Package cc.redberry.rings

Class Integers

java.lang.Object

cc.redberry.rings.ARing<BigInteger>

cc.redberry.rings.Integers

All Implemented Interfaces:

IParser<BigInteger>, Stringifiable<BigInteger>, Ring<BigInteger>, Serializable, Iterable<BigInteger>, Comparator<BigInteger>

public final class Integers
extends ARing<BigInteger>

The ring of integers (Z).

Since:

1.0

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static Integers	Integers	The ring of integers (Z)

Method Summary

Modifier and Type	Method	Description
BigInteger	abs(BigInteger el)	Returns the abs value of element (no copy)
BigInteger	add(BigInteger a, BigInteger b)	Add two elements
BigInteger	binomial(long n, long k)	Gives a binomial coefficient C(n, k)
BigInteger	cardinality()	Returns the number of elements in this ring (cardinality) or null if ring is infinite
BigInteger	characteristic()	Returns characteristic of this ring
protected Object	clone()
int	compare(BigInteger o1, BigInteger o2)
BigInteger	copy(BigInteger element)	Makes a deep copy of the specified element (for immutable instances the same reference returned).
BigInteger[]	createArray(int length)	Creates generic array of ring elements of specified length
BigInteger[][]	createArray2d(int length)	Creates 2d array of ring elements of specified length
BigInteger[][]	createArray2d(int m, int n)	Creates 2d array of ring elements of specified shape
BigInteger[]	divideAndRemainder(BigInteger a, BigInteger b)	Returns quotient and remainder of dividend / divider
boolean	equals(Object obj)
FactorDecomposition<BigInteger>	factor(BigInteger element)	Factor specified element
FactorDecomposition<BigInteger>	factorSquareFree(BigInteger element)	Square-free factorization of specified element
BigInteger	gcd(BigInteger a, BigInteger b)	Returns the greatest common divisor of two elements
BigInteger	getNegativeOne()	Returns negative unit element of this ring (minus one)
BigInteger	getOne()	Returns unit element of this ring (one)
BigInteger	getZero()	Returns zero element of this ring
int	hashCode()
boolean	isEuclideanRing()	Returns whether this ring is a Euclidean ring
boolean	isField()	Returns whether this ring is a field
boolean	isMinusOne(BigInteger bigInteger)	Tests whether specified element is minus one
boolean	isOne(BigInteger element)	Tests whether specified element is one (exactly)
boolean	isUnit(BigInteger element)	Tests whether specified element is a ring unit
boolean	isZero(BigInteger element)	Tests whether specified element is zero
Iterator<BigInteger>	iterator()	Returns iterator over ring elements (for finite rings, otherwise throws exception)
BigInteger	multiply(BigInteger a, BigInteger b)	Multiplies two elements
BigInteger	negate(BigInteger element)	Negates the given element
BigInteger	parse(String string)	Parse string into ring element
BigInteger	pow(BigInteger base, int exponent)	Returns base in a power of exponent (non negative)
BigInteger	pow(BigInteger base, long exponent)	Returns base in a power of exponent (non negative)
BigInteger	pow(BigInteger base, BigInteger exponent)	Returns base in a power of exponent (non negative)
protected Object	readResolve()
BigInteger	reciprocal(BigInteger element)	Gives the inverse element element ^ (-1)
BigInteger	remainder(BigInteger a, BigInteger b)	Returns the remainder of dividend / divider
int	signum(BigInteger element)	Returns -1 if element < 0, 0 if element == 0 and 1 if element > 0, where comparison is specified by Comparator.compare(Object, Object)
BigInteger	subtract(BigInteger a, BigInteger b)	Subtracts b from a
String	toString()
BigInteger	valueOf(long val)	Returns ring element associated with specified long
BigInteger	valueOf(BigInteger val)	Converts a value from other ring to this ring.
BigInteger	valueOfBigInteger(BigInteger val)	Returns ring element associated with specified integer

