Key words Standard bases
Computer algebra system
Springer Online Journal Archives 1860-2000
Abstract We describe an implementation of a general standard basis algorithm, valid for any monomial ordering compatible with the natural semigroup structure. We concentrate on new strategies which have proved useful, in particular in the non-wellordering case. Moreover, we describe the first implementation of Schreyer’s method to compute syzygies and compare it with other, more classical methods. Comparisons of the computing time of several examples in the system SINGULAR give hints as to which strategies should be used in different classes of examples.
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