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We consider the check of the involutive basis property in a polynomial context. In order to show that a finite generating set F of a polynomial ideal I is an involutive basis one must confirm two properties. Firstly, the set of leading terms of the elements of F has to be complete. Secondly, one has to prove that F is a Gröbner basis of I. The latter is the… (More)

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… (More)

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