edu.jas.gbmod

Class SolvableQuotient<C extends GcdRingElem<C>>

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

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).