require 'matrix'

class Affine

def initialize(m,v)
	@matrix=m
	@vector=v
end

  def ==(other)
    return false unless Affine === other
    @matrix == other.matrix and @vector == other.vector
  end
  alias eql? ==

  def +(n) # a is affine or number
    case(n)
    when Vector
      return Affine::new(@matrix,@vector+n)
    else
      return 1
    end
  end

  def -(n) # a is affine or number
    case(n)
    when Vector
      return Affine::new(@matrix,@vector-n)
    else
      return 1
    end
  end

  def *(n) # a is affine or number or vector
    case(n)
    when Numeric
      return Affine::new(@matrix*n,@vector*n)
    when Vector
      return @matrix*n+@vector
    when Affine
      return Affine::new(@matrix*n.matrix,@matrix*n.vector+@vector)
    else
      return 1
    end
  end

  def inverse
      i=@matrix.inverse
      return Affine::new(i,i*@vector*(-1))
  end
  alias inv inverse

  def determinant
    return @matrix.determinant
  end
  alias det determinant

  def trace
    return @matrix.trace
  end
  alias tr trace

  def to_s
    self.matrix.to_s+":"+self.vector.to_s
  end

attr_reader :matrix
attr_reader :vector

end #class