2019-07-10 23:48:52 +0200 received badge ● Popular Question (source) 2018-03-19 12:28:29 +0200 commented answer Dual Quaternion Algebra Thank you for your answer! I did have a problem using 'E' as the name variable but it worked out fine with E replaced by x. Also, what if I want to work with complex coefficients rather than real coefficients ? I want to be able to distinguish the Hamiltonian "I" from the complex "I" so that, for instance, the difference between them is non-zero. How could I do this ? 2018-03-19 12:24:15 +0200 received badge ● Supporter (source) 2018-03-16 15:31:27 +0200 received badge ● Student (source) 2018-03-16 02:26:29 +0200 asked a question Dual Quaternion Algebra Hello, I'm quite new to SAGE. I need to work with the algebra of dual quaternions. It can be defined in two equivalent ways: 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. The algebra of polynomials over the quaternions and variable e modulo e^2. For the first definition I tried to do this: P.=PolynomialRing(RR) S.=P.quo(e*e); F. = 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!