sadET VS autodiff

Then, each expression should carry enough information that you can call different member functions, such as derivative for their derivative, or conjugate to take its complex conjugate, etc. Now, the conjugate (and derivative) member function should somehow inherit its behaviour from the sub expressionss. You only need to define what conjugate means for the Number class, and then all other expressions, just apply this function to its sub expressions, until a Number is reached. I am not sure if this is detailed enough, but I apply this logic here. In this piece of code, I am using ETs to that define expressions, and then use these expressions to take their derivatives. This is an autodiff library (without dual numbers), which works well, but it suffers from the the problem; can't find a way to assign and reassign variables to expressions.

I completely agree. Specifying the metric rather than the Christoffel symbols would make it much easier for the users. Something like https://github.com/autodiff/autodiff might just work as the metric tensor is made up of primitives.

Old username :D So far I have been using Eigen for linear algebra and NLOPT for optimization algorithms. I have found "autodiff" that hopefully looks easy to use: https://github.com/autodiff/autodiff

Forward-mode differentiation is easy to implement in C++ with templates, operator overloading, and dual numbers (https://en.wikipedia.org/wiki/Automatic_differentiation#Auto...). Some libraries such as autodiff (https://github.com/autodiff/autodiff) and CppAD (https://github.com/coin-or/CppAD) use this method.

I was thinking of adding [autodiff](https://github.com/autodiff/autodiff) in the future, mainly because it works seamlessly with *Eigen*. One big advantage would be that I could use it for AD for NonlinearSystems as well.