Quaternion Conjugates

r""" q_reversal - reverse space, time and spacetime This is all done with conjugates. AUTHORS: -- Doug Sweetser (2009): Initial version. EXAMPLES: Test the various conjugates. sage: q1 = q(1, 2, 3, 4); q_time_rev = q(-1, 2, 3, 4); sage: q_space_rev = q(1, -2, -3, -4); q_spacetime_rev = q(-1, -2, -3, -4) sage: q1.conj()==q_space_rev True sage: q1.conj().negate() == q_time_rev True sage: q1.negate()==q_spacetime_rev True """ #***************************************************************************** # Copyright (C) 2009 Doug Sweetser <sweetser@alum.mit.edu> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #***************************************************************************** 

class q(list): def __init__(self,t,x,y,z): self.t = t self.x = x self.y = y self.z = z list.__init__(self,[t,x,y,z]) def __repr__(self): return "Quaternion tools." def show(self): print self.t, self.x, self.y, self.z def add(self, q2): return(q(self.t + q2.t, self.x + q2.x, self.y + q2.y, self.z + q2.z)); def scalar_div(self, d): return(q(self.t/d, self.x/d, self.y/d, self.z/d)); def scalar_x(self, d): return(q(self.t * d, self.x * d, self.y * d, self.z * d)); def conj(self): return q(self.t, -self.x, -self.y, -self.z) def conj_1(self): return q(-self.t, self.x, -self.y, -self.z) def conj_2(self): return q(-self.t, -self.x, self.y, -self.z) def conj_3(self): return q(-self.t, -self.x, -self.y, self.z) def negate(self): return q(-self.t, -self.x, -self.y, -self.z) 

q1 = q(1, 2, 3, 4); q_time_rev = q(-1, 2, 3, 4); q_space_rev = q(1, -2, -3, -4); q_spacetime_rev = q(-1, -2, -3, -4) q1.conj()==q_space_rev 

True

q1.conj().negate() == q_time_rev 

True

q1.negate()==q_spacetime_rev 

True

r""" The space, time and spacetime reflections all are well defined on the quaternion manifold H^1, even if one customarily things of them in R^4.