ABSTRACT
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15.1 Introduction The computer is an indispensable tool for a modern mathematician. It is not only useful for checking emails, or for writing articles, or for retrieving information from web services like Wikipedia, MathWorld, or Sloane’s celebrated online encyclopedia of integer sequences (OEIS [170]). The computer is also useful for computing. People working in applied mathematics seem to be more aware of this than people working in pure mathematics, perhaps because of the immediate impact numerical computations have in natural sciences and engineering. While numerical computations typically do not lead to rigorous proofs, symbolic computations do have proof quality. Symbolic computation and computer algebra can therefore be a valuable tool for people working in pure mathematics. And more than many other areas of pure mathematics, combinatorics can benefit from the advances that have been made in computer algebra in the past few decades. One reason may be that computer algebra
algorithms, just like all other algorithms, are applicable only to finite objects, and combinatorialists, unlike most other mathematicians, primarily study finite objects. Another reason may be that computer algebra algorithms developed during the past few decades are especially good at handling precisely those kinds of expressions, which tend to arise in the context of combinatorial problems.
