edu.jas.application

Class WordResidue<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.WordResidue<C>

All Implemented Interfaces:

AbelianGroupElem<WordResidue<C>>, Element<WordResidue<C>>, GcdRingElem<WordResidue<C>>, MonoidElem<WordResidue<C>>, NoncomRingElem<WordResidue<C>>, QuotPair<GenWordPolynomial<C>>, RingElem<WordResidue<C>>, Value<GenWordPolynomial<C>>, java.io.Serializable, java.lang.Comparable<WordResidue<C>>

public class WordResidue<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<WordResidue<C>>, NoncomRingElem<WordResidue<C>>, QuotPair<GenWordPolynomial<C>>, Value<GenWordPolynomial<C>>

WordResidue ring element based on GenWordPolynomial 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.
WordResidueRing<C>	ring WordResidue class factory data structure.
GenWordPolynomial<C>	val Value part of the element data structure.

Constructor Summary

Constructors

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

Method Summary

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

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

Field Detail

ring

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

WordResidue class factory data structure.

val

public final GenWordPolynomial<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

WordResidue

public WordResidue(WordResidueRing<C> r)

The constructor creates a WordResidue object from a ring factory.

Parameters:

r - solvable residue ring factory.

WordResidue

public WordResidue(WordResidueRing<C> r,
                   GenWordPolynomial<C> a)

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

Parameters:

r - solvable residue ring factory.

a - solvable polynomial.

WordResidue

public WordResidue(WordResidueRing<C> r,
                   GenWordPolynomial<C> a,
                   int u)

The constructor creates a WordResidue 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 WordResidueRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Returns:

factory for this Element.

See Also:

Element.factory()

value

public GenWordPolynomial<C> value()

Value. Returns the value.

Specified by:

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

See Also:

Value.value()

numerator

public GenWordPolynomial<C> numerator()

Numerator. Returns the value.

Specified by:

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

See Also:

QuotPair.numerator()

denominator

public GenWordPolynomial<C> denominator()

Denominator. Returns 1.

Specified by:

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

See Also:

QuotPair.denominator()

copy

public WordResidue<C> copy()

Clone this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is WordResidue zero.

Specified by:

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

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is WordResidue one.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is WordResidue unit.

Specified by:

isUnit in interface MonoidElem<WordResidue<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 WordResidue a constant.

Specified by:

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

Specified by:

isConstant in interface Value<GenWordPolynomial<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<WordResidue<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<WordResidue<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(WordResidue<C> b)

WordResidue comparison.

Specified by:

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

Specified by:

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

Parameters:

b - WordResidue.

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<WordResidue<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<WordResidue<C extends GcdRingElem<C>>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public WordResidue<C> abs()

WordResidue absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

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

WordResidue summation.

Specified by:

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

Parameters:

S - WordResidue.

Returns:

this+S.

negate

public WordResidue<C> negate()

WordResidue negate.

Specified by:

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

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

WordResidue signum.

Specified by:

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

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

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

WordResidue subtraction.

Specified by:

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

Parameters:

S - WordResidue.

Returns:

this-S.

divide

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

WordResidue left division.

Specified by:

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

Parameters:

S - WordResidue.

Returns:

left, with left*S = this

twosidedDivide

public WordResidue<C>[] twosidedDivide(WordResidue<C> S)

WordResidue two-sided division.

Specified by:

twosidedDivide in interface MonoidElem<WordResidue<C extends GcdRingElem<C>>>

Specified by:

twosidedDivide in interface NoncomRingElem<WordResidue<C extends GcdRingElem<C>>>

Parameters:

S - WordResidue.

Returns:

[left, right] with left*S*right + remainder = this.

rightDivide

public WordResidue<C> rightDivide(WordResidue<C> S)

WordResidue right division.

Specified by:

rightDivide in interface MonoidElem<WordResidue<C extends GcdRingElem<C>>>

Specified by:

rightDivide in interface NoncomRingElem<WordResidue<C extends GcdRingElem<C>>>

Parameters:

S - WordResidue.

Returns:

right, with S * right = this

inverse

public WordResidue<C> inverse()

WordResidue inverse.

Specified by:

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

Returns:

S with S = 1/this if defined.

See Also:

MonoidElem.inverse()

remainder

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

WordResidue remainder.

Specified by:

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

Parameters:

S - WordResidue.

Returns:

this - (this/S) * S.

rightRemainder

public WordResidue<C> rightRemainder(WordResidue<C> S)

WordResidue right remainder.

Specified by:

rightRemainder in interface MonoidElem<WordResidue<C extends GcdRingElem<C>>>

Specified by:

rightRemainder in interface NoncomRingElem<WordResidue<C extends GcdRingElem<C>>>

Parameters:

S - WordResidue.

Returns:

r = this - S * (S/right), where S * right = this.

twosidedRemainder

public WordResidue<C> twosidedRemainder(WordResidue<C> S)

WordResidue two-sided remainder.

Specified by:

twosidedRemainder in interface MonoidElem<WordResidue<C extends GcdRingElem<C>>>

Specified by:

twosidedRemainder in interface NoncomRingElem<WordResidue<C extends GcdRingElem<C>>>

Parameters:

S - WordResidue.

Returns:

r = this - left*S*right.

multiply

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

WordResidue multiplication.

Specified by:

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

Parameters:

S - WordResidue.

Returns:

this*S.

multiply

public WordResidue<C> multiply(GenWordPolynomial<C> S)

WordResidue multiplication.

Parameters:

S - GenWordPolynomial.

Returns:

this*S.

multiply

public WordResidue<C> multiply(C s)

multiply

public WordResidue<C> multiply(Word e)

WordResidue multiplication.

Parameters:

e - word.

Returns:

this*e.

monic

public WordResidue<C> monic()

WordResidue monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

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

Specified by:

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

Parameters:

b - other element.

Returns:

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