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Computing Gröbner bases within linear algebra. (English) Zbl 1260.68485
Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 11th international workshop, CASC 2009, Kobe, Japan, September 13–17, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04102-0/pbk). Lecture Notes in Computer Science 5743, 310-321 (2009).
Summary: In this paper, we present an alternative algorithm to compute Gröbner bases, which is based on computations on sparse linear algebra. Both S-polynomial computations and monomial reductions are computed in linear algebra simultaneously in this algorithm. So it can be implemented to any computational system which can handle linear algebra. For a given ideal in a polynomial ring, it calculates a Gröbner basis along with the corresponding term order appropriately.
For the entire collection see [Zbl 1175.68009].

MSC:
68W30 Symbolic computation and algebraic computation
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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