AXIOM: the scientific computation system
AXIOM: the scientific computation system
Algorithms for computer algebra
Algorithms for computer algebra
Theorems and algorithms: an interface between Isabelle and Maple
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
ML for the working programmer (2nd ed.)
ML for the working programmer (2nd ed.)
An OpenMath 1.0 implementation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
The Turing factorization of a rectangular matrix
ACM SIGSAM Bulletin
Coding Theory: The Essentials
A perspective on symbolic mathematical computing and artificial intelligence
Annals of Mathematics and Artificial Intelligence
DISCO '96 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
SigmaIT - A Strongly-Typed Embeddable Computer Algebra Library
DISCO '96 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Integrating Computer Algebra with Proof Planning
DISCO '96 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
A Certified Version of Buchberger's Algorithm
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
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The use of computer algebra is usually considered beneficial for mechanised reasoning in mathematical domains. We present a case study, in the application domain of coding theory, that supports this claim: the mechanised proofs depend on non-trivial algorithms from computer algebra and increase the reasoning power of the theorem prover. The unsoundness of computer algebra systems is a major problem in interfacing them to theorem provers. Our approach to obtaining a sound overall system is not blanket distrust but based on the distinction between algorithms we call sound and ad hoc respectively. This distinction is blurred in most computer algebra systems. Our experimental interface therefore uses a computer algebra library. It is based on formal specifications for the algorithms, and links the computer algebra library Sumit to the prover Isabelle. We give details of the interface, the use of the computer algebra system on the tactic-level of Isabelle and its integration into proof procedures.