edu.jas.arith

Class BigInteger

java.lang.Object

edu.jas.arith.BigInteger

All Implemented Interfaces:

Rational, AbelianGroupElem<BigInteger>, AbelianGroupFactory<BigInteger>, Element<BigInteger>, ElemFactory<BigInteger>, GcdRingElem<BigInteger>, MonoidElem<BigInteger>, MonoidFactory<BigInteger>, RingElem<BigInteger>, RingFactory<BigInteger>, java.io.Serializable, java.lang.Comparable<BigInteger>, java.lang.Iterable<BigInteger>

public final class BigInteger
extends java.lang.Object
implements GcdRingElem<BigInteger>, RingFactory<BigInteger>, java.lang.Iterable<BigInteger>, Rational

BigInteger class to make java.math.BigInteger available with RingElem respectively the GcdRingElem interface. Objects of this class are immutable. The SAC2 static methods are also provided.

Author:

Heinz Kredel

See Also:

BigInteger, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static BigInteger	ONE The constant 1.
static BigInteger	TWO The constant 2.
java.math.BigInteger	val The data structure.
static BigInteger	ZERO The constant 0.

Constructor Summary

Constructors

Constructor and Description
BigInteger() Constructor for BigInteger without parameters.
BigInteger(java.math.BigInteger a) Constructor for BigInteger from math.BigInteger.
BigInteger(long a) Constructor for BigInteger from long.
BigInteger(java.lang.String s) Constructor for BigInteger from String.

Method Summary

Modifier and Type	Method and Description
BigInteger	abs() Absolute value of this.
long	bitLength() Returns the number of bits in the representation of this BigInteger, including a sign bit.
static long	bitLength(long v) Returns the number of bits in the representation of a Long, including a sign bit.
java.math.BigInteger	characteristic() Characteristic of this ring.
int	compareTo(BigInteger b) Compare to BigInteger b.
BigInteger	copy() Clone this.
BigInteger	copy(BigInteger c) Copy BigInteger element c.
BigInteger	divide(BigInteger S) BigInteger divide.
BigInteger[]	egcd(BigInteger S) BigInteger extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
BigInteger	factory() Get the corresponding element factory.
BigInteger	fromInteger(java.math.BigInteger a) Get a BigInteger element from a math.BigInteger.
BigInteger	fromInteger(long a) Get a BigInteger element from long.
BigInteger	gcd(BigInteger S) BigInteger greatest common divisor.
java.util.List<BigInteger>	generators() Get a list of the generating elements.
BigInteger	getONE() Get the one element.
BigRational	getRational() Return a BigRational approximation of this Element.
java.math.BigInteger	getVal() Get the value.
BigInteger	getZERO() Get the zero element.
int	hashCode() Hash code for this BigInteger.
static BigInteger	IABS(BigInteger A) Absolute value.
static int	ICOMP(BigInteger A, BigInteger B) Integer comparison.
static BigInteger	IDIF(BigInteger A, BigInteger B) BigInteger subtract.
static BigInteger	IGCD(BigInteger A, BigInteger B) BigInteger greatest common divisor.
static BigInteger	INEG(BigInteger A) Negative value.
BigInteger	inverse() Integer inverse.
static BigInteger	IPROD(BigInteger A, BigInteger B) BigInteger multiply.
static BigInteger	IQ(BigInteger A, BigInteger B) BigInteger divide.
static BigInteger[]	IQR(BigInteger A, BigInteger B) Integer quotient and remainder.
static BigInteger	IRAND(int NL) BigInteger random.
static BigInteger	IREM(BigInteger A, BigInteger B) BigInteger remainder.
boolean	isAssociative() Query if this ring is associative.
boolean	isCommutative() Query if this ring is commutative.
boolean	isField() Query if this ring is a field.
boolean	isFinite() Is this structure finite or infinite.
static int	ISIGN(BigInteger A) Integer signum.
boolean	isONE() Is BigInteger number one.
static BigInteger	ISUM(BigInteger A, BigInteger B) BigInteger addition.
boolean	isUnit() Is BigInteger number unit.
boolean	isZERO() Is BigInteger number zero.
java.util.Iterator<BigInteger>	iterator() Get a BigInteger iterator.
long	longValue() Get the value as long.
BigInteger	multiply(BigInteger S) BigInteger multiply.
BigInteger	negate() Negate this.
BigInteger	parse(java.io.Reader r) BigInteger parse from Reader.
BigInteger	parse(java.lang.String s) BigInteger parse from String.
BigInteger[]	quotientRemainder(BigInteger S) BigInteger compute quotient and remainder.
BigInteger	random(int n) BigInteger random.
BigInteger	random(int n, java.util.Random rnd) BigInteger random.
BigInteger	remainder(BigInteger S) BigInteger remainder.
void	setAllIterator() Set the iteration algorithm to all elements.
void	setNonNegativeIterator() Set the iteration algorithm to non-negative elements.
BigInteger	shiftLeft(int n) BigInteger shift left.
int	signum() signum.
BigInteger	subtract(BigInteger S) BigInteger subtract.
BigInteger	sum(BigInteger S) BigInteger 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.
static BigInteger	valueOf(java.math.BigInteger a) Get a BigInteger element from a math.BigInteger.
static BigInteger	valueOf(long a) Get a BigInteger element from long.

