Class: Fraction

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

Overview

Mixed fraction

Constant Summary collapse

@@fractionSeparator =

“+”

" "

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_Frac, #to_N, #to_N0, #to_R, #to_Z

Instance Attribute Details

#a ⇒ Object

Returns the value of attribute a.



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# File 'lib/m500.rb', line 2202

def a
  @a
end

#absolute ⇒ Object

Returns the value of attribute absolute.



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# File 'lib/m500.rb', line 2202

def absolute
  @absolute
end

#b ⇒ Object

Returns the value of attribute b.



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# File 'lib/m500.rb', line 2202

def b
  @b
end

#integer ⇒ Object

Returns the value of attribute integer.



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# File 'lib/m500.rb', line 2202

def integer
  @integer
end

#properfraction ⇒ Object

Returns the value of attribute properfraction.



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# File 'lib/m500.rb', line 2202

def properfraction
  @properfraction
end

Class Method Details

.fractionSeparator ⇒ Object 



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# File 'lib/m500.rb', line 2148

def Fraction::fractionSeparator
  @@fractioinSeparator
end

.new!(a, b = Quotient(0,1), c = 1) ⇒ Object 



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# File 'lib/m500.rb', line 2140

def Fraction.new!(a, b = Quotient(0,1),c=1)
  if a.kind_of?(Array)
    new(a,"canonical form")
  else
    new(a, b,c)
  end
end

Instance Method Details

#*(a) ⇒ Object 



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# File 'lib/m500.rb', line 2275

def * (a)
  if a.kind_of?(Fraction)
    (self.to_Q*a.to_Q).to_Frac
  elsif a.kind_of?(Quotient)
    num =  @properfraction.numerator * a.numerator
    den =  @properfraction.denominator * a.denominator
    Fraction(num, den)
  elsif a.kind_of?(Integer) or a.kind_of?(Fixnum)
    if a == 0 then
      0 
    elsif a == 1 
      self
    else
      self * Fraction(Zahlen(a), Quotient(0,1))
    end
  elsif a.kind_of?(Float)
    self.to_f * a
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    naught
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity
  else
    x, y = a.coerce(self)
    (x * y).to_Frac
  end
end

#+(a) ⇒ Object 



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# File 'lib/m500.rb', line 2205

def + (a)
  if a.kind_of?(Fraction)
    if a.integer == 0 and a.properfraction == Quotient(0,1) then
      return self
    else
      (self.to_Q + a.to_Q).to_Frac
    end
  elsif a.kind_of?(Quotient)
    if a.numerator == 0 and a == Quotient(0,1) then
      return self
    else
      (self.to_Q + a).to_Frac
    end
  else
    (self.to_Q + a.to_Q).to_Frac
  end
end

#-(a) ⇒ Object 



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# File 'lib/m500.rb', line 2258

def - (a)
  if a.kind_of?(Fraction)
    if a.integer == 0 and a.properfraction == Quotient(0,1) then
      return self
    else
      (self.to_Q - a.to_Q).to_Frac
    end
  elsif a.kind_of?(Quotient)
    if a.numerator == 0 and a == Quotient(0,1) then
      return self
    else
      (self.to_Q - a).to_Frac
    end
  else
    (self.to_Q - a.to_Q).to_Frac
  end
end

#/(a) ⇒ Object 



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# File 'lib/m500.rb', line 2301

def / (a)
  if a.kind_of?(Fraction)
    self/a.to_Q
  elsif a.kind_of?(Quotient)
    num =  @properfraction.numerator * a.denominator
    den =  @properfraction.denominator * a.numerator
    Fraction(num, den) unless a.numerator == 0
    nan if a.numerator == 0
  elsif a.kind_of?(Integer) or a.kind_of?(Fixnum)
    self * Fraction.new!(1,a)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    nan
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    nan
  else
    x, y = a.coerce(self)
    (x / y).to_Frac
  end
end

