I have a set of (multivariate, nonlinear) equations which I want wo modify according to my own rules, i.e. not in a standard ways such as matlab's simplify function. I am looking for a mathematical symbolic programming language, which is able to do these things.
Most importantly, I want to do multivariate calculus and extract and change subexpressions of formulas in a user-defined way. I tried matlab symbolic toolbox, it is very intuitive but does not offer much functionality if one wants to do non-standard stuff. I also tried sympy but for a mathematician it seems complicated and not well developed. E.g. I did not even find a usable dot product function for vector-valued symbolic variables.
Does anyone have any advices about good symbolic programming language?
Thanks in advance to all.