Class ModInteger

java.lang.Object

edu.jas.arith.ModInteger

All Implemented Interfaces:

Modular, AbelianGroupElem<ModInteger>, Element<ModInteger>, GcdRingElem<ModInteger>, MonoidElem<ModInteger>, RingElem<ModInteger>, Serializable, Comparable<ModInteger>

public final class ModInteger
extends Object
implements GcdRingElem<ModInteger>, Modular

ModInteger class with GcdRingElem interface. Objects of this class are immutable. The SAC2 static methods are also provided.

See Also:

• BigInteger
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final ModIntegerRing	ring	ModIntegerRing reference.
final BigInteger	val	Value part of the element data structure.

Constructor Summary

Constructors

Constructor	Description
ModInteger(ModIntegerRing m)	The constructor creates a 0 ModInteger object from a given ModIntegerRing.
ModInteger(ModIntegerRing m, long a)	The constructor creates a ModInteger object from a ModIntegerRing and a long value part.
ModInteger(ModIntegerRing m, String s)	The constructor creates a ModInteger object from a ModIntegerRing and a String value part.
ModInteger(ModIntegerRing m, BigInteger a)	The constructor creates a ModInteger object from a ModIntegerRing and a value part.

Method Summary

Modifier and Type	Method	Description
ModInteger	abs()	ModInteger absolute value.
long	bitLength()	Returns the number of bits in the representation of this ModInteger, including a sign bit.
int	compareTo(ModInteger b)	ModInteger comparison.
ModInteger	copy()	Clone this.
ModInteger	divide(ModInteger S)	ModInteger divide.
ModInteger[]	egcd(ModInteger S)	ModInteger extended greatest common divisor.
boolean	equals(Object b)	Comparison with any other object.
ModIntegerRing	factory()	Get the corresponding element factory.
ModInteger	gcd(ModInteger S)	ModInteger greatest common divisor.
BigInteger	getInteger()	Return a BigInteger from this Element.
BigInteger	getModul()	Get the module part.
BigInteger	getSymmetricInteger()	Return a symmetric BigInteger from this Element.
BigInteger	getSymmetricVal()	Get the symmetric value part.
BigInteger	getVal()	Get the value part.
int	hashCode()	Hash code for this ModInteger.
ModInteger[]	hegcd(ModInteger S)	ModInteger half extended greatest common divisor.
ModInteger	inverse()	ModInteger inverse.
boolean	isONE()	Is ModInteger number one.
boolean	isUnit()	Is ModInteger number a unit.
boolean	isZERO()	Is ModInteger number zero.
static ModInteger	MIABS(ModInteger A)	ModInteger absolute value.
static int	MICOMP(ModInteger A, ModInteger B)	ModInteger comparison.
static ModInteger	MIDIF(ModInteger A, ModInteger B)	ModInteger subtraction.
static ModInteger	MIINV(ModInteger A)	ModInteger inverse.
static ModInteger	MINEG(ModInteger A)	ModInteger negative.
static ModInteger	MIPROD(ModInteger A, ModInteger B)	ModInteger product.
static ModInteger	MIQ(ModInteger A, ModInteger B)	ModInteger quotient.
static ModInteger	MIREM(ModInteger A, ModInteger B)	ModInteger remainder.
static int	MISIGN(ModInteger A)	ModInteger signum.
static ModInteger	MISUM(ModInteger A, ModInteger B)	ModInteger summation.
ModInteger	multiply(ModInteger S)	ModInteger multiply.
ModInteger	negate()	ModInteger negative.
ModInteger[]	quotientRemainder(ModInteger S)	Quotient and remainder by division of this by S.
ModInteger	remainder(ModInteger S)	ModInteger remainder.
int	signum()	ModInteger signum.
ModInteger	subtract(ModInteger S)	ModInteger subtraction.
ModInteger	sum(ModInteger S)	ModInteger 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.

Methods inherited from class Object

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

Methods inherited from interface MonoidElem

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

Methods inherited from interface RingElem

leftGcd, rightGcd

Field Details

ring

public final ModIntegerRing ring

ModIntegerRing reference.

val

public final BigInteger val

Value part of the element data structure.

Constructor Details

ModInteger

public ModInteger(ModIntegerRing m,
 BigInteger a)

The constructor creates a ModInteger object from a ModIntegerRing and a value part.

Parameters:

m - ModIntegerRing.

a - math.BigInteger.

ModInteger

public ModInteger(ModIntegerRing m,
 long a)

The constructor creates a ModInteger object from a ModIntegerRing and a long value part.

Parameters:

m - ModIntegerRing.

a - long.

ModInteger

public ModInteger(ModIntegerRing m,
 String s)

The constructor creates a ModInteger object from a ModIntegerRing and a String value part.

Parameters:

m - ModIntegerRing.

s - String.

ModInteger

public ModInteger(ModIntegerRing m)

The constructor creates a 0 ModInteger object from a given ModIntegerRing.

Parameters:

m - ModIntegerRing.

Method Details

getVal

public BigInteger getVal()

Get the value part.

Returns:

val.

getModul

public BigInteger getModul()

Get the module part.

Returns:

modul.

factory

public ModIntegerRing factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<ModInteger>

Returns:

factory for this Element.

See Also:

• Element.factory()

getSymmetricVal

public BigInteger getSymmetricVal()

Get the symmetric value part.

Returns:

val with -modul/2 ≤ val < modul/2.

getInteger

public BigInteger getInteger()

Return a BigInteger from this Element.

Specified by:

getInteger in interface Modular

Returns:

a BigInteger of this.

getSymmetricInteger

public BigInteger getSymmetricInteger()

Return a symmetric BigInteger from this Element.

