Class: Zahlen

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

Class Method Summary collapse

Instance Method Summary collapse

Methods included from SGML

#sgml_id, #tog_sgml_id

Methods inherited from Counting

#each, #factorial, #factorial_1, #hash

Methods inherited from Natural

#==, #div, #divmod, #gcd2, #gcdlcm, #hash, #is_0?, #lcm

Methods inherited from Numeric

#irrational?, #rational?, #sgml_id, #to_N0

Constructor Details

#initialize(a) ⇒ Zahlen

Returns a new instance of Zahlen.



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# File 'lib/m500.rb', line 1386

def initialize(a)
  if (a.kind_of?(Zahlen))
    @a = a.to_i
  elsif a.kind_of?(Fixnum) or a.kind_of?(Bignum)
    @a = a
  else
  end
end

Class Method Details

.new!(num) ⇒ Object 



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# File 'lib/m500.rb', line 1382

def Zahlen.new!(num)
  new(num)
end

Instance Method Details

#%(a) ⇒ Object 



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# File 'lib/m500.rb', line 1453

def % (a)
  self.to_i%(a.to_i)
end

#*(a) ⇒ Object 



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# File 'lib/m500.rb', line 1422

def * (a)
  if a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)
    Zahlen(self.to_i * a.to_i)
  elsif a.kind_of?(Quotient) or a.kind_of?(Fraction)
    a * Quotient(@a,1)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass) or a.nil?
    naught
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity
  else
    x , y = a.coerce(self)
    Zahlen(x * y)
  end
end

#**(a) ⇒ Object 



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# File 'lib/m500.rb', line 1445

def ** (a)
  if a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural)
    Zahlen(self.to_i ** a.to_i)
  else
    x, y = a.coerce(self)
    Zahlen(x ** y)
  end
end

#+(a) ⇒ Object 



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# File 'lib/m500.rb', line 1394

def + (a)
  if a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)
    Zahlen(self.to_i + a.to_i)
  elsif a.kind_of?(Quotient) or a.kind_of?(Fraction)
    a + Quotient(@a,1)
  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
  end
end

#-(a) ⇒ Object 



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# File 'lib/m500.rb', line 1408

def - (a)
  if a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)
    Zahlen(self.to_i - a.to_i)
  elsif a.kind_of?(Quotient) or a.kind_of?(Fraction)
    a - Quotient(@a,1)
  elsif a.kind_of?(NaughtClass) or a.kind_of?(EmptySetClass)
    self
  elsif a.kind_of?(NANClass) or a.kind_of?(InfinityClass)
    infinity*(-1) 
  else
    x, y = a.coerce(self)
    Zahlen(x - y)
  end
end

#/(a) ⇒ Object 



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# File 'lib/m500.rb', line 1436

def / (a)
  if (a.kind_of?(Zahlen) or a.kind_of?(Counting) or a.kind_of?(Natural) or a.kind_of?(Bignum) or a.kind_of?(Fixnum)) and self.to_i%(a.to_i) == 0
    Zahlen(self.to_i / a.to_i)
  elsif a.kind_of?(Quotient) or a.kind_of?(Fraction)
    self * Quotient(a.to_Q.denominator,a.to_Q.numerator)
  else
    emptySet
  end
end

#<=>(other) ⇒ Object 



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# File 'lib/m500.rb', line 1484

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

#abs ⇒ Object 



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# File 'lib/m500.rb', line 1456

def abs
  @a.to_i.abs
end

#coerce(other) ⇒ Object 



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# File 'lib/m500.rb', line 1468

def coerce(other)
#  if other.kind_of?(Float) then
#    other, @a
#  elsif other.kind_of?(Numeric)
#    return Zahlen.new!(other.to_i), self
#  else
#    other, @a 
#  end
  [other, @a]
end

#gcd(n) ⇒ Object 



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# File 'lib/m500.rb', line 1459

def gcd(n)
  g = nil
  if @a>0 then
    g = Natural( @a).gcd(n)
  else
    g = Natural(-1* @a).gcd(n)
  end
  g
end

#inspect ⇒ Object 



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# File 'lib/m500.rb', line 1522

def inspect
  sprintf("Zahlen(%s)", @a.to_s)
end

#next ⇒ Object 



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# File 'lib/m500.rb', line 1478

def next
  self + Zahlen(1)
end

#next_prime ⇒ Object 



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# File 'lib/m500.rb', line 1525

def next_prime
  emptySet
end

#succ ⇒ Object 



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# File 'lib/m500.rb', line 1481

def succ
  self.next
end

#to_Dec ⇒ Object 



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# File 'lib/m500.rb', line 1511

def to_Dec
  Decimal(@a,0,'0')
end

#to_f ⇒ Object 



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# File 'lib/m500.rb', line 1490

def to_f
  @a.to_f
end

#to_Frac ⇒ Object 



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# File 'lib/m500.rb', line 1505

def to_Frac
  Fraction(@a,Quotient(0,1))
end

#to_i ⇒ Object 



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# File 'lib/m500.rb', line 1487

def to_i
  @a.to_i
end

#to_K ⇒ Object 



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# File 'lib/m500.rb', line 1517

def to_K
  Kettenbruch(self.to_Frac)
end

#to_N ⇒ Object 



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# File 'lib/m500.rb', line 1499

def to_N
  Natural(@a)
end

#to_Q ⇒ Object 



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# File 'lib/m500.rb', line 1508

def to_Q
  Quotient(@a,1)
end

#to_R ⇒ Object 



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# File 'lib/m500.rb', line 1520

def to_R
end

#to_s ⇒ Object 



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# File 'lib/m500.rb', line 1496

def to_s
  @a.to_s
end

#to_s! ⇒ Object 



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# File 'lib/m500.rb', line 1493

def to_s!
  "Zahlen(#{@a})"
end

#to_sgml ⇒ Object 



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# File 'lib/m500.rb', line 1379

def to_sgml
  "<mn #{sgml_id}class='zahlen'>#{@a}</mn>"
end

#to_Sig ⇒ Object 



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# File 'lib/m500.rb', line 1514

def to_Sig
  Sigma(self.to_Q)
end

#to_Z ⇒ Object 



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# File 'lib/m500.rb', line 1502

def to_Z
  Zahlen(@a)
end