Class: Algebra::LocalizedRing

Inherits:
Object
  • Object
show all
Extended by:
AlgebraCreator
Includes:
AlgebraBase
Defined in:
lib/algebra/localized-ring.rb

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from AlgebraCreator

create, superior?, sysvar, wedge

Methods included from AlgebraBase

#+@, #-@, append_features, #coerce, #devide?, #ground, #ground=, #regulate, #unity, #unity?, #zero, #zero?

Constructor Details

#initialize(num, den = ground.unity) ⇒ LocalizedRing 



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# File 'lib/algebra/localized-ring.rb', line 113

def initialize(num, den = ground.unity)
  if den.respond_to?(:<=>) && den < ground.zero
    num = -num
    den = -den
  end
  @numerator = num
  @denominator = den
end

Instance Attribute Details

#denominator ⇒ Object (readonly)

Returns the value of attribute denominator.



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# File 'lib/algebra/localized-ring.rb', line 63

def denominator
  @denominator
end

#numerator ⇒ Object (readonly)

Returns the value of attribute numerator.



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# File 'lib/algebra/localized-ring.rb', line 62

def numerator
  @numerator
end

Class Method Details

.[](num, den = nil) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 69

def self.[](num, den = nil)
  den ? reduce(num, den) : unity * num
end

.create(ground) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 48

def self.create(ground)
  klass = super(ground)
  klass.sysvar(:reducible, true)
  klass
end

.reduce(num, den) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 73

def self.reduce(num, den)
  reducible ? simplify(num, den) : new(num, den)
end

.reducible ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 54

def self.reducible
  @@reducible
end

.reducible=(sw) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 58

def self.reducible=(sw)
  @@reducible = sw
end

.simplify(num, den) ⇒ Object

Raises:

  • (ZeroDivisionError) 


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# File 'lib/algebra/localized-ring.rb', line 77

def self.simplify(num, den)
  raise ZeroDivisionError, 'denometor is 0' if den.zero?
  return zero if num.zero?

  if ground.field?
    num /= den
    den = ground.unit
  elsif ground.ufd? # ground.euclidian?
    gcd = num.gcd(den)
    num /= gcd
    den /= gcd
    #      num = num.div(gcd)
    #      den = den.div(gcd)
  end

  # regulate the leading coefficient of polynomil
  if defined?(Polynomial) && ground <= Polynomial
    if ground.ground.field?
      m = den.lc
      num /= m
      den /= m
    elsif ground.ground.euclidian? # high cost!
      m = num.cont.gcd(den.cont)
      num /= m
      den /= m
    end
    #    elsif defined?(MPolynomial) && ground <= MPolynomial
  end

  #    if den.respond_to?(:<) and den < 0
  #      num = -num
  #      den = -den
  #    end
  new(num, den)
end

Instance Method Details

#*(o) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 148

def *(o)
  super do |o|
    num = @numerator * o.numerator
    den = @denominator * o.denominator
    self.class.reduce(num, den)
  end
end

#**(other) ⇒ Object

def % (o)

  raise ZeroDivisionError, "devided by 0" if o.zero?
  den, a, = @denominator.gcd_coeff(o)
  num = (@numerator * a) % o
  q, r = num.divmod den
  raise "#@denominator can not divide #@numerator mod #{o}" unless r.zero?
  q
end



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# File 'lib/algebra/localized-ring.rb', line 182

def **(other)
  case other
  when Integer
    if other > 0
      num = @numerator**other
      den = @denominator**other
      self.class.new(num, den)
    elsif other < 0
      num = @denominator**-other
      den = @numerator**-other
      self.class.new(num, den)
    elsif other.zero?
      unity
    end
  else
    x, y = other.coerce(self)
    x**y
  end
end

#+(o) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 132

def +(o)
  super do |o|
    num = @numerator * o.denominator
    num_o = o.numerator * @denominator
    self.class.reduce(num + num_o, @denominator * o.denominator)
  end
end

#-(o) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 140

def -(o)
  super do |o|
    num = @numerator * o.denominator
    num_o = o.numerator * @denominator
    self.class.reduce(num - num_o, @denominator * o.denominator)
  end
end

#/(o) ⇒ Object

Raises:

  • (ZeroDivisionError) 


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# File 'lib/algebra/localized-ring.rb', line 156

def /(o)
  raise ZeroDivisionError, 'devided by 0' if o.zero?
  super do |o|
    num = @numerator * o.denominator
    den = @denominator * o.numerator
    self.class.reduce(num, den)
  end
end

#==(o) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 126

def ==(o)
  super do |o|
    @numerator * o.denominator == o.numerator * @denominator
  end
end

#hash ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 243

def hash
  raise 'hash is undefined'
end

#inspect ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 238

def inspect
  to_s
  #    sprintf("%s(%s/%s)", self.class, @numerator.inspect, @denominator.inspect)
end

#monomial? ⇒ Boolean 



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# File 'lib/algebra/localized-ring.rb', line 65

def monomial?
  true
end

#need_paren_in_coeff? ⇒ Boolean 



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# File 'lib/algebra/localized-ring.rb', line 202

def need_paren_in_coeff?
  if @denominator.unity?
    if @numerator.respond_to?(:need_paren_in_coeff?)
      @numerator.need_paren_in_coeff?
    elsif @numerator.is_a?(Numeric)
      false
    else
      true
    end
  else
    false
  end
end

#pdivmod(other) ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 169

def pdivmod(other)
  [self / other, zero]
end

#simplify ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 122

def simplify
  self.class.simplify(@numerator, @denominator)
end

#to_s ⇒ Object 



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# File 'lib/algebra/localized-ring.rb', line 216

def to_s
  n = if @numerator.respond_to?(:need_paren_in_coeff?) &&
         @numerator.need_paren_in_coeff? &&
         !@denominator.unity?
        "(#{@numerator})"
      else
        @numerator.to_s
      end
  d = if @denominator.respond_to?(:need_paren_in_coeff?) &&
         @denominator.need_paren_in_coeff? &&
         !@denominator.is_a?(Integer)
        "(#{@denominator})"
      else
        @denominator.to_s
      end
  if @denominator.unity?
    n.to_s
  else
    n + '/' + d
  end
end

#unit? ⇒ Boolean 



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# File 'lib/algebra/localized-ring.rb', line 165

def unit?
  !zero? # some about
end