### quaternion-valued differential forms

I'm trying to define quaternion-valued differential forms in Sage. For example, take $e_0$, $e_1$, $e_2$, $e_3$ to be the quaternion generators and $d x^0$, $d x^1$, $d x^2$, $d x^3$ be the generators of the exterior algebra. So for example I'd like to be able to compute $d X \wedge d X^\dagger$, where $d X = e_0 d x^0 + e_1 d x^1 + e_2 d x^2 + e_3 d x^3$, $d X^\dagger = e_0 d x^0 - e_1 d x^1 - e_2 d x^2 - e_3 d x^3$.