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TitleComprehensive involutive systems.
Author(s) Vladimir P. Gerdt, Amir Hashemi
TypeBook, Chapter in Book, Conference Proceeding
AbstractIn this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal for the values of parameters in that cell. Using the Gerdt–Blinkov algorithm described in [6] for computing involutive bases and also the Montes DisPGB algorithm for computing comprehensive Gröbner systems [13], we present an algorithm for construction of comprehensive involutive systems. The proposed algorithm has been implemented in Maple, and we provide an illustrative example showing the step-by-step construction of comprehensive involutive system by our algorithm.
URL http://link.springer.com/chapter/10.1007%2F978-3-642-32973-9_9
PublisherBerlin: Springer
Translation No
Refereed No