How does one define a generic real valued function in Mathematica? In particular, I would like to utilize Mathematica to perform algebraic reductions that involve combinations of zj(q) = xj(q) + i yj(q) and D[zj(q),{q,n}] where xj(q), yj(q) and q are all generic real valued functions, and where j and n are integers; i is used here to represent the square root of -1. For example, by default Mathematica assumes these are complex valued functions, which, in turn, significantly effects the output of Simplify[] and and FullSimplify[]. Thanks in advance!
For example, by default Mathematica assumes these are complex valued
functions, which, in turn, significantly effects the output of
Simplify[] and and FullSimplify[].
I do not exactly understand the problem since you can use assumptions anytime telling it the domain of the variables. Also you can use ComplexExpand which expands expressions assuming all variables are real.
If you give specific example of what the problem is, this will help.
It could well be that I don’t know how to utilize Assumptions properly. For clarification - by generic I mean the functions zj(q) = xj(q) + i yj(q) are not defined algebraically, but they are specified as being real valued (which I’m sure you understood). I guess I need an example of how to do this.