edu.jas.arith

Class ModInt

java.lang.Object

edu.jas.arith.ModInt

All Implemented Interfaces:

Modular, AbelianGroupElem<ModInt>, Element<ModInt>, GcdRingElem<ModInt>, MonoidElem<ModInt>, RingElem<ModInt>, java.io.Serializable, java.lang.Comparable<ModInt>

public final class ModInt
extends java.lang.Object
implements GcdRingElem<ModInt>, Modular

ModInt class with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

ModInteger, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
ModIntRing	ring ModIntRing reference.
int	val Value part of the element data structure.

Constructor Summary

Constructors

Constructor and Description
ModInt(ModIntRing m) The constructor creates a 0 ModInt object from a given ModIntRing.
ModInt(ModIntRing m, java.math.BigInteger a) The constructor creates a ModInt object from a ModIntRing and a value part.
ModInt(ModIntRing m, int a) The constructor creates a ModInt object from a ModIntRing and a int value part.
ModInt(ModIntRing m, java.lang.Integer a) The constructor creates a ModInt object from a ModIntRing and a Int value part.
ModInt(ModIntRing m, long a) The constructor creates a ModInt object from a ModIntRing and a long value part.
ModInt(ModIntRing m, java.lang.Long a) The constructor creates a ModInt object from a ModIntRing and a Long value part.
ModInt(ModIntRing m, java.lang.String s) The constructor creates a ModInt object from a ModIntRing and a String value part.

Method Summary

Modifier and Type	Method and Description
ModInt	abs() ModInt absolute value.
int	bitLength() Returns the number of bits in the representation of this ModInt, including a sign bit.
int	compareTo(ModInt b) ModInt comparison.
ModInt	copy() Clone this.
ModInt	divide(ModInt S) ModInt divide.
ModInt[]	egcd(ModInt S) ModInteger extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
ModIntRing	factory() Get the corresponding element factory.
int	gcd(int T, int S) Int greatest common divisor.
ModInt	gcd(ModInt S) ModInteger greatest common divisor.
BigInteger	getInteger() Return a BigInteger from this Element.
int	getModul() Get the module part.
BigInteger	getSymmetricInteger() Return a symmetric BigInteger from this Element.
int	getSymmetricVal() Get the symmetric value part.
int	getVal() Get the value part.
int	hashCode() Hash code for this ModInt.
int[]	hegcd(int T, int S) Int half extended greatest common divisor.
ModInt	inverse() ModInt inverse.
boolean	isONE() Is ModInt number one.
boolean	isUnit() Is ModInt number a unit.
boolean	isZERO() Is ModInt number zero.
int	modInverse(int T, int m) Int modular inverse.
ModInt	multiply(ModInt S) ModInt multiply.
ModInt	negate() ModInt negative.
ModInt	remainder(ModInt S) ModInt remainder.
int	signum() ModInt signum.
ModInt	subtract(ModInt S) ModInt subtraction.
ModInt	sum(ModInt S) ModInt 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.

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, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

ring

public final ModIntRing ring

ModIntRing reference.

val

public final int val

Value part of the element data structure.

Constructor Detail

ModInt

public ModInt(ModIntRing m,
              java.math.BigInteger a)

The constructor creates a ModInt object from a ModIntRing and a value part.

Parameters:

m - ModIntRing.

a - math.BigInteger.

ModInt

public ModInt(ModIntRing m,
              int a)

The constructor creates a ModInt object from a ModIntRing and a int value part.

Parameters:

m - ModIntRing.

a - int.

ModInt

public ModInt(ModIntRing m,
              long a)

The constructor creates a ModInt object from a ModIntRing and a long value part.

Parameters:

m - ModIntRing.

a - long.

ModInt

public ModInt(ModIntRing m,
              java.lang.Integer a)

The constructor creates a ModInt object from a ModIntRing and a Int value part.

Parameters:

m - ModIntRing.

a - Int.

ModInt

public ModInt(ModIntRing m,
              java.lang.Long a)

The constructor creates a ModInt object from a ModIntRing and a Long value part.

