Integers (rings 2.5.7 API)

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 and Description

static Integers Integers
The ring of integers (Z)

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

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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, BigInteger exponent)` Returns `base` in a power of `exponent` (non negative)
`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)
`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(BigInteger val)` Converts a value from other ring to this ring.
`BigInteger`	`valueOf(long val)` Returns ring element associated with specified `long`
`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 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 java.util.Comparator
comparing, comparing, comparingDouble, comparingInt, comparingLong, naturalOrder, nullsFirst, nullsLast, reversed, reverseOrder, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable
forEach, spliterator

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

Class Integers

Field Summary

Method Summary

Methods inherited from class cc.redberry.rings.ARing

Methods inherited from class java.lang.Object

Methods inherited from interface cc.redberry.rings.Ring

Methods inherited from interface java.util.Comparator

Methods inherited from interface java.lang.Iterable

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

Field Detail

Integers

Method Detail

isField

isEuclideanRing

cardinality

characteristic

isUnit

add

subtract

negate

multiply

divideAndRemainder

remainder

reciprocal

pow

pow

pow

gcd

factorSquareFree

factor

valueOf

valueOf

getNegativeOne

isMinusOne

signum

abs

toString

iterator

binomial

readResolve

clone

equals

hashCode

getZero

getOne

isZero

isOne

parse

compare

createArray

createArray2d

createArray2d

valueOfBigInteger

copy