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, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

val

public final java.math.BigInteger val

The data structure.

ZERO

public static final BigInteger ZERO

The constant 0.

ONE

public static final BigInteger ONE

The constant 1.

TWO

public static final BigInteger TWO

The constant 2.

Constructor Detail

BigInteger

public BigInteger(java.math.BigInteger a)

Constructor for BigInteger from math.BigInteger.

Parameters:

a - java.math.BigInteger.

BigInteger

public BigInteger(long a)

Constructor for BigInteger from long.

Parameters:

a - long.

BigInteger

public BigInteger(java.lang.String s)

Constructor for BigInteger from String.

Parameters:

s - String.

BigInteger

public BigInteger()

Constructor for BigInteger without parameters.

Method Detail

getVal

public java.math.BigInteger getVal()

Get the value.

Returns:

val java.math.BigInteger.

longValue

public long longValue()

Get the value as long.

Returns:

val as long.

factory

public BigInteger factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<BigInteger>

Returns:

factory for this Element.

See Also:

Element.factory()

generators

public java.util.List<BigInteger> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<BigInteger>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<BigInteger>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

public BigInteger copy()

Clone this.

Specified by:

copy in interface Element<BigInteger>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

copy

public BigInteger copy(BigInteger c)

Copy BigInteger element c.

Specified by:

copy in interface ElemFactory<BigInteger>

Parameters:

c - BigInteger.

Returns:

a copy of c.

getZERO

public BigInteger getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<BigInteger>

Returns:

0.

getONE

public BigInteger getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<BigInteger>

Returns:

1.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<BigInteger>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<BigInteger>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<BigInteger>

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<BigInteger>

Returns:

characteristic of this ring.

fromInteger

public BigInteger fromInteger(java.math.BigInteger a)

Get a BigInteger element from a math.BigInteger.

Specified by:

fromInteger in interface ElemFactory<BigInteger>

Parameters:

a - math.BigInteger.

Returns:

a as BigInteger.

valueOf

public static BigInteger valueOf(java.math.BigInteger a)

Get a BigInteger element from a math.BigInteger.

Parameters:

a - math.BigInteger.

Returns:

a as BigInteger.

fromInteger

public BigInteger fromInteger(long a)

Get a BigInteger element from long.

Specified by:

fromInteger in interface ElemFactory<BigInteger>

Parameters:

a - long.

Returns:

a as BigInteger.

valueOf

public static BigInteger valueOf(long a)

Get a BigInteger element from long.

Parameters:

a - long.

Returns:

a as BigInteger.

isZERO

public boolean isZERO()

Is BigInteger number zero.

Specified by:

isZERO in interface AbelianGroupElem<BigInteger>

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is BigInteger number one.

Specified by:

isONE in interface MonoidElem<BigInteger>

Returns:

true if this is 1, else false.

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is BigInteger number unit.

Specified by:

isUnit in interface MonoidElem<BigInteger>

Returns:

true if this is a unit, 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<BigInteger>

Specified by:

toScript in interface ElemFactory<BigInteger>

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<BigInteger>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(BigInteger b)

Compare to BigInteger b.

Specified by:

compareTo in interface Element<BigInteger>

Specified by:

compareTo in interface java.lang.Comparable<BigInteger>

Parameters:

b - BigInteger.

Returns:

0 if this == b, 1 if this > b, -1 if this < b.

ICOMP

public static int ICOMP(BigInteger A,
                        BigInteger B)

Integer comparison.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

0 if A == B, 1 if A > B, -1 if A < B.

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<BigInteger>

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 BigInteger.

Specified by:

hashCode in interface Element<BigInteger>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public BigInteger abs()

Absolute value of this.

Specified by:

abs in interface AbelianGroupElem<BigInteger>

Returns:

|this|.

See Also:

AbelianGroupElem.abs()

IABS

public static BigInteger IABS(BigInteger A)

Absolute value.

Parameters:

A - BigInteger.

Returns:

abs(A).

negate

public BigInteger negate()

Description copied from interface: AbelianGroupElem

Negate this.

Specified by:

negate in interface AbelianGroupElem<BigInteger>

Returns:

- this.

INEG

public static BigInteger INEG(BigInteger A)

Negative value.

Parameters:

A - BigInteger.

Returns:

-A.

signum

public int signum()

signum.

Specified by:

signum in interface AbelianGroupElem<BigInteger>

Returns:

the sign of this.

See Also:

AbelianGroupElem.signum()

ISIGN

public static int ISIGN(BigInteger A)

Integer signum.

Parameters:

A - BigInteger.

