Package edu.jas.arith

Class BigRational

java.lang.Object

edu.jas.arith.BigRational

All Implemented Interfaces:

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

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

Immutable arbitrary-precision rational numbers. BigRational class based on BigInteger and implementing the RingElem interface. BigInteger is from java.math in the implementation. The SAC2 static methods are also provided.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
java.math.BigInteger	den	Denominator part of the data structure.
static BigRational	HALF	The Constant 1/2.
java.math.BigInteger	num	Numerator part of the data structure.
static BigRational	ONE	The Constant 1.
static BigRational	ZERO	The Constant 0.

Constructor Summary

Constructors

Modifier	Constructor	Description
	BigRational()	Constructor for a BigRational with no arguments.
	BigRational(long n)	Constructor for a BigRational from longs.
	BigRational(long n, long d)	Constructor for a BigRational from longs.
	BigRational(BigInteger n)	Constructor for a BigRational from jas.arith.BigIntegers.
	BigRational(BigInteger n, BigInteger d)	Constructor for a BigRational from jas.arith.BigIntegers.
	BigRational(java.lang.String s)	Constructor for a BigRational from String.
	BigRational(java.math.BigInteger n)	Constructor for a BigRational from math.BigIntegers.
protected	BigRational(java.math.BigInteger n, java.math.BigInteger d)	Constructor for a BigRational from math.BigIntegers.

Method Summary

Modifier and Type	Method	Description
BigRational	abs()	Rational number absolute value.
long	bitLength()	Returns the number of bits in the representation of this BigRational, including a sign bit.
java.math.BigInteger	ceil()	BigRational ceiling.
java.math.BigInteger	characteristic()	Characteristic of this ring.
int	compareTo(BigRational S)	Rational number comparison.
BigRational	copy()	Clone this.
BigRational	copy(BigRational c)	Copy BigRational element c.
java.math.BigInteger	denominator()	Get the denominator.
BigRational	divide(BigRational S)	Rational number quotient.
double	doubleValue()	Get this as a double.
BigRational[]	egcd(BigRational S)	BigRational extended greatest common divisor.
boolean	equals(java.lang.Object b)	Comparison with any other object.
BigRational	factory()	Get the corresponding element factory.
java.math.BigInteger	floor()	BigRational floor.
BigRational	fromInteger(long a)	Get a BigRational element from a long.
BigRational	fromInteger(BigInteger a)	Get a BigRational element from a arith.BigInteger.
BigRational	fromInteger(java.math.BigInteger a)	Get a BigRational element from a math.BigInteger.
BigRational	gcd(BigRational S)	Rational number greatest common divisor.
java.util.List<BigRational>	generators()	Get a list of the generating elements.
BigDecimal	getDecimal()	Get the decimal representation.
BigRational	getONE()	Get the one element.
BigRational	getRational()	Return a BigRational approximation of this Element.
BigRational	getZERO()	Get the zero element.
int	hashCode()	Hash code for this BigRational.
BigRational	inverse()	Rational number inverse.
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Query if this ring is commutative.
boolean	isEntier()	Is BigRational entier.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
boolean	isONE()	Is BigRational one.
boolean	isUnit()	Is BigRational unit.
boolean	isZERO()	Is BigRational zero.
java.util.Iterator<BigRational>	iterator()	Get a BigRational iterator.
BigRational	multiply(BigRational S)	Rational number product.
BigRational	negate()	Rational number negative.
java.math.BigInteger	numerator()	Get the numerator.
BigRational	parse(java.io.Reader r)	Parse rational number from Reader.
BigRational	parse(java.lang.String s)	Parse rational number from String.
BigRational[]	quotientRemainder(BigRational S)	Quotient and remainder by division of this by S.
BigRational	random(int n)	Rational number, random.
BigRational	random(int n, java.util.Random rnd)	Rational number, random.
static BigRational	reduction(java.math.BigInteger n, java.math.BigInteger d)	Rational number reduction to lowest terms.
BigRational	remainder(BigRational S)	Rational number remainder.
static BigRational	RNABS(BigRational R)	Rational number absolute value.
static int	RNCOMP(BigRational R, BigRational S)	Rational number comparison.
static java.math.BigInteger	RNDEN(BigRational R)	Rational number denominator.
static BigRational	RNDIF(BigRational R, BigRational S)	Rational number difference.
static void	RNDWR(BigRational R, int NL)	Rational number decimal write.
static BigRational	RNINT(java.math.BigInteger A)	Rational number from integer.
static BigRational	RNINV(BigRational R)	Rational number inverse.
static BigRational	RNNEG(BigRational R)	Rational number negative.
static java.math.BigInteger	RNNUM(BigRational R)	Rational number numerator.
static BigRational	RNPROD(BigRational R, BigRational S)	Rational number product.
static BigRational	RNQ(BigRational R, BigRational S)	Rational number quotient.
static BigRational	RNRAND(int NL)	Rational number, random.
static BigRational	RNRED(java.math.BigInteger n, java.math.BigInteger d)	Rational number reduction to lowest terms.
static int	RNSIGN(BigRational R)	Rational number sign.
static BigRational	RNSUM(BigRational R, BigRational S)	Rational number sum.
void	setAllIterator()	Set the iteration algorithm to all elements.
void	setDuplicatesIterator()	Set the iteration algorithm to allow duplicate elements.
void	setNoDuplicatesIterator()	Set the iteration algorithm to no duplicate elements.
void	setNonNegativeIterator()	Set the iteration algorithm to non-negative elements.
int	signum()	Rational number sign.
BigRational	subtract(BigRational S)	Rational number difference.
BigRational	sum(BigRational S)	Rational number sum.
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.
java.lang.String	toString(int n)	Get the decimal string representation with given precision.
java.util.Iterator<BigRational>	uniqueIterator()	Get a BigRational iterator with no duplicates.
static BigRational	valueOf(long a)	Get a BigRational element from a long.
static BigRational	valueOf(java.math.BigInteger a)	Get a BigRational element from a math.BigInteger.

