Package edu.jas.application

Class SolvableLocalResidue<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableLocalResidue<C>

All Implemented Interfaces:

AbelianGroupElem<SolvableLocalResidue<C>>, Element<SolvableLocalResidue<C>>, GcdRingElem<SolvableLocalResidue<C>>, MonoidElem<SolvableLocalResidue<C>>, QuotPair<GenPolynomial<C>>, RingElem<SolvableLocalResidue<C>>, Serializable, Comparable<SolvableLocalResidue<C>>

public class SolvableLocalResidue<C extends GcdRingElem<C>>
extends Object
implements GcdRingElem<SolvableLocalResidue<C>>, QuotPair<GenPolynomial<C>>

SolvableLocalResidue, that is a (left) rational function, based on pairs of GenSolvablePolynomial with GcdRingElem interface. Objects of this class are immutable.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
final GenSolvablePolynomial<C>	den	Denominator part of the element data structure.
private static final org.apache.logging.log4j.Logger	logger
final GenSolvablePolynomial<C>	num	Numerator part of the element data structure.
final SolvableLocalResidueRing<C>	ring	SolvableLocalResidue class factory data structure.

Constructor Summary

Constructors

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

Method Summary

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

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

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

ring

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

SolvableLocalResidue 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 Details

SolvableLocalResidue

public SolvableLocalResidue(SolvableLocalResidueRing<C> r)

The constructor creates a SolvableLocalResidue object from a ring factory.

Parameters:

r - ring factory.

SolvableLocalResidue

public SolvableLocalResidue(SolvableLocalResidueRing<C> r,
 GenSolvablePolynomial<C> n)

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

Parameters:

r - ring factory.

n - numerator solvable polynomial.

SolvableLocalResidue

public SolvableLocalResidue(SolvableLocalResidueRing<C> r,
 GenSolvablePolynomial<C> n,
 GenSolvablePolynomial<C> d)

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

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

SolvableLocalResidue

protected SolvableLocalResidue(SolvableLocalResidueRing<C> r,
 GenSolvablePolynomial<C> n,
 GenSolvablePolynomial<C> d,
 boolean isred)

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

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

isred - unused at the moment.

Method Details

factory

public SolvableLocalResidueRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<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<C extends GcdRingElem<C>>

See Also:

• QuotPair.numerator()

denominator

public GenSolvablePolynomial<C> denominator()

Denominator.

Specified by:

denominator in interface QuotPair<C extends GcdRingElem<C>>

See Also:

• QuotPair.denominator()

copy

public SolvableLocalResidue<C> copy()

Clone this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

• Object.clone()

isZERO

public boolean isZERO()

Is SolvableLocalResidue zero.

Specified by:

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

Returns:

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

See Also:

• AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is SolvableLocalResidue one.

Specified by:

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

Returns:

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

See Also:

• MonoidElem.isONE()

isUnit

public boolean isUnit()

Is SolvableLocalResidue a unit.

Specified by:

isUnit in interface MonoidElem<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 Quotient a constant.

Specified by:

isConstant in interface QuotPair<C extends GcdRingElem<C>>

Returns:

true, if this has constant numerator and denominator, else false.

toString

public String toString()

Get the String representation as RingElem.

Overrides:

toString in class Object

See Also:

• Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<C extends GcdRingElem<C>>

Returns:

script compatible representation for this Element.

See Also:

• Element.toScript()

toScriptFactory

public String toScriptFactory()

Get a scripting compatible string representation of the factory.

Specified by:

toScriptFactory in interface Element<C extends GcdRingElem<C>>

Returns:

script compatible representation for this ElemFactory.

See Also:

• Element.toScriptFactory()

compareTo

public int compareTo(SolvableLocalResidue<C> b)

SolvableLocalResidue comparison.

Specified by:

compareTo in interface Comparable<C extends GcdRingElem<C>>

Specified by:

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

Parameters:

b - SolvableLocalResidue.

Returns:

sign(this-b).

equals

public boolean equals(Object b)

Comparison with any other object.

Specified by:

equals in interface Element<C extends GcdRingElem<C>>

Overrides:

equals in class Object

Parameters:

b -

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<C extends GcdRingElem<C>>

Overrides:

hashCode in class Object

Returns:

the hashCode.

See Also:

• Object.hashCode()

abs

public SolvableLocalResidue<C> abs()

SolvableLocalResidue absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

• AbelianGroupElem.abs()

sum

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

SolvableLocalResidue summation.

Specified by:

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

Parameters:

S - SolvableLocalResidue.

Returns:

this+S.

negate

public SolvableLocalResidue<C> negate()

SolvableLocalResidue negate.

Specified by:

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

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

signum

public int signum()

SolvableLocalResidue signum.

Specified by:

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

Returns:

signum(this).

See Also:

• AbelianGroupElem.signum()

subtract

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

SolvableLocalResidue subtraction.

Specified by:

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

Parameters:

S - SolvableLocalResidue.

Returns:

this-S.

divide

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

SolvableLocalResidue division.

Specified by:

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

Parameters:

S - SolvableLocalResidue.

Returns:

this/S.

inverse

public SolvableLocalResidue<C> inverse()

SolvableLocalResidue inverse.

Specified by:

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

Returns:

S with S = 1/this.

See Also:

• MonoidElem.inverse()

remainder

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

SolvableLocalResidue remainder.

Specified by:

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

Parameters:

S - SolvableLocalResidue.

Returns:

this - (this/S)*S.

multiply

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

SolvableLocalResidue multiplication.

Specified by:

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

Parameters:

S - SolvableLocalResidue.

Returns:

this*S.

multiply

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

SolvableLocalResidue multiplication by GenSolvablePolynomial.

Parameters:

b - GenSolvablePolynomial.

Returns:

this*b.

multiply

public SolvableLocalResidue<C> multiply(C b)

SolvableLocalResidue multiplication by coefficient.

Parameters:

b - coefficient.

Returns:

this*b.

multiply

public SolvableLocalResidue<C> multiply(ExpVector e)

SolvableLocalResidue multiplication by exponent.

Parameters:

e - exponent vector.

Returns:

this*b.

monic

public SolvableLocalResidue<C> monic()

SolvableLocalResidue monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

Extended greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

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