Parameters:

m - ModIntRing.

a - long.

ModInt

public ModInt(ModIntRing m,
              java.lang.String s)

The constructor creates a ModInt object from a ModIntRing and a String value part.

Parameters:

m - ModIntRing.

s - String.

ModInt

public ModInt(ModIntRing m)

The constructor creates a 0 ModInt object from a given ModIntRing.

Parameters:

m - ModIntRing.

Method Detail

getVal

public int getVal()

Get the value part.

Returns:

val.

getModul

public int getModul()

Get the module part.

Returns:

modul.

factory

public ModIntRing factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<ModInt>

Returns:

factory for this Element.

See Also:

Element.factory()

getSymmetricVal

public int 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 ModInt copy()

Clone this.

Specified by:

copy in interface Element<ModInt>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is ModInt number zero.

Specified by:

isZERO in interface AbelianGroupElem<ModInt>

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is ModInt number one.

Specified by:

isONE in interface MonoidElem<ModInt>

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is ModInt number a unit.

Specified by:

isUnit in interface MonoidElem<ModInt>

Returns:

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

See Also:

MonoidElem.isUnit()

toString

public java.lang.String toString()

Get the String representation.

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<ModInt>

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<ModInt>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(ModInt b)

ModInt comparison.

Specified by:

compareTo in interface Element<ModInt>

Specified by:

compareTo in interface java.lang.Comparable<ModInt>

Parameters:

b - ModInt.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<ModInt>

Overrides:

equals in class java.lang.Object

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 ModInt.

Specified by:

hashCode in interface Element<ModInt>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public ModInt abs()

ModInt absolute value.

Specified by:

abs in interface AbelianGroupElem<ModInt>

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

negate

public ModInt negate()

ModInt negative.

Specified by:

negate in interface AbelianGroupElem<ModInt>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

ModInt signum.

Specified by:

signum in interface AbelianGroupElem<ModInt>

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

public ModInt subtract(ModInt S)

ModInt subtraction.

Specified by:

subtract in interface AbelianGroupElem<ModInt>

Parameters:

S - ModInt.

Returns:

this-S.

divide

public ModInt divide(ModInt S)

ModInt divide.

Specified by:

divide in interface MonoidElem<ModInt>

Parameters:

S - ModInt.

Returns:

this/S.

inverse

public ModInt inverse()

ModInt inverse.

Specified by:

inverse in interface MonoidElem<ModInt>

Returns:

S with S=1/this if defined.

Throws:

NotInvertibleException - if the element is not invertible.

See Also:

MonoidElem.inverse()

remainder

public ModInt remainder(ModInt S)

ModInt remainder.

Specified by:

remainder in interface MonoidElem<ModInt>

Parameters:

S - ModInt.

Returns:

remainder(this,S).

multiply

public ModInt multiply(ModInt S)

ModInt multiply.

Specified by:

multiply in interface MonoidElem<ModInt>

Parameters:

S - ModInt.

Returns:

this*S.

sum

public ModInt sum(ModInt S)

ModInt summation.

Specified by:

sum in interface AbelianGroupElem<ModInt>

Parameters:

S - ModInt.

Returns:

this+S.

gcd

public ModInt gcd(ModInt S)

ModInteger greatest common divisor.

Specified by:

gcd in interface RingElem<ModInt>

Parameters:

S - ModInteger.

Returns:

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

egcd

public ModInt[] egcd(ModInt S)

ModInteger extended greatest common divisor.

Specified by:

egcd in interface RingElem<ModInt>

Parameters:

S - ModInteger.

Returns:

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

gcd

public int gcd(int T,
               int S)

Int greatest common divisor.

Parameters:

T - int.

S - int.

Returns:

gcd(T,S).

hegcd

public int[] hegcd(int T,
                   int S)

Int half extended greatest common divisor.

Parameters:

T - int.

S - int.

Returns:

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

modInverse

public int modInverse(int T,
                      int m)

Int modular inverse.

Parameters:

T - int.

m - int.

Returns:

a with with a*T = 1 mod m.

bitLength

public int bitLength()

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

Returns:

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