Methods inherited from class cc.redberry.rings.ARing

isPerfectPower, perfectPowerBase, perfectPowerExponent

Methods inherited from class java.lang.Object

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

Methods inherited from interface java.util.Comparator

reversed, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface cc.redberry.rings.Ring

add, addMutable, createArray, createArray, createArray, createZeroesArray, createZeroesArray2d, decrement, divideExact, divideExactMutable, divideOrNull, extendedGCD, factorial, fillZeros, firstBezoutCoefficient, gcd, gcd, increment, isFinite, isFiniteField, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, multiplyMutable, negateMutable, quotient, randomElement, randomElement, randomElementTree, randomElementTree, randomNonZeroElement, setToValueOf, subtractMutable, valueOf

Methods inherited from interface cc.redberry.rings.io.Stringifiable

toString

Field Detail

Integers

public static final Integers Integers

The ring of integers (Z)

Method Detail

isField

public boolean isField()

Description copied from interface: Ring

Returns whether this ring is a field

Returns:

whether this ring is a field

isEuclideanRing

public boolean isEuclideanRing()

Description copied from interface: Ring

Returns whether this ring is a Euclidean ring

Returns:

whether this ring is a Euclidean ring

cardinality

public BigInteger cardinality()

Description copied from interface: Ring

Returns the number of elements in this ring (cardinality) or null if ring is infinite

Returns:

the number of elements in this ring (cardinality) or null if ring is infinite

characteristic

public BigInteger characteristic()

Description copied from interface: Ring

Returns characteristic of this ring

Returns:

characteristic of this ring

isUnit

public boolean isUnit(BigInteger element)

Description copied from interface: Ring

Tests whether specified element is a ring unit

Parameters:

element - the ring element

Returns:

whether specified element is a ring unit

See Also:

Ring.isOne(Object)

add

public BigInteger add(BigInteger a,
                      BigInteger b)

Description copied from interface: Ring

Add two elements

Parameters:

a - the first element

b - the second element

Returns:

a + b

subtract

public BigInteger subtract(BigInteger a,
                           BigInteger b)

Description copied from interface: Ring

Subtracts b from a

Parameters:

a - the first element

b - the second element

Returns:

a - b

negate

public BigInteger negate(BigInteger element)

Description copied from interface: Ring

Negates the given element

Parameters:

element - the ring element

Returns:

-val

multiply

public BigInteger multiply(BigInteger a,
                           BigInteger b)

Description copied from interface: Ring

Multiplies two elements

Parameters:

a - the first element

b - the second element

Returns:

a * b

divideAndRemainder

public BigInteger[] divideAndRemainder(BigInteger a,
                                       BigInteger b)

Description copied from interface: Ring

Returns quotient and remainder of dividend / divider

Parameters:

a - the dividend

b - the divider

Returns:

{quotient, remainder}

remainder

public BigInteger remainder(BigInteger a,
                            BigInteger b)

Description copied from interface: Ring

Returns the remainder of dividend / divider

Parameters:

a - the dividend

b - the divider

Returns:

the remainder of dividend / divider

reciprocal

public BigInteger reciprocal(BigInteger element)

Description copied from interface: Ring

Gives the inverse element element ^ (-1)

Parameters:

element - the element

Returns:

element ^ (-1)

pow

public BigInteger pow(BigInteger base,
                      int exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

pow

public BigInteger pow(BigInteger base,
                      long exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

pow

public BigInteger pow(BigInteger base,
                      BigInteger exponent)

Description copied from interface: Ring

Returns base in a power of exponent (non negative)

Parameters:

base - base

exponent - exponent (non negative)

Returns:

base in a power of exponent

gcd

public final BigInteger gcd(BigInteger a,
                            BigInteger b)

Description copied from interface: Ring

Returns the greatest common divisor of two elements

Parameters:

a - the first element

b - the second element

Returns:

gcd

factorSquareFree

public FactorDecomposition<BigInteger> factorSquareFree(BigInteger element)

Description copied from interface: Ring

Square-free factorization of specified element

factor

public FactorDecomposition<BigInteger> factor(BigInteger element)

Description copied from interface: Ring

Factor specified element

valueOf

public BigInteger valueOf(BigInteger val)

Description copied from interface: Ring

Converts a value from other ring to this ring. The result is not guarantied to be a new instance (i.e. val == valueOf(val) is possible).