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface edu.jas.structure.MonoidElem

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

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Field Detail

num

public final java.math.BigInteger num

Numerator part of the data structure.

den

public final java.math.BigInteger den

Denominator part of the data structure.

ZERO

public static final BigRational ZERO

The Constant 0.

ONE

public static final BigRational ONE

The Constant 1.

HALF

public static final BigRational HALF

The Constant 1/2.

Constructor Detail

BigRational

protected BigRational(java.math.BigInteger n,
                      java.math.BigInteger d)

Constructor for a BigRational from math.BigIntegers.

Parameters:

n - math.BigInteger.

d - math.BigInteger.

BigRational

public BigRational(java.math.BigInteger n)

Constructor for a BigRational from math.BigIntegers.

Parameters:

n - math.BigInteger.

BigRational

public BigRational(BigInteger n)

Constructor for a BigRational from jas.arith.BigIntegers.

Parameters:

n - edu.jas.arith.BigInteger.

BigRational

public BigRational(BigInteger n,
                   BigInteger d)

Constructor for a BigRational from jas.arith.BigIntegers.

Parameters:

n - edu.jas.arith.BigInteger.

d - edu.jas.arith.BigInteger.

BigRational

public BigRational(long n,
                   long d)

Constructor for a BigRational from longs.

Parameters:

n - long.

d - long.

BigRational

public BigRational(long n)

Constructor for a BigRational from longs.

Parameters:

n - long.

BigRational

public BigRational()

Constructor for a BigRational with no arguments.

BigRational

public BigRational(java.lang.String s)
            throws java.lang.NumberFormatException

Constructor for a BigRational from String.

Parameters:

s - String.

Throws:

java.lang.NumberFormatException

Method Detail

factory

public BigRational factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<BigRational>

Returns:

factory for this Element.

See Also:

Element.factory()

generators

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

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<BigRational>

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<BigRational>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

public BigRational copy()

Clone this.

Specified by:

copy in interface Element<BigRational>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

copy

public BigRational copy(BigRational c)

Copy BigRational element c.

Specified by:

copy in interface ElemFactory<BigRational>

Parameters:

c - BigRational.

Returns:

a copy of c.

getRational

public BigRational getRational()

Return a BigRational approximation of this Element.

Specified by:

getRational in interface Rational

Returns:

a BigRational approximation of this.

See Also:

Rational.getRational()

numerator

public java.math.BigInteger numerator()

Get the numerator.

Returns:

num.

denominator

public java.math.BigInteger denominator()

Get the denominator.

Returns:

den.

toString

public java.lang.String toString()

Get the string representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toString

public java.lang.String toString(int n)

Get the decimal string representation with given precision.

Parameters:

n - precision.

Returns:

decimal approximation.

getDecimal

public BigDecimal getDecimal()

Get the decimal representation.

Returns:

decimal.

doubleValue

public double doubleValue()

Get this as a double.

