edu.jas.application

Class SolvableLocal<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableLocal<C>

All Implemented Interfaces:

AbelianGroupElem<SolvableLocal<C>>, Element<SolvableLocal<C>>, GcdRingElem<SolvableLocal<C>>, MonoidElem<SolvableLocal<C>>, QuotPair<GenPolynomial<C>>, RingElem<SolvableLocal<C>>, java.io.Serializable, java.lang.Comparable<SolvableLocal<C>>

public class SolvableLocal<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<SolvableLocal<C>>, QuotPair<GenPolynomial<C>>

SolvableLocal ring element based on pairs of GenSolvablePolynomial with GcdRingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
GenSolvablePolynomial<C>	den Denominator part of the element data structure.
protected int	isunit Flag to remember if this local element is a unit. -1 is unknown, 1 is unit, 0 not a unit.
GenSolvablePolynomial<C>	num Numerator part of the element data structure.
SolvableLocalRing<C>	ring SolvableLocal class factory data structure.

Constructor Summary

Constructors

Modifier	Constructor and Description
	SolvableLocal(SolvableLocalRing<C> r) The constructor creates a SolvableLocal object from a ring factory.
	SolvableLocal(SolvableLocalRing<C> r, GenSolvablePolynomial<C> n) The constructor creates a SolvableLocal object from a ring factory and a numerator polynomial.
	SolvableLocal(SolvableLocalRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d) The constructor creates a SolvableLocal object from a ring factory and a numerator and denominator polynomial.
protected	SolvableLocal(SolvableLocalRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d, boolean isred) The constructor creates a SolvableLocal object from a ring factory and a numerator and denominator polynomial.

Method Summary

Modifier and Type	Method and Description
SolvableLocal<C>	abs() SolvableLocal absolute value.
int	compareTo(SolvableLocal<C> b) SolvableLocal comparison.
SolvableLocal<C>	copy() Clone this.
GenSolvablePolynomial<C>	denominator() Denominator.
SolvableLocal<C>	divide(SolvableLocal<C> S) SolvableLocal division.
SolvableLocal<C>[]	egcd(SolvableLocal<C> b) Extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
SolvableLocalRing<C>	factory() Get the corresponding element factory.
SolvableLocal<C>	gcd(SolvableLocal<C> b) Greatest common divisor.
int	hashCode() Hash code for this local.
SolvableLocal<C>	inverse() SolvableLocal inverse.
boolean	isConstant() Is Qoutient a constant.
boolean	isONE() Is SolvableLocal one.
boolean	isUnit() Is SolvableLocal unit.
boolean	isZERO() Is SolvableLocal zero.
SolvableLocal<C>	monic() SolvableLocal monic.
SolvableLocal<C>	multiply(C b) SolvableLocal multiplication by coefficient.
SolvableLocal<C>	multiply(ExpVector e) SolvableLocal multiplication by exponent.
SolvableLocal<C>	multiply(GenSolvablePolynomial<C> b) SolvableLocal multiplication by GenSolvablePolynomial.
SolvableLocal<C>	multiply(SolvableLocal<C> S) SolvableLocal multiplication.
SolvableLocal<C>	negate() SolvableLocal negate.
GenSolvablePolynomial<C>	numerator() Numerator.
SolvableLocal<C>	remainder(SolvableLocal<C> S) SolvableLocal remainder.
int	signum() SolvableLocal signum.
SolvableLocal<C>	subtract(SolvableLocal<C> S) SolvableLocal subtraction.
SolvableLocal<C>	sum(SolvableLocal<C> S) SolvableLocal 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

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, quotientRemainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

ring

public final SolvableLocalRing<C extends GcdRingElem<C>> ring

SolvableLocal 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.

isunit

protected int isunit

Flag to remember if this local element is a unit. -1 is unknown, 1 is unit, 0 not a unit.

Constructor Detail

SolvableLocal

public SolvableLocal(SolvableLocalRing<C> r)

The constructor creates a SolvableLocal object from a ring factory.

Parameters:

r - ring factory.

SolvableLocal

public SolvableLocal(SolvableLocalRing<C> r,
                     GenSolvablePolynomial<C> n)

The constructor creates a SolvableLocal object from a ring factory and a numerator polynomial. The denominator is assumed to be 1.

