Class IntegersZp

    • 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
      • 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)
      • 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)
      • 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
      • 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
      • 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