Top Level Namespace

Defined Under Namespace

Modules: Enumerable, SGML Classes: Array, Bignum, Counting, Decimal, EmptySetClass, Fixnum, Float, Fraction, InfinityClass, Kettenbruch, List, Matrix, NANClass, Natural, NaughtClass, Numeric, Quotient, Rational, Real, ST, Sequence, Set, Sigma, String, Symbolic_Prod, Symbolic_Term, Symbolic_statment, Tensor, Zahlen

Instance Method Summary collapse

Instance Method Details

#Counting(a) ⇒ Object 



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# File 'lib/m500.rb', line 585

def Counting(a)
  if (a.kind_of?(Fixnum) && a >= 0) or (a.kind_of?(Bignum) && a >= 0)
    Counting.new!(a)
  elsif  (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(NaughtClass))
    Counting.new!(0)
  elsif (a.kind_of?(InfinityClass))
    infinity
  elsif (a.kind_of?(String))
    Counting.new!(a.to_i)
  elsif a.kind_of?(Numeric)
    a.send :to_N0
  else
   EmptySet
  end
end

#Decimal(a, b = nil, c = '0', d = 0, e = 1) ⇒ Object 



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# File 'lib/m500.rb', line 700

def Decimal(a,b=nil,c='0',d=0,e=1)
  if a.kind_of?(Decimal)
    a
  elsif  (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(InfinityClass))
    infinity
  elsif a.kind_of?(String)
    a.to_Dec
  elsif (a.kind_of?(Fixnum) or a.kind_of?(Bignum)) and (b.kind_of?(Fixnum) or b.kind_of?(Bignum))
    if e<0 then
      Decimal.new!(a,b,c,d,-1)
    else
      if a<0 then
        Decimal.new!(a,b,c,d,-1)
      elsif a>0
        Decimal.new!(a,b,c,d,1)
      else
        Decimal.new!(0,b,c,d,1)
      end
    end
  elsif (a.kind_of?(Fixnum) or a.kind_of?(Bignum)) and b.nil?
    if e<0 then
      Decimal.new!(a,b,c,d,-1)
    else
      if a<0 then
        Decimal.new!(a,nil,c,0,-1)
      elsif a>0
        Decimal.new!(a,nil,c,0,1)
      else
        Decimal.new!(0,nil,c,0,1)
      end
    end
  elsif a.kind_of?(Numeric)
    a.send :to_Dec
  end
end

#emptySet ⇒ Object 



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# File 'lib/m500.rb', line 559

def emptySet
  EmptySetClass.new!
end

#Fraction(a, b = Quotient(0,1), c = 1) ⇒ Object 



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# File 'lib/m500.rb', line 660

def Fraction(a,b=Quotient(0,1),c=1)
  if  a.kind_of?(Zahlen) && b.kind_of?(Natural) then
    Fraction.new!(a,b,c)
  elsif a.kind_of?(Zahlen) && b.kind_of?(Quotient)
    if a>=0 and  b>=0 then
      Fraction.new!(a,b,c)
    elsif a<0 and b<0
      Fraction.new!(a*(-1),b*(-1),-1)
    else
      (a+b).to_Frac
    end
  elsif Integer === a && b.kind_of?(Quotient)
    if a>0 then
      Fraction.new!(Zahlen(a),b,c)
    else
      Fraction.new!(Zahlen(a*(-1)),b,-1*c)
    end
  elsif a.kind_of?(Quotient) && b == Quotient(0,1)
    Fraction.new!(a.numerator,a.denominator,c)
  elsif a.kind_of?(Fraction) && b == Quotient(0,1)
    a
  elsif a.kind_of?(String) && b == Quotient(0,1)
    a.to_Frac
  elsif  b == 1
    a
  elsif (a.kind_of?(NaughtClass))
    Fraction.new!(Zahlen(0),b)
  elsif  (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(InfinityClass))
    infinity
  else
    tmp = Quotient(a,b)
    unless a == b or -a==b then
      Fraction.new!(tmp.numerator,tmp.denominator)
    else
      a/b
    end
  end
end

