edu.jas.application

Class SolvableResidue<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableResidue<C>

All Implemented Interfaces:

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

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

SolvableResidue ring element based on 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
protected int	isunit Flag to remember if this residue element is a unit. -1 is unknown, 1 is unit, 0 not a unit.
SolvableResidueRing<C>	ring SolvableResidue class factory data structure.
GenSolvablePolynomial<C>	val Value part of the element data structure.

Constructor Summary

Constructors

Constructor and Description
SolvableResidue(SolvableResidueRing<C> r) The constructor creates a SolvableResidue object from a ring factory.
SolvableResidue(SolvableResidueRing<C> r, GenSolvablePolynomial<C> a) The constructor creates a SolvableResidue object from a ring factory and a polynomial.
SolvableResidue(SolvableResidueRing<C> r, GenSolvablePolynomial<C> a, int u) The constructor creates a SolvableResidue object from a ring factory, a polynomial and an indicator if a is a unit.

Method Summary

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

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

ring

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

SolvableResidue class factory data structure.

val

public final GenSolvablePolynomial<C extends GcdRingElem<C>> val

Value part of the element data structure.

isunit

protected int isunit

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

Constructor Detail

SolvableResidue

public SolvableResidue(SolvableResidueRing<C> r)

The constructor creates a SolvableResidue object from a ring factory.

Parameters:

r - solvable residue ring factory.

SolvableResidue

public SolvableResidue(SolvableResidueRing<C> r,
                       GenSolvablePolynomial<C> a)

The constructor creates a SolvableResidue object from a ring factory and a polynomial.

Parameters:

r - solvable residue ring factory.

a - solvable polynomial.

SolvableResidue

public SolvableResidue(SolvableResidueRing<C> r,
                       GenSolvablePolynomial<C> a,
                       int u)

The constructor creates a SolvableResidue object from a ring factory, a polynomial and an indicator if a is a unit.

Parameters:

r - solvable residue ring factory.

a - solvable polynomial.

u - isunit indicator, -1, 0, 1.

Method Detail

factory

public SolvableResidueRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Returns:

factory for this Element.

See Also:

Element.factory()

value

public GenSolvablePolynomial<C> value()

Value. Returns the value.

Specified by:

value in interface Value<GenPolynomial<C extends GcdRingElem<C>>>

See Also:

Value.value()

numerator

public GenSolvablePolynomial<C> numerator()

Numerator. Returns the value.

Specified by:

numerator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>

See Also:

QuotPair.numerator()

denominator

public GenSolvablePolynomial<C> denominator()

Denominator. Returns 1.

Specified by:

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

See Also:

QuotPair.denominator()

copy

public SolvableResidue<C> copy()

Clone this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is SolvableResidue zero.

Specified by:

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

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is SolvableResidue one.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is SolvableResidue unit.

Specified by:

isUnit in interface MonoidElem<SolvableResidue<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 SolvableResidue a constant.

Specified by:

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

Specified by:

isConstant in interface Value<GenPolynomial<C extends GcdRingElem<C>>>

Returns:

true if this.val is a constant polynomial, 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<SolvableResidue<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<SolvableResidue<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(SolvableResidue<C> b)

SolvableResidue comparison.

Specified by:

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

Specified by:

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

Parameters:

b - SolvableResidue.

Returns:

sign(this-b), 0 means that this and b are equivalent in this residue class ring.

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

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

Overrides:

equals in class java.lang.Object

Returns:

true means that this and b are equivalent in this residue class ring.

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this residue.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public SolvableResidue<C> abs()

SolvableResidue absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

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

SolvableResidue summation.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this+S.

negate

public SolvableResidue<C> negate()

SolvableResidue negate.

Specified by:

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

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

SolvableResidue signum.

Specified by:

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

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

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

SolvableResidue subtraction.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this-S.

divide

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

SolvableResidue division.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this/S.

inverse

public SolvableResidue<C> inverse()

SolvableResidue inverse.

Specified by:

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

Returns:

S with S = 1/this if defined.

See Also:

MonoidElem.inverse()

remainder

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

SolvableResidue remainder.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this - (this/S)*S.

multiply

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

SolvableResidue multiplication.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this*S.

multiply

public SolvableResidue<C> multiply(GenSolvablePolynomial<C> S)

SolvableResidue multiplication.

Parameters:

S - GenSolvablePolynomial.

Returns:

this*S.

multiply

public SolvableResidue<C> multiply(C s)

multiply

public SolvableResidue<C> multiply(ExpVector e)

SolvableResidue multiplication.

Parameters:

e - exponent.

Returns:

this*X^e.

monic

public SolvableResidue<C> monic()

SolvableResidue monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

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

Specified by:

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

Parameters:

b - other element.

Returns:

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