# modified at 2008.7.21
require 'matrix'

class RotationGroup

Element={
"1z" =>	Matrix[[1,0,0],[0,1,0],[0,0,1]],
"2x" =>	Matrix[[1,0,0],[0,-1,0],[0,0,-1]],
"2y" =>	Matrix[[-1,0,0],[0,1,0],[0,0,-1]],
"2z" =>	Matrix[[-1,0,0],[0,-1,0],[0,0,1]],
"2d" =>	Matrix[[0,1,0],[1,0,0],[0,0,-1]],
"2e" =>	Matrix[[0,-1,0],[-1,0,0],[0,0,-1]],
"3z" =>	Matrix[[0,1,0],[-1,-1,0],[0,0,1]],
"3r" =>	Matrix[[0,1,0],[0,0,1],[1,0,0]],
"4z" =>	Matrix[[0,1,0],[-1,0,0],[0,0,1]],
"6z" =>	Matrix[[1,1,0],[-1,0,0],[0,0,1]],
}

System={
"1" => "triclinic",
"2" => "monoclinic",
"222" => "orthorhombic",
"4" => "tetragonal",
"422" => "tetragonal",
"3" => "trigonal",
"32" => "trigonal",
"6" => "hexagonal",
"622" => "hexagonal",
"23" => "cubic",
"432" => "cubic",
}

Axis={
"1" => ["z"],
"2" => ["y"],
"222" => ["x","y","z"],
"4" => ["z"],
"422" => ["z","x","d"],
"3" => ["z"],
"32" => ["z","d","e"],
"6" => ["z"],
"622" => ["z","d","e"],
"23" => ["z","r"],
"432" => ["z","r","d"],
}

def initialize(s)
	@string=s.gsub(/\s/){""}
end

attr_reader :string

def rotation()
	return self
end

def system()
	System[rotation.string]
end

def axis()
	Axis[rotation.string]
end

def generator()
	g=@string.gsub(/m/){"-2"}
	ax=axis()
	a=[]
	i=0
	while g.size>0
		break unless m=/(-?\d'?)(\/(-2'?))?/.match(g)
		a.push(m[1]+ax[i])
		a.push(m[3]+ax[i]) if m[2]
		g=m.post_match
		i+=1
	end
	return a
end

def gen_matrix()
	g=generator()
	return g.collect{|e| Element[e]}
end

def position(pstn)
	a=[pstn]
	b=[""]
	while b.size>0
		b=[]
		for e1 in gen_matrix
			for e2 in a
				p=e1*e2
				b.push(p) unless a.include?(p)
			end
			a=(a+b).uniq
		end
	end
	return a
end

def element()
	return position(Element["1z"])
end

end # class


class Matrix

Direction={
#100
[1,0,0] => 'x',
[0,1,0] => 'y',
[0,0,1] => 'z',
#110
[0,1,1] => 'yz',
[1,0,1] => 'zx',
[1,1,0] => 'xy',
[0,1,-1] => 'y-z',
[1,0,-1] => 'z-x',
[1,-1,0] => 'x-y',
#111
[1,1,1] => 'xyz',
[-1,1,1] => '-xyz',
[1,-1,1] => 'x-yz',
[1,1,-1] => 'xy-z',
#hexa 100,010,110
[2,1,0] => '2xy',
[1,2,0] => 'x2y',
}
def operation
  rt=rotation.to_s.sub(/^\-2/){"m"}
  rt+=eigen unless rt=~/\-?1/
  return rt
end
def rotation
# trace=2cos(t)+1
	h={3=>1, -1=>2, 0=>3, 1=>4, 2=>6}
	t=self.tr
	d=self.det
	return h[t*d]*d
end
def eigen
  sign=self.det
  str=""
  for ve in Direction.keys
    v=Vector[*ve]
    if sign*self*v==v
      str=Direction[ve]
    end
  end
  return str
end
  def to_xyz
    char=["x","y","z"]
    a=[]
    for i in 0..2
      s=""
      for j in 0..2
        s+="+#{self[i,j]}#{char[j]}" unless self[i,j]==0
      end
      s="0" if s==""
      s.gsub!(/\+\-/){"-"}
      s.gsub!(/^\+/){""}
      s.gsub!(/1([x-z])/){"#{$1}"}
      a.push(s)
    end
    return a
  end

end #class