Returns:

this as a double

See Also:

Number.doubleValue()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<BigRational>

Specified by:

toScript in interface ElemFactory<BigRational>

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<BigRational>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

getZERO

public BigRational getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<BigRational>

Returns:

0 as BigRational.

getONE

public BigRational getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<BigRational>

Returns:

1 as BigRational.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<BigRational>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<BigRational>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<BigRational>

Returns:

true.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<BigRational>

Returns:

characteristic of this ring.

fromInteger

public BigRational fromInteger(java.math.BigInteger a)

Get a BigRational element from a math.BigInteger.

Specified by:

fromInteger in interface ElemFactory<BigRational>

Parameters:

a - math.BigInteger.

Returns:

BigRational from a.

fromInteger

public BigRational fromInteger(BigInteger a)

Get a BigRational element from a arith.BigInteger.

Parameters:

a - arith.BigInteger.

Returns:

BigRational from a.

valueOf

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

Get a BigRational element from a math.BigInteger.

Parameters:

a - math.BigInteger.

Returns:

BigRational from a.

fromInteger

public BigRational fromInteger(long a)

Get a BigRational element from a long.

Specified by:

fromInteger in interface ElemFactory<BigRational>

Parameters:

a - long.

Returns:

BigRational from a.

valueOf

public static BigRational valueOf(long a)

Get a BigRational element from a long.

Parameters:

a - long.

Returns:

BigRational from a.

isZERO

public boolean isZERO()

Is BigRational zero.

Specified by:

isZERO in interface AbelianGroupElem<BigRational>

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is BigRational one.

Specified by:

isONE in interface MonoidElem<BigRational>

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is BigRational unit.

Specified by:

isUnit in interface MonoidElem<BigRational>

Returns:

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

See Also:

MonoidElem.isUnit()

isEntier

public boolean isEntier()

Is BigRational entier.

Returns:

If this is an integer then true is returned, else false.

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<BigRational>

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 BigRational.

Specified by:

hashCode in interface Element<BigRational>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

RNRED

public static BigRational RNRED(java.math.BigInteger n,
                                java.math.BigInteger d)

Rational number reduction to lowest terms.

Parameters:

n - BigInteger.

d - BigInteger.

Returns:

a/b ~ n/d, gcd(a,b) = 1, b > 0.

reduction

public static BigRational reduction(java.math.BigInteger n,
                                    java.math.BigInteger d)

Rational number reduction to lowest terms.

Parameters:

n - BigInteger.

d - BigInteger.

Returns:

a/b ~ n/d, gcd(a,b) = 1, b > 0.

abs

public BigRational abs()

Rational number absolute value.

Specified by:

abs in interface AbelianGroupElem<BigRational>

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

RNABS

public static BigRational RNABS(BigRational R)

Rational number absolute value.

Parameters:

R - is a rational number.

Returns:

the absolute value of R.

compareTo

public int compareTo(BigRational S)

Rational number comparison.

Specified by:

compareTo in interface java.lang.Comparable<BigRational>

Specified by:

compareTo in interface Element<BigRational>

Parameters:

S - BigRational.

Returns:

SIGN(this-S).

RNCOMP

public static int RNCOMP(BigRational R,
                         BigRational S)

Rational number comparison.

Parameters:

R - BigRational.

S - BigRational.

Returns:

SIGN(R-S).

RNDEN

public static java.math.BigInteger RNDEN(BigRational R)

Rational number denominator.

Parameters:

R - BigRational.

Returns:

R.denominator().

subtract

public BigRational subtract(BigRational S)

Rational number difference.

Specified by:

subtract in interface AbelianGroupElem<BigRational>

Parameters:

S - BigRational.

Returns:

this-S.

RNDIF

public static BigRational RNDIF(BigRational R,
                                BigRational S)

Rational number difference.

Parameters:

R - BigRational.

S - BigRational.

Returns:

R-S.

RNDWR

public static void RNDWR(BigRational R,
                         int NL)

Rational number decimal write. R is a rational number. n is a non-negative integer. R is approximated by a decimal fraction D with n decimal digits following the decimal point and D is written in the output stream. The inaccuracy of the approximation is at most (1/2)*10**-n.

Parameters:

R -

NL -

RNINT

public static BigRational RNINT(java.math.BigInteger A)

Rational number from integer.

Parameters:

A - BigInteger.

Returns:

A/1.

inverse

public BigRational inverse()

Rational number inverse.

Specified by:

inverse in interface MonoidElem<BigRational>

Returns:

1/this.

See Also:

MonoidElem.inverse()

RNINV

public static BigRational RNINV(BigRational R)

Rational number inverse.

