Computer algebra systems

A computer algebra system (CAS) or symbolic computation system is a system of software packages that facilitates symbolic mathematics. Typically, these systems include

• arbitrary precision (bignum) arithmetic, allowing for instance to evaluate pi to 10,000 digits.
• symbolic manipulation engine, to simplify algebraic expressions, differentiate and integrate functions and solve equations
• graphing facility, to produce graphs of functions, typically in two and three dimensions
• linear algebra subsystem, to allow matrix computations and solving of systems of linear equations
• high level programming language, allowing users to implement their own algorithms

More advanced examples usually include more sophisticated tools, including Gröbner basis packages for manipulating ideals in polynomial rings, which is essential for many advanced real-world applications involving differential equations, robotics, and so forth, as well as packages for working at a high level with vectors and tensors.