SymPy is a Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live or SymPy Gamma.
License: Open Source
SymPy is an open-source Python library that excels in symbolic mathematics and is more suited for users familiar with programming, while Mathcad offers a user-friendly interface and robust numerical capabilities, making it ideal for engineers and scientists who prefer a more visual approach. The choice between the two largely depends on the user's background and specific needs.