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>>, Serializable, Comparable<SolvableResidue<C>>

public class SolvableResidue<C extends GcdRingElem<C>>
extends 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.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected int	isunit	Flag to remember if this residue element is a unit.
final SolvableResidueRing<C>	ring	SolvableResidue class factory data structure.
final GenSolvablePolynomial<C>	val	Value part of the element data structure.

Constructor Summary

Constructors

Constructor	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	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(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(SolvableResidue<C> S)	SolvableResidue multiplication.
SolvableResidue<C>	multiply(ExpVector e)	SolvableResidue multiplication.
SolvableResidue<C>	multiply(GenSolvablePolynomial<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.
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.
GenSolvablePolynomial<C>	value()	Value.

Methods inherited from class Object

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

Methods inherited from interface MonoidElem

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

Methods inherited from interface RingElem

leftGcd, rightGcd

Field Details

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 Details

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 Details

factory

public SolvableResidueRing<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()

value

public GenSolvablePolynomial<C> value()

Value. Returns the value.

Specified by:

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

See Also:

• Value.value()

numerator

public GenSolvablePolynomial<C> numerator()

Numerator. Returns the value.

Specified by:

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

See Also:

• QuotPair.numerator()

denominator

public GenSolvablePolynomial<C> denominator()

Denominator. Returns 1.

Specified by:

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

See Also:

• QuotPair.denominator()

copy

public SolvableResidue<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 SolvableResidue 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 SolvableResidue 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 SolvableResidue 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 SolvableResidue a constant.

Specified by:

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

Specified by:

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

Returns:

true if this.val is a constant polynomial, 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(SolvableResidue<C> b)

SolvableResidue comparison.

Specified by:

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

Specified by:

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

Overrides:

hashCode in class Object

Returns:

the hashCode.

See Also:

• Object.hashCode()

abs

public SolvableResidue<C> abs()

SolvableResidue absolute value.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this+S.

negate

public SolvableResidue<C> negate()

SolvableResidue negate.

Specified by:

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

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

signum

public int signum()

SolvableResidue signum.

Specified by:

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

Parameters:

S - SolvableResidue.

Returns:

this/S.

inverse

public SolvableResidue<C> inverse()

SolvableResidue inverse.

Specified by:

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

Parameters:

b - other element.

Returns:

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