupElem.abs()
  - sum
```
public SolvableQuotient<C> sum(SolvableQuotient<C> S)
```
    SolvableQuotient summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - SolvableQuotient.
    
    Returns:
    
    this+S.
  - negate
```
public SolvableQuotient<C> negate()
```
    SolvableQuotient negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    -this.
    
    See Also:
    
    AbelianGroupElem.negate()
  - signum
```
public int signum()
```
    SolvableQuotient signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    signum(this).
    
    See Also:
    
    AbelianGroupElem.signum()
  - subtract
```
public SolvableQuotient<C> subtract(SolvableQuotient<C> S)
```
    SolvableQuotient subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - SolvableQuotient.
    
    Returns:
    
    this-S.
  - divide
```
public SolvableQuotient<C> divide(SolvableQuotient<C> S)
```
    SolvableQuotient division.
    
    Specified by:
    
    divide in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - SolvableQuotient.
    
    Returns:
    
    this/S.
  - inverse
```
public SolvableQuotient<C> inverse()
```
    SolvableQuotient inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Returns:
    
    S with S = 1/this.
    
    See Also:
    
    MonoidElem.inverse()
  - remainder
```
public SolvableQuotient<C> remainder(SolvableQuotient<C> S)
```
    SolvableQuotient remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - SolvableQuotient.
    
    Returns:
    
    this - (this/S)*S.
  - quotientRemainder
```
public SolvableQuotient<C>[] quotientRemainder(SolvableQuotient<C> S)
```
    Quotient and remainder by division of this by S.
    
    Parameters:
    
    S - a SolvableQuotient
    
    Returns:
    
    [this/S, this - (this/S)*S].
  - multiply
```
public SolvableQuotient<C> multiply(SolvableQuotient<C> S)
```
    SolvableQuotient multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - SolvableQuotient.
    
    Returns:
    
    this*S.
  - multiply
```
public SolvableQuotient<C> multiply(GenSolvablePolynomial<C> b)
```
    SolvableQuotient multiplication by GenSolvablePolynomial.
    
    Parameters:
    
    b - GenSolvablePolynomial.
    
    Returns:
    
    this*b.
  - multiply
```
public SolvableQuotient<C> multiply(C b)
```
    SolvableQuotient multiplication by coefficient.
    
    Parameters:
    
    b - coefficient.
    
    Returns:
    
    this*b.
  - multiply
```
public SolvableQuotient<C> multiply(ExpVector e)
```
    SolvableQuotient multiplication by exponent.
    
    Parameters:
    
    e - exponent vector.
    
    Returns:
    
    this*b.
  - monic
```
public SolvableQuotient<C> monic()
```
    SolvableQuotient monic.
    
    Returns:
    
    this with monic value part.
  - gcd
```
public SolvableQuotient<C> gcd(SolvableQuotient<C> b)
```
    Greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<SolvableQuotient<C extends GcdRingElem<C>>>
    
    Parameters:
    
    b - other element.
    
    Returns:
    
    gcd(this,b).
  - egcd
```
public SolvableQuotient<C>[] egcd(SolvableQuotient<C> b)
```
    Extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<SolvableQuotient<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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Summary:
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Constr |
Method

Detail:
Field |
Constr |
Method

Class SolvableQuotient<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

num

den

Constructor Detail

SolvableQuotient

SolvableQuotient

SolvableQuotient

Method Detail

factory

numerator

denominator

copy

isZERO

isONE

isUnit

isConstant

toString

toScript

toScriptFactory

compareTo

equals

hashCode

rightFraction

isRightFraction

abs

sum

negate

signum

subtract

divide

inverse

remainder

quotientRemainder

multiply

multiply

multiply

multiply

monic

gcd

egcd