Parameters:

R - BigRational.

Returns:

1/R.

negate

public BigRational negate()

Rational number negative.

Specified by:

negate in interface AbelianGroupElem<BigRational>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

RNNEG

public static BigRational RNNEG(BigRational R)

Rational number negative.

Parameters:

R - BigRational.

Returns:

-R.

RNNUM

public static java.math.BigInteger RNNUM(BigRational R)

Rational number numerator.

Parameters:

R - BigRational.

Returns:

R.numerator().

multiply

public BigRational multiply(BigRational S)

Rational number product.

Specified by:

multiply in interface MonoidElem<BigRational>

Parameters:

S - BigRational.

Returns:

this*S.

RNPROD

public static BigRational RNPROD(BigRational R,
                                 BigRational S)

Rational number product.

Parameters:

R - BigRational.

S - BigRational.

Returns:

R*S.

divide

public BigRational divide(BigRational S)

Rational number quotient.

Specified by:

divide in interface MonoidElem<BigRational>

Parameters:

S - BigRational.

Returns:

this/S.

RNQ

public static BigRational RNQ(BigRational R,
                              BigRational S)

Rational number quotient.

Parameters:

R - BigRational.

S - BigRational.

Returns:

R/S.

remainder

public BigRational remainder(BigRational S)

Rational number remainder.

Specified by:

remainder in interface MonoidElem<BigRational>

Parameters:

S - BigRational.

Returns:

this-(this/S)*S

quotientRemainder

public BigRational[] quotientRemainder(BigRational S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<BigRational>

Parameters:

S - a rational number

Returns:

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

random

public BigRational random(int n)

Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.

Specified by:

random in interface ElemFactory<BigRational>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

Returns:

a random BigRational.

random

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

Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.

Specified by:

random in interface ElemFactory<BigRational>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random BigRational.

RNRAND

public static BigRational RNRAND(int NL)

Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.

Parameters:

NL - such that 0 ≤ A, B ≤ (2ⁿ-1).

Returns:

a random BigRational.

signum

public int signum()

Rational number sign.

Specified by:

signum in interface AbelianGroupElem<BigRational>

Returns:

the sign of this.

See Also:

AbelianGroupElem.signum()

RNSIGN

public static int RNSIGN(BigRational R)

Rational number sign.

Parameters:

R - BigRational.

Returns:

R.signum().

sum

public BigRational sum(BigRational S)

Rational number sum.

Specified by:

sum in interface AbelianGroupElem<BigRational>

Parameters:

S - BigRational.

Returns:

this+S.

RNSUM

public static BigRational RNSUM(BigRational R,
                                BigRational S)

Rational number sum.

Parameters:

R - BigRational.

S - BigRational.

Returns:

R+S.

parse

public BigRational parse(java.lang.String s)

Parse rational number from String.

Specified by:

parse in interface ElemFactory<BigRational>

Parameters:

s - String.

Returns:

BigRational from s.

parse

public BigRational parse(java.io.Reader r)

Parse rational number from Reader.

Specified by:

parse in interface ElemFactory<BigRational>

Parameters:

r - Reader.

Returns:

next BigRational from r.

gcd

public BigRational gcd(BigRational S)

Rational number greatest common divisor.

Specified by:

gcd in interface RingElem<BigRational>

Parameters:

S - BigRational.

Returns:

gcd(this,S).

egcd

public BigRational[] egcd(BigRational S)

BigRational extended greatest common divisor.

Specified by:

egcd in interface RingElem<BigRational>

Parameters:

S - BigRational.

Returns:

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

ceil

public java.math.BigInteger ceil()

BigRational ceiling.

Returns:

ceiling of this.

floor

public java.math.BigInteger floor()

BigRational floor.

Returns:

floor of this.

bitLength

public long bitLength()

Returns the number of bits in the representation of this BigRational, including a sign bit. For positive BigRational, this is equivalent to num.bitLength()+den.bitLength().)

Returns:

number of bits in the representation of this BigRational, 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.

setNoDuplicatesIterator

public void setNoDuplicatesIterator()

Set the iteration algorithm to no duplicate elements.

setDuplicatesIterator

public void setDuplicatesIterator()

Set the iteration algorithm to allow duplicate elements.

iterator

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

Get a BigRational iterator.

Specified by:

iterator in interface java.lang.Iterable<BigRational>

Returns:

a iterator over all rationals.

uniqueIterator

public java.util.Iterator<BigRational> uniqueIterator()

Get a BigRational iterator with no duplicates.

Returns:

a iterator over all rationals without duplicates.