Returns:

signum(A).

subtract

public BigInteger subtract(BigInteger S)

BigInteger subtract.

Specified by:

subtract in interface AbelianGroupElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

this-S.

IDIF

public static BigInteger IDIF(BigInteger A,
                              BigInteger B)

BigInteger subtract.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

A-B.

divide

public BigInteger divide(BigInteger S)

BigInteger divide.

Specified by:

divide in interface MonoidElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

this/S.

IQ

public static BigInteger IQ(BigInteger A,
                            BigInteger B)

BigInteger divide.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

A/B.

inverse

public BigInteger inverse()

Integer inverse. R is a non-zero integer. S=1/R if defined else throws not invertible exception.

Specified by:

inverse in interface MonoidElem<BigInteger>

Returns:

x with this * x = 1, if it exists.

See Also:

MonoidElem.inverse()

remainder

public BigInteger remainder(BigInteger S)

BigInteger remainder.

Specified by:

remainder in interface MonoidElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

this - (this/S)*S.

IREM

public static BigInteger IREM(BigInteger A,
                              BigInteger B)

BigInteger remainder.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

A - (A/B)*B.

quotientRemainder

public BigInteger[] quotientRemainder(BigInteger S)

BigInteger compute quotient and remainder. Throws an exception, if S == 0.

Specified by:

quotientRemainder in interface MonoidElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

BigInteger[] { q, r } with this = q S + r and 0 ≤ r < |S|.

IQR

public static BigInteger[] IQR(BigInteger A,
                               BigInteger B)

Integer quotient and remainder. A and B are integers, B ne 0. Q is the quotient, integral part of A/B, and R is the remainder A-B*Q. Throws an exception, if B == 0.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

BigInteger[] { q, r } with A = q B + r and 0 ≤ r < |B|

gcd

public BigInteger gcd(BigInteger S)

BigInteger greatest common divisor.

Specified by:

gcd in interface RingElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

gcd(this,S).

egcd

public BigInteger[] egcd(BigInteger S)

BigInteger extended greatest common divisor.

Specified by:

egcd in interface RingElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

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

IGCD

public static BigInteger IGCD(BigInteger A,
                              BigInteger B)

BigInteger greatest common divisor.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

gcd(A,B).

random

public BigInteger random(int n)

BigInteger random.

Specified by:

random in interface ElemFactory<BigInteger>

Parameters:

n - such that 0 ≤ r ≤ (2ⁿ-1).

Returns:

r, a random BigInteger.

random

public BigInteger random(int n,
                         java.util.Random rnd)

BigInteger random.

Specified by:

random in interface ElemFactory<BigInteger>

Parameters:

n - such that 0 ≤ r ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

r, a random BigInteger.

IRAND

public static BigInteger IRAND(int NL)

BigInteger random.

Parameters:

NL - such that 0 ≤ r ≤ (2ⁿ-1).

Returns:

r, a random BigInteger.

multiply

public BigInteger multiply(BigInteger S)

BigInteger multiply.

Specified by:

multiply in interface MonoidElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

this*S.

shiftLeft

public BigInteger shiftLeft(int n)

BigInteger shift left.

Parameters:

n - bits to shift.

Returns:

this << n.

IPROD

public static BigInteger IPROD(BigInteger A,
                               BigInteger B)

BigInteger multiply.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

A*B.

sum

public BigInteger sum(BigInteger S)

BigInteger summation.

Specified by:

sum in interface AbelianGroupElem<BigInteger>

Parameters:

S - BigInteger.

Returns:

this+S.

ISUM

public static BigInteger ISUM(BigInteger A,
                              BigInteger B)

BigInteger addition.

Parameters:

A - BigInteger.

B - BigInteger.

Returns:

A+B.

parse

public BigInteger parse(java.lang.String s)

BigInteger parse from String.

Specified by:

parse in interface ElemFactory<BigInteger>

Parameters:

s - String.

Returns:

Biginteger from s.

parse

public BigInteger parse(java.io.Reader r)

BigInteger parse from Reader.

Specified by:

parse in interface ElemFactory<BigInteger>

Parameters:

r - Reader.

Returns:

next Biginteger from r.

getRational

public BigRational getRational()

Return a BigRational approximation of this Element.

Specified by:

getRational in interface Rational

Returns:

a BigRational approximation of this.

bitLength

public long bitLength()

Returns the number of bits in the representation of this BigInteger, including a sign bit. For positive BigIntegers, this is equivalent to (ceil(log2(this+1))+1).)

Returns:

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

bitLength

public static long bitLength(long v)

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

Parameters:

v - value.

Returns:

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

setAllIterator

public void setAllIterator()

Set the iteration algorithm to all elements.

setNonNegativeIterator

public void setNonNegativeIterator()

Set the iteration algorithm to non-negative elements.

iterator

public java.util.Iterator<BigInteger> iterator()

Get a BigInteger iterator.

Specified by:

iterator in interface java.lang.Iterable<BigInteger>

Returns:

a iterator over all integers.