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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:

  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:

P.<e>=PolynomialRing(RR)
S.<e>=P.quo(e*e); 
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!