#infinity ⇒ Object 



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# File 'lib/m500.rb', line 565

def infinity
  InfinityClass.new!
end

#Kettenbruch(a, b = '', c = 1, leicht = true) ⇒ Object 



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# File 'lib/m500.rb', line 737

def Kettenbruch(a,b='',c=1,leicht=true)
  if a.kind_of?(Kettenbruch)
    a
  elsif a.kind_of?(Array)
    b = a.shift
    b<0 ?  Kettenbruch.new!(-1*b,a) : Kettenbruch.new!(b,a)
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    a
  elsif a.kind_of?(String)
    a.to_K
  elsif a.kind_of?(Proc)
    a
  elsif (a.kind_of?(Fixnum) or a.kind_of?(Bignum)) and b.kind_of?(String)
    if (a>0 and c<0) or (a<0 and c>0) then
      Kettenbruch.new!(a,b,-1)
    else
      Kettenbruch.new!(a,b,1)
    end
  elsif a.kind_of?(Quotient) and b==''
    if a.to_Z == emptySet then
      (a>0 and c<0) or (a<0 and c>0) ?  Kettenbruch.new!(a.abs,b,-1): Kettenbruch.new!(a.abs,b,1)
    else
      Kettenbruch(a.to_Z,b,c)
    end
    elsif (a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural))and b==''
    (a>0 and c<0) or (a<0 and c>0) ?  Kettenbruch.new!(a.abs,[],-1): Kettenbruch.new!(a.abs,[],1)
  end
end

#List(a = nil, &b) ⇒ Object 



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# File 'lib/M500_containers.rb', line 7

def List(a=nil,&b)
  b ?  List.new!(a) {b} : List.new!(a)
end

#Matrix(m, n) ⇒ Object 



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# File 'lib/m500.rb', line 771

def Matrix(m,n)
  Matrix.instanciate(m,n)
end

#nan ⇒ Object 



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# File 'lib/m500.rb', line 562

def nan
  NANClass.new!
end

#Natural(a) ⇒ Object 



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# File 'lib/m500.rb', line 568

def Natural(a)
  if (a.kind_of?(Natural))
    a
  elsif (a.kind_of?(NaughtClass)) or (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(InfinityClass))
    infinity
  elsif (a.kind_of?(String))
    Natural.new!(a.to_i)
  elsif (a.kind_of?(Fixnum) && a >= 1) or (a.kind_of?(Bignum) && a >= 1)
    Natural.new!(a)
  elsif  a.kind_of?(Numeric)
    a.send :to_N
  else
    EmptySet
  end
end

#naught ⇒ Object 



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# File 'lib/m500.rb', line 556

def naught
  NaughtClass.new!
end

#Quotient(a, b = 1) ⇒ Object 



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# File 'lib/m500.rb', line 619

def Quotient(a,b=1)
  if b < 0
    a = -a 
    b = -b
  end
  if b == 0 or b.kind_of?(NaughtClass)
    return infinity
  elsif (a.kind_of?(NaughtClass))
    Quotient(0,1)
  elsif  (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(InfinityClass))
    infinity
  elsif a.kind_of?(Quotient) && b == 1
    a
  elsif a.kind_of?(Numeric) && (b.kind_of?(Quotient)||b.kind_of?(Fraction)) # =8=
    a/b
  elsif (a.kind_of?(String))
    re = /(\-*\d+)\/(\d+)/
    md = re.match(a)
    Quotient.new!(md[1].to_i,md[2].to_i)
  elsif a.kind_of?(Float)
    tmp =  a.to_s.scan(/\d+/)
    m= tmp.at(1).length
    (Quotient.new!(((tmp.at(0).to_i)*(10**m)) + tmp.at(1).to_i,10**m)/(Quotient(b,1)))  
  elsif b.kind_of?(Quotient) && a == 1
    Quotient.new!(b.denominator,b.numerator)
  elsif Zahlen(a).kind_of?(Numeric) and Natural(b).kind_of?(Numeric)
    unless a == b
      Quotient.new!(Zahlen(a),Natural(b)) 
    else
      Quotient.new!(Zahlen(a),Natural(b)) 
    end
  elsif a.kind_of?(Quotient) && b.kind_of?(Quotient)
    return a/b
  elsif a.kind_of?(Numeric)
    a.send :to_Q
  else
    emptySet
  end
end

