Class: Quotient

Inherits:
Numeric show all
Includes:
SGML
Defined in:
lib/m500.rb

Constant Summary collapse

@@delta = 
0

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from SGML

#sgml_id, #tog_sgml_id

Methods inherited from Numeric

#irrational?, #rational?, #sgml_id, #to_N, #to_N0, #to_Q, #to_R

Instance Attribute Details

#a ⇒ Object

Returns the value of attribute a.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def a
  @a
end

#abs1 ⇒ Object

Returns the value of attribute abs1.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def abs1
  @abs1
end

#b ⇒ Object

Returns the value of attribute b.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def b
  @b
end

#deltaIter ⇒ Object

Returns the value of attribute deltaIter.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def deltaIter
  @deltaIter
end

#denominator ⇒ Object

Returns the value of attribute denominator.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def denominator
  @denominator
end

#numerator ⇒ Object

Returns the value of attribute numerator.



1570
1571
1572
 
# File 'lib/m500.rb', line 1570

def numerator
  @numerator
end

Class Method Details

.new!(a, b = 1) ⇒ Object 



1535
1536
1537
1538
1539
1540
1541
 
# File 'lib/m500.rb', line 1535

def Quotient.new!(a, b = 1)
  if a.kind_of?(Quotient) && b == 1
    a
  else
    new(a, b)
  end
end

Instance Method Details

#%(other) ⇒ Object 



1690
1691
1692
1693
 
# File 'lib/m500.rb', line 1690

def % (other)
  value = (self / other).to_i
  return self - other * value
end

#*(a) ⇒ Object 



1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
 
# File 'lib/m500.rb', line 1624

def * (a)
  if a == 0 or ( @numerator == 0 and @denominator == 1)
    return Quotient(0,1)
  elsif a.kind_of?(Quotient)
    abs = @abs1 * a.abs1
    num = @numerator * a.numerator
    den = @denominator * a.denominator
    Quotient(num*abs, den)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    naught
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity
  elsif (a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)) 
    if a ==1 then
      self
    else
      self * Quotient(a, 1)
    end
  elsif a.kind_of?(Float)
    self * a.to_Q
  else
    x, y = a.coerce(self)
    x * y
  end
end

#**(other) ⇒ Object 



1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
 
# File 'lib/m500.rb', line 1667

def ** (other)
  if other.kind_of?(Quotient)
    Float(self) ** other
  elsif other.kind_of?(Integer)
    if other > 0
      num = @numerator ** other
      den = @denominator ** other
    elsif other < 0
      num = @denominator ** -other
      den = @numerator ** -other
    elsif other == 0
      num = 1
      den = 1
    end
    tmp = Quotient.new!(num, den)
    Quotient(tmp.numerator,tmp.denominator)
  elsif other.kind_of?(Float)
    Float(self) ** other
  else
    x, y = other.coerce(self)
    x ** y
  end
end

#+(a) ⇒ Object 



1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
 
# File 'lib/m500.rb', line 1576

def + (a)
  if a == 0
    return self
  elsif @numerator == 0 and @denominator == 1
    return a.to_Q
  elsif a.kind_of?(Fraction)
    self + a.to_Q 
  elsif a.kind_of?(Quotient)
    num = (@numerator*@abs1) * (a.denominator)
    num_a = (a.numerator*a.abs1) * @denominator
    Quotient(num + num_a, @denominator * a.denominator)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    self
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity
  elsif (a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum))
    self + Quotient(a, 1)
  elsif a.kind_of?(Float)
    Float(self) + a
  else
    x, y = a.coerce(self)
    x + y
  end
end

#-(a) ⇒ Object 



1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
 
# File 'lib/m500.rb', line 1600

def - (a)
  if a == 0
    return self
  elsif @numerator == 0 and @denominator == 1
    return a.to_Q
  else
    if a.kind_of?(Quotient)
      num = (@numerator*@abs1) * (a.denominator)
      num_a = (a.numerator*a.abs1) * @denominator
      Quotient(num - num_a, @denominator * a.denominator)
    elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass) or a == 0
      self
    elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
      infinity*(-1)
    elsif (a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)) 
      self - Quotient.new!(a, 1)
    elsif a.kind_of?(Float)
      Float(self) - a
    else
      x, y = a.coerce(self)
      x - y
    end
  end
end

