Package cc.redberry.rings

Class ImageRing<F,​I>

java.lang.Object
cc.redberry.rings.ImageRing<F,​I>
All Implemented Interfaces:
IParser<I>, Stringifiable<I>, Ring<I>, Serializable, Iterable<I>, Comparator<I>
Direct Known Subclasses:
MultipleFieldExtension
public class ImageRing<F,​I>
extends Object
implements Ring<I>
A ring obtained via isomorphism specified by image(Object) and inverse(Object) functions.
See Also:
Serialized Form

  • Field Details

    • ring

      public final Ring<F> ring
      the ring

    • imageFunc

      public final Function<F,​I> imageFunc

    • inverseFunc

      public final Function<I,​F> inverseFunc

  • Constructor Details

  • Method Details

    • image

      public I image​(F el)

    • image

      public I[] image​(F[] el)

    • inverse

      public F inverse​(I el)

    • inverse

      public F[] inverse​(I[] el)

    • isField

      public boolean isField()
      Description copied from interface: Ring
      Returns whether this ring is a field
      Specified by:
      isField in interface Ring<F>
      Returns:
      whether this ring is a field

    • isEuclideanRing

      public boolean isEuclideanRing()
      Description copied from interface: Ring
      Returns whether this ring is a Euclidean ring
      Specified by:
      isEuclideanRing in interface Ring<F>
      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
      Specified by:
      cardinality in interface Ring<F>
      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
      Specified by:
      characteristic in interface Ring<F>
      Returns:
      characteristic of this ring

    • isPerfectPower

      public boolean isPerfectPower()
      Description copied from interface: Ring
      Returns whether the cardinality is a perfect power (p^k with k > 1)
      Specified by:
      isPerfectPower in interface Ring<F>
      Returns:
      whether the cardinality is a perfect power (p^k with k > 1)

    • perfectPowerBase

      public BigInteger perfectPowerBase()
      Description copied from interface: Ring
      Returns base so that cardinality == base^exponent or null if cardinality is not finite
      Specified by:
      perfectPowerBase in interface Ring<F>
      Returns:
      base so that cardinality == base^exponent or null if cardinality is not finite

    • perfectPowerExponent

      public BigInteger perfectPowerExponent()
      Description copied from interface: Ring
      Returns exponent so that cardinality == base^exponent or null if cardinality is not finite
      Specified by:
      perfectPowerExponent in interface Ring<F>
      Returns:
      exponent so that cardinality == base^exponent or null if cardinality is not finite

    • add

      public I add​(I a, I b)
      Description copied from interface: Ring
      Add two elements
      Specified by:
      add in interface Ring<F>
      Parameters:
      a - the first element
      b - the second element
      Returns:
      a + b

    • subtract

      public I subtract​(I a, I b)
      Description copied from interface: Ring
      Subtracts b from a
      Specified by:
      subtract in interface Ring<F>
      Parameters:
      a - the first element
      b - the second element
      Returns:
      a - b

    • multiply

      public I multiply​(I a, I b)
      Description copied from interface: Ring
      Multiplies two elements
      Specified by:
      multiply in interface Ring<F>
      Parameters:
      a - the first element
      b - the second element
      Returns:
      a * b

    • negate

      public I negate​(I element)
      Description copied from interface: Ring
      Negates the given element
      Specified by:
      negate in interface Ring<F>
      Parameters:
      element - the ring element
      Returns:
      -val

    • increment

      public I increment​(I element)
      Description copied from interface: Ring
      Returns element + 1
      Specified by:
      increment in interface Ring<F>
      Parameters:
      element - the element
      Returns:
      element + 1

    • decrement

      public I decrement​(I element)
      Description copied from interface: Ring
      Returns element - 1
      Specified by:
      decrement in interface Ring<F>
      Parameters:
      element - the element
      Returns:
      element - 1

    • add

      public I add​(I... elements)
      Description copied from interface: Ring
      Total of the array of elements
      Specified by:
      add in interface Ring<F>
      Parameters:
      elements - elements to sum
      Returns:
      sum of the array

