Class BigRational

java.lang.Object
edu.jas.arith.BigRational
All Implemented Interfaces:
Rational, AbelianGroupElem<BigRational>, AbelianGroupFactory<BigRational>, Element<BigRational>, ElemFactory<BigRational>, GcdRingElem<BigRational>, MonoidElem<BigRational>, MonoidFactory<BigRational>, RingElem<BigRational>, RingFactory<BigRational>, Serializable, Comparable<BigRational>, Iterable<BigRational>
public final class BigRational extends Object implements GcdRingElem<BigRational>, RingFactory<BigRational>, Rational, Iterable<BigRational>
Immutable arbitrary-precision rational numbers. BigRational class based on BigInteger and implementing the RingElem interface. BigInteger is from java.math in the implementation. The SAC2 static methods are also provided.
See Also:

  • Field Details

    • num

      public final BigInteger num
      Numerator part of the data structure.

    • den

      public final BigInteger den
      Denominator part of the data structure.

    • ZERO

      public static final BigRational ZERO
      The Constant 0.

    • ONE

      public static final BigRational ONE
      The Constant 1.

    • HALF

      public static final BigRational HALF
      The Constant 1/2.

    • random

      private static final Random random

    • nonNegative

      private boolean nonNegative

    • duplicates

      private boolean duplicates

  • Constructor Details

    • BigRational

      protected BigRational(BigInteger n, BigInteger d)
      Constructor for a BigRational from math.BigIntegers.
      Parameters:
      n - math.BigInteger.
      d - math.BigInteger.

    • BigRational

      public BigRational(BigInteger n)
      Constructor for a BigRational from math.BigIntegers.
      Parameters:
      n - math.BigInteger.

    • BigRational

      public BigRational(BigInteger n)
      Constructor for a BigRational from jas.arith.BigIntegers.
      Parameters:
      n - edu.jas.arith.BigInteger.

    • BigRational

      public BigRational(BigInteger n, BigInteger d)
      Constructor for a BigRational from jas.arith.BigIntegers.
      Parameters:
      n - edu.jas.arith.BigInteger.
      d - edu.jas.arith.BigInteger.

    • BigRational

      public BigRational(long n, long d)
      Constructor for a BigRational from longs.
      Parameters:
      n - long.
      d - long.

    • BigRational

      public BigRational(long n)
      Constructor for a BigRational from longs.
      Parameters:
      n - long.

    • BigRational

      public BigRational()
      Constructor for a BigRational with no arguments.

    • BigRational

      public BigRational(String s) throws NumberFormatException
      Constructor for a BigRational from String.
      Parameters:
      s - String.
      Throws:
      NumberFormatException

  • Method Details

    • factory

      public BigRational factory()
      Get the corresponding element factory.
      Specified by:
      factory in interface Element<BigRational>
      Returns:
      factory for this Element.
      See Also:

    • generators

      public List<BigRational> generators()
      Get a list of the generating elements.
      Specified by:
      generators in interface ElemFactory<BigRational>
      Returns:
      list of generators for the algebraic structure.
      See Also:

    • isFinite

      public boolean isFinite()
      Is this structure finite or infinite.
      Specified by:
      isFinite in interface ElemFactory<BigRational>
      Returns:
      true if this structure is finite, else false.
      See Also:

    • copy

      public BigRational copy()
      Clone this.
      Specified by:
      copy in interface Element<BigRational>
      Returns:
      Creates and returns a copy of this Element.
      See Also:

    • copy

      public BigRational copy(BigRational c)
      Copy BigRational element c.
      Specified by:
      copy in interface ElemFactory<BigRational>
      Parameters:
      c - BigRational.
      Returns:
      a copy of c.

    • getRational

      public BigRational getRational()
      Return a BigRational approximation of this Element.
      Specified by:
      getRational in interface Rational
      Returns:
      a BigRational approximation of this.
      See Also:

    • numerator

      public BigInteger numerator()
      Get the numerator.
      Returns:
      num.

    • denominator

      public BigInteger denominator()
      Get the denominator.
      Returns:
      den.

