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 Details

    • Integers

      public static final Integers Integers
      The ring of integers (Z)

  • Method Details

    • 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