#/(a) ⇒ Object 



1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
 
# File 'lib/m500.rb', line 1649

def / (a)
  if (@numerator == 0 and @denominator == 1)
    return Quotient(0,1)
  elsif a.kind_of?(Quotient)
    abs = @abs1 * a.abs1
    num = @numerator * a.denominator
    den = @denominator * a.numerator
    Quotient(num*abs, den)
  elsif a.kind_of?(Integer)
    raise ZeroDivisionError, "division by zero" if a == 0
    self / Quotient.new!(a, 1)
  elsif a.kind_of?(Float)
    Float(self) / a
  else
    x, y = a.coerce(self)
    x / y
  end
end

#<=>(other) ⇒ Object 



1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
 
# File 'lib/m500.rb', line 1723

def <=> (other)
  if @setdelta then
    @@delta = Quotient(((other - self).abs)/@deltaIter) if (other.abs1 == 1 and self.abs1 == 1) or  (other.abs1 == -1 and self.abs1 == -1)
    @@delta = Quotient((Quotient(other.numerator,other.denominator) + Quotient(self.numerator,self.denominator))/@deltaIter) if (other.abs1 == 1 and self.abs1 == -1) or  (other.abs1 == -1 and self.abs1 == 1)
  end
  @setdelta = false
  if other.kind_of?(Quotient)
    num = (@numerator*@abs1) * other.denominator
    num_o = (other.numerator*other.abs1) * @denominator
    v = num- num_o
    if v > 0
      return 1
    elsif v < 0
      return  -1
    else
  return 0
    end
  elsif other.kind_of?(Integer)
    return self <=> Quotient.new!(other, 1)
  elsif other.kind_of?(Float)
    return Float(self) <=> other
  elsif defined? other.coerce
    x, y = other.coerce(self)
    return x <=> y
  else
    return nil
  end
end

#==(other) ⇒ Object 



1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
 
# File 'lib/m500.rb', line 1701

def == (other)
  if other.kind_of?(Quotient)
    @numerator == other.numerator and @denominator == other.denominator
  elsif other.kind_of?(Integer)
    self == Quotient.new!(other, 1)
  elsif other.kind_of?(Float)
    Float(self) == other
  else
    other.to_i == self.to_i
  end
end

#===(other) ⇒ Object 



1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
 
# File 'lib/m500.rb', line 1712

def === (other)
  if other.kind_of?(Quotient)
    @a == other.a and @b == other.b
    return 1
  elsif other.kind_of?(Quotient)
    @numerator == other.numerator and @denominator == other.denominator
    return -1
  else
    return 0
  end
end

#abs ⇒ Object 



1698
1699
1700
 
# File 'lib/m500.rb', line 1698

def abs
  @abs1 = -1 ? Quotient.new!(@numerator, @denominator)   : self
end

#coerce(other) ⇒ Object 



1754
1755
1756
1757
1758
1759
1760
1761
1762
 
# File 'lib/m500.rb', line 1754

def coerce(other)
  if Natural === other or Counting === other or Zahlen === other
    [Quotient(other,1),self]
  elsif Fixnum === other
    [other, self.to_f]
  else
    [Float(other),self.to_f]
  end
end

#diavmod(other) ⇒ Object 



1694
1695
1696
1697
 
# File 'lib/m500.rb', line 1694

def diavmod(other)
  value = (self / other).to_i
  return value, self - other * value
end

#hash ⇒ Object 



1830
1831
1832
 
# File 'lib/m500.rb', line 1830

def hash
  @numerator.hash ^ @denominator.hash ^ @abs.hash
end

#inspect ⇒ Object 



1827
1828
1829
 
# File 'lib/m500.rb', line 1827

def inspect
  @abs1 == -1 ?  sprintf("Quotient(-%s, %s)", @numerator.inspect, @denominator.inspect) :     sprintf("Quotient(%s, %s)", @numerator.inspect, @denominator.inspect)
end

