Handbook of theoretical computer science (vol. B)
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
IMPS: an interactive mathematical proof system
Journal of Automated Reasoning
Commutative algebra in the Mizar system
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
A Machine-Checked Implementation of Buchberger's Algorithm
Journal of Automated Reasoning
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
A verified Common Lisp implementation of Buchberger's algorithm in ACL2
Journal of Symbolic Computation
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We argue that for building mathematical knowledge repositories a broad development of theories is of major importance. Organizing mathematical knowledge in theories is an obvious approach to cope with the immense number of topics, definitions, theorems, and proofs in a general repository that is not restricted to a special field. However, concrete mathematical objects are often reinterpreted as special instances of a general theory, in this way reusing and refining existing developments. We believe that in order to become widely accepted mathematical knowledge management systems have to adopt this flexibility and to provide collections of well-developed theories. As an example we describe the Mizar development of the theory of Gröbner bases, a theory which is built upon the theory of polynomials, ring (ideal) theory, and the theory of rewriting systems. Here, polynomials are considered both as ring elements and elements of rewriting systems. Both theories (and polynomials) already have been formalized in Mizar and are therefore refined and reused. Our work also includes a number of theorems that, to our knowledge, have been proved mechanically for the first time.