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Dual Quaternion Algebra


I'm quite new to SAGE.

I need to work with the algebra of dual quaternions. It can be defined in two equivalent ways:

  1. The algebra of quaternions over the dual numbers. Dual numbers are elements of the form a+be where a and b are real and e is such that e^2=0.

  2. The algebra of polynomials over the quaternions and variable e modulo e^2.

For the first definition I tried to do this:

F.<I,J,K> = QuaternionAlgebra(S, -1,-1)

For some reason this doesn't work. What is the best way to define this Dual Quaternion Algebra in SAGE ?

Thank you for your help!