    • toString

      public String toString()
      Get the string representation.
      Overrides:
      toString in class Object
      See Also:

    • toString

      public String toString(int n)
      Get the decimal string representation with given precision.
      Parameters:
      n - precision.
      Returns:
      decimal approximation.

    • getDecimal

      public BigDecimal getDecimal()
      Get the decimal representation.
      Returns:
      decimal.

    • doubleValue

      public double doubleValue()
      Get this as a double.
      Returns:
      this as a double
      See Also:

    • toScript

      public String toScript()
      Get a scripting compatible string representation.
      Specified by:
      toScript in interface Element<BigRational>
      Specified by:
      toScript in interface ElemFactory<BigRational>
      Returns:
      script compatible representation for this Element.
      See Also:

    • toScriptFactory

      public String toScriptFactory()
      Get a scripting compatible string representation of the factory.
      Specified by:
      toScriptFactory in interface Element<BigRational>
      Returns:
      script compatible representation for this ElemFactory.
      See Also:

    • getZERO

      public BigRational getZERO()
      Get the zero element.
      Specified by:
      getZERO in interface AbelianGroupFactory<BigRational>
      Returns:
      0 as BigRational.

    • getONE

      public BigRational getONE()
      Get the one element.
      Specified by:
      getONE in interface MonoidFactory<BigRational>
      Returns:
      1 as BigRational.

    • isCommutative

      public boolean isCommutative()
      Query if this ring is commutative.
      Specified by:
      isCommutative in interface MonoidFactory<BigRational>
      Returns:
      true.

    • isAssociative

      public boolean isAssociative()
      Query if this ring is associative.
      Specified by:
      isAssociative in interface MonoidFactory<BigRational>
      Returns:
      true.

    • isField

      public boolean isField()
      Query if this ring is a field.
      Specified by:
      isField in interface RingFactory<BigRational>
      Returns:
      true.

    • characteristic

      public BigInteger characteristic()
      Characteristic of this ring.
      Specified by:
      characteristic in interface RingFactory<BigRational>
      Returns:
      characteristic of this ring.

    • fromInteger

      public BigRational fromInteger(BigInteger a)
      Get a BigRational element from a math.BigInteger.
      Specified by:
      fromInteger in interface ElemFactory<BigRational>
      Parameters:
      a - math.BigInteger.
      Returns:
      BigRational from a.

    • fromInteger

      public BigRational fromInteger(BigInteger a)
      Get a BigRational element from a arith.BigInteger.
      Parameters:
      a - arith.BigInteger.
      Returns:
      BigRational from a.

    • valueOf

      public static BigRational valueOf(BigInteger a)
      Get a BigRational element from a math.BigInteger.
      Parameters:
      a - math.BigInteger.
      Returns:
      BigRational from a.

    • fromInteger

      public BigRational fromInteger(long a)
      Get a BigRational element from a long.
      Specified by:
      fromInteger in interface ElemFactory<BigRational>
      Parameters:
      a - long.
      Returns:
      BigRational from a.

    • valueOf

      public static BigRational valueOf(long a)
      Get a BigRational element from a long.
      Parameters:
      a - long.
      Returns:
      BigRational from a.

    • isZERO

      public boolean isZERO()
      Is BigRational zero.
      Specified by:
      isZERO in interface AbelianGroupElem<BigRational>
      Returns:
      If this is 0 then true is returned, else false.
      See Also:

    • isONE

      public boolean isONE()
      Is BigRational one.
      Specified by:
      isONE in interface MonoidElem<BigRational>
      Returns:
      If this is 1 then true is returned, else false.
      See Also:

    • isUnit

      public boolean isUnit()
      Is BigRational unit.
      Specified by:
      isUnit in interface MonoidElem<BigRational>
      Returns:
      If this is a unit then true is returned, else false.
      See Also:

    • isEntier

      public boolean isEntier()
      Is BigRational entier.
      Returns:
      If this is an integer then true is returned, else false.

