Symbolic computation manipulates mathematical expressions and objects instead of reducing everything to numerical answers. It turns formulas into other formulas, making relationships visible and preserving general solutions. SymPy provides a practical shortcut: it performs the symbolic mathematics and can convert resulting formulas into source code. section 1.7 section 1.5
Underspecified systems
A system of linear equations may describe a line, plane, or hyperplane rather than one point. Symbolic computation can retain that geometric object as the solution, whereas numerical methods generally seek a single set of numbers. This is useful for understanding families of solutions, but symbolic solving can become extremely slow: even an 8 × 8 system may take a long time. section 3.2.2
Use symbolic computation when:
- You need a general formula rather than one evaluated result. section 1.7
- A solution is naturally a geometric object such as a line or plane. section 3.2.2
- You can accept slower computation in exchange for symbolic structure, or split a problem into symbolic and numerical stages. section 3.2.2
