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, #to_Z

Instance Attribute Details

#a ⇒ Object

Returns the value of attribute a.



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# File 'lib/m500.rb', line 1500

def a
  @a
end

#abs1 ⇒ Object

Returns the value of attribute abs1.



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# File 'lib/m500.rb', line 1500

def abs1
  @abs1
end

#b ⇒ Object

Returns the value of attribute b.



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# File 'lib/m500.rb', line 1500

def b
  @b
end

#deltaIter ⇒ Object

Returns the value of attribute deltaIter.



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# File 'lib/m500.rb', line 1500

def deltaIter
  @deltaIter
end

#denominator ⇒ Object

Returns the value of attribute denominator.



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# File 'lib/m500.rb', line 1500

def denominator
  @denominator
end

#numerator ⇒ Object

Returns the value of attribute numerator.



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# File 'lib/m500.rb', line 1500

def numerator
  @numerator
end

Class Method Details

.new!(a, b = 1) ⇒ Object 



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# File 'lib/m500.rb', line 1465

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 



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# File 'lib/m500.rb', line 1620

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

#*(a) ⇒ Object 



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# File 'lib/m500.rb', line 1554

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 



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# File 'lib/m500.rb', line 1597

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 



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# File 'lib/m500.rb', line 1506

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 



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# File 'lib/m500.rb', line 1530

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 



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# File 'lib/m500.rb', line 1579

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 



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# File 'lib/m500.rb', line 1653

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 



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# File 'lib/m500.rb', line 1631

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 



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# File 'lib/m500.rb', line 1642

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 



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# File 'lib/m500.rb', line 1628

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

#coerce(other) ⇒ Object 



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# File 'lib/m500.rb', line 1684

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 



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# File 'lib/m500.rb', line 1624

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

#hash ⇒ Object 



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# File 'lib/m500.rb', line 1758

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

#inspect ⇒ Object 



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# File 'lib/m500.rb', line 1755

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) 


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# File 'lib/m500.rb', line 1693

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

#q2Dec(remainder) ⇒ Object 



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# File 'lib/m500.rb', line 1714

def q2Dec(remainder)
  maxcount =1000
  kmcount = 0
  ret = nil
  until (@remainders.member?(remainder) and @remainders.index(remainder)!= 0) or (kmcount > maxcount + 100) do    # =8= KM
    break if remainder == 0
    @remainders << remainder
    @reg2 << remainder.div(@denominator.to_i)
    remainder = remainder.remainder(@denominator.to_i)*10 
    kmcount += 1   # =8= KM
  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,"[")
    @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) # =8= KM
    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) # =8= KM
    end
  end
  eval(ret)
end

#setdelta ⇒ Object 



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# File 'lib/m500.rb', line 1503

def setdelta
  @setdelta = true
end

#succ ⇒ Object 



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# File 'lib/m500.rb', line 1681

def succ
  self + @@delta
end

#to_Dec ⇒ Object 



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# File 'lib/m500.rb', line 1705

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

#to_f ⇒ Object 



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

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

#to_Frac ⇒ Object 



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# File 'lib/m500.rb', line 1702

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

#to_i ⇒ Object 



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# File 'lib/m500.rb', line 1696

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

#to_K ⇒ Object 



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# File 'lib/m500.rb', line 1711

def to_K
  Kettenbruch(self.to_Frac)
end

#to_s ⇒ Object 



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# File 'lib/m500.rb', line 1748

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

#to_s! ⇒ Object 



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# File 'lib/m500.rb', line 1745

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

#to_sgml ⇒ Object 



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# File 'lib/m500.rb', line 1462

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

#to_Sig ⇒ Object 



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# File 'lib/m500.rb', line 1708

def to_Sig
  Sigma(self)
end