IntegersZp (rings 2.5.7 API)

java.lang.Object
- cc.redberry.rings.ARing<BigInteger>
- - cc.redberry.rings.IntegersZp

All Implemented Interfaces:

IParser<BigInteger>, Stringifiable<BigInteger>, Ring<BigInteger>, Serializable, Iterable<BigInteger>, Comparator<BigInteger>
```
public final class IntegersZp
extends ARing<BigInteger>
```
Ring of integers modulo some modulus.

Since:

1.0

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

BigInteger modulus
The modulus.

Fields
Modifier and Type	Field and Description
`BigInteger`	`modulus` The modulus.

Constructor Summary

Constructors
Constructor and Description

IntegersZp(BigInteger modulus)
Creates Zp ring for specified modulus.

IntegersZp(long modulus)
Creates Zp ring for specified modulus.

Constructors
Constructor and Description
`IntegersZp(BigInteger modulus)` Creates Zp ring for specified modulus.
`IntegersZp(long modulus)` Creates Zp ring for specified modulus.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`BigInteger`	`add(BigInteger a, BigInteger b)` Add two elements
`IntegersZp64`	`asMachineRing()` Converts to a `IntegersZp64`
`IntegersZp64`	`asZp64()` Returns machine integer ring or null if modulus is larger than `long`
`BigInteger`	`cardinality()` Returns the number of elements in this ring (cardinality) or null if ring is infinite
`BigInteger`	`characteristic()` Returns characteristic of this ring
`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`	`divide(BigInteger a, BigInteger b)`
`BigInteger[]`	`divideAndRemainder(BigInteger a, BigInteger b)` Returns quotient and remainder of `dividend / divider`
`boolean`	`equals(Object o)`
`FactorDecomposition<BigInteger>`	`factor(BigInteger element)` Factor specified element
`FactorDecomposition<BigInteger>`	`factorSquareFree(BigInteger element)` Square-free factorization of specified element
`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`	`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`	`modulus(BigInteger val)` Returns `val mod this.modulus`
`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
`IntegersZp`	`perfectPowerBaseDomain()` Returns ring for `ARing.perfectPowerBase()` or `this` if modulus is not a perfect power
`BigInteger`	`randomElement(org.apache.commons.math3.random.RandomGenerator rnd)` Returns a random element from this ring
`BigInteger`	`reciprocal(BigInteger element)` Gives the inverse element `element ^ (-1)`
`BigInteger`	`remainder(BigInteger a, BigInteger b)` Returns the remainder of `dividend / divider`
`BigInteger`	`subtract(BigInteger a, BigInteger b)` Subtracts `b` from `a`
`BigInteger`	`symmetricForm(BigInteger value)` Converts `value` to a symmetric representation of Zp
`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
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface cc.redberry.rings.Ring
abs, add, addMutable, createArray, createArray, createArray, createZeroesArray, createZeroesArray2d, decrement, divideExact, divideExactMutable, divideOrNull, extendedGCD, factorial, fillZeros, firstBezoutCoefficient, gcd, gcd, gcd, getNegativeOne, increment, isFinite, isFiniteField, isMinusOne, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, multiplyMutable, negateMutable, pow, pow, pow, quotient, randomElement, randomElementTree, randomElementTree, randomNonZeroElement, setToValueOf, signum, 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
  - modulus
```
public final BigInteger modulus
```
    The modulus.
- Constructor Detail
  - IntegersZp
```
public IntegersZp(BigInteger modulus)
```
    Creates Zp ring for specified modulus.
    
    Parameters:
    
    modulus - the modulus
  - IntegersZp
```
public IntegersZp(long modulus)
```
    Creates Zp ring for specified modulus.
    
    Parameters:
    
    modulus - the modulus
- 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)
  - modulus
```
public BigInteger modulus(BigInteger val)
```
    Returns val mod this.modulus
    
    Parameters:
    
    val - the integer
    
    Returns:
    
    val mod this.modulus
  - symmetricForm
```
public BigInteger symmetricForm(BigInteger value)
```
    Converts value to a symmetric representation of Zp
    
    Parameters:
    
    value - field element
    
    Returns:
    
    value in a symmetric representation of Zp
  - asMachineRing
```
public IntegersZp64 asMachineRing()
```
    Converts to a IntegersZp64
  - 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}
  - divide
```
public BigInteger divide(BigInteger a,
                         BigInteger b)
```
  - 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)
  - 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
  - randomElement
```
public BigInteger randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Description copied from interface: Ring
    
    Returns a random element from this ring
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random element from this ring
  - iterator
```
public Iterator<BigInteger> iterator()
```
    Description copied from interface: Ring
    
    Returns iterator over ring elements (for finite rings, otherwise throws exception)
  - perfectPowerBaseDomain
```
public IntegersZp perfectPowerBaseDomain()
```
    Returns ring for ARing.perfectPowerBase() or this if modulus is not a perfect power
    
    Returns:
    
    ring for ARing.perfectPowerBase() or this if modulus is not a perfect power
  - asZp64
```
public IntegersZp64 asZp64()
```
    Returns machine integer ring or null if modulus is larger than long
    
    Returns:
    
    machine integer ring or null if modulus is larger than long
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - equals
```
public boolean equals(Object o)
```
    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 IntegersZp

Field Summary

Constructor 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

modulus

Constructor Detail

IntegersZp

IntegersZp

Method Detail

isField

isEuclideanRing

cardinality

characteristic

isUnit

modulus

symmetricForm

asMachineRing

add

subtract

negate

multiply

divideAndRemainder

divide

remainder

reciprocal

factorSquareFree

factor

valueOf

valueOf

randomElement

iterator

perfectPowerBaseDomain

asZp64

toString

equals

hashCode

getZero

getOne

isZero

isOne

parse

compare

createArray

createArray2d

createArray2d

valueOfBigInteger

copy