=begin
  # sample-quotientfield04.rb

  require "algebra"
  
  F13 = ResidueClassRing(Integer, 13)
  F = RationalFunctionField(F13, "x")
  x = F.var
  AF = AlgebraicExtensionField(F, "a") {|a| a**2 - 2*x}
  a = AF.var
  
  p( (a/4*x + AF.unity/2)/(x**2 + a*x + 1) +
    (-a/4*x + AF.unity/2)/(x**2 - a*x + 1) )
  #=> (-x^3 + x^2 + 1)/(x^4 + 11x^3 + 2x^2 + 1)
((<_|CONTENTS>))
=end
