  We discuss parabolic versions of Euler's identity e^{it}=cos t + i sin t. A
purely algebraic approach based on dual numbers is known to produce a very
trivial relation e^{pt} = 1+pt. Therefore we use a geometric setup of parabolic
rotations to recover the corresponding non-trivial algebraic framework. Our
main tool is Moebius transformations which turn out to be closely related to
induced representations of the group SL(2,R).
  Keywords: complex numbers, dual numbers, double numbers, linear algebra,
invariant, computer algebra, GiNaC