Parameters:

val - some element from any ring

Returns:

this ring element associated with specified val

valueOf

public BigInteger valueOf(long val)

Description copied from interface: Ring

Returns ring element associated with specified long

Parameters:

val - machine integer

Returns:

ring element associated with specified long

getNegativeOne

public BigInteger getNegativeOne()

Description copied from interface: Ring

Returns negative unit element of this ring (minus one)

Returns:

-1

isMinusOne

public boolean isMinusOne(BigInteger bigInteger)

Description copied from interface: Ring

Tests whether specified element is minus one

Parameters:

bigInteger - the ring element

Returns:

whether specified element is minus one

signum

public final int signum(BigInteger element)

Description copied from interface: Ring

Returns -1 if element < 0, 0 if element == 0 and 1 if element > 0, where comparison is specified by Comparator.compare(Object, Object)

Parameters:

element - the element

Returns:

-1 if element < 0, 0 if element == 0 and 1 otherwise

abs

public BigInteger abs(BigInteger el)

Description copied from interface: Ring

Returns the abs value of element (no copy)

toString

public String toString()

Overrides:

toString in class Object

iterator

public Iterator<BigInteger> iterator()

Description copied from interface: Ring

Returns iterator over ring elements (for finite rings, otherwise throws exception)

binomial

public BigInteger binomial(long n,
                           long k)

Gives a binomial coefficient C(n, k)

readResolve

protected Object readResolve()

clone

protected Object clone()
                throws CloneNotSupportedException

Overrides:

clone in class Object

Throws:

CloneNotSupportedException

equals

public boolean equals(Object obj)

Specified by:

equals in interface Comparator<BigInteger>

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

getZero

public final BigInteger getZero()

Description copied from interface: Ring

Returns zero element of this ring

Returns:

0

getOne

public final BigInteger getOne()

Description copied from interface: Ring

Returns unit element of this ring (one)

Returns:

1

isZero

public final boolean isZero(BigInteger element)

Description copied from interface: Ring

Tests whether specified element is zero

Parameters:

element - the ring element

Returns:

whether specified element is zero

isOne

public final boolean isOne(BigInteger element)

Description copied from interface: Ring

Tests whether specified element is one (exactly)

Parameters:

element - the ring element

Returns:

whether specified element is exactly one

See Also:

Ring.isUnit(Object)

parse

public final BigInteger parse(String string)

Description copied from interface: Ring

Parse string into ring element

Parameters:

string - string

Returns:

ring element

See Also:

Coder

compare

public final int compare(BigInteger o1,
                         BigInteger o2)

createArray

public final BigInteger[] createArray(int length)

Description copied from interface: Ring

Creates generic array of ring elements of specified length

Parameters:

length - array length

Returns:

array of ring elements of specified length

createArray2d

public final BigInteger[][] createArray2d(int length)

Description copied from interface: Ring

Creates 2d array of ring elements of specified length

Parameters:

length - array length

Returns:

2d array of ring elements of specified length

createArray2d

public final BigInteger[][] createArray2d(int m,
                                          int n)

Description copied from interface: Ring

Creates 2d array of ring elements of specified shape

Parameters:

m - result length

n - length of each array in the result

Returns:

2d array E[m][n]

valueOfBigInteger

public final BigInteger valueOfBigInteger(BigInteger val)

Description copied from interface: Ring

Returns ring element associated with specified integer

Parameters:

val - integer

Returns:

ring element associated with specified integer

copy

public BigInteger copy(BigInteger element)

Description copied from interface: Ring

Makes a deep copy of the specified element (for immutable instances the same reference returned).

Parameters:

element - the element

Returns:

deep copy of specified element