    • multiply

      public I multiply​(I... elements)
      Description copied from interface: Ring
      Multiplies the array of elements
      Specified by:
      multiply in interface Ring<F>
      Parameters:
      elements - the elements
      Returns:
      product of the array

    • abs

      public I abs​(I el)
      Description copied from interface: Ring
      Returns the abs value of element (no copy)
      Specified by:
      abs in interface Ring<F>

    • copy

      public I copy​(I element)
      Description copied from interface: Ring
      Makes a deep copy of the specified element (for immutable instances the same reference returned).
      Specified by:
      copy in interface Ring<F>
      Parameters:
      element - the element
      Returns:
      deep copy of specified element

    • divideAndRemainder

      public I[] divideAndRemainder​(I dividend, I divider)
      Description copied from interface: Ring
      Returns quotient and remainder of dividend / divider
      Specified by:
      divideAndRemainder in interface Ring<F>
      Parameters:
      dividend - the dividend
      divider - the divider
      Returns:
      {quotient, remainder}

    • quotient

      public I quotient​(I dividend, I divider)
      Description copied from interface: Ring
      Returns the quotient of dividend / divider
      Specified by:
      quotient in interface Ring<F>
      Parameters:
      dividend - the dividend
      divider - the divider
      Returns:
      the quotient of dividend / divider

    • remainder

      public I remainder​(I dividend, I divider)
      Description copied from interface: Ring
      Returns the remainder of dividend / divider
      Specified by:
      remainder in interface Ring<F>
      Parameters:
      dividend - the dividend
      divider - the divider
      Returns:
      the remainder of dividend / divider

    • reciprocal

      public I reciprocal​(I element)
      Description copied from interface: Ring
      Gives the inverse element element ^ (-1)
      Specified by:
      reciprocal in interface Ring<F>
      Parameters:
      element - the element
      Returns:
      element ^ (-1)

    • getZero

      public I getZero()
      Description copied from interface: Ring
      Returns zero element of this ring
      Specified by:
      getZero in interface Ring<F>
      Returns:
      0

    • getOne

      public I getOne()
      Description copied from interface: Ring
      Returns unit element of this ring (one)
      Specified by:
      getOne in interface Ring<F>
      Returns:
      1

    • isZero

      public boolean isZero​(I element)
      Description copied from interface: Ring
      Tests whether specified element is zero
      Specified by:
      isZero in interface Ring<F>
      Parameters:
      element - the ring element
      Returns:
      whether specified element is zero

    • isOne

      public boolean isOne​(I element)
      Description copied from interface: Ring
      Tests whether specified element is one (exactly)
      Specified by:
      isOne in interface Ring<F>
      Parameters:
      element - the ring element
      Returns:
      whether specified element is exactly one
      See Also:
      Ring.isUnit(Object)

    • isUnit

      public boolean isUnit​(I element)
      Description copied from interface: Ring
      Tests whether specified element is a ring unit
      Specified by:
      isUnit in interface Ring<F>
      Parameters:
      element - the ring element
      Returns:
      whether specified element is a ring unit
      See Also:
      Ring.isOne(Object)

    • valueOf

      public I valueOf​(long val)
      Description copied from interface: Ring
      Returns ring element associated with specified long
      Specified by:
      valueOf in interface Ring<F>
      Parameters:
      val - machine integer
      Returns:
      ring element associated with specified long

    • valueOfBigInteger

      public I valueOfBigInteger​(BigInteger val)
      Description copied from interface: Ring
      Returns ring element associated with specified integer
      Specified by:
      valueOfBigInteger in interface Ring<F>
      Parameters:
      val - integer
      Returns:
      ring element associated with specified integer

    • valueOf

      public I valueOf​(I 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).
      Specified by:
      valueOf in interface Ring<F>
      Parameters:
      val - some element from any ring
      Returns:
      this ring element associated with specified val