#Real(a, &block) ⇒ Object 



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# File 'lib/m500.rb', line 249

def Real(a,&block)
  if a.kind_of?(Real)
    a 
  elsif a.kind_of?(Array)
    rez = Real.new!(Quotient(0,1),block)
    rez.continuedFraction = a.to_s
    rez.update_eval = proc{|k0,k,ret,irrat|  (k0..k).to_a.each{|n| n==k0 ? ret << irrat.call(n): ret << ","+ irrat.call(n)}; ret = "[" + ret + "]";eval(Real::gcontinuedFractionFactory(eval(ret)))}
    rez.updateApprox{ 
      @k0 = 1
      @k = 12
      @rat += update_eval.call(@k0,@k,@continuedFraction,@irrat).to_Q
    }
  elsif a.kind_of?(Quotient)
    Real.new!(a,block)
  elsif a.kind_of?(Natural) or a.kind_of?(Counting) or a.kind_of?(Zahlen) or a.kind_of?(Fraction) or a.kind_of?(Decimal)
  elsif
    Real.new!(a.to_Q,block)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass) or a.kind_of?(NilClass)
    a unless b
    new(Quotinet(0,1),block)
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    a
  end
end

#Sequence(a) ⇒ Object 



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# File 'lib/M500_containers.rb', line 13

def Sequence(a)
  Sequence.new(a)
end

#Set(a, &b) ⇒ Object 



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# File 'lib/M500_containers.rb', line 10

def Set(a,&b)
  b ?  Set.new!(a) {b} :  Set.new!(a)
end

#Sigma(a, &block) ⇒ Object 



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# File 'lib/M500_containers.rb', line 16

def Sigma(a,&block)
  if a.kind_of?(Sigma)
    a 
  elsif a.kind_of?(Quotient)
    Sigma.new!(a,block)
  elsif a.kind_of?(Natural) or a.kind_of?(Counting) or a.kind_of?(Zahlen) or a.kind_of?(Fraction) or a.kind_of?(Decimal)
  elsif
    Sigma.new!(a.to_Q,block)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptyListClass) or a.kind_of?(NilClass)
    a unless b
    new(Quotinet(0,1),block)
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    a
  end
end

#Symbolic_Prod(a, b) ⇒ Object 



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# File 'lib/m500.rb', line 768

def Symbolic_Prod(a,b)
  Symbolic_Prod.new(a,b)
end

#Symbolic_Term(a, b) ⇒ Object 



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# File 'lib/m500.rb', line 765

def Symbolic_Term(a,b)
  Symbolic_Term.new(a,b)
end

#Tensor(m, *args) ⇒ Object 



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# File 'lib/m500.rb', line 774

def Tensor(m,*args)
  Tensor.new!(m,*args)
end

#Zahlen(a) ⇒ Object 



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# File 'lib/m500.rb', line 602

def Zahlen(a)
  if a.kind_of?(Zahlen)
     a
  elsif  (a.kind_of?(EmptySetClass))
    emptySet
  elsif (a.kind_of?(NaughtClass))
    Zahlen.new!(0)
  elsif (a.kind_of?(InfinityClass))
    infinity
  elsif a.kind_of?(Fixnum) or a.kind_of?(Bignum)
    Zahlen.new!(a)
  elsif a.kind_of?(Numeric)
    a.send :to_Z
  else
    emptySet
  end
end