    • equals

      public boolean equals(Object b)
      Comparison with any other object.
      Specified by:
      equals in interface Element<BigRational>
      Overrides:
      equals in class Object
      Parameters:
      b -
      Returns:
      true if this is equal to b, else false.
      See Also:

    • hashCode

      public int hashCode()
      Hash code for this BigRational.
      Specified by:
      hashCode in interface Element<BigRational>
      Overrides:
      hashCode in class Object
      Returns:
      the hashCode.
      See Also:

    • RNRED

      public static BigRational RNRED(BigInteger n, BigInteger d)
      Rational number reduction to lowest terms.
      Parameters:
      n - BigInteger.
      d - BigInteger.
      Returns:
      a/b ~ n/d, gcd(a,b) = 1, b > 0.

    • reduction

      public static BigRational reduction(BigInteger n, BigInteger d)
      Rational number reduction to lowest terms.
      Parameters:
      n - BigInteger.
      d - BigInteger.
      Returns:
      a/b ~ n/d, gcd(a,b) = 1, b > 0.

    • abs

      public BigRational abs()
      Rational number absolute value.
      Specified by:
      abs in interface AbelianGroupElem<BigRational>
      Returns:
      the absolute value of this.
      See Also:

    • RNABS

      public static BigRational RNABS(BigRational R)
      Rational number absolute value.
      Parameters:
      R - is a rational number.
      Returns:
      the absolute value of R.

    • compareTo

      public int compareTo(BigRational S)
      Rational number comparison.
      Specified by:
      compareTo in interface Comparable<BigRational>
      Specified by:
      compareTo in interface Element<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      SIGN(this-S).

    • RNCOMP

      public static int RNCOMP(BigRational R, BigRational S)
      Rational number comparison.
      Parameters:
      R - BigRational.
      S - BigRational.
      Returns:
      SIGN(R-S).

    • RNDEN

      public static BigInteger RNDEN(BigRational R)
      Rational number denominator.
      Parameters:
      R - BigRational.
      Returns:
      R.denominator().

    • subtract

      public BigRational subtract(BigRational S)
      Rational number difference.
      Specified by:
      subtract in interface AbelianGroupElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      this-S.

    • RNDIF

      public static BigRational RNDIF(BigRational R, BigRational S)
      Rational number difference.
      Parameters:
      R - BigRational.
      S - BigRational.
      Returns:
      R-S.

    • RNDWR

      public static void RNDWR(BigRational R, int NL)
      Rational number decimal write. R is a rational number. n is a non-negative integer. R is approximated by a decimal fraction D with n decimal digits following the decimal point and D is written in the output stream. The inaccuracy of the approximation is at most (1/2)*10**-n.
      Parameters:
      R -
      NL -

    • RNINT

      public static BigRational RNINT(BigInteger A)
      Rational number from integer.
      Parameters:
      A - BigInteger.
      Returns:
      A/1.

    • inverse

      public BigRational inverse()
      Rational number inverse.
      Specified by:
      inverse in interface MonoidElem<BigRational>
      Returns:
      1/this.
      See Also:

    • RNINV

      public static BigRational RNINV(BigRational R)
      Rational number inverse.
      Parameters:
      R - BigRational.
      Returns:
      1/R.

    • negate

      public BigRational negate()
      Rational number negative.
      Specified by:
      negate in interface AbelianGroupElem<BigRational>
      Returns:
      -this.
      See Also:

    • RNNEG

      public static BigRational RNNEG(BigRational R)
      Rational number negative.
      Parameters:
      R - BigRational.
      Returns:
      -R.

    • RNNUM

      public static BigInteger RNNUM(BigRational R)
      Rational number numerator.
      Parameters:
      R - BigRational.
      Returns:
      R.numerator().

    • multiply

      public BigRational multiply(BigRational S)
      Rational number product.
      Specified by:
      multiply in interface MonoidElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      this*S.

    • RNPROD

      public static BigRational RNPROD(BigRational R, BigRational S)
      Rational number product.
      Parameters:
      R - BigRational.
      S - BigRational.
      Returns:
      R*S.

    • divide

      public BigRational divide(BigRational S)
      Rational number quotient.
      Specified by:
      divide in interface MonoidElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      this/S.

    • RNQ

      public static BigRational RNQ(BigRational R, BigRational S)
      Rational number quotient.
      Parameters:
      R - BigRational.
      S - BigRational.
      Returns:
      R/S.