    • iterator

      public Iterator<I> iterator()
      Description copied from interface: Ring
      Returns iterator over ring elements (for finite rings, otherwise throws exception)
      Specified by:
      iterator in interface Iterable<F>
      Specified by:
      iterator in interface Ring<F>

    • gcd

      public I gcd​(I a, I b)
      Description copied from interface: Ring
      Returns the greatest common divisor of two elements
      Specified by:
      gcd in interface Ring<F>
      Parameters:
      a - the first element
      b - the second element
      Returns:
      gcd

    • extendedGCD

      public I[] extendedGCD​(I a, I b)
      Description copied from interface: Ring
      Returns array of [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b)
      Specified by:
      extendedGCD in interface Ring<F>

    • lcm

      public I lcm​(I a, I b)
      Description copied from interface: Ring
      Returns the least common multiple of two elements
      Specified by:
      lcm in interface Ring<F>
      Parameters:
      a - the first element
      b - the second element
      Returns:
      lcm

    • gcd

      public I gcd​(I... elements)
      Description copied from interface: Ring
      Returns greatest common divisor of specified elements
      Specified by:
      gcd in interface Ring<F>
      Parameters:
      elements - the elements
      Returns:
      gcd

    • gcd

      public I gcd​(Iterable<I> elements)
      Description copied from interface: Ring
      Returns greatest common divisor of specified elements
      Specified by:
      gcd in interface Ring<F>
      Parameters:
      elements - the elements
      Returns:
      gcd

    • signum

      public int signum​(I 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)
      Specified by:
      signum in interface Ring<F>
      Parameters:
      element - the element
      Returns:
      -1 if element < 0, 0 if element == 0 and 1 otherwise

    • factorSquareFree

      public FactorDecomposition<I> factorSquareFree​(I element)
      Description copied from interface: Ring
      Square-free factorization of specified element
      Specified by:
      factorSquareFree in interface Ring<F>

    • factor

      public FactorDecomposition<I> factor​(I element)
      Description copied from interface: Ring
      Factor specified element
      Specified by:
      factor in interface Ring<F>

    • parse

      public I parse​(String string)
      Description copied from interface: Ring
      Parse string into ring element
      Specified by:
      parse in interface IParser<F>
      Specified by:
      parse in interface Ring<F>
      Parameters:
      string - string
      Returns:
      ring element
      See Also:
      Coder

    • pow

      public I pow​(I base, int exponent)
      Description copied from interface: Ring
      Returns base in a power of exponent (non negative)
      Specified by:
      pow in interface Ring<F>
      Parameters:
      base - base
      exponent - exponent (non negative)
      Returns:
      base in a power of exponent

    • pow

      public I pow​(I base, long exponent)
      Description copied from interface: Ring
      Returns base in a power of exponent (non negative)
      Specified by:
      pow in interface Ring<F>
      Parameters:
      base - base
      exponent - exponent (non negative)
      Returns:
      base in a power of exponent

    • pow

      public I pow​(I base, BigInteger exponent)
      Description copied from interface: Ring
      Returns base in a power of exponent (non negative)
      Specified by:
      pow in interface Ring<F>
      Parameters:
      base - base
      exponent - exponent (non negative)
      Returns:
      base in a power of exponent

    • factorial

      public I factorial​(long num)
      Description copied from interface: Ring
      Gives a product of valueOf(1) * valueOf(2) * .... * valueOf(num)
      Specified by:
      factorial in interface Ring<F>
      Parameters:
      num - the number
      Returns:
      valueOf(1) * valueOf(2) * .... * valueOf(num)

    • randomElement

      public I randomElement​(org.apache.commons.math3.random.RandomGenerator rnd)
      Description copied from interface: Ring
      Returns a random element from this ring
      Specified by:
      randomElement in interface Ring<F>
      Parameters:
      rnd - the source of randomness
      Returns:
      random element from this ring

    • compare

      public int compare​(I o1, I o2)
      Specified by:
      compare in interface Comparator<F>

    • equals

      public boolean equals​(Object o)
      Specified by:
      equals in interface Comparator<F>
      Overrides:
      equals in class Object

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object