Specified by:

getSymmetricInteger in interface Modular

Returns:

a symmetric BigInteger of this.

copy

public ModInteger copy()

Clone this.

Specified by:

copy in interface Element<ModInteger>

Returns:

Creates and returns a copy of this Element.

See Also:

• Object.clone()

isZERO

public boolean isZERO()

Is ModInteger number zero.

Specified by:

isZERO in interface AbelianGroupElem<ModInteger>

Returns:

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

See Also:

• AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is ModInteger number one.

Specified by:

isONE in interface MonoidElem<ModInteger>

Returns:

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

See Also:

• MonoidElem.isONE()

isUnit

public boolean isUnit()

Is ModInteger number a unit.

Specified by:

isUnit in interface MonoidElem<ModInteger>

Returns:

If this is a unit then true is returned, else false.

See Also:

• MonoidElem.isUnit()

toString

public String toString()

Get the String representation.

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<ModInteger>

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<ModInteger>

Returns:

script compatible representation for this ElemFactory.

See Also:

• Element.toScriptFactory()

compareTo

public int compareTo(ModInteger b)

ModInteger comparison.

Specified by:

compareTo in interface Comparable<ModInteger>

Specified by:

compareTo in interface Element<ModInteger>

Parameters:

b - ModInteger.

Returns:

sign(this-b).

MICOMP

public static int MICOMP(ModInteger A,
 ModInteger B)

ModInteger comparison.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

sign(this-b).

equals

public boolean equals(Object b)

Comparison with any other object.

Specified by:

equals in interface Element<ModInteger>

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 ModInteger.

Specified by:

hashCode in interface Element<ModInteger>

Overrides:

hashCode in class Object

Returns:

the hashCode.

See Also:

• Object.hashCode()

abs

public ModInteger abs()

ModInteger absolute value.

Specified by:

abs in interface AbelianGroupElem<ModInteger>

Returns:

the absolute value of this.

See Also:

• AbelianGroupElem.abs()

MIABS

public static ModInteger MIABS(ModInteger A)

ModInteger absolute value.

Parameters:

A - ModInteger.

Returns:

the absolute value of A.

negate

public ModInteger negate()

ModInteger negative.

Specified by:

negate in interface AbelianGroupElem<ModInteger>

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

MINEG

public static ModInteger MINEG(ModInteger A)

ModInteger negative.

Parameters:

A - ModInteger.

Returns:

-A.

signum

public int signum()

ModInteger signum.

Specified by:

signum in interface AbelianGroupElem<ModInteger>

Returns:

signum(this).

See Also:

• AbelianGroupElem.signum()

MISIGN

public static int MISIGN(ModInteger A)

ModInteger signum.

Parameters:

A - ModInteger

Returns:

signum(A).

subtract

public ModInteger subtract(ModInteger S)

ModInteger subtraction.

Specified by:

subtract in interface AbelianGroupElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

this-S.

MIDIF

public static ModInteger MIDIF(ModInteger A,
 ModInteger B)

ModInteger subtraction.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

A-B.

divide

public ModInteger divide(ModInteger S)

ModInteger divide.

Specified by:

divide in interface MonoidElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

this/S.

MIQ

public static ModInteger MIQ(ModInteger A,
 ModInteger B)

ModInteger quotient.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

A/B.

inverse

public ModInteger inverse()

ModInteger inverse.

Specified by:

inverse in interface MonoidElem<ModInteger>

Returns:

S with S=1/this if defined.

Throws:

NotInvertibleException - if the element is not invertible.

See Also:

• MonoidElem.inverse()

MIINV

public static ModInteger MIINV(ModInteger A)

ModInteger inverse.

Parameters:

A - is a non-zero integer.

Returns:

S with S=1/A if defined.

See Also:

• MonoidElem.inverse()

remainder

public ModInteger remainder(ModInteger S)

ModInteger remainder.

Specified by:

remainder in interface MonoidElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

remainder(this,S).

MIREM

public static ModInteger MIREM(ModInteger A,
 ModInteger B)

ModInteger remainder.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

A - (A/B)*B.

quotientRemainder

public ModInteger[] quotientRemainder(ModInteger S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<ModInteger>

Parameters:

S - a modular integer

Returns:

[this/S, this - (this/S)*S].

multiply

public ModInteger multiply(ModInteger S)

ModInteger multiply.

Specified by:

multiply in interface MonoidElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

this*S.

MIPROD

public static ModInteger MIPROD(ModInteger A,
 ModInteger B)

ModInteger product.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

A*B.

sum

public ModInteger sum(ModInteger S)

ModInteger summation.

Specified by:

sum in interface AbelianGroupElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

this+S.

MISUM

public static ModInteger MISUM(ModInteger A,
 ModInteger B)

ModInteger summation.

Parameters:

A - ModInteger.

B - ModInteger.

Returns:

A+B.

gcd

public ModInteger gcd(ModInteger S)

ModInteger greatest common divisor.

Specified by:

gcd in interface RingElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

gcd(this,S).

hegcd

public ModInteger[] hegcd(ModInteger S)

ModInteger half extended greatest common divisor.

Parameters:

S - ModInteger.

Returns:

[ gcd(this,S), a ] with a*this + b*S = gcd(this,S) for some b.

egcd

public ModInteger[] egcd(ModInteger S)

ModInteger extended greatest common divisor.

Specified by:

egcd in interface RingElem<ModInteger>

Parameters:

S - ModInteger.

Returns:

[ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).

bitLength

public long bitLength()

Returns the number of bits in the representation of this ModInteger, including a sign bit. For positive ModIntegers, this is equivalent to val.bitLength().)

Returns:

number of bits in the representation of this ModInteger, including a sign bit.