#is_0? ⇒ Boolean

Returns:

  • (Boolean) 


1763
1764
1765
 
# File 'lib/m500.rb', line 1763

def is_0?
  @numerator === 0 and  @denominator === 1 ? true : false
end

#q2Dec(remainder) ⇒ Object 



1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
 
# File 'lib/m500.rb', line 1787

def q2Dec(remainder)
  maxcount =1000
  kmcount = 0
  ret = nil
  until (@remainders.member?(remainder) and @remainders.index(remainder)!= 0) or (kmcount > maxcount + 100) do 
    break if remainder == 0
    @remainders << remainder
    @reg2 << remainder.div(@denominator.to_i)
    remainder = remainder.remainder(@denominator.to_i)*10 
    kmcount += 1 
  end
 @reg2.shift
  if remainder == 0
    if @abs1 ==1 then
      ret = "Decimal('#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}')"
    elsif @abs1 == -1
      ret = "Decimal('-#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}')"
    end
  else
    @reg2.insert(@remainders.find_index(remainder)-1,"[")  unless (kmcount > maxcount + 100)
    if @abs1 ==1 then
      ret = "Decimal('#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}]')" unless (kmcount > maxcount + 100)
      ret = "Decimal('#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}[0]')" if (kmcount > maxcount + 100)
    elsif @abs1 == -1
      ret = "Decimal('-#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}]')" unless (kmcount > maxcount + 100)
      ret = "Decimal('#{@numerator.div(@denominator)}#{Decimal::decimalSeparator}#{@reg2.join}[0]')" if (kmcount > maxcount + 100)
    end
  end
  eval(ret)
end

#setdelta ⇒ Object 



1573
1574
1575
 
# File 'lib/m500.rb', line 1573

def setdelta
  @setdelta = true
end

#succ ⇒ Object 



1751
1752
1753
 
# File 'lib/m500.rb', line 1751

def succ
  self + @@delta
end

#to_Dec ⇒ Object 



1775
1776
1777
 
# File 'lib/m500.rb', line 1775

def to_Dec
  @to_Dec ||= q2Dec(@numerator.remainder(@denominator))
end

#to_f ⇒ Object 



1769
1770
1771
 
# File 'lib/m500.rb', line 1769

def to_f
  @numerator.to_f/@denominator.to_f
end

#to_Frac ⇒ Object 



1772
1773
1774
 
# File 'lib/m500.rb', line 1772

def to_Frac
  self >= 0 ? Fraction(Zahlen(@numerator),Natural(@denominator),1) : Fraction(Zahlen(@numerator),Natural(@denominator),-1)
end

#to_i ⇒ Object 



1766
1767
1768
 
# File 'lib/m500.rb', line 1766

def to_i
  Integer(@numerator.div(@denominator))
end

#to_K ⇒ Object 



1781
1782
1783
 
# File 'lib/m500.rb', line 1781

def to_K
  Kettenbruch(self.to_Frac)
end

#to_s ⇒ Object 



1820
1821
1822
1823
1824
1825
1826
 
# File 'lib/m500.rb', line 1820

def to_s
  if @b == 1
    (@a*@abs1).to_s
  else
    "#{@numerator*@abs1}/#{@denominator}"
  end
end

#to_s! ⇒ Object 



1817
1818
1819
 
# File 'lib/m500.rb', line 1817

def to_s!
  "Quotient(#{(@a*@abs1).to_s},#{@b.to_s})"
end

#to_sgml ⇒ Object 



1532
1533
1534
 
# File 'lib/m500.rb', line 1532

def to_sgml
  "<mfrac #{sgml_id}class='quotient'><mn>#{@numerator*@abs1}</mn> <mn>#{@denominator}</mn></mfrac>"
end

#to_Sig ⇒ Object 



1778
1779
1780
 
# File 'lib/m500.rb', line 1778

def to_Sig
  Sigma(self)
end

#to_Z ⇒ Object 



1784
1785
1786
 
# File 'lib/m500.rb', line 1784

def to_Z
  self.denominator == 1 ? Zahlen(self.numerator) : emptySet
end