=begin
  # sample-quotientfield03.rb

  require "algebra"
  
  F13 = ResidueClassRing(Integer, 13)
  F = AlgebraicExtensionField(F13, "a") {|a| a**2 - 2}
  a = F.var
  RF = RationalFunctionField(F, "x")
  x = RF.var
  
  p( (a/4*x + RF.unity/2)/(x**2 + a*x + 1) +
    (-a/4*x + RF.unity/2)/(x**2 - a*x + 1) )
  #=> 1/(x**4 + 1)
=end
