Symbolic computation deals with the computation of mathematical objects symbolically. This means that the mathematical objects are represented exactly, not approximately, and mathematical expressions with unevaluated variables are left in symbolic form.
I admit to being frustrated by the SymPy documentation. It does an adequate job of explaining "what" (i.e. the mechanics of each function or class), but I cannot read it to get an idea of the "how" or "why" questions, of how to best use SymPy to accomplish my goals.
An oversimplified explanation. SymPy is a non-interactive toolkit for balancing the numerical coefficients of a system of nonlinear equations. FYI a "system" in this sense is a math term. I also found that SymPy is too niche because it's not interactive.
> SymPy is a Python library for symbolic mathematics.
Both the release notes as well as the readme of the github repository don't explain it (or at least I couldn't find it).