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doi:10.1006/jsco.2001.0478 
Copyright © 2002 Elsevier Science Ltd. All rights reserved.
Regular Article
Continuously Parameterized Symmetries and Buchberger’s Algorithm
Received 5 September 1996;
accepted 13 June 2001. ;
Available online 27 February 2002.
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Abstract
Systems of polynomial equations often have symmetries. In solving such a system using Buchberger’s algorithm, the symmetries are neglected. Incorporating symmetries into the solution process enables us to solve larger problems than with Buchberger’s algorithm alone. This paper presents a method that shows how this can be achieved and also gives an algorithm that brings together continuously parameterized symmetries with Buchberger’s algorithm.
