Numerical Error

When we store and manipulate numbers on a computer we are subject them to different types of errors. Understanding and mitigating these errors is the art of making good numerical methods.

Symbolic Representation

If we could use an infinite number of digits or represent numbers and functions symbolically (e.g., as \(1/3\), \(\pi\), or \(\sqrt{2}\)), round-off error would not be an issue. This is the approach taken by symbolic computation tools like Mathematica, Maple, and Python’s sympy module, which delay numerical evaluation until absolutely necessary.

Question: What are the pros and cons of using symbolic representation?