Library that implements automatic simplification of algebraic expressions in C#.
To get an idea of the kinds of expressions it handles, see the tests in this file.
The automatic simplification algorithm comes from the book "Computer Algebra and Symbolic Computation: Mathematical Methods" by Joel S. Cohen.
GiNaC and SymbolicC++ are of course very inspirational.
The projects "PSE 5E ..." are examples and problems from the textbook "Physics for Scientists and Engineers, 5th Edition" by Serway and Jewett.
Here's a walk-through of solving a physics problem.
A slightly more complex walk-through.
This paper by members of the GiNaC team gets into some reasons to consider using general purpose programming languages for computer algebra. Here's a quote:
The traditional split into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages.
Computer Algebra and Symbolic Computation: Elementary Algorithms by Joel S. Cohen
Computer Algebra and Symbolic Computation: Mathematical Methods by Joel S. Cohen
GiNaC (C++)
SymbolicC++ (C++)
ComputerAlgebra (C++)
Math.NET Symbolics (F#)
SymPy (Python)