Module: Algebra::AlgebraBase

Included in:
LocalizedRing, MPolynomial, MatrixAlgebra, Polynomial, ResidueClassRing
Defined in:
lib/algebra/algebraic-system.rb

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.append_features(klass) ⇒ Object

private :regulate



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# File 'lib/algebra/algebraic-system.rb', line 113

def self.append_features(klass)
  def klass.field?
    !method_defined?(:divmod) # may be overwrited
  end

  def klass.euclidian?
    method_defined?(:divmod) #  may be overwrited
  end

  def klass.ufd?
    euclidian? #  may be overwrited
  end

  def klass.zero
    new(ground.zero)
  end

  def klass.unity
    new(ground.unity)
  end

  def klass.regulate(x)
    if x.is_a? self
      x
    elsif y = ground.regulate(x)
      new(y)
            end
  end
  super
end

Instance Method Details

#*(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 180

def *(other)
  if o = regulate(other)
    yield o
  else
    x, y = other.coerce(self)
    x * y
  end
end

#**(n) ⇒ Object Also known as: ^ 



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# File 'lib/algebra/algebraic-system.rb', line 198

def **(n)
  if !n.is_a?(Integer) || n < 0
    raise 'index must be non negative integer'
  elsif n == 0
    return unity
  elsif n == 1
    self
  else
    q, r = n.divmod 2
    x = self**q
    x *= x
    x *= self if r > 0
    x
  end
end

#+(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 162

def +(other)
  if o = regulate(other)
    yield o
  else
    x, y = other.coerce(self)
    x + y
  end
end

#+@ ⇒ Object

Operations



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# File 'lib/algebra/algebraic-system.rb', line 145

def +@
  self
end

#-(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 171

def -(other)
  if o = regulate(other)
    yield o
  else
    x, y = other.coerce(self)
    x - y
  end
end

#-@ ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 149

def -@
  zero - self
end

#/(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 189

def /(other)
  if o = regulate(other)
    yield o
  else
    x, y = other.coerce(self)
    x / y
  end
end

#==(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 153

def ==(other)
  if o = regulate(other)
    yield o
  else
    x, y = other.coerce(self)
    x == y
  end
end

#coerce(other) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 216

def coerce(other)
  if x = regulate(other)
    [x, self]
  else
    raise "(ALG.SYS) can't coerce: (#{self.class}).coerce(#{other.class}) : (#{self}).coerce(#{other})"
  end
end

#devide?(other) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/algebraic-system.rb', line 97

def devide?(other)
  if self.class.field?
    true
  elsif self.class.euclidian?
    _q, r = other.divmod(self)
    r.zero?
  else
    raise "don't konw #{self} divides #{other}"
  end
end

#ground ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 89

def ground
  self.class.ground
end

#ground=(bf) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 93

def ground=(bf)
  self.class.ground = bf
end

#regulate(x) ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 108

def regulate(x)
  self.class.regulate(x)
end

#unit? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/algebraic-system.rb', line 81

def unit?
  unity == self || -unity == self
end

#unity ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 73

def unity
  self.class.unity
end

#unity? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/algebraic-system.rb', line 85

def unity?
  unity == self
end

#zero ⇒ Object 



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# File 'lib/algebra/algebraic-system.rb', line 69

def zero
  self.class.zero
end

#zero? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/algebraic-system.rb', line 77

def zero?
  zero == self
end