solving for the center of the real quaternions

edit

I'm trying out Sage on quaternions, on the problem of finding the center of the real Hamiltonian quaternions $\mathbb{H}$. So what I tried was:

Q.<i,j,k> = QuaternionAlgebra(SR, -1, -1)

a1, b1, c1, d1 = SR.var('a1, b1, c1, d1', domain = RR)
a2, b2, c2, d2 = SR.var('a2, b2, c2, d2', domain = RR)

q1 = a1 + b1*i + c1*j + d1*k
q2 = a2 + b2*i + c2*j + d2*k

solve(q1*q2 - q2*q1, a1, b1, c1, d1)

which rewarded me with:

TypeError                                 Traceback (most recent call last)
<ipython-input-6-8a6c0ff8f7d0> in <module>()
      9 q2 = a2 + b2*i + c2*j + d2*k
     10 
---> 11 solve(q1*q2 - q2*q1, [a1, b1, c1, d1])

/home/sage/sage/local/lib/python3.7/site-packages/sage/symbolic/relation.py in solve(f, *args, **kwds)
   1045 
   1046     if not isinstance(f, (list, tuple)):
-> 1047         raise TypeError("The first argument must be a symbolic expression or a list of symbolic expressions.")
   1048 
   1049     # f is a list of such expressions or equations

TypeError: The first argument must be a symbolic expression or a list of symbolic expressions.

Well, OK, that's not a symbolic expression:

sage: type(q1*q2 - q2*q1)
<class 'sage.algebras.quatalg.quaternion_algebra_element.QuaternionAlgebraElement_generic'>

At least this looks right:

sage: q1*q2 - q2*q1
((c1 - d1)*(c2 + d2) - (c1 + d1)*(c2 - d2))*i + (2*b2*d1 - 2*b1*d2)*j + (-(a2 + b2)*(c1 + d1) + (a2 - b2)*(c1 + d1) + (a1 + b1)*(c2 + d2) - (a1 - b1)*(c2 + d2) + 2*b2*d1 - 2*b1*d2)*k

I can figure out the answer from the last line, but was hoping for something like $b_1 = c_1 = d_1 = 0$. Not sure how this works.

update: Updated to Sage 9.1.