    • remainder

      public BigRational remainder(BigRational S)
      Rational number remainder.
      Specified by:
      remainder in interface MonoidElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      this-(this/S)*S

    • quotientRemainder

      public BigRational[] quotientRemainder(BigRational S)
      Quotient and remainder by division of this by S.
      Specified by:
      quotientRemainder in interface MonoidElem<BigRational>
      Parameters:
      S - a rational number
      Returns:
      [this/S, this - (this/S)*S].

    • random

      public BigRational random(int n)
      Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
      Specified by:
      random in interface ElemFactory<BigRational>
      Parameters:
      n - such that 0 ≤ A, B ≤ (2n-1).
      Returns:
      a random BigRational.

    • random

      public BigRational random(int n, Random rnd)
      Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
      Specified by:
      random in interface ElemFactory<BigRational>
      Parameters:
      n - such that 0 ≤ A, B ≤ (2n-1).
      rnd - is a source for random bits.
      Returns:
      a random BigRational.

    • RNRAND

      public static BigRational RNRAND(int NL)
      Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
      Parameters:
      NL - such that 0 ≤ A, B ≤ (2n-1).
      Returns:
      a random BigRational.

    • signum

      public int signum()
      Rational number sign.
      Specified by:
      signum in interface AbelianGroupElem<BigRational>
      Returns:
      the sign of this.
      See Also:

    • RNSIGN

      public static int RNSIGN(BigRational R)
      Rational number sign.
      Parameters:
      R - BigRational.
      Returns:
      R.signum().

    • sum

      public BigRational sum(BigRational S)
      Rational number sum.
      Specified by:
      sum in interface AbelianGroupElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      this+S.

    • RNSUM

      public static BigRational RNSUM(BigRational R, BigRational S)
      Rational number sum.
      Parameters:
      R - BigRational.
      S - BigRational.
      Returns:
      R+S.

    • parse

      public BigRational parse(String s)
      Parse rational number from String.
      Specified by:
      parse in interface ElemFactory<BigRational>
      Parameters:
      s - String.
      Returns:
      BigRational from s.

    • parse

      public BigRational parse(Reader r)
      Parse rational number from Reader.
      Specified by:
      parse in interface ElemFactory<BigRational>
      Parameters:
      r - Reader.
      Returns:
      next BigRational from r.

    • gcd

      public BigRational gcd(BigRational S)
      Rational number greatest common divisor.
      Specified by:
      gcd in interface RingElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      gcd(this,S).

    • egcd

      public BigRational[] egcd(BigRational S)
      BigRational extended greatest common divisor.
      Specified by:
      egcd in interface RingElem<BigRational>
      Parameters:
      S - BigRational.
      Returns:
      [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).

    • ceil

      public BigInteger ceil()
      BigRational ceiling.
      Returns:
      ceiling of this.

    • floor

      public BigInteger floor()
      BigRational floor.
      Returns:
      floor of this.

    • bitLength

      public long bitLength()
      Returns the number of bits in the representation of this BigRational, including a sign bit. For positive BigRational, this is equivalent to num.bitLength()+den.bitLength().)
      Returns:
      number of bits in the representation of this BigRational, including a sign bit.

    • setAllIterator

      public void setAllIterator()
      Set the iteration algorithm to all elements.

    • setNonNegativeIterator

      public void setNonNegativeIterator()
      Set the iteration algorithm to non-negative elements.

    • setNoDuplicatesIterator

      public void setNoDuplicatesIterator()
      Set the iteration algorithm to no duplicate elements.

    • setDuplicatesIterator

      public void setDuplicatesIterator()
      Set the iteration algorithm to allow duplicate elements.

    • iterator

      public Iterator<BigRational> iterator()
      Get a BigRational iterator.
      Specified by:
      iterator in interface Iterable<BigRational>
      Returns:
      a iterator over all rationals.

    • uniqueIterator

      public Iterator<BigRational> uniqueIterator()
      Get a BigRational iterator with no duplicates.
      Returns:
      a iterator over all rationals without duplicates.