Package cc.redberry.rings

Class Rationals<E>

java.lang.Object
cc.redberry.rings.Rationals<E>
All Implemented Interfaces:
IParser<Rational<E>>, Stringifiable<Rational<E>>, Ring<Rational<E>>, Serializable, Iterable<Rational<E>>, Comparator<Rational<E>>
public final class Rationals<E>
extends Object
implements Ring<Rational<E>>
The ring of rationals (Q).
Since:
1.0
See Also:
Serialized Form

  • Field Details

    • ring

      public final Ring<E> ring
      Ring that numerator and denominator belongs to

  • Constructor Details

    • Rationals

      public Rationals​(Ring<E> ring)

  • Method Details

    • mkNumerator

      public Rational<E> mkNumerator​(E num)
      Gives rational with a given numerator and unit denominator

    • mkNumerator

      public Rational<E> mkNumerator​(long num)
      Gives rational with a given numerator and unit denominator

    • mkDenominator

      public Rational<E> mkDenominator​(E den)
      Gives rational with a given denominator and unit numerator

    • mkDenominator

      public Rational<E> mkDenominator​(long den)
      Gives rational with a given denominator and unit numerator

    • mk

      public Rational<E> mk​(E num, E den)
      Gives rational with a given numerator and denominator

    • mk

      public Rational<E> mk​(long num, long den)
      Gives rational with a given numerator and denominator

    • isField

      public boolean isField()
      Description copied from interface: Ring
      Returns whether this ring is a field
      Specified by:
      isField in interface Ring<E>
      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<E>
      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<E>
      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<E>
      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<E>
      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<E>
      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<E>
      Returns:
      exponent so that cardinality == base^exponent or null if cardinality is not finite

    • add

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

    • subtract

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

    • multiply

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

    • negate

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

    • signum

      public int signum​(Rational<E> 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<E>
      Parameters:
      element - the element
      Returns:
      -1 if element < 0, 0 if element == 0 and 1 otherwise

    • divideAndRemainder

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

    • reciprocal

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

    • gcd

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

    • factorSquareFree

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

    • factor

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

    • getZero

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

    • getOne

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

    • isZero

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

    • isOne

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

    • isUnit

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

    • valueOf

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

    • valueOfBigInteger

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

    • copy

      public Rational<E> copy​(Rational<E> 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<E>
      Parameters:
      element - the element
      Returns:
      deep copy of specified element

    • valueOf

      public Rational<E> valueOf​(Rational<E> 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<E>
      Parameters:
      val - some element from any ring
      Returns:
      this ring element associated with specified val

    • createArray2d

      public Rational<E>[][] createArray2d​(int length)
      Description copied from interface: Ring
      Creates 2d array of ring elements of specified length
      Specified by:
      createArray2d in interface Ring<E>
      Parameters:
      length - array length
      Returns:
      2d array of ring elements of specified length

    • createArray2d

      public Rational<E>[][] createArray2d​(int m, int n)
      Description copied from interface: Ring
      Creates 2d array of ring elements of specified shape
      Specified by:
      createArray2d in interface Ring<E>
      Parameters:
      m - result length
      n - length of each array in the result
      Returns:
      2d array E[m][n]

    • compare

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

    • getNegativeOne

      public Rational<E> getNegativeOne()
      Description copied from interface: Ring
      Returns negative unit element of this ring (minus one)
      Specified by:
      getNegativeOne in interface Ring<E>
      Returns:
      -1

    • createArray

      public Rational<E>[] createArray​(int length)
      Description copied from interface: Ring
      Creates generic array of ring elements of specified length
      Specified by:
      createArray in interface Ring<E>
      Parameters:
      length - array length
      Returns:
      array of ring elements of specified length

    • randomElement

      public Rational<E> 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<E>
      Parameters:
      rnd - the source of randomness
      Returns:
      random element from this ring

    • randomElementTree

      public Rational<E> randomElementTree​(org.apache.commons.math3.random.RandomGenerator rnd)
      Description copied from interface: Ring
      If this ring has a complicated nested structure, this method guaranties that the resulting random element will reflect ring complicated structure, i.e. the result will be roughly as complicated as the ring is
      Specified by:
      randomElementTree in interface Ring<E>
      Returns:
      random element from this ring

    • iterator

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

    • equals

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

    • hashCode

      public int hashCode()
      Overrides:
      hashCode in class Object

    • toString

      public String toString​(IStringifier<Rational<E>> stringifier)
      Description copied from interface: Stringifiable
      convert this to string with the use of stringifier
      Specified by:
      toString in interface Stringifiable<E>

    • toString

      public String toString()
      Overrides:
      toString in class Object