Parameters:

r - ring factory.

n - numerator polynomial.

SolvableLocal

public SolvableLocal(SolvableLocalRing<C> r,
                     GenSolvablePolynomial<C> n,
                     GenSolvablePolynomial<C> d)

The constructor creates a SolvableLocal object from a ring factory and a numerator and denominator polynomial.

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

SolvableLocal

protected SolvableLocal(SolvableLocalRing<C> r,
                        GenSolvablePolynomial<C> n,
                        GenSolvablePolynomial<C> d,
                        boolean isred)

The constructor creates a SolvableLocal 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.

Method Detail

factory

public SolvableLocalRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<SolvableLocal<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 SolvableLocal<C> copy()

Clone this.

Specified by:

copy in interface Element<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is SolvableLocal zero.

Specified by:

isZERO in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

If this is 0 then true is returned, else false.

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is SolvableLocal one.

Specified by:

isONE in interface MonoidElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

If this is 1 then true is returned, else false.

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is SolvableLocal unit.

Specified by:

isUnit in interface MonoidElem<SolvableLocal<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<SolvableLocal<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<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(SolvableLocal<C> b)

SolvableLocal comparison.

Specified by:

compareTo in interface Element<SolvableLocal<C extends GcdRingElem<C>>>

Specified by:

compareTo in interface java.lang.Comparable<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

b - SolvableLocal.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<SolvableLocal<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 local.

Specified by:

hashCode in interface Element<SolvableLocal<C extends GcdRingElem<C>>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public SolvableLocal<C> abs()

SolvableLocal absolute value.

Specified by:

abs in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

public SolvableLocal<C> sum(SolvableLocal<C> S)

SolvableLocal summation.

Specified by:

sum in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

S - SolvableLocal.

Returns:

this+S.

negate

public SolvableLocal<C> negate()

SolvableLocal negate.

Specified by:

negate in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

SolvableLocal signum.

Specified by:

signum in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

public SolvableLocal<C> subtract(SolvableLocal<C> S)

SolvableLocal subtraction.

Specified by:

subtract in interface AbelianGroupElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

S - SolvableLocal.

Returns:

this-S.

divide

public SolvableLocal<C> divide(SolvableLocal<C> S)

SolvableLocal division.

Specified by:

divide in interface MonoidElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

S - SolvableLocal.

Returns:

this/S.

inverse

public SolvableLocal<C> inverse()

SolvableLocal inverse.

Specified by:

inverse in interface MonoidElem<SolvableLocal<C extends GcdRingElem<C>>>

Returns:

S with S = 1/this if defined.

See Also:

MonoidElem.inverse()

remainder

public SolvableLocal<C> remainder(SolvableLocal<C> S)

SolvableLocal remainder.

Specified by:

remainder in interface MonoidElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

S - SolvableLocal.

Returns:

this - (this/S)*S.

multiply

public SolvableLocal<C> multiply(SolvableLocal<C> S)

SolvableLocal multiplication.

Specified by:

multiply in interface MonoidElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

S - SolvableLocal.

Returns:

this*S.

multiply

public SolvableLocal<C> multiply(GenSolvablePolynomial<C> b)

SolvableLocal multiplication by GenSolvablePolynomial.

Parameters:

b - GenSolvablePolynomial.

Returns:

this*b.

multiply

public SolvableLocal<C> multiply(C b)

SolvableLocal multiplication by coefficient.

Parameters:

b - coefficient.

Returns:

this*b.

multiply

public SolvableLocal<C> multiply(ExpVector e)

SolvableLocal multiplication by exponent.

Parameters:

e - exponent vector.

Returns:

this*b.

monic

public SolvableLocal<C> monic()

SolvableLocal monic.

Returns:

this with monic value part.

gcd

public SolvableLocal<C> gcd(SolvableLocal<C> b)

Greatest common divisor.

Specified by:

gcd in interface RingElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

public SolvableLocal<C>[] egcd(SolvableLocal<C> b)

Extended greatest common divisor. Note: Not implemented, throws UnsupportedOperationException.

Specified by:

egcd in interface RingElem<SolvableLocal<C extends GcdRingElem<C>>>

Parameters:

b - other element.

Returns:

[ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).