I think ca_tribonacci_constant should just create an element of the simple number field generated by qqbar_tribonacci_constant.

Other than that it looks good.

I considered that, too. But then I modeled Tc in analogy to the golden ratio.
With my latest commit, it should be fine now.

Instead of the old output:

Evaluating Tc as ca:
1.83929 {(a+b+1)/3 where a = 3.30906 [Pow(36.2337 {3*c+19}, 0.333333 {1/3})], b = 1.20880 [Pow(1.76631 {-3*c+19}, 0.333333 {1/3})], c = 5.74456 [c^2-33=0]}

the example code now gives:

Evaluating Tc as ca:
1.83929 {a where a = 1.83929 [a^3-a^2-a-1=0]}

which at least looks much more useful indeed.

In case of the golden ratio, the expression in terms of radicals is much simpler than here and hence the difference between both representations probably not such a big deal. What do you think, should we represent it as element of Q[a] where a^2 - a - 1 = 0?

I probably do not see through the details and consequences to really judge.
My main argument might just be for the sake of consistency.

BTW: I could try to do the changes if you agree.