# Algebraic Extension Field
#
#   by Shin-ichiro Hara
#
# Version 1.00 (2002.02.27)

require "algebra/polynomial"
#require "algebra/m-polynomial"
require "algebra/residue-class-ring"
require "algebra/polynomial"

module Algebra
  def AlgebraicExtensionField(field, var = "x", &b)
    AlgebraicExtensionField.create(field, var, &b)
  end
  module_function :AlgebraicExtensionField

  class AlgebraicExtensionField < ResidueClassRing
    def self.create(field, var_obj)
      poly_ring = Algebra.Polynomial(field, var_obj)

      modulus = yield(poly_ring.var)
      klass = super(poly_ring, modulus)

#      def klass.var; self[ground.var]; end
      klass.sysvar :var, klass[klass.ground.var]
      klass.sysvar :base, field

      if Algebra::AlgebraicExtensionField >= field
	env_ring = Algebra.Polynomial(field.env_ring, var_obj)
	klass.sysvar :def_polys, field.def_polys + [modulus]
      else
	env_ring = poly_ring
	klass.sysvar :def_polys, [modulus]
      end

      poly_ring.class_eval <<-__DEF__
      def abs_lift
	if Algebra::AlgebraicExtensionField >= ground
	  project(self.class.env_ring) {|c, n| c.abs_lift }
	else
	  project(self.class.env_ring) {|c, n| c }
	end
      end
      __DEF__
      poly_ring.sysvar :env_ring, env_ring
      klass.sysvar :env_ring, env_ring

      klass
    end

    def [](n)
      lift[n]
    end

    def abs_lift
      Algebra::AlgebraicExtensionField >= self.class.base ? lift.abs_lift : lift
    end

    def self.to_ary
      [self, var]
    end
  end

################# 2 ###################

  def AlgebraicExtensionField2(field, var = nil, &b)
    AlgebraicExtensionField2.create(field, var, &b)
  end
  module_function :AlgebraicExtensionField2

  class AlgebraicExtensionField2 < ResidueClassRing
    def self.create(field, var_obj)
      poly_ring = Algebra.Polynomial(field, var_obj)
      modulus = yield(poly_ring.var)
      x = modulus.var

      if modulus.deg == 2
        a = modulus[1] / 2 / modulus[2]
        modulus = modulus.evaluate(x + a)
        var_obj ||= "√(" + (modulus[0]/modulus[2]).to_s + ")"

        poly_ring = Algebra.Polynomial(field, var_obj)
        x = poly_ring.var
        modulus = x**2 + a**2
      else
        a = 0
        var_obj ||= "x"
      end
      klass = super(poly_ring, modulus)
      klass.sysvar :root, klass[x + a]

#      def klass.var; self[ground.var]; end

      klass.sysvar :var, klass[klass.ground.var]
      klass.sysvar :base, field

      if Algebra::AlgebraicExtensionField >= field
	env_ring = Algebra.Polynomial(field.env_ring, var_obj)
	klass.sysvar :def_polys, field.def_polys + [modulus]
      else
	env_ring = poly_ring
	klass.sysvar :def_polys, [modulus]
      end

      poly_ring.class_eval <<-__DEF__
      def abs_lift
	if Algebra::AlgebraicExtensionField >= ground
	  project(self.class.env_ring) {|c, n| c.abs_lift }
	else
	  project(self.class.env_ring) {|c, n| c }
	end
      end
      __DEF__
      poly_ring.sysvar :env_ring, env_ring
      klass.sysvar :env_ring, env_ring

      klass
    end

    def [](n)
      lift[n]
    end

    def abs_lift
      Algebra::AlgebraicExtensionField >= self.class.base ? lift.abs_lift : lift
    end

    def self.to_ary
      [self, var]
    end
  end

end

if $0 == __FILE__
end