I like this. I think AD can be extended in a fairly straightforward manner to stochastic differentials, e.g. Ito formula. Has anybody looked into this? That could be interesting for finance applications.
This could also be interesting for use in other differential algebras. In particular, extending it to higher degree differential forms could be nice. For the latter, you would need to be able to take linear combinations of epsilons. Is that currently possible? For example, e = e1 + e2 e^2 = e1*e2 + e2*e1 = 0 => e1*e2 = -e2*e1 That would be cool.
