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

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 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 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 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 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).