Algebraic computation

Also called Formula Manipulation or Symbolic Computation. Existing programs or systems in this area allow us or one to transform mathematical expressions in symbolic form, hence in an exact way, as opposed to numerical and hence limited-precision floating point computation. Primarily designed for applications in theoretical physics or mathematics, these systems, which are usually interactive, can be used in any area where straightforward but tedious or lengthy calculations with formulae are required. Typical operations include differentiation and integration, linear algebra and matrix calculus, polynomials, or the simplification of algebraic expressions.

Well known systems for algebraic computation are, amongst others, Macsyma MACSYMA87, Maple Char91, MathematicaWolfram91, or Reduce Hearn95, Rayna87. These systems have different scope and facilities, and some are easier to use or to access than others. Mathematica is a commercial package; Maple is available through another commercial package, Matlab (Symbolic Math Toolbox). For introductory reading, and many further references, e.g. Buchberger83 or Davenport88.