Bugs, Errors, and Unexpected Results in Computer Algebra Packages

Walter Kraemer

University of Wuppertal, Germany

The following is a citation from the Description and aims of the Dagstuhl Seminar on "Algebraic and Numerical Algorithms and Computer-assisted Proofs": "In contrast, most algorithms in computer algebra are 'never failing', that is they are proved to provide a solution for any input, and the maximum computing time for this is estimated a priori."

The focus of the talk is the reliablity of the computer algebra system Maple. We show that 'never failing' algorithms may be the theory but concerning actual implementations such a statement seems not to be drawn from life.