#<=>(other) ⇒ Object 



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# File 'lib/m500.rb', line 2378

def <=>(other)
  self.to_Q <=>other.to_Q
end

#addition(a) ⇒ Object 



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# File 'lib/m500.rb', line 2222

def addition (a)
  if a.kind_of?(Fraction)
    if a.integer == 0 and a.properfraction == Quotient(0,1) then
      return self
    else
      abs = 0
      temp = Quotient(@absolute *@properfraction.numerator,@properfraction.denominator) + Quotient(a.absolute * a.properfraction.numerator, a.properfraction.denominator)
      temp2 = Fraction(temp.numerator,temp.denominator)
      pfrac = temp2.properfraction
      int = (@absolute*@integer) + (a.absolute*a.integer) + (temp2.integer)
      if int.abs>1 and int>0
        abs = 1
      elsif int.abs>1 and int<0
        abs= -1
      else
        abs = (@absolute * a.absolute)
      end
      Fraction.new!([abs,int.abs.to_i,pfrac],"canonical form")
    end
  elsif a.kind_of?(Quotient)
    num = @properfraction.numerator * a.denominator
    num_a = a.numerator * @properfraction.denominator
    Fraction(num + num_a, @properfraction.denominator * a.denominator)
  elsif a.kind_of?(Integer)or a.kind_of?(Fixnum)
   a == 0 ? self: self + Fraction.new!(a, Quotient(0,1))
  elsif a.kind_of?(Float)
    Float(self) + a
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    self
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity
  else
    x, y = a.coerce(self)
    (x + y).to_Frac
  end
end

#coerce(other) ⇒ Object 



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# File 'lib/m500.rb', line 2320

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

#hash ⇒ Object 



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# File 'lib/m500.rb', line 2381

def hash
  @absolute.hash ^ @integer.hash ^ @properfraction.hash
end

#inspect ⇒ Object 



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# File 'lib/m500.rb', line 2365

def inspect
  if @absolute == 1
    sprintf("Fraction(\"%s %s/%s\")",(@integer).to_s,@properfraction.numerator, @properfraction.denominator)
  elsif  @absolute == -1
      sprintf("Fraction(\"-1(%s %s/%s)\")",(@integer).to_s,@properfraction.numerator, @properfraction.denominator)
  end
end

#is_0? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/m500.rb', line 2331

def is_0?
  @integer === 0 and @properfraction.is_0? ? true : false
end

#setdelta ⇒ Object 



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# File 'lib/m500.rb', line 2372

def setdelta
  self.to_Q.setdelta
end

#succ ⇒ Object 



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# File 'lib/m500.rb', line 2375

def succ
  self.to_Q.succ
end

#to_Dec ⇒ Object 



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# File 'lib/m500.rb', line 2337

def to_Dec
  self.to_Q.to_Dec
end

#to_f ⇒ Object 



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# File 'lib/m500.rb', line 2340

def to_f
  self.to_Q.to_f
end

#to_K ⇒ Object 



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# File 'lib/m500.rb', line 2346

def to_K
  Kettenbruch(self)
end

#to_Q ⇒ Object 



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# File 'lib/m500.rb', line 2334

def to_Q
  @to_Q ||= Quotient(@absolute*@integer,1) + (@properfraction*@absolute)
end

#to_s ⇒ Object 



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# File 'lib/m500.rb', line 2349

def to_s
  t = ""
  unless a.nil? or b.nil?
    t = "#{@a.to_s}/#{@b.to_s} = "
  end
  if @b == 1
    @a.to_s
  elsif @absolute <0
    "#{t}#{@absolute}*(#{@integer} + (#{@properfraction}))"
  else
    "#{t}#{@integer.to_s} + (#{@properfraction.to_s})"
  end
end

#to_sgml ⇒ Object 



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# File 'lib/m500.rb', line 2152

def to_sgml
  "<mn #{sgml_id}class='mixed_fraction'><mn>#{@integer.to_s}</mn>#{@properfraction.to_sgml}<mn>"
end

#to_Sig ⇒ Object 



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# File 'lib/m500.rb', line 2343

def to_Sig
  Sigma(self.to_Q)
end