I need to compute Slater determinants. I'm wondering if I would benefit from assigning each of my functions to a variable prior to computation. I'm working with Slater determinants, but my question goes beyond them and applies to the computation of any determinant.
Say I have functions $f_n[x]$ which are sums of complex exponentials. If I want to compute the determinant of an $N\times N$ matrix, should I use the expanded form of $f_n[x]$ or variables ($a_1,a_2,b_1,b_2$, etc.), or else? Does Mathematica benefit from prior "simplification" of the matrix or not?
At the moment, I'm not concerned with speed because the systems I work with contain few electrons, but that will change.